JP6834727B2 - Planning equipment, planning methods, and programs - Google Patents

Description

The present invention relates to a planning apparatus, a planning method, and a program, and is particularly suitable for use in collecting a plurality of products in a lot to produce or process a plurality of products in lot units.

When formulating a production plan for a product in the manufacturing industry, it is often the case that a production plan is formulated so that a plurality of products are grouped into an appropriate number of lots on an appropriate scale and manufactured in lot units.
Here, as an example of the case where a plurality of products are collectively manufactured in a lot, a case where continuous casting is performed in a steelmaking factory will be described.

At a steelmaking factory, hot metal supplied from a blast furnace is charged into a converter and oxygen is blown to remove carbon in the hot metal to produce molten steel. This is called primary refining. Next, the molten steel is injected into a container called a ladle and transported to a secondary refining process. The amount of molten steel for a full ladle is called a charge. As a secondary refining step, for example, there is an RH (Ruhrstahl Heraeus) step, in which a molten steel is circulated in a vacuum tube to remove an impure gas in the molten steel into a vacuum to adjust the composition of the molten steel. When the secondary refining process is completed, the ladle is transported to the continuous casting machine. In a continuous casting machine, a semi-finished slab is manufactured by injecting molten steel from a ladle into a mold and cooling it at the same time. In a continuous casting machine, it is possible to continuously cast a plurality of charges, and a group of a plurality of charges that are continuously cast is called a cast. Further, continuous casting of molten steel having a plurality of charges is called continuous casting. If the number of continuous castings is increased too much, the components of the continuous casting machine (refractory of tundish, mold, immersion nozzle, etc.) will be melted. Therefore, continuous casting is performed according to the degree of melting damage, which differs depending on the type of product. The number of charges to be carried out must be determined appropriately.

The slabs produced in the continuous casting machine are called slabs and are transported to the rolling process. In the rolling process, the slab is reheated by a heating furnace, rolled to a thickness of several millimeters by a rolling mill at a high temperature, and wound into a coil. Depending on the shape and hardness of the slab, the number of slabs that can be continuously rolled by the rolling mill is limited. A group of slabs that are continuously rolled by a rolling mill is called an opportunity.
Information such as composition, shape, and desired hot rolling date is given to each slab from order information, and lots such as casts and chances are organized in consideration of constraints in the steelmaking process and the rolling process.

Further, in recent years, attempts have been made to shorten the lead time and reduce the heat loss by making the cast, which is a lot of the steelmaking process, the same as the chance of being a lot of the rolling process. When performing such an operation, it is necessary to determine a cast knitting (slab to be included in each cast) that simultaneously satisfies the constraints in the steelmaking process and the rolling process.

In cast knitting, by incorporating a large number of slabs into the cast and increasing the lot size, the number of continuous castings is increased, the number of slab defective parts at the start and end of continuous casting is reduced, and the preparation time required for the start of recasting It is expected that the production volume will increase due to the reduction of. On the other hand, there are restrictions on the slabs that can be incorporated into the same cast depending on conditions such as the composition, shape, and desired date of hot spreading. For this reason, it is required to perform cast formation with as large a lot as possible within the range satisfying the constraint conditions.

Casting work generally deals with hundreds or thousands of slabs, resulting in a large number of slab combinations. Therefore, it takes a long time for the planner to perform the cast formation that satisfies all the constraints.
Therefore, there is a technique described in Patent Document 1 as a technique for automatically performing cast knitting.
Patent Document 1 discloses that each charge is represented by a node, a network is created in which the charges that can be tyed and cast are represented by directed branches, and the route that is the longest cast is searched for on the network. Has been done.

Japanese Unexamined Patent Publication No. 2012-11451

However, in the technique described in Patent Document 1, there is no description about a method of collecting slabs into a charge, and cast knitting is performed based on the information of the given charge. Therefore, if the charges are not properly organized, the optimum cast organization result may not be obtained. As described above, since there are many combinations of slabs, if the charge is properly included in the cast in the technique described in Patent Document 1, the problem scale becomes too large and the calculation time may become long.

As described above, in the conventional technology, a casting (production) plan for casting (producing) slabs (products) in cast (lot) units by collecting a plurality of slabs (products) in a cast (lot) is created. It was not easy to make a plan in a practical calculation time without significantly reducing the accuracy of. Further, when a plurality of slabs (products) are put together in a cast (lot), it is required that many slabs (products) are included in the cast (lot).
The present invention has been made in view of the above problems, and a plan for producing or processing a product in lot units can be made within a practical calculation time without significantly reducing the planning accuracy. The purpose is to allow many products to be planned for inclusion in the lot.

The planning device of the present invention is a planning device that creates a plan for collectively producing or processing a plurality of products in units of lots, and is information on the plurality of products, and is a manufacturing condition of the product. The same group represented by using the acquisition means for acquiring the product information including the above and the manufacturing conditions of the product included in the product information acquired by the acquisition means as a condition that the product can be included in the same group. A group creation means for creating a plurality of product groups by grouping the plurality of products based on the inclusion conditions, a product selection means for selecting a part of the plurality of product groups created by the group creation means, and a product selection means. Among the subsets of the product group selected by the product selection means, the subset that satisfies the same lot inclusion condition expressed by using the manufacturing conditions as a condition that the product group can be included in the same lot is first. The first lot candidate derivation means derived as the lot candidate and the first optimum lot candidate which is the optimum lot candidate from the first lot candidate derived by the first lot candidate derivation means are first selected. The first optimization means derived by performing the first optimization calculation that maximizes or minimizes the value of the objective function within the range satisfying the constraint equation of, and the first optimization means by the first optimization means. When the first determination means for determining whether or not the result of the optimization calculation has converged and the first determination means determine that the result of the first optimization calculation has not converged, the first determination means. The first redefinition means for redefining the product group included in the first optimum lot candidate derived by the first optimization means as one product group, and the first determination means for the first determination means. The product group included in the first optimum lot candidate derived by the first optimization means when it is determined that the result of the first optimization calculation by the optimization means has converged. A result of comparing a predetermined attribute and a threshold of the first optimum lot candidate from the product and the product constituting the product group not included in the first optimum lot candidate, and the first. Based on the result of comparing a predetermined attribute of the product group not included in the optimum lot candidate with the threshold value, a set for extracting an embedded candidate product which is a candidate product to be further incorporated into the optimum lot candidate. Selection of embedded candidate products that selects at least one of the embedded candidate product extracting means and the embedded candidate products extracted by the embedded candidate product extracting means. It is said that the selection means, the built-in candidate product selected by the built-in candidate product selection means, and the result of the first optimization calculation by the first optimization means have converged by the first determination means. Among the subsets of the first optimum lot candidates derived by the first optimization means at the time of determination and the first optimum lot candidates that do not include the embedded candidate product, the same lot is included. A second lot candidate derivation means that derives a subset satisfying the conditions as a second lot candidate, and a second lot candidate that is an optimum lot candidate from the second lot candidate derived by the second lot candidate derivation means. The second optimization means for deriving the optimum lot candidate of the above by performing the second optimization calculation that maximizes or minimizes the value of the objective function within the range that satisfies the second constraint equation, and the second The second determination means for determining whether or not the result of the second optimization calculation by the optimization means has converged, and the second determination means have not converged the result of the second optimization calculation. When the determination is made, the second redefinition means for redefining the product group included in the second optimum lot candidate derived by the second optimization means as one product group, and the second redefinition means. When it is determined by the determination means of the above that the result of the second optimization calculation has converged, the second optimum lot candidate derived by the second optimization means is set as the optimum lot, and which of the optimum lots is used. The objective function includes an output means for outputting information indicating whether or not the product is included, and the objective function includes at least the number of lots as a lot candidate derivation evaluation index, and the first constraint equation is The number of the product groups included in the first optimum lot candidate and the number of the product groups selected by the product selection means are the same, and the same product group is different. The second constraint formula includes a formula formulated not to be included in the optimum lot candidate, and the second constraint formula is based on the number of product groups included in the second optimum lot candidate and the first determination means. The number of products included in the first optimum lot candidate derived by the first optimization means when it is determined that the result of the first optimization calculation by the first optimization means has converged. The product selection means includes the formula that is the same as, and that the same product group is not included in the different second lot candidates, and the product selection means is described by the first redefinition means. If the product group is redefined, the first redefinition move All of the product groups redefined by the step and a part of the unselected product groups are selected, and the embedded candidate product selection means is the product by the second redefinition means. When the group is redefined, the unselected embedded candidate product is selected, and the embedded candidate product extraction means converges the result of the first optimization calculation by the first optimization means. The result of comparing the predetermined attributes of the first optimum lot candidate derived by the first optimization means at the time of determination with the threshold value and the product not included in the first optimum lot candidate. Based on the result of comparing a predetermined attribute of the group with the threshold value, the embedded candidate product is extracted, the product group is redefined by the first redefinition means, and the product is redefined by the product selection means. The selection of the group, the derivation of the first lot candidate by the first lot candidate derivation means, and the first optimization calculation by the first optimization means are performed by the first determination means. It is repeated until it is determined that the result of the optimization calculation by the first optimization means has converged, the redefinition of the product group by the second redefinition means and the set by the incorporation candidate product selection means. The selection of the inclusion candidate product, the derivation of the second lot candidate by the second lot candidate derivation means, and the second optimization calculation by the second optimization means are performed by the second determination means. The second optimization calculation by the second optimization means is repeated until it is determined that the result of the second optimization calculation has converged.

The plan creation method of the present invention is a plan creation method for creating a plan for collectively producing or processing a plurality of products in units of lots by a plan creation device, and the acquisition means of the plan creation device is the plurality. The acquisition process as a condition for acquiring the product information including the manufacturing conditions of the product and the group creating means of the planning apparatus can include the product in the same group. A group creation step of creating a plurality of product groups by grouping the plurality of products based on the same group inclusion condition represented by using the manufacturing conditions of the product included in the product information acquired by the above. The product selection step in which the product selection means of the planning apparatus selects a part of the plurality of product groups created by the group creation step , and the first lot candidate derivation means of the planning apparatus are the product selection. Among the subsets of the product group selected by the process, the subset that satisfies the same lot inclusion condition expressed by using the manufacturing conditions as a condition that the product group can be included in the same lot is selected as the first lot candidate. The first lot candidate derivation step derived as, and the first optimization means of the planning apparatus are candidates for the optimum lot from the first lot candidates derived by the first lot candidate derivation step. The first optimization step and the plan for deriving the first optimum lot candidate by performing the first optimization calculation that maximizes or minimizes the value of the objective function within the range that satisfies the first constraint equation. The first determination means of the creation apparatus includes a first determination step of determining whether or not the result of the first optimization calculation by the first optimization step has converged, and a first determination step of the plan creation apparatus. When the redefinition means of is determined by the first determination step that the result of the first optimization calculation has not converged, the first optimum lot derived by the first optimization step is derived. The first redefinition step of redefining the product group included in the candidates as one product group and the built-in candidate product extraction means of the planning device are optimized by the first determination step. With the product constituting the product group included in the first optimum lot candidate derived by the first optimization process when it is determined that the result of the first optimization calculation by the process has converged. From the products constituting the product group that are not included in the first optimum lot candidate, the predetermined attributes and thresholds of the first optimum lot candidate Based on the result of comparing the above and the result of comparing the predetermined attribute of the product group not included in the first optimum lot candidate with the threshold value, a product that is a candidate to be further incorporated into the optimum lot candidate. The embedded candidate product extraction step for extracting the embedded candidate product and the embedded candidate product selection means of the planning device are at least one of the embedded candidate products extracted by the embedded candidate product extraction step. The embedded candidate product selection step of selecting the above, and the second lot candidate derivation means of the planning apparatus are based on the embedded candidate product selected by the embedded candidate product selection step and the first determination step. Among the first optimum lot candidates derived by the first optimization step when it is determined that the result of the first optimization calculation by the first optimization step has converged, the incorporation candidate Among the subsets with the first optimum lot candidate that does not include the product, the second lot candidate derivation step of deriving the subset satisfying the same lot inclusion condition as the second lot candidate, and the first of the planning apparatus. The second optimum lot candidate, which is a candidate for the optimum lot from the second lot candidate derived by the second lot candidate derivation step, is selected by the second optimization means within a range satisfying the second constraint equation. The second optimization step derived by performing the second optimization calculation that maximizes or minimizes the value of the objective function and the second determination means of the planning apparatus are based on the second optimization step. The second determination step of determining whether or not the result of the second optimization calculation has converged and the second redefinition means of the planning apparatus are the second optimization by the second determination step. When it is determined that the result of the chemical calculation has not converged, the product group included in the second optimum lot candidate derived by the second optimization step is redefined as one product group. The redefinition step of the above and the output means of the planning apparatus are derived by the second optimization step when it is determined by the second determination step that the result of the second optimization calculation has converged. The second optimum lot candidate is set as the optimum lot, and has an output step of outputting information indicating which product is included in the optimum lot, and the objective function includes at least the number of lots. It is an objective function included as a candidate derivation evaluation index, and the first constraint formula includes the number of the product groups included in the first optimum lot candidate and the number of the product groups selected by the product selection process. Is the same and the same product group The second constraint formula includes the formula that the loop is not included in the first optimum lot candidate, and the second constraint formula includes the number of the product groups included in the second optimum lot candidate. The first optimum lot derived by the first optimization step when it is determined by the first determination step that the result of the first optimization calculation by the first optimization step has converged. The product selection step includes the formula that the number of the products included in the candidates is the same and that the same product group is not included in the different second lot candidates. When the product group is redefined by the first redefinition step, all of the product groups redefined by the first redefinition step and a part of the unselected product groups. When the product group is redefined by the second redefinition step, the embedded candidate product selection step selects an unselected embedded candidate product and extracts the embedded candidate product. Is a predetermined attribute of the first optimum lot candidate derived by the first optimization step when it is determined that the result of the first optimization calculation by the first optimization step has converged. Based on the result of comparing with the threshold and the result of comparing the predetermined attribute of the product group not included in the first optimum lot candidate with the threshold, the embedded candidate product is extracted. The redefinition of the product group by the first redefinition step, the selection of the product group by the product selection step, the derivation of the first lot candidate by the first lot candidate derivation step, and the first. The first optimization calculation by the optimization step of the above is repeated until it is determined by the first determination step that the result of the optimization calculation by the first optimization step has converged, and the second. Redefinition of the product group by the redefinition step of the above, selection of the incorporation candidate product by the incorporation candidate product selection process, derivation of the second lot candidate by the second lot candidate derivation process, The second optimization calculation by the second optimization step is repeated until it is determined by the second determination step that the result of the second optimization calculation by the second optimization step has converged. It is characterized by being done.

The program of the present invention is characterized in that a computer functions as each means of the planning apparatus.

According to the present invention, a plan for producing or processing products in lot units is made so that more products are included in the lot within a practical calculation time without significantly reducing the planning accuracy. Can be done.

It is a figure explaining an example of the outline of the method of making a cast plan. It is a figure which shows an example of the functional structure of the cast knitting apparatus in the premise form. It is a figure which shows the 1st example of a slab information. It is a figure which shows an example of the slab information after sorting. It is a figure which shows an example of the slab group information. It is a figure which shows an example of the slab group information after sorting. It is a figure which conceptually shows an example of the method of solving a set partitioning problem. It is a figure explaining a matrix conceptually. It is a figure which shows an example of the slab group information after redefinition. It is a figure which conceptually shows an example of the slab group which cannot be incorporated into a cast piece (redefined slab group). It is a figure which shows the 1st example of the functional structure of a cast knitting apparatus. It is a figure which shows an example of the embedded candidate slab group conceptually. It is a flowchart explaining the 1st example of a plan making method. It is a flowchart following FIG. 13-1. It is a flowchart explaining an example of the process of step S1302. It is a figure which shows an example of the drafting result of a cast plan in a table format. It is a figure which shows the 2nd example of the functional structure of the cast knitting apparatus. It is a figure which conceptually shows an example of the method of calculation, storage, and destruction of a constraint violation amount. It is a figure which shows an example of the constraint violation amount about a cast weight. It is a figure which shows the constraint violation amount about a cast weight by a box plot. It is a figure which shows the upper limit value of each constraint condition and the number of pairs, in tabular form. It is a figure which represented the constraint violation amount of each constraint condition obtained from the result of the first calculation by a box plot. It is a figure which represented the constraint violation amount of each constraint condition obtained from the result of the second calculation by a box plot. It is the figure which represented the constraint violation amount of each constraint condition obtained from the result of the 3rd calculation by a box plot. It is a flowchart explaining the 2nd example of the plan making method. It is a flowchart following FIG. 24-1.

[Prerequisite form]
The present inventors have proposed a technique described in Patent Document 1 in Japanese Patent Application No. 2016-104543, which can formulate a cast plan in a short time without significantly reducing the planning accuracy. An embodiment of the present invention is a technique premised on the technique described in Japanese Patent Application No. 2016-104543. Therefore, before the description of the embodiment of the present invention, among the techniques described in Japanese Patent Application No. 2016-104543, the technique that is the premise of the embodiment of the present invention will be described as a premise embodiment.

In the following, as a production plan, a case where a cast plan for a continuous casting machine is created (that is, cast knitting is performed) will be described as an example. In this case, "slab" corresponds to "product", "cast" corresponds to "lot", and "casting" corresponds to "manufacturing". In addition, "product" refers to a product in which raw materials have been modified, and is not limited to final products and the like on the market. For example, intermediate products (semi-finished products) are also included in "products".

(Overview)
The outline of the premise form will be described.
FIG. 1 is a diagram illustrating an outline of an outline of a method for creating a cast plan in a premise form.
Slab information including the manufacturing conditions of the slab is associated with each of the plurality of slabs scheduled to be manufactured during the planning period. Based on this slab information, each of the plurality of slabs is grouped so that the slabs whose production conditions match within a predetermined range belong to the same slab group.

In FIG. 1, the slab group No. 1 that identifies the slab group thus obtained is shown. And the slab group No. The number of slabs belonging to the slab group (number of slabs) and the slab group No. Indicates the earliest (earliest day) of the desired hot-spreading dates given as one of the manufacturing conditions for slabs belonging to the slab group of. The slab manufactured by the continuous casting machine is placed in the yard and then hot-rolled in the hot rolling process of the next step. The day desired by the factory as the day for performing this hot rolling is the desired day for hot rolling. That is, the desired hot-rolling date is the delivery date of the slab to the hot-rolling factory. The desired hot-rolling date is set based on, for example, the delivery date of the coil obtained by winding the hot-rolled steel sheet obtained by hot rolling to the customer, the operating status of the equipment of the hot-rolling line, and the like.

In the example shown in FIG. 1, the slab groups are sorted in order from the earliest desired hot extension date (earliest date). In FIG. 1, for convenience of explanation, the order in which the slab groups are arranged in order from the earliest desired hot extension date (earliest date) and the slab group No. Is the same as.
Next, a part of a plurality of slab groups is selected to create a subset of the selected slab groups. In the example shown in FIG. 1, 10 slab groups are selected from the 27 slab groups having the earliest desired hot-spreading date (earliest date), and a subset of these 10 slab groups is created. For each of these subsets, it is determined whether or not the conditions (constraints) that can be manufactured by the same cast are satisfied, and the subsets that satisfy this condition are set as cast candidates.

Next, the optimum combination of cast candidates is derived from the cast candidates by solving the optimization problem. The details of the optimization problem will be described later. In the following description, the optimum cast candidate thus obtained will be referred to as a “cast piece” as necessary.
FIG. 1 shows that the cast pieces 101a to 101d were obtained as a result of the calculation of such an optimization problem (the result of the "first division optimization"). In FIG. 1, one quadrangle shown in the cast pieces 101a to 101r indicates a slab group constituting the cast piece, and the numbers in the quadrangle indicate the slab group No. of the slab group. Is shown.

Next, each of the cast pieces 101a to 101d is redefined as a new slab group, and all the new slab groups and some of the unselected slab groups are selected, and the selected slab group is selected. Create a subset of. In the example shown in FIG. 1, 6 slab groups are selected from the 17 unselected slab groups having the earliest desired hot extension date (earliest date), and 4 new slab groups and 6 of these are selected. Create a subset of the Slavic groups. As described above, among these subsets, a subset that satisfies the conditions (constraints) that can be included in the same cast is set as a cast candidate, and the optimum combination of cast candidates (cast pieces) is selected from the cast candidates. , Derived by solving the optimization problem.

FIG. 1 shows that the cast pieces 101e to 101h were obtained as a result of the calculation of this optimization problem (the result of the “second division optimization”). In FIG. 1, the portion that has already been derived as a cast piece and has become a new slab group is shown by painting it in gray.
Next, each of the cast pieces 101e to 101h thus obtained is redefined as a new slab group. Then, the cast pieces 101i-101m and 101n-101r are derived in this order by the same procedure as described above. In this way, the slab group is gradually added to the cast piece while maintaining the cast piece already derived, and the size of the cast piece is increased. Actually, the order of the slab groups included in the cast is determined based on the width of the slabs belonging to the slab group, but here, the size of the cast pieces is expanded while maintaining the cast pieces already derived. To show the situation in an easy-to-understand manner, the newly added slab group is connected behind the cast piece that has already been created, without sorting by width.

When the slab group included in the cast piece derived as described above satisfies a predetermined convergence determination condition, the cast piece is determined as a cast. In the example shown in FIG. 1, it is assumed that the convergence test condition is satisfied when all the slab groups are included in any of the cast pieces. Therefore, the cast pieces 101n to 101r are cast. From the cast obtained in this way, the cast to which each slab belongs is output as the result of planning the cast plan.
Note that FIG. 1 shows the concept of the premise form, and does not necessarily correspond to the contents described below. For example, the number of slabs included in the slab group shown in FIG. 1 and the contents of the desired hot spreading date (earliest date) are different from those shown in FIGS. 3 to 6.

(Cast knitting device 200)
FIG. 2 is a diagram showing an example of a functional configuration of the cast knitting device 200 in the premise form. The hardware of the cast knitting device 200 is realized by using, for example, an information processing device including a CPU, a ROM, a RAM, an HDD, and various interfaces, or dedicated hardware.

<Slab information acquisition department 201>
The slab information acquisition unit 201 acquires and stores the slab information. The slab information acquisition unit 201 acquires slab information by, for example, operating the cast knitting device 200 by an operator, receiving slab information transmitted from an external device, or reading slab information stored in a portable storage medium. To do.

FIG. 3 is a diagram showing an example of the slab information 300.
In FIG. 3, the slab information 300 refers to the slab No. , Material, slab weight, slab width, slab thickness, coil width, coil thickness, coil length, and desired date of hot spreading are interrelated information. Slab information is given individually for each slab to be planned.

Slab No. Is a number that identifies the slab.
The material indicates the components of the slab and the like. Here, the material is represented by a symbol that identifies the material.
The slab weight, slab width, and slab thickness are the weight, width, and thickness of the slab, respectively. The material, slab weight, slab width, slab thickness, and desired hot spreading date are manufacturing conditions in the slab manufacturing process (continuous casting process).

The coil width, coil thickness, and coil length are the slab Nos. The width, thickness, and length of the coil obtained by hot rolling the slab identified by. The coil width, coil thickness, coil length, and desired hot rolling date are manufacturing conditions in a step (hot rolling step) after the step of manufacturing the slab. As described above, the desired hot rolling date is the date desired by the factory as the date for hot rolling.

<Slab group creation department 202>
The slab group creation unit 202 is included in the slab information 300 so that slabs having matching manufacturing conditions within a predetermined range belong to the same slab group based on the slab information 300 acquired by the slab information acquisition unit 201. Group each of the slabs.
First, the slab group creation unit 202 rearranges the slabs (records) of the slab information 300 based on at least one of the slab manufacturing conditions included in the slab information 300. In this embodiment, the slabs (records) of the slab information 300 are rearranged in order from the slab having the earliest desired date of hot extension. FIG. 4 is a diagram showing an example of the slab information 400 in which the slabs (records) of the slab information 300 shown in FIG. 3 are rearranged in order from the earliest desired hot spreading date. In order to show the relationship between FIGS. 3 and 4 in an easy-to-understand manner, the same slab No. Is attached. However, in FIG. 4, the slab No. in the top row is No. Is set to "1", and the slab Nos. May be reattached. Further, in the slabs (records) having the same desired date of hot extension, the slabs may be sorted based on the item to be emphasized next to the desired date of hot extension.

Next, the slab group creation unit 202 selects one of the unselected slabs (records) included in the slab information 400 sorted as described above, which is the highest slab. That is, the slab group creation unit 202 selects one of the unselected slabs (records) included in the slab information 400 that has the earliest desired hot extension date.

Next, the slab group creation unit 202 determines whether or not there is a slab group to which the slab selected from the slab information 400 can be added among the slab groups already created. As described above, in the present embodiment, slabs having matching slab production conditions within a predetermined range are included in the same slab group.
Specifically, in the present embodiment, the slab group creating unit 202 selects from the slab information 400 among the slab groups already created when all the following determination conditions (A1) to (D1) are satisfied. Determine that there is a slab group to which slabs can be added.

(A1) The maximum value of the difference between the slab width (slab width) included in the already created slab group and the slab width (slab width) selected from the slab information 400 is 100 [mm] or less.
(B1) The maximum value of the difference between the slab thickness (slab thickness) included in the already created slab group and the slab thickness (slab thickness) selected from the slab information 400 is 2 [mm] or less.
(C1) The maximum value of the difference between the desired heat extension date of the slab included in the already created slab group and the desired heat extension date of the slab selected from the slab information 400 is 2 [days] or less.
(D1) The material of the slab included in the already created slab group and the material of the slab selected from the slab information 400 are the same.

When the slab group creation unit 202 determines that there is no slab group that can add the slab selected from the slab information 400 among the slab groups that have already been created, the slab group creation unit 202 creates a new slab group and selects the slab group. Include the slab in the new slab group created.
On the other hand, if there is a slab group to which the slab selected from the slab information 400 can be added to the already created slab group, the slab group creation unit 202 sets the slab included in the slab group and the selected slab. It is determined whether or not the total number of sheets is equal to or less than the upper limit value. Since the rolling rolls are worn in the hot rolling process, there is a limit to the number of slabs of the same width band that are continuously hot-rolled at the same chance. Therefore, in this embodiment, an upper limit is set for the number of slabs to be included in one slab group. In this embodiment, this upper limit is set to 40 [sheets] or less.

The slab group creation unit 202 creates a new slab group when the total number of slabs included in the slab group to which the slab selected from the slab information 400 can be added and the number of the selected slabs is not less than the upper limit value. Include the selected slab in the new slab group created.
On the other hand, when the total number of slabs included in the slab group to which the slab selected from the slab information 400 can be added and the number of the selected slabs is equal to or less than the upper limit, the slab group creation unit 202 attaches the selected slab to the slab. Include in slab group.

The slab group creation unit 202 selects one slab at the top of the slab information 400 from among the unselected slabs (records) included in the slab information 400 sorted in order from the earliest desired hot extension date. Then, the above processing is executed, and the slab included in the slab information 400 is included in any slab group.

FIG. 5 is a diagram showing an example of slab group information 500 created from the slab information 400 shown in FIG. The slab group information 500 is a list of slab groups.
In FIG. 5, the slab group information 500 refers to the slab group No. , Material, slab width (maximum, minimum), slab thickness (maximum, minimum), slab weight, coil length, desired hot spreading date (earliest, latest), and number of slabs correlate with each other This is the information that was given.

Slab group No. Is a number that identifies the slab group.
The material is a material of a slab belonging to the slab group. In this embodiment, slabs of the same material belong to one slab group according to the condition (D1) described above.
The maximum value of the slab width means the maximum value of the width (slab width) of the slab included in the slab group. The minimum value of the slab width means the minimum value of the width (slab width) of the slab included in the slab group.

The maximum value of the slab thickness means the maximum value of the slab thickness (slab thickness) included in the slab group. The minimum value of the slab thickness means the minimum value of the slab thickness (slab thickness) included in the slab group.
The slab weight is the total value of the slab weights (slab weights) included in the slab group.

The coil length is the total value of the coil lengths of the slabs included in the slab group.
The earliest desired date for hot extension is the earliest desired date for hot extension of slabs included in the slab group. The latest desired hot extension date is the latest of the desired hot extension dates of the slabs included in the slab group.
The slab group creation unit 202 creates the slab group information 500 as described above.

As described above, in this embodiment, a plurality of slab groups are combined to form a cast. Therefore, if the production conditions of the slabs belonging to one slab group (for example, at least one of the slab thickness, the slab width, and the desired rolling date) vary, the slab production conditions are also used in the cast combining these. The variation becomes large. Therefore, in the present embodiment, the slab group creation unit 202 rearranges the records (slabs) of the slab information 300 according to at least one value of the slab manufacturing conditions included in the slab information 300 (in this embodiment, the desired hot extension date). , Determine the slab group to which the slab belongs in the sorted order. In this way, it is possible to prevent slabs having significantly different production conditions from belonging to the same slab group.

<Slab group selection unit 203>
The slab group selection unit 203 rearranges the slab groups (records) of the slab group information 500 created by the slab group creation unit 202 in order from the slab group having the earliest desired hot extension date. FIG. 6 is a diagram showing an example of slab group information 600 in which the slab groups (records) of the slab group information 500 shown in FIG. 5 are rearranged in order from the earliest desired hot-spreading date. In order to show the relationship between FIGS. 5 and 6 in an easy-to-understand manner, in FIGS. 5 and 6, the same slab group No. Is attached. However, in FIG. 6, the slab group No. 1 in the top row is shown. Is set to "1", and the slab group Nos. May be reattached.

The slab group selection unit 203 selects a predetermined number of slab groups (records) included in the slab group information 600 sorted as described above in order from the upper slab group (record). That is, the slab group selection unit 203 sets a predetermined number of a part of the slab groups (records) included in the slab group information 600 sorted as described above in order from the earliest desired hot-extending date. Just select.

When the number of selected slab groups per time (the predetermined number) is "5" and the slab group selection unit 203 selects the first slab group, the slab group information 600 shown in FIG. 6 Select the slab group on the 1st to 5th lines. The case of selecting the slab group from the second time onward will be described later. Since the calculation time required for the optimization calculation becomes longer as the number of slab groups to be selected increases, the number of slab groups to be selected is set to at least 2 or more based on the time allowed for this calculation.

<Cast candidate derivation unit 204>
The cast candidate derivation unit 204 derives a cast candidate from the slab group selected by the slab group selection unit 203.
First, the cast candidate derivation unit 204 enumerates all possible combinations (subsets) of slab groups from the set of slab groups selected by the slab group selection unit 203. When the number of slab group selections per time in the slab group selection unit 203 is "5", the cast candidate derivation unit 204 has 32 (= ²⁵ ) combinations (subsets) of slab groups (subset). Subsets) are listed.

Next, the cast candidate derivation unit 204 determines whether or not all of the following (A2) to (E2) constraint conditions are satisfied for each of the listed slab group combinations (subsets), and only those that satisfy the conditions. Is adopted as a cast candidate.

(A2) Material restrictions The materials of the slabs included in the combination (subset) of the slab groups do not contain any materials that are prohibited from being included in the same cast.
For example, if the slab of material A and the slab of material C cannot be included in the same cast, the combination of the slab group to which the slab of material A belongs and the slab group to which the slab of material C belongs violates the material restriction. Therefore, it is not adopted as a cast candidate.

(B2) Cast weight The total weight of the slabs included in the combination (subset) of slab groups does not exceed the upper limit of the weight of (one) cast.
For example, when the upper limit of the cast weight is 1300 [ton], the slab group No. 1 shown in FIG. The total slab weight of the slab groups of "1", "2", "5", and "3" is 1321.7 [ton], so the combination (subset) of these slab groups is adopted as a cast candidate. Not done.

In this embodiment, since the slabs contained in the same cast are hot-rolled in the hot rolling process as the same lot (chance), it is necessary to derive a cast that satisfies the restrictions generated during hot rolling. is there. Therefore, in this embodiment, the following constraint conditions (C2) to (E2) are adopted.

(C2) Coil length The total coil length of the slabs included in the combination (subset) of the slab groups does not exceed the upper limit value.
For example, when the upper limit value is 100 [km], the slab group No. 1 shown in FIG. The total coil length of the slab groups of "1", "2", "5", and "3" is 104.7 [km], so the combination (subset) of these slab groups is a cast candidate. Not adopted.

(D2) Width shift constraint The difference in width between the two slabs that are in phase with each other when sorted in the rolling order is less than or equal to the upper limit.
In the hot rolling process, there may be a restriction that hot rolling must be performed in order from the slab having the largest width, that is, so-called narrow down. In this case, when the slabs included in the slab group combination (subset) are rearranged in order from the one with the widest slab width, the difference between the widths (slab widths) of the two slabs before and after each other must be equal to or less than the upper limit. is there. For example, when this upper limit value is 150 [mm], the slab group No. Considers whether or not the Slavic groups (subsets) of "2" and "5" can be adopted as cast candidates. Slab group No. The minimum value of the slab width of the slab group of "2" is 1600 [mm], and the slab group No. The maximum value of the slab width of the slab group of "5" is 1400 [mm]. Therefore, when the slabs included in these slab groups are rearranged so as to be narrow down, a difference of 200 [mm] or more occurs as a difference in slab width between any of the slabs. Therefore, the combination (subset) of these Slavic groups is not adopted as a cast candidate.

(E2) Constraints on the number of slabs with the same width The number of slabs whose width difference is less than or equal to a certain value is less than or equal to the upper limit.
If a large number of slabs having a width difference of a certain value or less are included in the same chance, the coil shape may be deteriorated due to the wear of the rolling roll, and the quality of the coil may be deteriorated. Therefore, a constraint condition is provided that the number of slabs having a width difference of a certain value or less is not more than the upper limit value. For example, when the number of slabs having a width difference of 100 [mm] or less is 40 [sheets] or less as the same width constraint, the slab group No. In the slab groups (subsets) of "2" and "4", the number of slabs having a slab width in the range of 1600 [mm] to 1700 [mm] is 49 [sheets]. Therefore, the combination (subset) of these Slavic groups is not adopted as a cast candidate.

<Optimization unit 205>
The optimization unit 205 derives the optimum combination of cast candidates (cast pieces) from the cast candidates derived by the cast candidate derivation unit 204 by solving the optimization problem. In this embodiment, the set partitioning problem is used as the optimization problem.

FIG. 7 is a diagram conceptually showing an example of a method for solving a set partitioning problem.
As shown in FIG. 7, it is assumed that a set M composed of m elements is given (the black circle in FIG. 7 is one element). In the example shown in FIG. 7, 10 elements are given (m = 10). In this embodiment, one element corresponds to one slab group.

Next, n subsets are derived as subsets of set M. For example, all possible combinations of elements are subsets. However, instead of all possible combinations of elements as subsets, some combinations may be used as subsets. In FIG. 7, for convenience of notation, only subsets 701a to 701g are shown. In this embodiment, one subset corresponds to one cast candidate.
Next, an evaluation index (cost) is derived for each of these n subsets.

Next, the combination of subsets in which the sum of the evaluation index (cost) values is optimal is set as the optimum solution. The smaller the value of the evaluation index is, the more desirable the problem setting is, the minimum value is optimal, and conversely, the larger the value of the evaluation index is, the more desirable the problem setting is, the maximum value is optimal. FIG. 7 shows that the subsets 701a, 701d, and 701f are optimal solutions. In this embodiment, each of these subsets corresponds to a cast piece.
In the partition of a set problem, the optimum solution is generally derived under the constraint that the same element is not duplicated in a plurality of subsets. As shown in FIG. 7, the 10 elements are included in only one of the subsets.
Since the partitioning problem itself can be realized by a known technique, detailed description thereof will be omitted here.

On the premise of the above, an example of the processing performed by the optimization unit 205 will be described.
In this embodiment, the optimization problem (set partitioning problem) for deriving the optimum cast (cast piece) is formulated by the following equations (1) to (3). That is, in this embodiment, the optimization unit 205 determines when the value of the objective function f of the following equation (1) is minimized within a range satisfying the constraint equations of the following equations (2) and (3). Derivation of the variable x _j. The optimization problem (partitioning problem) can be solved by, for example, a known mixed integer programming method, and a commercial solver (cplex or the like) can be used at that time.

_{Here, let i ∈ N I be} the set of slab groups i included in the cast candidate j, and let j ∈ N _J be the set of cast candidates j. Further, the decision variable x _{j is a 0-1 variable (x j} ∈ {0, 1}) that becomes “1” when the cast candidate j is adopted as the cast piece and becomes “0” when the cast candidate j is not adopted. To do. Further, c _j represents an evaluation value of the cast candidate j. In this embodiment, the evaluation value c _j is expressed by the following equation (4).
c _j = C _W x W + C _T x T + C _D x D + C _N- C _S x S ... (4)

In the equation (4), W is the difference between the maximum value and the minimum value of the slab width (slab width) included in the cast candidate j. C _W is a weighting factor for W.
T is the difference between the maximum value and the minimum value of the slab thickness (slab thickness) included in the cast candidate j. C _T is a weighting factor for T.
D is the difference between the average value of the desired hot-spreading date of the slab included in the cast candidate j and the earliest date. C _D is a weighting factor for D.

_CN is a weighting factor for the number of casts. As described above, the decision variable x _j is a 0-1 variable that becomes “1” when the cast candidate j is adopted as the cast piece and becomes “0” when the cast candidate j is not adopted. Therefore, in the calculation of Eq. (1), _{the integrated value of the coefficient} of determination x j is the number of casts. Thus, by integrating the value obtained by multiplying the weight coefficient C _N in decision variables x _j, it is possible to evaluate the number of casts.
S is the number of slabs included in the cast candidate j. C _S is a weighting factor for S. As the number of slabs contained in one cast increases, the yield improves. Therefore, the evaluation value c _j of the cast candidate j becomes a value indicating that the evaluation is high (the value becomes smaller in the equation (4)). ).
The weighting coefficients C _W , C _T , C _D , C _N , and C _S are preset depending on how much each evaluation item is emphasized, and represent the balance of evaluation among each evaluation item.

For example, the slab group Nos. 500 and 600 of the slab group information 500 and 600 shown in FIGS. 5 and 6 are shown. _{The evaluation value c j} of the cast candidate j composed of the Slavic groups of "1" and "2" is as follows. First, W is 200 (= 1700-1500). Further, T is 0 (= 250-250). Further, D is 0.4 (= 1.4-1). Here, when obtaining D, the slab group No. The average value of the desired hot-spreading dates of the slabs included in the "1" and "2" slab groups is assumed to be June 1.4. Further, S is 37 (= 9 + 28).
From the above, for _{example, C W = 1, C T} = 1, C D = 200, C N = 1000, if a C _S = 1, the evaluation value c _j is, 1243 (= 1 × 200 + 1 × 0 + 200 × 0.4 + 1000-1 × 37).

In (2) and (3), M _i is the number of slabs which belong to the selected slab group i as cast candidate j. H _MAX is the upper limit of the number of slabs. Equation (2) _{i ∈ N I and} M i ≧ H _{MAX is when the number of slabs M i} belonging to the slab group i is equal to or greater than the upper limit value H _MAX for each of the slab groups i included in the cast candidate j. Means that equation (2) is applied. Further, in equation (3), _{i ∈ N I and} M i <H _{MAX , the number of slabs M i} belonging to the slab group i is less than the upper limit value H _MAX for each of the slab groups i included in the cast candidate j. In this case, it means that the equation (3) is applied.

_{The A ij} of the equations (2) and (3) is a matrix having the slab group i as a row and the cast candidate j as a column, and has "0" or "1" as an element.
FIG. 8 is a diagram conceptually explaining the _{matrix A ij.}
In FIG. 8, each column shows a slab group i included in one cast candidate j. A "1" is given to the row corresponding to the slab group i included in the cast candidate j, and a "0" is given to the row corresponding to the slab group i not included in the cast candidate j. For example, cast candidate 1 (j = 1) includes slab groups 1 and 2 (i = 1, 2), and does not include other slab groups.

The result of such assignment of "1" or "0" for each of the cast candidates j derived by the cast candidate derivation unit 204 is the matrix A _ij . The part below the arrow line in FIG. 8 indicates that the evaluation value c _j and the determination variable x _j can be obtained for each cast candidate j.
In the example shown in FIG. 8, the matrix A _ij is represented by the following equation (5).

Therefore, the constraint condition of the equation (2) _{indicates that the slab group i in which the number of slabs M i} belonging to the slab belongs to the upper limit value H _MAX or more is always adopted once as the slab group to be included in the cast piece.
On the other hand, (3) the constraints slab group i number M _i belonging slab is less than the upper limit value H _MAX are either employed once the slab group including cast piece, or not employed once (The number of hires is 0 (zero)).
The optimization unit 205 _{executes the derivation of the determination variable x j} as described above every time the cast candidate is derived by the cast candidate derivation unit 204. The cast candidate j corresponding to the decision variable x _j given "1" becomes a cast piece.

<Judgment unit 206>
The determination unit 206 determines whether or not the result of the optimization calculation in the optimization unit 205 satisfies the convergence test condition.
In this embodiment, a slab group creation unit 202 or a slab group redefinition unit 207, which will be described later, is created in any of the cast candidates j (cast pieces) corresponding to the determination variable x _{j given "1" (.} When all of the latest) slab groups are included one by one, it is determined that the result of the optimization calculation in the optimization unit 205 satisfies the convergence test condition, and if not, the optimization in the optimization unit 205 is performed. It is assumed that the result of the conversion calculation does not satisfy the convergence test condition.

As a result of this determination, if the result of the optimization calculation in the optimization unit 205 satisfies the convergence test condition, the determination unit 206 is given a "1" in the result of the optimization calculation in the optimization unit 205. The cast candidate j (cast piece) corresponding to _{x j is confirmed as a cast.} Then, the determination unit 206 activates the output unit 208.
On the other hand, when the result of the optimization calculation in the optimization unit 205 does not satisfy the convergence test condition, the determination unit 206 activates the slab group redefinition unit 207.

<Slab group redefinition unit 207>
The slab group redefinition unit 207 has a plurality of slabs included in the cast candidate j (cast piece) corresponding _{to the determination variable x j} given "1" as the (latest) result of the optimization calculation in the optimization unit 205. Redefining the group as one slab group is performed individually for each cast candidate j (cast piece).
FIG. 9 is a diagram showing an example of the slab group information 900 after the slab group is redefined.
In FIG. 9, in the slab group information 500 shown in FIG. 5, the slab group No. The slab groups of "1" and "2" are included in the first cast piece, and the slab group No. The slab groups of "3" and "4" were included in the second cast piece, and the slab group No. The case where the slab group of "5" is included in the third cast piece is shown as an example.

The slab group No. included in the first cast piece. Takes as an example the case where the slab groups of "1" and "2" are combined into one and a new slab group is redefined, and the slab group information 500 shown in FIG. 5 and the slab group information 900 shown in FIG. 9 are taken as an example. Explain the relationship with.

The slab group redefinition unit 207 has a slab group No. From the maximum and minimum values of the slab widths of the slab groups of "1" and "2", 1700 and 1500 are derived as the maximum and minimum values of the slab width of the new slab group, respectively.
The slab group redefinition unit 207 has a slab group No. From the maximum and minimum values of the slab thickness of the slab groups of "1" and "2", 250 and 250 are derived as the maximum and minimum values of the slab thickness of the new slab group, respectively.

The slab group redefinition unit 207 has a slab group No. Adds the slab weights of the slab groups "1" and "2" to derive 736.4 (= 185.3 + 551.1) as the slab weight of the new slab group.
The slab group redefinition unit 207 has a slab group No. Adds the coil lengths of the slab groups "1" and "2" to derive 62.2 (= 25.4 + 36.8) as the coil length of the new slab group.

The slab group redefinition unit 207 has a slab group No. From the earliest and latest desired rolling dates of the "1" and "2" slab groups to the earliest and latest desired rolling dates of the new slab group, June 1 and June 2, respectively. Derive the day.
The slab group redefinition unit 207 has a slab group No. Adds the number of slabs in the slab groups of "1" and "2" to derive 37 (= 9 + 28) as the number of slabs in the new slab group.
The slab group No. However, the material of the slab groups of "1" and "2" is "A", so it is not changed.

The slab group redefinition unit 207 has set the slab group No. 207 of the slab group information 500 shown in FIG. Deleted the slab groups of "1" and "2", and the slab group consisting of the material, slab width, slab thickness, slab weight, coil length, desired hot spreading date, and number of slabs derived as described above ( A slab group No. that newly generates a record) and identifies the slab group (record). Is given to the slab group (record). In FIG. 9, the slab group No. Is a new slab group slab group No. redefined from the "1" and "2" slab groups. As an example, the case where "1" is given is shown.

The slab group No. included in the second cast piece. However, a new slab group can be obtained in the same manner for the slab groups of "3" and "4". In FIG. 9, the slab group No. of the slab group information 500 shown in FIG. 5 is shown. Is a new slab group slab group No. redefined from the "3" and "4" slab groups. As an example, the case where "2" is given is shown.

The slab group included in the third cast piece is the slab group No. Is only the "5" Slavic group. Therefore, the slab group No. For the slab group with "5", the slab group No. Only changed. In FIG. 9, the slab group No. of the slab group information 500 shown in FIG. 5 is shown. Is a new slab group redefined from the "5" slab group No. As an example, the case where "3" is given is shown.

In addition, the slab group No. of the slab group information 500 shown in FIG. For the slab groups of "6" to "10", the slab group No. Only changed. In FIG. 9, the slab group No. of the slab group information 500 shown in FIG. 5 is shown. Is a new slab group slab group No. redefined from the slab groups "6" to "10". As an example, the case where "4" to "8" are given is shown.

Then, the slab group selection unit 203 selects a part of the slab groups from the slab group information 900 composed of the slab groups redefined as described above, and the cast candidate derivation unit 204 selects from the selected slab group. , The cast candidate is derived, the optimization unit 205 derives the cast piece from the cast candidate, and the determination unit 206 determines whether or not the result of the optimization calculation in the optimization unit 205 satisfies the convergence determination condition. If the determination is made and the result of the optimization calculation in the optimization unit 205 does not satisfy the convergence determination condition, the slab group redefinition unit 207 will perform a plurality of slab groups included in the cast piece obtained by the optimization unit 205. Is redefined as one slab group. The above processing is repeated by the determination unit 206 until the result of the optimization calculation in the optimization unit 205 is determined to satisfy the convergence test condition. Here, when the number of selections of the slab group at one time is "5" and the slab group selection unit 203 selects the slab group from the second time onward, one line of the slab group information 900 shown in FIG. Select the slab group from the 1st to the 5th line.

By doing so, as shown in FIG. 1, every time the optimization calculation is performed in the optimization unit 205, the cast piece 101a-101d → the cast piece 101e-101h → the cast piece 101i-101m. The size of the piece gradually increases, and finally the cast piece 101n-101r becomes a cast.

If you try to derive a cast from all the slab groups included in the slab group information 500 at once, the number of combinations of slab groups will be enormous (that is, the problem scale will increase), and the cast will be performed within a practical calculation time. It is not easy to derive. On the other hand, in this embodiment, a part of the slab group included in the slab group information 500 is selected to derive a cast piece, and the slab group included in the derived cast piece is redefined as one slab group. The size of the cast piece is gradually increased by repeatedly taking in the unselected slab group and deriving the cast piece to the maximum. Therefore, even for a large-scale problem, the cast plan can be derived in a practical calculation time. In addition, since the slab groups are sorted in advance according to the items that are important in operation, the cast pieces are generated and the slab groups are redefined in the sorted order, so that the variation of the important items in the generated cast pieces is suppressed. This makes it possible to minimize the decrease in accuracy due to dividing the problem and finding the solution as described above.

<Output unit 208>
The output unit 208 determines that the result of the optimization calculation in the optimization unit 205 satisfies the convergence test condition by the determination unit 206, and when the cast is confirmed, the information of the slab included in each cast is used in the cast plan. Output as a planning result. The output unit 208 displays the slab information included in each cast by displaying at least one of the display on the computer display, the transmission to the external device, and the storage in the internal or external storage medium. Is output. For example, the output unit 208 has the cast No. 2, which is a number for identifying the cast, as an item of the slab information 300 shown in FIG. The information added with can be output as the information of the slab included in each cast.

As shown in equation (3), there may be slab groups not included in the cast. That is, there may be a case where the above-mentioned convergence test condition cannot be satisfied. In such a situation, the output unit 208 can output the information of the slab group not included in such a cast together. Thereby, the operator can instruct by the operation of the cast knitting device 200 which cast of the cast plan derived as described above the slab group (the slab included in the slab) is to be incorporated. As a result, the cast knitting device 200 can include the slab group in the designated cast. Alternatively, instead of doing so, the slab group may be included in the cast plan in the next planning period.

In addition, for example, cast pieces for all the numbers of slab groups i so that the calculation converges even when a so-called remainder occurs, in which slabs cannot be incorporated into any cast as described above. When the ratio of the number of slab groups i included in any of the above (that is, the adoption rate of the slab group i to the cast piece) is equal to or more than a predetermined ratio, it may be determined that the convergence determination condition is satisfied. In addition, the ratio of the number of slabs in the slab group i included in any of the cast pieces to the number of slabs in all the slab groups i (that is, the adoption rate of the slabs in the cast pieces) is equal to or higher than a predetermined ratio. In some cases, it may be determined that the convergence determination condition is satisfied.

Further, the adoption rate of the slab group i (slab) for the cast piece is defined as the ratio of the weight of the slab contained in the slab group i included in any of the cast pieces to the weight of the slab contained in all the slab group i. May be good. Further, the adoption rate of the slab group i (slab) to the cast piece is set to the total coil length of the slabs included in all the slab groups i, and the slab included in the slab group i included in any of the cast pieces. It may be a ratio of the total coil lengths.

In addition, the difference between the value of the objective function f obtained as a result of the previous optimization calculation and the value of the objective function f obtained as a result of the current optimization calculation is less than or equal to a predetermined value, or the previous optimization. When the value of the objective function f obtained as a result of the calculation and the value of the objective function f obtained as a result of the optimization calculation this time are the same, it may be determined that the convergence determination condition is satisfied.

(Summary of premise form)
As described above, in the present embodiment, among the slabs included in the slab information 300, the slabs having the same manufacturing conditions within a predetermined range (slabs satisfying all the determination conditions of (A1) to (D1)) are the same. Each of the slabs included in the slab information 300 is grouped so as to belong to the group. Therefore, even when there are many slabs to be created for the cast plan, it is possible to suppress an increase in calculation time.

Further, in this embodiment, a part of a plurality of slab groups is selected in order from the earliest desired hot-spreading date. Then, among the selected slab groups, those satisfying the conditions (all the constraint conditions of (A2) to (E2)) that can be included in the same cast are derived as cast candidates. Objective function f that has _{a decision variable x j} , which is a variable indicating whether or not to adopt a cast candidate (as a cast piece or a cast), _{and an evaluation value c i} expressed using an evaluation index including the number of casts. The decision variable x _j that minimizes is derived by performing the optimization calculation. As a constraint in the optimization calculation, the number of slab groups included in the optimum cast candidate and the number of slab groups selected prior to deriving the cast candidate are the same, and the same slab group is used. Adopt the condition that they are not included in different cast candidates. The slab groups included in the cast candidates adopted by such optimization calculation are combined into one as a new slab group (that is, the slab group is redefined). The above process is repeated until the result of the optimization calculation converges.

In this way, a part of the slab group is taken in and the size of the cast piece is gradually increased to create the final cast plan. Therefore, compared to the case where the cast is derived from the slab group at once and the cast plan is created. The cast plan can be derived with a practical calculation time, and the calculation time required to create the cast plan can be shortened. In addition, the slab groups are sorted in advance according to items that are important in terms of operation, such as the earliest date of the desired hot extension date, and the cast pieces are generated and the slab groups are redefined in the sorted order. It is possible to suppress the variation of the emphasized items, and it is possible to minimize the decrease in accuracy due to dividing the cast knitting problem and finding the solution.

Further, in the present embodiment, the constraint condition at the time of the optimization calculation is made different depending on whether or not _{the number of slabs included in the slab group is equal to or more than the upper limit value H MAX.}
That is, the following restrictions are imposed on the slab group in which the number of slabs contained is equal to _{or greater than the upper limit value H MAX.} That is, for slab groups having the same content, a constraint is imposed so that the number of slab groups included in the optimum cast candidates and the number of love groups selected prior to deriving the cast candidates are the same. Therefore, a slab group to which a large number of slabs belong is likely to be adopted as a cast piece. Therefore, the calculation time can be further shortened.

On the other hand, the following restrictions are imposed on slab groups in which the number of slabs contained is _{not equal to or greater than the upper limit H MAX.} That is, for slab groups having the same content, a constraint is imposed that the number of slab groups included in the optimum cast candidates is less than or equal to the number of slab groups selected prior to deriving the cast candidates. This allows the slab group selected prior to deriving the cast candidate to not be included in the optimal cast candidate. Therefore, it is possible to prevent a slab group to which a small number of slabs belong from being included in an unfavorable cast piece.

Further, in this embodiment, among the slab groups, those satisfying the constraint conditions of (C2) coil length, (D2) width shift constraint, and (E2) same width number constraint are adopted as cast candidates. Therefore, the cast, which is a lot in the steelmaking process, can be the same as the chance, which is a lot in the hot rolling process. Therefore, for example, it is possible to prevent the slab from staying in the yard for a long time before being hot-rolled in the hot rolling process. Thereby, for example, it is possible to shorten the manufacturing construction period and suppress the fuel intensity of the heating furnace in the heat spreading process by lowering the temperature of the slab.

[First Embodiment]
As described above, in the premise form, in order to reduce the problem scale of the optimization problem, the calculation time is calculated by solving the optimization problem in units of slab groups in which slabs whose manufacturing conditions match within a predetermined range are aggregated. Can be shortened. In the premise form, as shown in FIG. 1, each time the optimization calculation is performed in the optimization unit 205, the size of the cast piece is as follows: cast piece 101a-101d → cast piece 101e-101h → cast piece 101i-101m. Gradually expands. In this case, as described above, the constraints of (A2) material constraint, (B2) cast weight, (C2) coil length, (D2) width shift constraint, and (E2) same width number constraint are not satisfied, and the cast candidate is not satisfied. The derivation unit 204 may generate a slab group that cannot be incorporated into any cast piece (slab group redefined by the slab group redefinition unit 207).

FIG. 10 is a diagram conceptually showing an example of a slab group that cannot be incorporated into a cast piece (slab group redefined by the slab group redefinition unit 207). Here, for the sake of simplicity, it is assumed that the constraints are (B2) cast weight and (C2) coil length. Further, it is assumed that the upper limit value of the cast weight and the upper limit value of the coil length are 1300 [ton] and 100 [km] exemplified in the premise form, respectively.

As shown in FIG. 10, it is assumed that two slab groups 1001 and 1002 are redefined by the slab group redefinition unit 207 by iterative calculation. In this case, it will be described whether or not the cast candidate derivation unit 204 can combine the slab groups 1003 with the slab groups 1001 and 1002 to make cast candidates.
As shown in FIG. 10, the total weight of the slabs constituting the slab group 1001 (cast weight shown in FIG. 10) is 1200 [ton], and the total weight of the slabs constituting the slab group 1003 (slab Gr weight shown in FIG. 10). ) Is 250 [ton]. Therefore, when the slab group 1003 is combined with the slab group 1001, the total weight (cast weight) of the slabs constituting the combined slab group becomes 1450 [ton], which exceeds the upper limit of 1300 [ton]. .. Therefore, the slab group 1003 cannot be incorporated into the slab group 1001.

The total length of the slab coil constituting the slab group 1002 (coil length shown in FIG. 10) is 85 [km], and the total length of the slab coil constituting the slab group 1003 (coil length shown in FIG. 10) is 20. It is [km]. Therefore, when the slab group 1003 is combined with the slab group 1002, the total length (coil length) of the coils of the slabs constituting the combined slab group becomes 105 [km], which exceeds the upper limit of 100 [km]. .. Therefore, the slab group 1003 cannot be incorporated into the slab group 1002.

As described above, in the premise form, the calculation ends as the slab group 1003 is not incorporated into any of the slab groups 1001 and 1002 (that is, does not become a cast candidate). As described above, in such a case, the premise form allows the operator to instruct which cast of the cast plan the slab included in the slab group not included in the cast is to be included in.

In the cast formation problem, it is desirable to automatically incorporate more slabs into the cast to form a large cast. Therefore, in the embodiment of the present invention described below, more slabs can be automatically incorporated into the cast. By doing so, it is possible to realize that the slab is automatically incorporated into the cast so that the capacity of the cast (the size of the cast determined by the cast weight and the coil length) is as close as possible to the upper limit thereof. Can be expected.

The first embodiment of the present invention will be described below. In the following description, the same parts as those of the premise form will be omitted in detail by adding the same reference numerals as those given in FIGS. 1 to 10.

(Cast knitting device 1100)
FIG. 11 is a diagram showing an example of a functional configuration of the cast knitting device 1100 according to the present embodiment. The hardware of the cast knitting apparatus 1100 is realized by using, for example, an information processing apparatus including a CPU, a ROM, a RAM, an HDD, and various interfaces, and dedicated hardware.

<Slab information acquisition department 201>
The slab information acquisition unit 201 is the same as that described in the premise form, and acquires the slab information 300 (see FIG. 3).
<Slab group creation department 202>
The slab group creation unit 202 is the same as that described in the premise form, and based on the slab information 300, the slab information 300 is provided with the slab information 300 so that the slabs whose manufacturing conditions match within a predetermined range belong to the same slab group. Each of the included slabs is grouped to create slab group information 500 (see FIG. 5).

<Slab group selection unit 203>
The slab group selection unit 203 is the same as that described in the premise form, and the slab group information 600 in which the slab groups (records) of the slab group information 500 are rearranged in order from the slab group having the earliest desired hot extension date. A predetermined number of a part of the included slab groups (records) is selected in order from the upper slab group (record) (see FIG. 6).

<First cast candidate derivation unit 204>
The first cast candidate derivation unit 204 is the same as the cast candidate derivation unit 204 described in the premise form, but the name is changed for convenience of notation. From the slab group selected by the slab group selection unit 203, the first cast candidate derivation unit 204 has all the constraint conditions (A2) to (E2) described in the section <Cast candidate derivation unit 204> of the premise form. A combination of slab groups satisfying is derived as a cast candidate.

<First optimization unit 205>
The first optimization unit 205 is the same as the optimization unit 205 described in the premise form, but the name is changed for convenience of notation. The first optimization unit 205 derives the optimum combination of cast candidates (cast pieces) from the cast candidates derived by the first cast candidate derivation unit 204 by solving the set partitioning problem. _{Specifically, the first optimization unit 205 sets the coefficient of determination x j} when the value of the objective function f of the equation (1) is minimized within the range satisfying the constraint equations of the equations (2) and (3). Derived. As described above, the coefficient of determination variable x _{j is a 0-1 variable (x j} ∈ {0, 1}) which is “1” when the cast candidate j is adopted as the cast piece and “0” when the cast candidate j is not adopted. ).

<First determination unit 206>
The first determination unit 206 is the same as the determination unit 206 described in the premise form, but the name is changed for convenience of notation. The first determination unit 206 determines whether or not the result of the optimization calculation in the first optimization unit 205 satisfies the convergence test condition. However, in the first determination unit 206, the adoption rate of the slabs for the cast pieces (= (total number of slabs incorporated in each cast piece ÷ total number of slabs included in the slab information) × 100) is equal to or higher than a predetermined ratio. If, it is determined that the result of the optimization calculation in the first optimization unit 205 satisfies the convergence test condition, and if not, the result of the optimization calculation in the first optimization unit 205 converges. It shall be determined that the determination conditions are not satisfied. The predetermined ratio is preset depending on how much the slab group i is allowed to be taken into the cast piece. For example, 70 [%] can be adopted as a predetermined ratio. When the adoption rate of the slab group i for the cast piece is 100%, the convergence test condition described in the premise form (whether or not all of the slab groups are included in one of the cast pieces). The same convergence test conditions as (judgment). When the first determination unit 206 determines that the result of the optimization calculation in the first optimization unit 205 satisfies the convergence test condition, the first determination unit 206 activates the built-in candidate slab group presence / absence determination unit 1101 described later.

<First slab group redefinition unit 207>
The first slab group redefinition unit 207 is the same as the slab group redefinition unit 207 described in the premise form, but the name is changed for convenience of notation. The first slab group redefinition unit 207 is activated when the first determination unit 206 determines that the result of the optimization calculation in the first optimization unit 205 does not satisfy the convergence test condition. The first slab group redefinition unit 207 is a cast candidate j (cast piece) corresponding _{to the determination variable x j} given “1” as the (latest) result of the optimization calculation in the first optimization unit 205. The plurality of slab groups included in the above are redefined as one slab group individually for each of the cast candidates j (cast pieces).

Then, the slab group selection unit 203 selects a part of the slab groups from the slab group information 900 (see FIG. 9) composed of the redefined slab groups, and the first cast candidate derivation unit 204 is selected. A cast candidate is derived from the slab group, the first optimization unit 205 derives a cast piece from the cast candidate, and the first determination unit 206 performs optimization calculation in the first optimization unit 205. Determines whether or not the result of the above satisfies the convergence determination condition, and if the result of the optimization calculation in the first optimization unit 205 does not satisfy the convergence determination condition, the first slab group redefinition unit 207 Redefines a plurality of slab groups included in the cast piece obtained by the first optimization unit 205 as one slab group. The above processing is repeated by the first determination unit 206 until the result of the optimization calculation in the first optimization unit 205 is determined to satisfy the convergence test condition.

<Incorporation candidate slab group presence / absence determination unit 1101>
As described above, the built-in candidate slab group presence / absence determination unit 1101 is activated when the first determination unit 206 determines that the result of the optimization calculation in the first optimization unit 205 satisfies the convergence test condition. .. When the built-in candidate slab group presence / absence determination unit 1101 is determined by the first determination unit 206 to satisfy the convergence test condition from the slab groups included in the slab group information 500 created by the slab group creation unit 202. The slab group not included in the cast piece derived by the first optimization unit 205 is extracted (immediately before the determination).

Next, the built-in candidate slab group presence / absence determination unit 1101 includes a slab group included in the cast piece derived by the first optimization unit 205 when the first determination unit 206 determines that the convergence determination condition is satisfied. Based on the result of comparing the predetermined attribute and the threshold value of the above, and the result of comparing the predetermined attribute and the threshold value of the extracted slab group, the cast piece and the candidate slab group to be incorporated in the slab group are included. Determine if it exists. As a result of this determination, if there is an embedded candidate slab group, the embedded candidate slab group presence / absence determination unit 1101 extracts the embedded candidate slab group. In the present embodiment, the cast piece and the slab group whose capacity is less than the threshold value are set as the embedded candidate slab group. More specifically, the cast piece and the slab group in which the total weight of the cast piece and the slab included in the slab group is less than the weight of one charge are defined as the incorporation candidate slab group.

FIG. 12 is a diagram conceptually showing an example of an embedded candidate slab group. It is assumed that one quadrangle shown in FIG. 12 represents one slab group. Further, it is assumed that the broken line indicates the threshold value (weight of one charge).
In FIG. 12, it is assumed that the cast pieces 1201 to 1207 are cast pieces derived from _{the result of the optimization calculation (determination variable x j) in the first optimization unit 205 when the convergence test condition is satisfied.} .. It is assumed that the slab groups 1208 and 1209 are slab groups included in the slab group information 500 created by the slab group creation unit 202 but not included in the derived cast pieces 1201 to 1207.

In the example shown in FIG. 12, since the cast pieces 1206 and 1207 and the slab groups 1208 and 1209 are less than the threshold value (weight of one charge), they are candidates for incorporation slab groups. As described above, not only the slab groups 1208 and 1209 not included in the cast piece but also the cast pieces 1206 and 1207 can be embedded candidate slab groups. When the embedded candidate slab group presence / absence determination unit 1101 extracts the embedded candidate slab group as described above, the embedded candidate slab group disassembly unit 1102 is activated.

<Built-in candidate slab group disassembly unit 1102>
The embedded candidate slab group disassembling unit 1102 decomposes each of the embedded candidate slab groups extracted by the embedded candidate slab group presence / absence determination unit 1101 into one slab. The embedded candidate slab group disassembly unit 1102 registers each disassembled slab as an embedded candidate slab in the embedded candidate slab list.

<Built-in candidate slab selection unit 1103>
The embedded candidate slab selection unit 1103 selects one unselected embedded candidate slab from the embedded candidate slabs registered in the embedded candidate slab list by the embedded candidate slab group decomposition unit 1102.
The selection order of the embedded candidate slabs is not particularly limited, but for example, the selection order of the embedded candidate slabs can be determined based on the slab weight, the coil length, or the desired hot spreading date. The slab weight, coil length, and desired date of hot spreading are included in the slab information 300 (see FIG. 3).

For example, when determining the selection order of candidate slabs to be incorporated as a guideline, the weight of the cast should be as close as possible to the maximum weight of the cast (the maximum value of the total weight of the slabs allowed in one cast). The heavy embedded candidate slab can be preferentially selected. On the other hand, when the selection order of the embedded candidate slabs is determined with the guideline of increasing the number of slabs to be included in the cast, conversely, the embedded candidate slabs having a light slab weight are preferentially selected. When determining the selection order of the candidate slabs to be incorporated, the guideline is to approach the maximum coil length (the maximum value of the coil length that can be rolled in one lot (one chance) in the hot rolling process) as much as possible. Built-in candidate slabs with a long length can be preferentially selected. On the other hand, when the selection order of slabs is determined with the guideline of increasing the number of coils to be rolled in one lot (one chance) in the hot rolling process, conversely, the embedded candidate slabs having a short coil length are given priority. select. For the desired hot extension date, select the earliest desired hot extension date embedded candidate slab.

<Second cast candidate derivation unit 1104>
The second cast candidate derivation unit 1104 has a cast candidate slab group among the cast pieces derived by the first optimization unit 205 when the first determination unit 206 determines that the convergence determination condition is satisfied. All possible combinations (subsets) of the cast pieces not extracted as the embedded candidate slab group by the determination unit 1101 and the embedded candidate slabs selected by the embedded candidate slab selection unit 1103 are listed.

Next, the second cast candidate derivation unit 1104 has all the constraint conditions (A2) to (E2) described in the section <Cast candidate derivation unit 204> of the premise form among the listed combinations (subsets). A combination that satisfies is derived as a cast candidate.

<Second optimization unit 1105>
The second optimization unit 1105 derives the optimum combination of cast candidates (cast pieces) from the cast candidates derived by the second cast candidate derivation unit 1104 by solving the set partitioning problem. The method of solving the set partitioning problem is the same as that of the optimization unit 205 (first optimization unit 205). That is, the second optimization unit 1105 derives the _coefficient of determination x j when the value of the objective function f of the equation (1) is minimized within the range satisfying the constraint equations of the equations (2) and (3). To do. As described above, the coefficient of determination variable x _{j is a 0-1 variable (x j} ∈ {0, 1}) which is “1” when the cast candidate j is adopted as the cast piece and “0” when the cast candidate j is not adopted. ).

In the first optimization unit 205, the number of slab groups selected by the slab group selection unit 203 is included in the combination of the optimum cast candidates (cast pieces) derived by the first optimization unit 205. The optimum combination of cast candidates (cast pieces) is determined according to equations (2) and (3) so that the number of slab groups is equal to or greater than the number of slab groups. On the other hand, in the second optimization unit 1105, the optimum cast candidate (cast piece) derived by the first optimization unit 205 when the first determination unit 206 determines that the convergence determination condition is satisfied. Among them, the number of slab groups included in the combination of cast candidates not including the embedded candidate slab group is included in the combination of the optimum cast candidates (cast pieces) derived by the second optimization unit 1105. The number of embedded candidate slabs equal to or greater than the number of slabs and selected by the embedded candidate slab selection unit 1103 is the optimum cast candidate (cast piece) derived by the second optimization unit 1105. The optimum combination of cast candidates (cast pieces) is determined according to Eqs. (2) and (3) so as to be equal to or more than the number of embedded candidate slabs included in the combination of.

<Second determination unit 1106>
The second determination unit 1106 determines whether or not the result of the optimization calculation in the second optimization unit 1105 satisfies the convergence test condition.
In the present embodiment, when the cast candidate is derived and the optimum cast candidate (cast piece) combination is derived for all the embedded candidate slabs registered in the embedded candidate slab list, the convergence judgment condition is set. It shall be determined that the condition is satisfied. When the second determination unit 1106 determines that the result of the optimization calculation in the second optimization unit 1105 does not satisfy the convergence test condition, the second determination unit 1106 activates the second slab group redefinition unit 1107. If this is not the case, the output unit 1108, which will be described later, is activated.

<Second slab group redefinition unit 1107>
The second slab group redefinition unit 1107, like the slab group redefinition unit 207 (first slab group redefinition unit 207), is the (latest) result of the optimization calculation in the second optimization unit 1105. Redefining a plurality of slab groups included in the cast candidate j (cast piece) corresponding to the determination variable x _j given "1" as one slab group is defined for each of the cast candidates j (cast piece). Perform individually to generate slab group information. Since the slab group information can be generated in the same manner as described with reference to the slab group information 900 of FIG. 9, detailed description thereof will be omitted here.

Then, the embedded candidate slab selection unit 1103 selects one unselected embedded candidate slab from the embedded candidate slabs registered in the embedded candidate slab list by the embedded candidate slab group decomposition unit 1102, and the first The cast candidate derivation unit 1104 of 2 derives a cast candidate from the selected embedded candidate slab and the cast piece which is a slab group redefined by the second slab group redefinition unit 1107, and the second cast candidate is derived. The optimization unit 1105 of the above derives a cast piece from the cast candidate, and the second determination unit 1106 determines whether or not the result of the optimization calculation in the second optimization unit 1105 satisfies the convergence determination condition. If the determination is made and the result of the optimization calculation in the second optimization unit 1105 does not satisfy the convergence determination condition, the second slab group redefinition unit 1107 is obtained by the second optimization unit 1105. A plurality of slab groups contained in a cast piece are redefined as one slab group. The above processing is repeated by the second determination unit 1106 until the result of the optimization calculation in the second optimization unit 1105 is determined to satisfy the convergence test condition.

<Output unit 1108>
The output unit 1108 is included in each cast when the second determination unit 1106 determines that the result of the optimization calculation in the second optimization unit 1105 satisfies the convergence test condition and the cast is confirmed. Output slab information as a result of casting plan. The output unit 1108 contains information on the slab included in each cast by, for example, displaying on a computer display, transmitting to an external device, and storing at least one of internal or external storage media. Is output. For example, the output unit 1108 has a cast No. 1108, which is a number for identifying the cast, as an item of the slab information 300 shown in FIG. The information added with can be output as the information of the slab included in each cast.

Further, in the present embodiment, more slabs are incorporated into the cast as compared with the premise embodiment, but all the embedded candidate slabs are still not incorporated into the cast, and there may be embedded candidate slabs that are not incorporated into the cast. Occurs. In such a case, the output unit 1108 can output the information of the embedded candidate slab not included in such a cast together, as in the premise form. Thereby, the operator can instruct which cast of the cast plan derived as described above to incorporate the embedding candidate slab by operating the cast knitting apparatus 1100. As a result, the cast knitting device 1100 can include the built-in candidate slab in the designated cast. Further, instead of doing so, the embedded candidate slab may be included in the cast plan in the next planning target period.

(flowchart)
An example of the plan creation method performed by the cast knitting apparatus 1100 will be described with reference to the flowcharts of FIGS. 13-1 and 13-2.
First, in step S1301 of FIG. 13-1, the slab information acquisition unit 201 acquires the slab information 300 (see FIG. 3).
Next, in step S1302, the slab group creation unit 202 creates a slab group by grouping each of the slabs included in the slab information 300 acquired in step S1301 and derives the slab group information 500 (FIG. 5). reference). Details of step S1302 will be described later with reference to FIG.

Next, in step S1303, the slab group selection unit 203 rearranges the slab groups (records) of the slab group information 500 created in step S1302 in order from the slab group having the earliest desired hot extension date. From 600 (see FIG. 6), a predetermined number of slab groups are selected in order from the earliest desired hot-spreading date.
Next, in step S1304, the first cast candidate derivation unit 204 derives from the slab group selected in step S1303 those satisfying all the constraint conditions (A2) to (E2) described above as cast candidates. ..

Next, in step S1305, the first optimization unit 205 determines when the value of the objective function f of the equation (1) is minimized within the range satisfying the constraint equations of the equations (2) and (3). The cast piece is derived by deriving the variable x _j.
Next, in step S1306, the first determination unit 206 determines whether or not the result of the optimization calculation in step S1305 satisfies the convergence test condition. As described above, in the present embodiment, the first determination unit 206 determines that the convergence test condition is satisfied when the adoption rate of the slab group for the cast piece is equal to or higher than a predetermined ratio.

As a result of this determination, if the result of the optimization calculation does not satisfy the convergence test condition, the process proceeds to step S1307. Proceeding to step S1307, the first slab group redefinition unit 207 is included in the cast candidate j (cast piece) corresponding _{to the determination variable x j} given “1” as the result of the optimization calculation in step S1305. Redefining a plurality of slab groups as one slab group is performed individually for each cast candidate j (cast piece), the slab group is redefined, and slab group information 900 is generated (see FIG. 9). .. Then, the process returns to step S1303, and the processes after step S1303 are performed using the slab group information 900 of the redefined slab group.

If it is determined in step S1306 that the result of the optimization calculation satisfies the convergence test condition, the process proceeds to step S1308 of FIG. 13-2. Proceeding to step S1308, when the embedded candidate slab group presence / absence determination unit 1101 determines in step S1306 that the convergence test condition is satisfied in the slab group included in the slab group information 500 created in step S1302. It is determined whether or not there is a slab group not included in the cast piece derived in step S1305. As a result of this determination, if there is no slab group not included in the cast piece, step S1309 is omitted and the process proceeds to step S1310 described later. On the other hand, if there is a slab group not included in the cast piece, the process proceeds to step S1309.

Proceeding to step S1309, the embedded candidate slab group presence / absence determination unit 1101 is derived from the slab group information 500 created in step S1302 in step S1305 when it is determined in step S1306 that the convergence test condition is satisfied. Extract slab groups that are not included in the cast pieces. Then, the process proceeds to step S1310.

Proceeding to step S1310, the embedded candidate slab group presence / absence determination unit 1101 has an embedded candidate slab group among the cast pieces derived in step S1305 when it is determined in step S1306 that the convergence test condition is satisfied. Judge whether or not. When the process proceeds from step S1309 to step S1310, the embedded candidate slab group presence / absence determination unit 1101 further determines whether or not there is an embedded candidate slab group among the slab groups extracted in step S1309. As described above, in the present embodiment, the cast piece and the slab group in which the total weight of the cast piece and the slab included in the slab group is less than the weight of one charge is defined as the incorporation candidate slab group. As a result of this determination, if there is no embedded candidate slab group, the process of steps S1311 to S1317 is omitted and the process proceeds to step S1318 described later. On the other hand, if there is an embedded candidate slab group, the process proceeds to step S1311.

Next, when the process proceeds to step S1311, the embedded candidate slab group presence / absence determination unit 1101 extracts the embedded candidate slab group.
Next, in step S1312, the embedded candidate slab group disassembling unit 1102 decomposes each of the embedded candidate slab groups extracted in step S1311 into one slab, and each disassembled slab is used as an embedded candidate slab. Register in the embedded candidate slab list.
Next, in step S1313, the embedded candidate slab selection unit 1103 selects one unselected embedded candidate slab from the embedded candidate slabs registered in the embedded candidate slab list by the embedded candidate slab group decomposition unit 1102. Select a sheet.

Next, in step S1314, the second cast candidate deriving unit 1104 is a cast candidate slab group incorporated in step S1311 among the cast pieces derived in step S1305 when it is determined in step S1306 that the convergence determination condition is satisfied. All possible combinations (subsets) of the cast pieces not extracted as and the built-in candidate slabs selected in step S1313 are listed. Then, the second cast candidate derivation unit 1104 derives the combinations satisfying all the constraint conditions (A2) to (E2) described above as cast candidates for each of the listed combinations (subsets).

Next, in step S1315, the second optimization unit 1105 determines when the value of the objective function f of the equation (1) is minimized within the range satisfying the constraint equations of the equations (2) and (3). The cast piece is derived by deriving the variable x _j.
Next, in step S1316, the second determination unit 1106 determines whether or not the result of the optimization calculation in step S1315 satisfies the convergence test condition. As described above, in the present embodiment, the second determination unit 1106 satisfies the convergence test condition when the processes of steps S1313 to S1317 are completed for all the slabs registered in the embedded candidate slab list in step S1312. Is determined.

As a result of this determination, if the result of the optimization calculation does not satisfy the convergence test condition, the process proceeds to step S1317. Proceeding to step S1317, the second slab group redefinition unit 1107 is included in the cast candidate j (cast piece) corresponding _{to the determination variable x j} given “1” as the result of the optimization calculation in step S1315. Redefining a plurality of slab groups as one slab group is performed individually for each cast candidate j (cast piece), the slab group is redefined, and slab group information is generated. Then, the process returns to step S1313, and the processes after step S1313 are performed using the slab group information of the redefined slab group and the unselected embedded candidate slab.

Then, if it is determined in step S1316 that the result of the optimization calculation satisfies the convergence test condition, the process proceeds to step S1318 of FIG. 13-2. Proceeding to step S1318, the output unit 1108 outputs the slab information included in each cast as the result of planning the cast plan. Then, the process according to the flowchart of FIG. 13-2 is completed.

FIG. 14 is a flowchart illustrating an example of the process of step S1302 of FIG. 13-1.
First, in step S1401, the slab group creation unit 202 rearranges the slabs (records) included in the slab information 300 acquired in step S1301 of FIG. 13-1 in order from the slab having the earliest desired hot extension date (FIG. 4). See slab information 400 shown in.
Next, in step S1402, the slab group creation unit 202 sets “0 (zero)” in the variable k that specifies the rows of the rearranged slab information 400.

Next, in step S1403, the slab group creation unit 202 adds "1" to the variable k that specifies the rows of the rearranged slab information 400.
Next, in step S1404, the slab group creating unit 202 sets the slabs registered in the k-th line of the rearranged slab information 400 in the slab group already created. Determine if there is a slab group that can be added. As described in the section of <Slab group creation unit 202> of the premise form, in the present embodiment, when all the determination conditions of (A1) to (D1) are satisfied, the slab group already created is included in the slab group. Determines that there is a slab group to which the selected slab can be added.

As a result of this determination, if there is no slab group to which the slab registered in the kth line of the sorted slab information 400 can be added to the already created slab group, the process proceeds to step S1405. Proceeding to step S1405, the slab group creation unit 202 creates a new slab group, and includes the slab registered in the kth line of the sorted slab information 400 in the created new slab group. Then, the process proceeds to step S1408, which will be described later.

On the other hand, as a result of the determination in step S1404, if there is a slab group to which the slab registered in the kth line of the rearranged slab information 400 can be added, the process proceeds to step S1406. Proceeding to step S1406, the slab group creation unit 202 increases the number of slabs included in the slab group determined to be able to be added in step S1404 and the number of slabs registered in the kth line of the sorted slab information 400. Determine if the total is less than or equal to the upper limit.

As a result of this determination, if the total number of slabs is equal to or less than the upper limit value, the process proceeds to step S1407. Proceeding to step S1407, the slab group creation unit 202 includes the slab registered in the k-th row of the rearranged slab information 400 in the slab group determined in step S1404 that the slab can be added. Then, the process proceeds to step S1408, which will be described later.

On the other hand, if it is determined in step S1406 that the total number of slabs is not equal to or less than the upper limit value, the process proceeds to step S1405 described above. As described above, in step S1405, the slab group creation unit 202 creates a new slab group, and the slabs registered in the kth line of the rearranged slab information 400 are converted into the created new slab group. include. Then, the process proceeds to step S1408.

Proceeding to step S1408, the slab group creation unit 202 determines whether or not all the slabs included in the rearranged slab information 400 are assigned to any slab group. As a result of this determination, if all the slabs included in the sorted slab information 400 are not assigned to any of the slab groups, the process returns to step S1403. Then, the processes of steps S1403 to S1408 are repeated until all the slabs included in the rearranged slab information 400 are assigned to any of the slab groups.

When all the slabs included in the slab information 400 sorted as described above are assigned to any slab group, the slab group information 500 is obtained (see FIG. 5). Then, in step S1409, the slab group creation unit 202 outputs the slab group information 500 to the slab group selection unit 203. Then, the process proceeds to step S1303 of FIG. 13-1.

(Example)
Next, an embodiment of the present embodiment will be described.
In this embodiment, a cast plan was drawn up for each of the premise method and the method of the present embodiment for 1018 slabs. FIG. 15 is a diagram showing the result. Specifically, FIG. 15 (a) shows the result of the cast plan drafted by the method of the premise form, and FIG. 15 (b) shows the result of the cast plan drafted by the method of the present embodiment.

In FIGS. 15 (a) and 15 (b), No is a cast identification number. The cast weight filling rate of each cast is the ratio of the total value of the slab weights (see FIG. 3) of the slabs contained in the cast to the maximum weight of the cast as a percentage. As described above, the maximum weight of the cast is the maximum weight of the slab allowed in one cast. The coil length filling rate of each cast is the ratio of the total length of the slab coils (see FIG. 3) included in the cast to the maximum coil length expressed as a percentage. The maximum coil length is the maximum value of the coil length that can be rolled in one lot (one chance) in the hot rolling process.

As shown in FIG. 15A, as a result of the cast plan devised by the premise method, eight casts were created, and a total of 829 slabs were incorporated into any of these eight casts. Therefore, the number of candidate slabs to be incorporated (slabs not incorporated into any cast) was 189 (= 1018-829). When the method of the present embodiment (process of FIG. 13-2) was applied to this result, a total of 893 slabs were incorporated into the cast, and the number of candidate slabs to be incorporated was reduced to 125 (= 1018-893). .. In addition, as shown in FIG. 15 (b), No. In the casts 1, 2 and 7, the slab weight filling rate or the coil length filling rate was improved.

As described above, the method of the present embodiment makes it possible to allocate more slabs to the cast. Further, the calculation time by the method of the premise form was 924 seconds, whereas the total calculation time of the method of the premise form and the method of the present embodiment (processing of FIG. 13-2) was 991 seconds. Therefore, even if the method of the present embodiment (process of FIG. 13-2) is added, it is possible to formulate a more suitable cast plan without significantly extending the calculation time.

(Summary)
As described above, in the present embodiment, slabs whose manufacturing conditions match within a predetermined range are set as the same slab group, and slab groups satisfying the conditions that can be included in the same cast are derived as cast candidates, and the optimum cast is performed. Derivation of candidates as cast pieces. From the slab group not included in the cast piece derived in this way and the cast piece, the embedding candidate slab group is extracted, and the embedding candidate slab group is converted into each slab (embedding candidate slab). Disassemble. Then, among the cast pieces that are not in the built-in candidate slab group, the built-in candidate slab is incorporated into the cast piece that satisfies the conditions that can be included in the same cast to make it a cast candidate, and the optimum cast candidate is derived as a cast piece. And update the cast pieces (ie redefine the slab group). Such processing is performed for all embedded candidate slabs. Therefore, in addition to the effect explained in the section (Summary of premise form), the effect that more slabs can be automatically incorporated into the cast can be obtained within a practical calculation time.

(Modification example)
<Modification example 1>
In the present embodiment, when the adoption rate of the slab for the cast piece is equal to or higher than a predetermined ratio, the result of the optimization calculation in the first optimization unit 205 determines the convergence test condition. The case where it is determined that the condition is satisfied has been described as an example. Here, the "predetermined ratio" may be 100% (that is, all slabs are included in the cast piece). As a result of the optimization calculation in the first optimization unit 205, even if all the slabs are included in the cast piece, the cast piece may be a candidate slab group to be incorporated. Judgment conditions can be adopted (see cast pieces 1206 and 1207 in FIG. 12).

In addition, when the ratio of the total number of slab groups i included in any of the cast pieces to the total number of slab groups i is equal to or greater than a predetermined ratio, it may be determined that the convergence test condition is satisfied. Further, the adoption rate of the slab group i (slab) for the cast piece is defined as the ratio of the weight of the slab contained in the slab group i included in any of the cast pieces to the weight of the slab contained in all the slab group i. May be good. Further, the adoption rate of the slab group i (slab) to the cast piece is set to the total coil length of the slabs included in all the slab groups i, and the slab included in the slab group i included in any of the cast pieces. It may be a ratio of the total coil lengths. Further, the difference between the value of the objective function f obtained as a result of the previous optimization calculation and the value of the objective function f obtained as a result of the current optimization calculation is less than or equal to a predetermined value, or the previous optimization. When the value of the objective function f obtained as a result of the calculation and the value of the objective function f obtained as a result of the optimization calculation this time are the same, it may be determined that the convergence determination condition is satisfied.

<Modification 2>
In the present embodiment, the second determination unit 1106 derives the cast candidate and the optimum combination of cast candidates (cast pieces) for all the embedded candidate slabs registered in the embedded candidate slab list. When this is done, a case where it is determined that the convergence test condition is satisfied has been described as an example. However, it is not always necessary to do this. For example, when the adoption rate of the slab group i to the cast piece is equal to or higher than a predetermined ratio, it may be determined that the convergence test condition is satisfied, or the adoption rate of the slab to the cast piece is equal to or higher than the predetermined ratio. In some cases, it may be determined that the convergence test condition is satisfied.

Here, when the same conditions are set in the first determination unit 206 and the second determination unit 1106 except for the threshold value (the predetermined ratio) as the convergence determination condition, the threshold value in the second determination unit 1106 (the above). It is preferable that the predetermined ratio) is made larger than the threshold value (predetermined ratio) in the first determination unit 206. As described in the present embodiment, when the threshold value (the predetermined ratio) with respect to the adoption rate of the slab in the cast piece in the first determination unit 206 is 70 [%], the slab in the second determination unit 1106 The threshold value (the predetermined ratio) with respect to the adoption rate of the cast piece can be set to, for example, 80 [%].

In addition, as described in the first modification, the adoption rate of the slab group i (slab) for the cast piece may be specified by the weight of the slab or the coil length.

<Modification example 3>
In the present embodiment, the embedded candidate slab selection unit 1103 has been described by taking as an example a case where the embedded candidate slabs are selected one by one. However, this is not always the case, and a plurality of embedded candidate slabs may be selected at a time. In this case, the second cast candidate derivation unit 1104 enumerates all possible combinations (subsets) of the cast piece and one or more embedded candidate slabs. Further, the number of embedded candidate slabs selected by the embedded candidate slab selection unit 1103 may not be fixed, but may be different depending on, for example, the number of repetitions of the processes of steps S1313 to S1316 shown in FIG. 13-2. ..

<Modification example 4>
In the present embodiment, the case where the second cast candidate derivation unit 1104 enumerates all possible combinations (subsets) of the cast piece and the embedded candidate slab has been described as an example. However, at least a plurality of these combinations may be listed, if not all. For example, at least one of a combination of cast pieces and a combination of one or more cast pieces and a built-in candidate slab may be further listed. For example, all combinations that can be taken as a combination of cast pieces, a combination of embedded candidate slabs, and a combination of cast pieces and embedded candidate slabs may be listed.

<Modification 5>
In the present embodiment, the built-in candidate slab group presence / absence determination unit 1101 sets the cast piece and the cast piece and the slab group in which the total weight of the slabs included in the slab group is less than the weight of one charge into the built-in candidate slab. The case of making a group has been described as an example. However, it is not always necessary to do this. For example, the size (for example, the total length of the slab coils in the cast piece and the slab group) may be used instead of the total weight of the cast piece and the slab included in the slab group. Further, when the quantity of the cast piece and the slab included in the slab group is equal to or less than a certain threshold value, it may be used as an embedded candidate slab group.

<Modification 6>
In the present embodiment, a case where the slabs (records) of the slab information 300 are rearranged in order from the slab having the earliest desired date for hot extension has been described as an example. However, if the slabs (records) of the slab information 300 are rearranged based on the slab manufacturing conditions included in the slab information 300, this is not always necessary. In the rolling process, the operation of rolling from a wide slab to a narrow slab is generally performed, but the smaller the amount of change in the slab width rolled back and forth, the more stable the operation tends to be. Therefore, for example, the slabs (records) having the narrowest slab width may be sorted in order. By doing so, the variation in the slab width within the same cast is suppressed, and the operation is stabilized. For numerical values such as slab width, slab thickness, and slab weight, the slabs (records) are sorted so that the numerical values are in descending or ascending order. On the other hand, for materials that are represented by symbols, for example, the slabs (records) are sorted so that the symbols are in ascending or descending order according to the dictionary order (alphabetical order or Japanese syllabary order).
The above is the same when the slab group selection unit 203 rearranges the slab groups (records) of the slab group information 500.

<Modification 7>
In the present embodiment, when all the determination conditions (A1) to (D1) described above are satisfied, a case where a slab selected from the slab information 400 is included in the already created slab group is taken as an example. explained. However, it is determined whether or not to include the slab selected from the slab information 400 in the already created slab group based on the determination condition determined based on the slab manufacturing conditions included in the slab information 300. If so, it is not always necessary to do this. For example, the condition (D1) may be omitted.

<Modification 8>
In the present embodiment, for each of the listed slab group combinations (subsets), a case where only those satisfying all the constraint conditions (A2) to (E2) described above are adopted as cast candidates will be described as an example. did. However, this is not always necessary if a cast candidate that satisfies the conditions (constraints) that can be included in the same cast is adopted. For example, at least one of (B2) to (E2) may be adopted.

<Modification 9>
In the present embodiment, the case where the number of slab groups selected by the slab group selection unit 203 is constant has been described as an example. However, the number of slab groups selected by the slab group selection unit 203 may be different. When the processes of steps S1303 to S1306 shown in FIG. 13-1 are repeated, the number of slabs belonging to the slab group increases due to the redefinition of the slab group. Then, since cast candidates that do not satisfy the above-mentioned constraints (A2) to (E2) are likely to occur, the number of cast candidates is reduced, and the processing time per step S1303 to S1306 is shortened. It becomes a tendency. Therefore, the process shown in steps S1303 to S1307 shown in FIG. 13-1 may be repeated, and the number of slab groups selected by the slab group selection unit 203 may be increased as the number of slabs included in the slab group increases. As a result, the decrease in the number of cast candidates derived in step S1304 is suppressed, a cast piece is obtained as an optimization result from a larger number of combinations, and the number of repeated calculations in steps S1303 to S1307 until convergence is required. It becomes possible to suppress.

<Modification example 10>
In the present embodiment, the constraints (C2) to (E2) are taken as examples as the constraints for hot rolling the slabs contained in the same cast as the same lot (chance) in the hot rolling process. I mentioned and explained in. However, the constraint condition for hot rolling the slabs contained in the same cast as the same lot (chance) in the hot rolling process is at least one of the constraint conditions (C2) to (E2). It may be included. For example, it is possible to determine which of the constraints (C2) to (E2) to be adopted according to the slab and equipment to be hot-rolled.

<Modification 11>
In the present embodiment, the difference W between the maximum value and the minimum value of the slab width of the slab included in the cast candidate j, the difference T between the maximum value and the minimum value of the slab thickness of the slab included in the cast candidate j, and the cast candidate j. The case where the difference D between the average value of the desired hot spreading date and the earliest date of the slab included in the slab and the number of casts is used as an evaluation index of the cast candidate j has been described as an example. However, when creating a production plan for products produced in lot units, if the number of lots is evaluated, other evaluation indexes may be appropriately determined. That is, in the example of the present embodiment, the evaluation index may include at least the number of casts. Further, in addition to or in place of the difference D between the average value of the desired hot extension date of the slab included in the cast candidate j and the earliest date, the latest and earliest days of the desired hot extension date of the slab included in the cast candidate j. The difference from the above may be used as an evaluation index. In addition, the material may be included in the evaluation index.

<Modification example 12>
In the present embodiment, it is premised that there are not a plurality of slab groups i having the same contents (that is, slab groups i having the same combination of slabs), so that the right side of the constraint equations of equations (2) and (3) The value of was set to "1". However, for example, when there are a plurality of slab groups i having the same contents, the value on the right side of the constraint equations of the equations (2) and (3) is the number. For example, when there are two slab groups i having the same contents, a constraint expression in which the value on the right side of the constraint expressions of the equations (2) and (3) is "2" is given as the constraint expression for the slab group i. .. By doing so, even if there are a plurality of slab groups i having the same content, the slab group to be included in the optimum cast candidate can be determined according to the number of slabs to which the slab belongs.

<Modification example 13>
When the number of slabs to be the target of the cast plan is large, it is preferable to create a slab group as described in this embodiment. This is because the calculation time can be shortened as described above. However, for example, if the number of slabs to be cast is not large, it is not necessary to create a slab group.

<Modification 14>
In the present embodiment, an upper limit of the calculation time in one optimization calculation is set, and when the calculation time in one optimization calculation reaches the upper limit, the solution obtained at that time is optimized. You may consider it as a good cast candidate.

<Modification 15>
In this embodiment, the case of creating a cast plan has been described as an example. However, the method described in the present embodiment can be applied to a production plan of a plurality of products produced in lot units by collecting a plurality of products in a lot, other than the cast plan.

For example, the method described in this embodiment may be applied to a plate production plan (cutting problem). After rolling the slab to the target plate thickness, the rolled slab is sheared according to the order to obtain a thick plate. Therefore, it is necessary to decide which slab to cut out from which slab. Such contents will be prepared as a plank production plan. In this case, the "thick plate" corresponds to the "product", the "slab" corresponds to the "lot", and the "shearing (cutting)" corresponds to the "manufacturing". Further, when the total weight of the planks sheared from one slab does not sufficiently reach the slab weight, the slab can be regarded as a candidate lot for incorporation.

The plate information corresponding to the slab information includes, for example, manufacturing conditions such as the material, size, and delivery date of the plate. As a condition corresponding to (A2) to (E2), a condition (constraint condition) capable of cutting out a thick plate from the same slab is given. This constraint includes, for example, that the same slab does not contain a thick plate different from a predetermined material, that the total weight of the thick plate does not exceed the upper limit, and that the thickness of the thick plate contained in the same slab. Can be included to have a thickness within a predetermined range. A slab that meets this constraint is a slab candidate. It is also possible to group thick plates. For example, the plank group can be created by replacing the "desired rolling date" described in the present embodiment with the "delivery date" and performing the process described in the section of the slab group creating unit 202. In addition to the number of slabs, the evaluation index at the time of optimization can include, for example, a surplus portion of the slabs. The surplus part of the slab is a part of the slab that does not become any thick plate after being cut out from the slab. The smaller the surplus portion of this slab, the higher the evaluation value. In addition, as described in the present embodiment, an evaluation index using the size and delivery date of the product (thick plate) can be adopted. Further, the constraint equation at the time of the optimization calculation can be set in the same manner as the constraint equation in the cast plan (see equations (2) and (3)). For example, as a constraint equation corresponding to Eq. (2), the number of thick plates (or thick plate groups) included in the optimum slab candidates and the slab candidates are derived for the thick plates (or thick plate groups) having the same contents. It is possible to adopt a constraint equation formulated to have the same number of slabs (or slab groups) selected prior to.

Further, the method described in the present embodiment may be applied to the heat spread plan (chance formation problem). It is necessary to determine multiple slabs for continuous hot rolling. The unit of these multiple slabs is called a chance. In this case, the "hot-rolled plate (coil)" corresponds to the "product", the "chance" corresponds to the "lot", and the "rolling" corresponds to the "manufacturing". Also, if the quantity, weight, or rolling length of hot rolled sheets assigned to one chance is not sufficient. The chance can be regarded as a candidate lot for incorporation, and the hot-rolled plate (coil) manufactured by the chance can be regarded as a candidate product for incorporation. The hot-rolled plate information corresponding to the slab information includes, for example, manufacturing conditions such as the material of the hot-rolled plate (coil), the size of the slab, the size of the hot-rolled plate (coil), and the desired hot-rolling date. As the conditions corresponding to (A2) to (E2), for example, (C2) to (E2) can be used. Opportunities that meet this constraint are candidates. It is also possible to group the heat-rolled plates. For example, the hot-rolled plate group can be created by performing the process described in the section of the slab group creating unit 202. The number of chances can be used as an evaluation index at the time of optimization. In addition, as described in the present embodiment, an evaluation index using the size of the product (hot-rolled plate) and the desired hot-rolling date can be adopted. Further, the constraint equation at the time of the optimization calculation can be set in the same manner as the constraint equation in the cast plan (see equations (2) and (3)). For example, as a constraint equation corresponding to Eq. (2), the number of hot-rolled plates (or hot-rolled plate groups) included in the optimum chance candidates and the chances for the hot-rolled plates (or hot-rolled plate groups) having the same contents. A constraint equation can be adopted that is formulated to have the same number of hot-rolled plates (or hot-rolled plate groups) selected prior to deriving the candidates.

Further, the application target of the method described in the present embodiment is not limited to a plan for collectively producing a plurality of products in lot units, but is a plan for processing a plurality of products collectively in lot units. May be good.
For example, the method described in this embodiment may be applied to a mountain stand creation plan (mountain stand problem). It is necessary to determine the mountain to which each slab belongs and the position (stacking stage) of each slab in each mountain when multiple slabs are divided into multiple piles and piled up using a transport device such as a crane in a steel material storage area (yard). There is. Create such contents as a mountain stand plan. In this case, the "slab" corresponds to the "product", the "mountain" corresponds to the "lot", and the "mountain stand (transportation of the slab by the transport device)" corresponds to the "processing". Further, when the quantity of the slabs assigned to one pile does not reach a certain threshold value, the pile can be regarded as a candidate lot for incorporation, and the slabs constituting the pile can be regarded as a candidate product for incorporation. As the slab information, the slab information 300 described in the present embodiment can be used. As a condition (constraint condition) corresponding to (A2) to (E2), a condition in which "cast" in (A2) to (E2) is replaced with "mountain" can be included. Mountains that meet this constraint are candidates for mountains. As in the present embodiment, slabs can be grouped to create a slab group. In addition to the number of ridges, for example, the number of ridges can be included as the evaluation index at the time of optimization. Mountain climbing means temporarily placing a slab in a place different from the final place when making a mountain. The smaller the number of piles, the higher the evaluation value. In addition, as described in the present embodiment, an evaluation index using the size of the slab and the desired date of hot spreading can be adopted. Further, the constraint equation at the time of optimization calculation can be set in the same manner as the constraint equation in the cast plan (see equations (2) and (3)).

<Modification 16>
In this embodiment, an optimization problem that minimizes the value of the objective function f has been described as an example. However, for example, it may be an optimization problem that maximizes the value of the objective function f by multiplying the right side of the equation (1) by (-1).

[Second Embodiment]
Next, the second embodiment will be described. In the first embodiment, the embedded candidate slab group is decomposed into individual slabs (embedded candidate slabs), and the cast piece that does not become the embedded candidate slab group and the embedded candidate slab are optimally composed. By solving the combination of cast candidates as a set partitioning problem, the number of slabs incorporated in the cast can be increased. As a result, it is possible to incorporate the surplus slab into the cast piece within the range where the constraint condition is allowed.

However, in the first embodiment, when the constraint condition of each cast approaches the upper limit value or the lower limit value, the embedding candidate slab cannot be incorporated into any cast, and finally, it is incorporated into any cast. A slab that cannot be generated occurs. In such a case, the operator may review the upper limit value or the lower limit value of the constraint condition and perform the optimization calculation again. This is because, for example, as described above, the (D2) width transition constraint is a constraint that the difference between the widths of the two slabs that are in phase with each other when the slabs are sorted in order from the one with the widest slab width is equal to or less than a certain upper limit value. However, if it deviates slightly from the upper limit, there is no problem in operation, and it is an acceptable constraint depending on the degree of deviation from the upper limit.

However, when incorporating a built-in candidate slab that was not incorporated into any cast by the method of the first embodiment into each cast, the operator needs to know which constraint condition causes how much violation. If this is not possible, the constraint condition correction policy for executing the optimization calculation cannot be obtained again, and the constraint condition correction and the optimization calculation will be repeated by trial and error, which may take a long time for the planning work. is there.

Therefore, in the present embodiment, the amount of violation of the constraint condition for each cast of the embedded candidate slab that is not incorporated in any cast (combination of the optimum cast candidate (cast piece)) in the first embodiment is obtained. By displaying the above, the operator can easily determine the modification policy of the constraint condition. As described above, in the present embodiment, the amount of constraint violation for each cast of the embedded candidate slab that is not incorporated in any of the casts is calculated and displayed for the first embodiment, and the operator is displayed according to the result. The main difference is that it adds recalculation using the constraints modified by the operation of. Therefore, in the description of the present embodiment, detailed description will be omitted by assigning the same reference numerals as those given in FIGS. 1 to 15 to the same parts as those in the premise embodiment and the first embodiment. Here, the constraint condition that can be modified is a constraint condition that can be quantified. In the present embodiment, the (B2) cast weight, (C2) coil length, and (D2) width shift constraint described in the premise are the constraints that can be modified, and the other constraints cannot be modified. This will be described by taking as an example.

(Cast knitting device 1600)
FIG. 16 is a diagram showing an example of a functional configuration of the cast knitting device 1600 according to the present embodiment. The hardware of the cast knitting apparatus 1600 is realized by using, for example, an information processing apparatus including a CPU, ROM, RAM, HDD, and various interfaces, and dedicated hardware.

<Second cast candidate derivation unit 1601>
Similar to the second cast candidate derivation unit 1104 of the first embodiment, the second cast candidate derivation unit 1601 is the first optimum when it is determined by the first determination unit 206 that the convergence determination condition is satisfied. Among the cast pieces derived by the chemical conversion unit 205, the cast pieces not extracted as the embedded candidate slab group by the embedded candidate slab group presence / absence determination unit 1101 or redefined by the second slab group redefinition unit 1107. All possible combinations (subsets) of the cast piece, which is a slab group, and the embedded candidate slabs selected by the embedded candidate slab selection unit 1103 are listed, and among the listed combinations (subsets). A combination satisfying all the constraint conditions of (A2) to (E2) is derived as a cast candidate.

The second cast candidate derivation unit 1601 of the present embodiment performs the following processing when the listed combinations (subsets) do not satisfy the constraint conditions (A2) to (E2). I do.
First, the second cast candidate derivation unit 1601 sets the embedded candidate slab among the constraints (A2) to (E2) for the cast piece and the embedded candidate slab constituting the combination (subset). Derivation and storage of constraints that are not satisfied when incorporated into a cast piece.

Next, the second cast candidate derivation unit 1601 calculates the violation amount of the constraint conditions that are not satisfied when the embedded candidate slab is incorporated into the cast piece among the constraint conditions (B2) to (E2). ,Remember. Here, the violation amount of the constraint condition is the amount of deviation from the upper limit value or the lower limit value of the constraint condition. For example, if (B2) the upper limit of the cast weight is 1300 [ton], and the weight of the cast piece becomes 1400 [ton] when the built-in candidate slab is incorporated into the cast piece, the built-in candidate The amount of violation of the constraint condition when the slab is incorporated into the cast piece is 100 (= 1400-1300) [ton]. In this embodiment, since the (A1) material constraint cannot be quantified, it is excluded from the calculation target of the violation amount of the constraint condition. Further, in the present embodiment, the second cast candidate derivation unit 1601 is a constraint condition that can be quantified even if it is a constraint condition that cannot be modified. (E2) A constraint condition for the same width number constraint. Calculate and memorize the violation amount of. In the following description, the violation amount of the constraint condition is referred to as the constraint violation amount as necessary. In addition, the constraint condition that is not satisfied when the embedded candidate slab is incorporated into the cast piece is referred to as a violation constraint condition as necessary.

<Second optimization unit 1602>
Similar to the first optimization unit 1105, the second optimization unit 1602 selects the optimum combination of cast candidates (cast pieces) from the cast candidates derived by the second cast candidate derivation unit 1104. Derived by solving the partition of a set problem.
In the second optimization unit 1602 of the present embodiment, in addition to the above processing, when the result of the optimization calculation of this time (latest) and the result of the previous optimization calculation immediately before the change are different. Perform the following processing. If the combinations (subsets) listed by the second cast candidate derivation unit 1601 include combinations that satisfy all the constraint conditions (A2) to (E2), the result of the previous optimization calculation and the current time The result of the optimization calculation will be different.

Further, in the present embodiment, when the result of the previous optimization calculation and the result of the current optimization calculation are different, the second optimization unit 1602 is based on the current optimization calculation of the second optimization unit 1602. Discards the violation constraint condition and constraint violation amount calculated and stored by the second cast candidate derivation unit 1601 before the time of the optimization calculation for the cast piece to be incorporated in the embedded candidate slab. To do.
Hereinafter, a specific example of the method of calculating, storing, and discarding the constraint violation amount by the second cast candidate derivation unit 1601 and the second optimization unit 1602 will be described with reference to FIG.
FIG. 17 is a diagram conceptually showing an example of a method of calculating, storing, and discarding a constraint violation amount. In FIG. 17B, x indicates that the constraint condition is not satisfied when the built-in candidate slab is incorporated in the cast piece shown next to it, and ○ indicates that the built-in candidate slab is incorporated in the cast piece shown next to it. It is shown that the constraint condition is satisfied even if the above is incorporated.

In FIG. 17, among the cast pieces derived by the first optimization unit 205 when it is determined by the first determination unit 206 that the convergence determination condition is satisfied, the cast pieces are incorporated by the incorporation candidate slab group presence / absence determination unit 1101. It is assumed that the cast pieces that are not extracted as the candidate slab group or the cast pieces that are the slab group redefined by the second slab group redefinition unit 1107 are the cast pieces 1701a to 1701d. Further, it is assumed that the embedded candidate slabs 1702a, 1702b, 1702c are selected in this order by the embedded candidate slab selection unit 1103.

In this case, since there are three embedded candidate slabs 1702a, 1702b, and 1702c, the embedded candidate slab selection unit 1103, the second cast candidate derivation unit 1601, the second optimization unit 1602, and the second determination unit 1106, And the process of the second slab group redefinition unit 1107 is repeated three times. The first, second, and third rounds of FIG. 17B show the number of repetitions.

First, in the first round, the embedded candidate slab 1702a does not satisfy any of the constraints (A2) to (E2) even if it is incorporated into any of the cast pieces 1701a to 1701d (FIG. 17 (FIG. 17). b) See x shown next to the embedded candidate slab 1702a in the first round). In this case, the second cast candidate deriving unit 1601 restricts which of the combinations of the cast pieces 1701a to 1701d and the built-in candidate slab 1702a when the built-in candidate slab 1702a is incorporated into the cast pieces 1701a to 1701d. Derivation and storage of whether the condition is not satisfied (that is, the violation constraint condition). Further, the second cast candidate derivation unit 1601 violates the constraint condition (constraint) that is not satisfied when the built-in candidate slab 1702a is incorporated into the cast pieces 1701a to 1701d among the constraint conditions (B2) to (E2). Violation amount) is calculated and stored.

The second optimization unit 1602 derives the optimum combination of cast candidates (cast pieces) from the cast candidates derived by the second cast candidate derivation unit 1601 by solving the set partitioning problem. Here, since there is no change in the cast pieces 1701a to 1701d, the result of the optimization calculation is the same between the previous time and this time. If there is no change in the cast piece between the previous time and this time, the second optimization unit 1602 may not perform the optimization calculation.

In the first round, since the processing has not been completed for all of the embedded candidate slabs 1702a to 1702c, in the second determination unit 1106, the result of the optimization calculation in the second optimization unit 1602 satisfies the convergence test condition. Judge that there is no. Then, the second slab group redefinition unit 1107 redefines the slab group (cast piece). In the first round, there is no change in the cast pieces 1701a to 1701c, so the cast pieces 1701a to 1701d are adopted as they are.

Next, in the second round, when the built-in candidate slab 1702b is incorporated into the cast piece 1701c, it satisfies all the constraints of (A2) to (E2), and becomes the other cast pieces 1701a, 1701b, 1701d. When incorporated, some of the constraints (A2) to (E2) are not satisfied (○, × shown next to the incorporation candidate slab 1702b in the second round of FIG. 17 (b). See).

In this case, the second cast candidate derivation unit 1601 determines that the built-in candidate slab 1702b satisfies all the constraint conditions (A2) to (E2) when incorporated into the cast piece 1701c. , Cast candidate slab 1702b among the constraint conditions (violation constraint conditions) that are not satisfied when the embedded candidate slab 1702b is incorporated into the cast pieces 1701a, 1701b, 1701d and the constraint conditions (B2) to (E2). If the violation amount of the constraint condition (constraint violation amount) that is not satisfied when incorporated in the pieces 1701a, 1701b, 1701d is stored, they are discarded. This is because the built-in candidate slab 1702b is incorporated into the cast piece 1701c, so that this information is unnecessary.

The second optimization unit 1602 derives the optimum combination of cast candidates (cast pieces) from the cast candidates derived by the second cast candidate derivation unit 1601 by solving the set partitioning problem. Here, the cast pieces 1701a, 1701b, 1701d are the same as those in the first round. On the other hand, the built-in candidate slab 1702b is incorporated in the cast piece 1701c.

In the second round, since the processing has not been completed for all of the embedded candidate slabs 1702a to 1702c, in the second determination unit 1106, the result of the optimization calculation in the second optimization unit 1602 satisfies the convergence test condition. Judge that there is no. Then, the second slab group redefinition unit 1107 redefines the slab group (cast piece). In the second round, the second slab group redefinition unit 1107 redefines the cast piece 1701c in which the built-in candidate slab 1702b is incorporated as a new slab group (cast piece 1701c'). Since there is no change in the other cast pieces 1701a, 1701b, 1701d, the cast pieces 1701a, 1701b, 1701d are adopted as they are.

In addition, the second optimization unit 1602 uses the second cast candidate derivation unit 1601 in the first round with respect to the cast piece 1701c that was the target of incorporating the embedded candidate slab 1702b in the second round of optimization calculation. Discard the calculated and stored violation constraint condition and constraint violation amount. That is, the second optimization unit 1602 discards the violation constraint condition and the constraint violation amount when the built-in candidate slab 1702a is incorporated into the cast piece 1701c.

Next, in the third round, the built-in candidate slab 1702c does not satisfy any of the constraints (A2) to (E2) even if it is incorporated into any of the cast pieces 1701a, 1701b, 1701c', 1701d. (See x shown next to the embedded candidate slab 1702c in the first round of FIG. 17 (c)). In this case, the second cast candidate deriving unit 1601 casts the embedded candidate slab 1702c into the cast pieces 1701a, 1701b, 1701c', respectively, for the cast pieces 1701a, 1701b, 1701c', 1701d and the embedded candidate slab 1702c, respectively. Which constraint condition is not satisfied when incorporated in 1701d (that is, a violation constraint condition) is derived and stored. Further, the second cast candidate derivation unit 1601 does not satisfy the constraint conditions of (B2) to (E2) when the built-in candidate slab 1702c is incorporated into the cast pieces 1701a, 1701b, 1701c', 1701d. Calculate and store the violation amount (constraint violation amount) of.

The second optimization unit 1602 derives the optimum combination of cast candidates (cast pieces) from the cast candidates derived by the second cast candidate derivation unit 1601 by solving the set partitioning problem. Here, since there is no change in the cast pieces 1701a, 1701b, 1701c', 1701d, the result of the optimization calculation is the same between the previous time and this time. As described above, since the processing is completed for all of the embedded candidate slabs 1702a to 1702c, the second determination unit 1106 determines that the result of the optimization calculation in the second optimization unit 1602 satisfies the convergence test condition.

In the example shown in FIG. 17, the constraint violation amount when the built-in candidate slab 1702a is incorporated in the cast piece 1701a, the constraint violation amount when the built-in candidate slab 1702a is incorporated in the cast piece 1701b, and the set in the cast piece 1701d. The amount of constraint violation when the inclusion candidate slab 1702a is incorporated is stored (without being discarded). Further, the amount of constraint violation when the built-in candidate slab 1702c is incorporated in the cast piece 1701a, the amount of constraint violation when the built-in candidate slab 1702c is incorporated in the cast piece 1701b, and the amount of constraint violation when the built-in candidate slab 1702c is incorporated in the cast piece 1701c' The constraint violation amount when the built-in candidate slab 1702c is incorporated in the cast piece 1701d and the constraint violation amount when the built-in candidate slab 1702c is incorporated are stored (without being discarded). That is, of the eight cases indicated by x in the first and third rounds of FIG. 17B, seven cases excluding the case where the built-in candidate slab 1702a is incorporated in the cast piece 1701c of the first round. Constraints and the amount of constraint violations are stored.

<Output unit 1603>
When all the embedded candidate slabs are incorporated into any of the cast pieces, the output unit 1603 formulates a cast plan by using the information of the slabs included in each cast as in the output unit 1108 of the first embodiment. Output as a result.
On the other hand, when at least one of the embedded candidate slabs is not incorporated in the cast piece, the output unit 1603 incorporates which embedded candidate slab into which cast piece for each of the constraints (B2) to (D2). In that case, information indicating how much the constraint violation amount is displayed is displayed.

FIG. 18 is a diagram showing an example of the amount of constraint violation regarding (B2) cast weight. FIG. 18 shows that, for example, when the built-in candidate slab 2 is incorporated into the cast piece of Cast 6, the constraint violation amount becomes 0.4 [ton]. The numerical value of each cell in FIG. 18 is information obtained when the second determination unit 1106 determines that the result of the optimization calculation in the second optimization unit 1602 satisfies the convergence test condition. .. Information as shown in FIG. 18 can be obtained for the other constraints (C2) to (D2).

FIG. 18 shows information showing, for example, how much constraint violation amount is obtained when which embedded candidate slab is incorporated into which cast piece for each constraint condition (B2) to (D2). As shown, it can be represented by a table. In addition, the output unit 1603 graphically displays information indicating for each of the constraint conditions (B2) to (D2) how much the constraint violation amount is when the embedded candidate slab is incorporated into which cast piece. can do. FIG. 19 is a box plot showing the amount of constraint violation for the (B2) cast weight shown in FIG. As shown in FIG. 19, the output unit 1603 may display information indicating how much constraint violation amount is obtained when which embedded candidate slab is incorporated into which cast piece by box plot. Further, the output unit 1603 displays slab information of the slab constituting each cast piece and the built-in candidate slab. For example, the output unit 1603 can pop up a list of slab information of the slabs constituting the cast by clicking the cast column (Cast1 or the like) in FIGS. 18 and 19. Similarly, the output unit 1603 can pop up a list of slab information of the embedded candidate slab by clicking the column of the embedded candidate slab (embedded candidate slab 1 or the like) in FIG.

From the information shown in FIGS. 18 and 19, the operator can grasp which constraint condition violates to what extent, and can correct the constraint condition to be corrected from the constraint conditions (B2) to (D2). And the correction value of the upper limit of the constraint condition can be determined without trial and error.
Further, when the embedded candidate slab is incorporated into the cast piece and cannot be corrected, if the constraint conditions of (A2) and (E2) are violated, the output unit 1603 adds which embedded candidate slab to which cast in addition to the above information. When incorporated into a piece, information indicating whether the constraint condition is violated may be displayed. This display may be performed on the same screen as the information shown in FIGS. 18 and 19, or may be performed on a different screen.

<Constraint input unit 1604>
The constraint condition input unit 1604 is the constraint condition to be modified from the constraint conditions (B2) to (D2) that can be modified based on the operator's operation on the user interface of the cast knitting device 1600, and the upper limit of the constraint condition. Correct the value Enter the value. Then, when there is an input by the constraint condition input unit 1604, the slab group selection unit 203, the first cast candidate derivation unit 204, the first optimization unit 205, the first determination unit 206, and the first slab group described above are received. Redefinition unit 207, embedding candidate slab group presence / absence determination unit 1101, embedding candidate slab group decomposition unit 1102, embedding candidate slab selection unit 1103, second cast candidate derivation unit 1601, second optimization unit 1602, first The processing of the determination unit 1106 of 2, the second slab group redefinition unit 1107, and the output unit 1603 is performed again. At this time, the first cast candidate derivation unit 204 and the second cast candidate derivation unit 1601 derive the optimum combination of cast candidates by using the modified constraint conditions. In addition, the second cast candidate derivation unit 1601 calculates the constraint violation amount using the modified constraint conditions.

FIG. 20 shows the upper limit value of each constraint condition and the number of residuals in a tabular form when the above calculation is repeated three times (that is, when the correction value is input twice by the constraint condition input unit 1604). It is a figure shown by. In FIG. 20, the number of times is the number of repeated calculations. The coil length indicates (C2) the upper limit of the coil length. The cast weight indicates (B2) the upper limit of the cast weight. The width shift indicates the upper limit value of the (D2) width shift constraint. The number of set remainders indicates the number of built-in candidate slabs that were not incorporated into any cast piece as a result of the optimization calculation by the second optimization unit 1602. 21, FIG. 22, and FIG. 23 are box plots of the amount of constraint violation of each constraint condition (B2) to (D2) obtained from the results of the first, second, and third calculations shown in FIG. 20, respectively. It is a representation figure.

Specifically, FIGS. 21 (a), 21 (b), and 21 (c) are obtained from the results of the first calculation shown in FIG. 20, respectively, (C2) the amount of violation of the coil length constraint (B2). ) The amount of the constraint violation of the cast weight and (D2) the amount of the constraint violation of the width shift constraint are shown. 22 (a), 22 (b), and 22 (c) are the amount of (C2) coil length constraint violation and (B2) cast weight obtained from the result of the second calculation shown in FIG. 20, respectively. The amount of constraint violation and (D2) the amount of constraint violation of the width shift constraint are shown. 23 (a), 23 (b), and 23 (c) are the amount of (C2) coil length constraint violation and (B2) cast weight obtained from the result of the third calculation shown in FIG. 20, respectively. The amount of constraint violation and (D2) the amount of constraint violation of the width shift constraint are shown.

As shown in FIGS. 21 (b) and 21 (c), in the first calculation, a constraint violation regarding the cast weight and width shift constraint occurs. Since no constraint violation has occurred with respect to the coil length, the targets for which the constraint conditions are relaxed are (B2) cast weight and (D2) width shift constraint. Therefore, first, as a result of performing the second calculation by relaxing the upper limit of the (B2) cast weight from 2100 [ton] to 2400 [ton], the number of surpluses is 12 to 9 as shown in FIG. Reduced to. As shown in FIG. 22 (c), in the second calculation, the (D2) width shift constraint is violated, so the upper limit of the (D2) width shift constraint is changed from 90 [mm] to 100 [mm]. It was relaxed and the third calculation was performed. As a result, as shown in FIG. 20, the number of surplus sets was reduced from 9 to 1.

For example, in FIG. 21, no matter which built-in candidate slab is incorporated in the cast piece of Cast 5, nothing is shown for Cast 5 because the constraint conditions of (B2) to (D2) are not violated. .. This is because if each embedded candidate slab is incorporated into the cast piece of Cast5, it violates other constraint conditions (for example, (A2) material constraint), so that each embedded candidate slab cannot be incorporated into the cast piece of Cast5. Represents that. By displaying information indicating which embedding candidate slab is included in which cast piece to violate the other constraints, the operator understands why the embedding candidate slab cannot be incorporated into the Cast 5 cast piece. be able to.
Further, here, the case where the upper limit value of the constraint condition is corrected in the order of (B2) cast weight, (C2) coil length, and (D2) width shift constraint is shown as an example, but the upper limit value of the constraint condition is shown. The order of correction can be determined by the operator and is arbitrary. Further, the upper limit of a plurality of constraint conditions may be modified at once.

(flowchart)
An example of the plan creation method performed by the cast knitting apparatus 1600 will be described with reference to the flowcharts of FIGS. 24-1 and 24-2.
Since step S2401 of FIG. 24-1 to step S2412 of FIG. 24-2 are the same as steps S1301 to 13-2 of FIG. 13-1, detailed description thereof will be omitted here. If it is determined in step S2410 that there is no embedded candidate slab group, the process proceeds to step S2424 described later.

When the embedded candidate slab is registered in the embedded candidate slab list in step S2412, the process proceeds to step S2413. Proceeding to step S2413, the embedded candidate slab selection unit 1103 selects one unselected embedded candidate slab from the embedded candidate slabs registered in the embedded candidate slab list.
Next, in step S2414, the second cast candidate deriving unit 1601 is a cast candidate slab group incorporated in step S2411 among the cast pieces derived in step S2405 when it is determined in step S2406 that the convergence determination condition is satisfied. All possible combinations (subsets) of the cast pieces not extracted as and the built-in candidate slabs selected in step S2413 are listed.

Next, in step S2415, the second cast candidate derivation unit 1601 determines whether or not there is a combination satisfying all the constraint conditions (A2) to (E2) in the listed combinations (subsets). To do. As a result of this determination, if there is a combination satisfying all the constraint conditions of (A2) to (E2) among the listed combinations (subsets), the process proceeds to step S2416. Proceeding to step S2416, as in step S1315 of FIG. 13-2, the second cast candidate derivation unit 1601 performs all of the above-mentioned (A2) to (E2) for each of the listed combinations (subsets). A combination that satisfies the constraint conditions is derived as a cast candidate. Then, the process proceeds to step S2418, which will be described later.

On the other hand, if none of the listed combinations (subsets) satisfy all the constraint conditions of (A2) to (E2), the process proceeds to step S2417. Proceeding to step S2417, the second cast candidate derivation unit 1601 incorporates the cast pieces and the incorporation candidate slabs constituting the combination (subset) among the constraints (A2) to (E2). When the candidate slab is incorporated into the cast piece, which constraint condition is not satisfied (that is, the violation constraint condition) is derived and stored. In addition, the second cast candidate derivation unit 1601 violates the constraint conditions (constraint violation amount) that are not satisfied when the embedded candidate slab is incorporated into the cast piece among the constraint conditions (B2) to (E2). ) Is calculated and memorized. Then, the process proceeds to step S2418.

Proceeding to step S2418, the second optimization unit 1602 determines that the value of the objective function f in Eq. (1) is minimized within the range satisfying the constraint equations in Eqs. (2) and (3). The cast piece is derived by deriving _{x j.}
Next, in step S2419, whether or not the second optimization unit 1602 has a change between the result of the optimization calculation of the latest step S2418 and the result of the optimization calculation of the immediately preceding step S2418 ( That is, whether or not there is a difference between the cast piece derived in the latest step S2418 and the cast piece derived in the previous step S2418) is determined. If there is no change in the result of the optimization calculation as a result of this determination, step S2420 is omitted and the process proceeds to step S2421 described later.

On the other hand, if there is a change in the result of the optimization calculation, the process proceeds to step S2420. Proceeding to step S2420, the second optimization unit 1602 performs the optimization calculation of the previous step S2418 with respect to the cast piece that was the target of incorporating the embedded candidate slab in the optimization calculation of this step S2418. Discard the violation constraint condition and constraint violation amount previously calculated and stored in step S2417. Then, the process proceeds to step S2421.

Proceeding to step S2421, the second determination unit 1106 determines whether or not the result of the optimization calculation in step S2418 satisfies the convergence test condition. In the present embodiment as well as in the first embodiment, the second determination unit 1106 determines that all the slabs registered in the embedded candidate slab list in step S2412 have completed the processes of steps S2413 to S2422. It is determined that the convergence test condition is satisfied.

As a result of this determination, if the result of the optimization calculation does not satisfy the convergence test condition, the process proceeds to step S2422. Proceeding to step S2422, the second slab group redefinition unit 1107 is included in the cast candidate j (cast piece) corresponding _{to the determination variable x j} given “1” as the result of the optimization calculation in step S2418. Redefining a plurality of slab groups as one slab group is performed individually for each cast candidate j (cast piece), the slab group is redefined, and slab group information is generated. Then, the process returns to step S2413, and the processes after step S2413 are performed using the slab group information of the redefined slab group and the unselected embedded candidate slab.

Then, if it is determined in step S2421 that the result of the optimization calculation satisfies the convergence test condition, the process proceeds to step S2423. Proceeding to step S2423, the output unit 1603 determines whether or not all the embedded candidate slabs registered in the embedded candidate slab list have been incorporated into any of the cast pieces. As a result of this determination, if all the embedded candidate slabs registered in the embedded candidate slab list are incorporated into any of the cast pieces, the process proceeds to step S2424. Proceeding to step S2424, the output unit 1603 outputs the slab information included in each cast as the result of planning the cast plan. Then, the process according to the flowchart of FIG. 24-2 is completed.

On the other hand, if any of all the embedded candidate slabs registered in the embedded candidate slab list is not incorporated in any of the cast pieces, the process proceeds to step S2425. Proceeding to step S2425, the output unit 1603 indicates, for each of the constraint conditions (B2) to (D2), how much the constraint violation amount is when which embedded candidate slab is incorporated into which cast piece. Etc., output information that guides the operator to correct the constraint conditions (see FIGS. 18, 19, etc.).
Next, in step S2426, the constraint condition input unit 1604 inputs the constraint condition to be modified and the modification value of the upper limit value of the constraint condition from the constraint conditions of (B2) to (D2) that can be modified. Determine if it is. As a result of this determination, if the constraint condition to be corrected and the correction value of the upper limit value of the constraint condition are not input, the process according to the flowchart of FIG. 24-2 ends. For example, when the operation of the operator with respect to the user interface of the cast knitting apparatus 1600 is instructed to end the processing according to the flowcharts of FIGS. Assuming that the correction value of the value is not input, the process according to the flowchart of FIG. 24-2 ends.

On the other hand, when the constraint condition to be corrected and the correction value of the upper limit value of the constraint condition are input, the process returns to step S2403. Then, the processing after step S2403 is performed using the modified constraint condition.
(Summary)
As described above, in the present embodiment, the amount of constraint violation when the built-in candidate slab is incorporated into each cast piece is extracted and displayed. Therefore, in addition to the effects described in the first embodiment, the following effects are obtained. For example, it is possible to reduce inefficient work such as changing the threshold value (upper limit value or lower limit value) of a constraint condition that does not cause a violation and repeating the optimization calculation, and the constraint condition that becomes a bottleneck in the previous calculation condition. Can be specified to modify the threshold of the constraint. Therefore, it is possible to efficiently formulate a cast plan with a small number of embedded candidate slabs that are not incorporated into any cast piece.

(Modification example)
<Modification example 1>
In the present embodiment, the cases where the constraints that can be modified are (B2) cast weight, (C2) coil length, and (D2) width shift constraint have been described as an example. However, the constraints that can be modified are not necessarily limited to these constraints as long as they can be quantified. For example, when the range of the component value of each slab is specified as the material constraint, the material constraint is quantified and can be included in the constraint condition that can be modified.

<Modification 2>
Further, in the present embodiment, when the result of the previous optimization calculation and the result of the current optimization calculation are different, the cast piece that is the target of incorporating the embedded candidate slab in the current optimization calculation is subjected to. An example has been described in which the violation constraint condition and the constraint violation amount calculated and stored by the second cast candidate derivation unit 1601 are discarded before the time of the optimization calculation. However, it is not always necessary to do this. Two other examples are shown below.

As a first example, it is not necessary to discard such a violation constraint condition and a constraint violation amount. In this case, the output unit 1603, including the amount of the constraint violation, restricts which embedded candidate slab is incorporated into which cast piece for each of the constraint conditions (B2) to (D2). Display information indicating whether it is a violation amount using graphs and tables. In the example shown in FIG. 17, the constraint violation amount when the built-in candidate slab 1702a is incorporated into the cast piece 1701c is also stored without being discarded. That is, in the first example, the amount of constraint violation in the eight cases indicated by x in the first and third rounds of FIG. 17B is stored.

As a second example, the violation constraint condition and the constraint violation amount may be obtained after the determination of the second determination unit 1106 without being obtained by the second cast candidate derivation unit 1601. In this case, the constraint violation amount calculation unit is arranged between the second determination unit 1106 and the output unit 1603 in FIG. The constraint violation amount calculation unit is not incorporated into any cast piece as a result of the optimization calculation of the second optimization unit 1602 when, for example, the second determination unit 1106 determines that the convergence test condition is satisfied. Identify the candidate slabs to be incorporated. Then, the constraint violation amount calculation unit identifies the cast piece obtained as a result of the optimization calculation of the second optimization unit 1602 when the second determination unit 1106 determines that the convergence test condition is satisfied. Calculate the amount of constraint violation when the embedded candidate slab is incorporated. Further, in this case, for example, in the flowchart of FIG. 24-2, the processing of steps S2415, S2417, S2419, and S2420 becomes unnecessary, and the constraint violation amount calculation unit described above between steps S2421 and S2423. Perform the processing.

In the example shown in FIG. 17, the amount of constraint violation when the built-in candidate slab 1702a is incorporated into the cast piece 1701c'is stored. That is, in the second example, among the eight cases indicated by x in the first and third rounds of FIG. 17B, the built-in candidate slab 1702a was incorporated into the cast piece 1701c of the first round. The amount of constraint violation is stored in seven cases excluding the case and in a total of eight cases when the built-in candidate slab 1702a is incorporated in the cast piece 1701c'.

<Modification example 3>
In the present embodiment, the case where the constraint conditions ((B2) to (D2)) when deriving the cast candidate are to be modified has been described as an example. However, among the determination conditions ((A1) to (D1)) when creating the slab group, the determination conditions (for example, (A1) to (C1)) that can be quantified may be included in the modification target. In this case, the constraint condition input unit 1604 corrects, for example, from the constraint conditions (B2) to (D2) that can be modified and the determination conditions (A1) to (C1) that can be modified. Enter the judgment condition / constraint condition to be used and the correction value of the upper limit value of the judgment condition / constraint condition. When the upper limit value of the determination condition is modified, the slab group creation unit 202 recreates the slab group based on the upper limit value of the modified determination condition.

Further, in this case, the flowcharts of FIGS. 24-1 and 24-2 are changed as follows, for example. First, in step S2426, has the constraint condition input unit 1604 input the constraint condition to be modified and the modification value of the upper limit value of the constraint condition from the constraint conditions of (B2) to (D2) that can be modified? It is determined whether or not, and whether or not the determination condition to be modified and the modification value of the upper limit value of the determination condition are input from the determination conditions (A1) to (C1) that can be modified. As a result of this determination, when the constraint condition to be modified and the modification value of the upper limit value of the constraint condition are input from the constraint conditions (B2) to (D2) that can be modified, the process returns to step S2403. .. Further, in step S2426, when the determination condition to be modified and the modification value of the upper limit value of the determination condition are input from the determination conditions (A1) to (C1) that can be modified, step S2402 is performed. go back. In this case, the constraint condition input unit 1604 sets the determination condition to be modified and the modification value of the upper limit value of the determination condition from the determination conditions (A1) to (C1) that can be modified to the slab group creation unit 202. Output (in FIG. 16, an arrow line from the constraint condition input unit 1604 to the slab group creation unit 202 is added). If these inputs are not made, the process according to the flowchart of FIG. 24-2 ends. In addition, among the judgment conditions ((A1) to (D1)) when creating a slab group, the judgment conditions that can be quantified (for example, (A1) to (C1)) are targeted for modification, and cast candidates are derived. It is not necessary to include the constraint conditions ((B2) to (D2)) in the modification.

<Modification example 4>
In the present embodiment, a case where the constraint violation amount is calculated and displayed has been described as an example. However, the number of constraint violations may be calculated and displayed in addition to or instead of the amount of constraint violations. Here, the number of constraint violations is the number of combinations of the embedded candidate slab and the cast piece for each constraint condition, and is the number of combinations that do not satisfy the constraint condition when the embedded candidate slab is incorporated into the cast piece. Similar to the case of discarding the constraint violation amount in the present embodiment, the combination of the cast piece to which the embedded candidate slab is incorporated by the optimization calculation of the second optimization unit 1602 and the embedded candidate slab is used. The number, which is a number and is counted before the time of the optimization calculation, may be subtracted from the number of constraint violations. Further, it is not necessary to perform such subtraction as in the first example of the second modification. Further, as in the second example of the modification 2, the cast piece finally determined after the determination by the second determination unit 1106 and the built-in candidate slab that was not incorporated in any of the cast pieces. The number of combinations may be the number of constraint violations. Explaining the case of FIG. 17 as an example, in the example of the present embodiment, the number of constraint violations is 7. In the first example of the second modification, the number of constraint violations is eight. In the second example of the modification 2, the number of constraint violations is eight. That is, the number of constraint violations output (displayed) for one constraint condition corresponds to the number of constraint violations output (displayed) for one constraint condition, respectively.
In addition, in this embodiment as well, various modifications described in the first embodiment can be adopted.

[Other variants]
The embodiment of the present invention described above can be realized by executing a program by a computer. Further, a computer-readable recording medium on which the program is recorded and a computer program product such as the program can also be applied as an embodiment of the present invention. As the recording medium, for example, a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a non-volatile memory card, a ROM, or the like can be used.
In addition, the embodiments of the present invention described above are merely examples of embodiment in carrying out the present invention, and the technical scope of the present invention should not be construed in a limited manner by these. It is a thing. That is, the present invention can be implemented in various forms without departing from the technical idea or its main features.

[Relationship with claims]
The relationship between the matters described in the present embodiment and the claims is listed below. It should be noted that the present invention is not limited to the following, as described in the modified examples and the like.
The planning apparatus corresponds to, for example, the cast knitting apparatus 1100.
The acquisition means is realized, for example, by using the slab information acquisition unit 201.
The product information corresponds to, for example, the slab information 300.
The group creation means is realized, for example, by using the slab group creation unit 202. The same group inclusion condition is realized, for example, by using the determination conditions (A1) to (D1).
The product selection means is realized, for example, by using the slab group selection unit 203.
The first lot candidate derivation means is realized by using, for example, the first cast candidate derivation unit 204. The same lot inclusion condition is realized, for example, by using the constraint conditions (A2) to (E2) (see also variants 8 and 15 of the first embodiment).
The first optimization means is realized, for example, by using the first optimization unit 205.
The objective function used in the first optimization means is realized by, for example, Eq. (1).
The lot candidate derivation evaluation index used in the first optimization means is realized by, for example, each term of the equation (4) (see also modification 11 and the like).
The first constraint equation is realized by, for example, the equations (2) and (3) used in the first optimization unit 205.
The first optimum lot candidate is realized by, for example, a combination of the optimum cast candidates (cast pieces) derived by the first optimization unit 205.
The first determination means is realized, for example, by using the first determination unit 206 (see also the first modification of the first embodiment).
The first redefinition means is realized, for example, by using the first slab group redefinition unit 207.
The embedded candidate product extraction means is realized by using, for example, the embedded candidate slab group presence / absence determination unit 1101 and the embedded candidate slab group decomposition unit 1102. The embedded candidate products correspond to, for example, the embedded candidate slab groups, and the embedded candidate slab groups are, for example, the slab groups constituting the cast pieces 1206 and 1207, and the slab groups 1208 and 1209, respectively. The predetermined attribute corresponds to the total weight of the slab (see also variant 5 and the like of the first embodiment).
The embedded candidate product selection means is realized, for example, by using the embedded candidate slab selection unit 1103 (see also the modification 3 of the first embodiment).
The second lot candidate derivation means is realized, for example, by using the second cast candidate derivation unit 1104.
The second optimization means is realized, for example, by using the second optimization unit 1105.
The objective function used in the second optimization means is realized by, for example, Eq. (1).
The lot candidate derivation evaluation index used in the second optimization means is realized by, for example, each term of the equation (4).
The second constraint equation is realized by, for example, the equations (2) and (3) used in the second optimization unit 1105 (see also the modified example 2 of the first embodiment).
The second optimum lot candidate is realized by, for example, a combination of the optimum cast candidates (cast pieces) derived by the second optimization unit 1105.
The second determination means is realized, for example, by using the second determination unit 1106.
The second redefinition means is realized, for example, by using the second slab group redefinition unit 1107.
The output means is realized, for example, by using the output unit 1108.
The group creating means is realized, for example, by using the slab group creating unit 202 (see also the modified example 13 of the first embodiment).
The product group corresponds to the slab group.
The calculation means is realized, for example, by using the second cast candidate derivation unit 1601 (see also the second embodiment, the second embodiment, the third modification, and the like).
The constraints / judgment conditions are realized by, for example, the judgment conditions of (A1) to (D1) and the constraint conditions of (A2) to (E2) (see also the modification 3 of the second embodiment). The constraints / judgment conditions that can be quantified are realized by, for example, the judgment conditions (A1) to (C1) and the constraint conditions (B2) to (D2) (modification example 3 of the second embodiment, etc.). See also).
The product violation information is realized by using, for example, the amount of product violation and the number of product violations (see Modification 4 of the second embodiment).
For example, when the first determination unit 206 determines that the convergence determination condition is satisfied, the embedded target product group determines the presence or absence of the incorporation candidate slab group among the cast pieces derived by the first optimization unit 205. It is realized by using a cast piece that is not extracted as an embedded candidate slab group by the unit 1101 or a cast piece that is a slab group redefined by the second slab group redefinition unit 1107.
The input means is realized, for example, by using the constraint condition input unit 1604 (see also the modification 3 of the second embodiment).
When the output means has a subset of the embedded candidate product and the embedded target product group that satisfies the same lot inclusion condition, the embedded candidate product and the same lot inclusion condition are set. Not outputting the constraint violation information based on the subset of the embedded target product group other than the embedded target product group constituting the satisfied subset and the embedded candidate product is, for example, the constraint output in step S2425. The violation amount is the constraint violation amount not discarded in step S2420 among the constraint violation amounts stored in step S2417 (that is, in the combination (subset) listed in step S2414 in step S2415). , (A2) to (E2), if there is a combination that satisfies all the constraint conditions, the process of step S2417 is not performed).

1100: Cast knitting device, 201: Slab information acquisition unit, 202: Slab group creation unit, 203: Slab group selection unit, 204: First cast candidate derivation unit, 205: First optimization unit, 206: First 207: First slab group redefinition unit, 1101: Embedded candidate slab group presence / absence determination unit 1102: Embedded candidate slab group decomposition unit 1103: Embedded candidate slab selection unit 1104-1601: 2 cast candidate derivation unit. 1105 ・ 1602: 2nd optimization unit, 1106: 2nd judgment unit, 1107: 2nd slab group redefinition unit, 1108 ・ 1603: output unit, 300: slab information, 400: slab information after sorting , 500: slab group information, 600: slab group information after sorting, 900: slab group information after redefinition, 1201 to 1207: cast piece, 1208 to 1209: slab group, 1604: constraint condition input unit, 1701a to 1701d: Cast piece, 1702a to 1702b: Built-in candidate slab

Claims (17)

A planning device that creates a plan for producing or processing multiple products together in lot units.
An acquisition means for acquiring product information including manufacturing conditions of the product, which is information on the plurality of products.
The plurality of products are grouped based on the same group inclusion condition expressed by using the manufacturing condition of the product included in the product information acquired by the acquisition means as a condition that the product can be included in the same group. Group creation means to create multiple product groups by
A product selection means for selecting a part of the plurality of product groups created by the group creation means, and
Among the subsets of the product group selected by the product selection means, the first subset that satisfies the same lot inclusion condition expressed by using the manufacturing conditions as a condition that the product group can be included in the same lot. The first lot candidate derivation means to be derived as a lot candidate of
From the first lot candidate derived by the first lot candidate derivation means, the first optimum lot candidate, which is a candidate for the optimum lot, is selected by maximizing the value of the objective function within a range satisfying the first constraint equation. The first optimization means derived by performing the first optimization calculation to minimize, and
A first determination means for determining whether or not the result of the first optimization calculation by the first optimization means has converged,
When it is determined by the first determination means that the result of the first optimization calculation has not converged, the product included in the first optimum lot candidate derived by the first optimization means. The first redefinition means to redefine a group as one product group,
The first optimum lot derived by the first optimization means when it is determined by the first determination means that the result of the first optimization calculation by the first optimization means has converged. A predetermined attribute and threshold value of the first optimum lot candidate from the product constituting the product group included in the candidate and the product constituting the product group not included in the first optimum lot candidate. Based on the result of comparing the above and the result of comparing the predetermined attribute of the product group not included in the first optimum lot candidate with the threshold value, the candidate is further incorporated into the candidate of the optimum lot. Embedded candidate product extraction means for extracting embedded candidate products that are products, and
An embedded candidate product selection means for selecting at least one of the embedded candidate products extracted by the embedded candidate product extraction means, and an embedded candidate product selecting means.
When it is determined that the embedded candidate product selected by the embedded candidate product selection means and the result of the first optimization calculation by the first optimizing means have converged by the first determining means. Of the subset of the first optimum lot candidate derived by the first optimization means and the first optimum lot candidate that does not include the embedded candidate product, the portion satisfying the same lot inclusion condition. A second lot candidate derivation means for deriving the set as a second lot candidate,
From the second lot candidate derived by the second lot candidate derivation means, the second optimum lot candidate, which is a candidate for the optimum lot, is selected by maximizing the value of the objective function within a range satisfying the second constraint equation. A second optimization means derived by performing a second optimization calculation to minimize,
A second determination means for determining whether or not the result of the second optimization calculation by the second optimization means has converged,
When it is determined by the second determination means that the result of the second optimization calculation has not converged, the product included in the second optimum lot candidate derived by the second optimization means. A second redefinition means that redefines a group as a product group,
When it is determined by the second determination means that the result of the second optimization calculation has converged, the second optimum lot candidate derived by the second optimization means is set as the optimum lot, and the optimum lot is used. It has an output means for outputting information indicating which said product is included in the lot.
The objective function is an objective function that includes at least the number of lots as a lot candidate derivation evaluation index.
In the first constraint formula, the number of the product groups selected by the product selection means is equal to or greater than the number of the product groups included in the first optimum lot candidate, and is the same. Includes an equation formulated that the product group is not included in the different first optimal lot candidates.
The second constraint equation is derived by the first optimization means when it is determined by the first determination means that the result of the first optimization calculation by the first optimization means has converged. Among the first optimum lot candidates, the number of the product groups included in the first optimum lot candidate not including the embedded candidate product is the number of the product groups included in the second optimum lot candidate. The number of the embedded candidate products equal to or greater than the number and selected by the embedded candidate product selection means is the same as the number of the embedded candidate products included in the second optimum lot candidate. Or more, and includes an expression formulated that the same product group is not included in the different second lot candidates.
When the product group is redefined by the first redefinition means, the product selection means includes all of the product groups redefined by the first redefinition means and the unselected product group. Select some of our product groups and
When the product group is redefined by the second redefinition means, the embedded candidate product selection means selects an unselected embedded candidate product.
The embedded candidate product extraction means is the first one derived by the first optimization means when it is determined that the result of the first optimization calculation by the first optimization means has converged. The set is based on the result of comparing the predetermined attribute of the optimum lot candidate with the threshold value and the result of comparing the predetermined attribute of the product group not included in the first optimum lot candidate with the threshold value. Extract candidate products
The redefinition of the product group by the first redefinition means, the selection of the product group by the product selection means, the derivation of the first lot candidate by the first lot candidate derivation means, and the first. The first optimization calculation by the optimization means of the above is repeated until it is determined by the first determination means that the result of the optimization calculation by the first optimization means has converged.
The product group is redefined by the second redefinition means, the embedded candidate product is selected by the embedded candidate product selection means, and the second lot candidate is derived by the second lot candidate derivation means. In the second optimization calculation by the second optimization means, it is determined by the second determination means that the result of the second optimization calculation by the second optimization means has converged. A planning device characterized in that it is repeated until the end. The group creating means rearranges the plurality of product groups based on the manufacturing conditions of the product included in the product information acquired by the acquisition means.
1. The product selection means is characterized in that a part of the plurality of product groups sorted by the group creation means is selected in a preset number in ascending or descending order in the sorting order. The planning device described in. The planning apparatus according to claim 1 or 2, wherein the group creating means does not exceed a predetermined upper limit value for the number of the products included in the product group. The manufacturing conditions include at least one of the material, size, weight, and delivery date of the product.
The lot candidate derivation evaluation index according to any one of claims 1 to 3, further comprising an evaluation index for evaluating at least one of the material, size, weight, and delivery date of the product. Planning device. The first determination means includes a case where the first optimum lot candidate includes products in a predetermined ratio or more among the plurality of products, and the case where the first optimum lot candidate is maximized or minimized by the first optimization calculation. The first case where the difference between the value in the previous first optimization calculation of the objective function and the value in the first optimization calculation this time is less than or equal to a predetermined value. Judging that the result of the optimization calculation of
The second determination means derives the second lot candidate by the second lot candidate derivation means and the second optimization by the second optimization means for all of the embedded candidate products. and if the calculated and is performed, when any one of the case where the product group of more than a predetermined ratio among the plurality of product groups to a second optimal lot candidates included, the second The planning apparatus according to any one of claims 1 to 4, wherein it is determined that the result of the optimization calculation of is converged. Further having a calculation means for calculating constraint violation information indicating that the constraint / judgment condition, which is at least one of the same lot inclusion condition and the same group inclusion condition, is not satisfied.
The calculation means calculates at least one of the constraint violation amount and the constraint violation number as the constraint violation information.
The constraint violation amount is the amount of deviation from the upper limit value or the lower limit value of the constraint / judgment condition that can be quantified when the embedding candidate product is incorporated into the embedding target product group for each constraint / judgment condition. It is represented in
The number of constraint violations represents the number of subsets of the subset of the candidate product to be embedded and the product group to be incorporated that do not satisfy the constraint / judgment condition for each constraint / judgment condition.
The product group to be incorporated is derived by the first optimization means when it is determined by the first determination means that the result of the first optimization calculation by the first optimization means has converged. The product group that constitutes the first optimum lot candidate that does not include the embedded candidate product among the first optimum lot candidates, or is redefined as one product group by the second redefinition means. This is the product group mentioned above.
When the constraint violation information is calculated by the calculation means, the output means outputs the constraint violation information calculated by the calculation means instead of the information indicating which product is included in the optimum lot. The planning apparatus according to any one of claims 1 to 5, wherein the planning apparatus is to be used. The constraint / judgment condition includes the same lot inclusion condition.
After the constraint violation information is output by the output means, the output means further includes an input means for inputting a correction value of the upper limit value or the lower limit value of the same lot inclusion condition.
When the correction value of the upper limit value or the lower limit value of the same lot inclusion condition is input by the input means, the first lot candidate is derived by the first lot candidate derivation means and the first lot candidate is derived based on the correction value. The first optimization calculation by the first optimization means, the determination by the first determination means, the redefinition of the product group by the first redefinition means, and the incorporation candidate product extraction means. Extraction of the embedded candidate product by the above, selection of the embedded candidate product by the embedded candidate product selection means, derivation of the second lot candidate by the second lot candidate derivation means, and calculation by the calculation means. The calculation of the constraint violation information, the second optimization calculation by the second optimization means, the determination by the second determination means, and the redefinition of the product group by the second redefinition means. The planning apparatus according to claim 6, wherein the output is performed by the output means. The constraint / judgment condition includes the same group inclusion condition in addition to or in place of the same lot inclusion condition.
The input means inputs the correction value of the upper limit value or the lower limit value of the same group inclusion condition in addition to or instead of the correction value of the upper limit value or the lower limit value of the same lot inclusion condition.
When the correction value of the upper limit value or the lower limit value of the same group inclusion condition is input by the input means, the group creation means creates the plurality of product groups and the first lot based on the correction value. The derivation of the first lot candidate by the candidate derivation means, the first optimization calculation by the first optimization means, the determination by the first determination means, and the said by the first redefinition means. Redefining the product group, extracting the embedded candidate product by the embedded candidate product extracting means, selecting the embedded candidate product by the embedded candidate product selecting means, and using the second lot candidate deriving means. Derivation of the second lot candidate, calculation of the constraint violation information by the calculation means, the second optimization calculation by the second optimization means, determination by the second determination means, and the above. The planning apparatus according to claim 7, wherein the product group is redefined by the second redefinition means and the output is performed by the output means. When the output means has a subset of the embedded candidate product and the embedded target product group that satisfies the same lot inclusion condition, the embedded candidate product and the same lot inclusion condition are set. Any of claims 6 to 8 characterized in that the constraint violation information based on the subset of the embedded target product group other than the embedded target product group constituting the satisfied subset and the embedded candidate product is not output. The planning apparatus according to item 1. The planning apparatus according to any one of claims 6 to 9, wherein the output means outputs the constraint violation information as a graph or a table. The planning apparatus according to any one of claims 1 to 10, wherein the predetermined attribute is the number of products, weight, or size. Claims 1 to 11 are characterized in that the embedded candidate product selection means selects the unselected embedded candidate product based on the weight, size, or delivery date of the unselected embedded candidate product. The planning apparatus according to any one of the above items. The planning apparatus according to any one of claims 1 to 12, wherein the embedded candidate product selection means simultaneously selects one or a plurality of unselected embedded candidate products. The product is a slab cast in a continuous casting machine.
The lot is a cast that is a group of charges that are continuously cast.
The planning apparatus according to any one of claims 1 to 13, wherein the plan is a cast plan indicating the cast to which the slab belongs. The same lot inclusion condition is that the total weight of the slab does not exceed the upper limit value specified in advance, and the sum of the lengths of the coils manufactured by rolling the slab exceeds the upper limit value specified in advance. The difference between the widths of the slabs that are in phase with each other when the slabs are rearranged in the rolling order is less than or equal to the specified upper limit, and the number of slabs whose width difference is less than a certain value is predetermined. The planning apparatus according to claim 14, further comprising at least one of not more than or equal to a specified upper limit value. It is a planning method that uses a planning device to create a plan for producing or processing multiple products in units of lots.
The acquisition means of the planning apparatus is the acquisition process of acquiring the product information including the manufacturing conditions of the products, which is the information of the plurality of products.
The group creating means of the planning apparatus includes the same group represented by using the manufacturing condition of the product included in the product information acquired by the acquisition process as a condition that the product can be included in the same group. A group creation process for creating a plurality of product groups by grouping the plurality of products based on conditions, and
A product selection step in which the product selection means of the planning apparatus selects a part of the plurality of product groups created by the group creation step, and
The manufacturing conditions are used as a condition that the first lot candidate derivation means of the planning apparatus can include the product group in the same lot among the subsets of the product group selected by the product selection step. A first lot candidate derivation process for deriving a subset satisfying the same lot inclusion condition as a first lot candidate,
The first optimization means of the planning apparatus first constrains the first optimum lot candidate, which is a candidate for the optimum lot from the first lot candidate derived by the first lot candidate derivation step. The first optimization step derived by performing the first optimization calculation that maximizes or minimizes the value of the objective function within the range that satisfies the equation, and
The first determination means of the planning apparatus includes a first determination step of determining whether or not the result of the first optimization calculation by the first optimization step has converged.
When it is determined by the first determination step that the result of the first optimization calculation has not converged , the first redefinition means of the planning apparatus is derived by the first optimization step. The first redefinition step of redefining the product group included in the first optimum lot candidate as one product group, and
When the built-in candidate product extraction means of the planning apparatus determines that the result of the first optimization calculation by the first optimization step has converged by the first determination step, the first From the product constituting the product group included in the first optimum lot candidate derived by the optimization step, and the product constituting the product group not included in the first optimum lot candidate. Based on the result of comparing the predetermined attribute of the first optimum lot candidate with the threshold value and the result of comparing the predetermined attribute of the product group not included in the first optimum lot candidate with the threshold value. Then, the embedded candidate product extraction process for extracting the embedded candidate product, which is a candidate product to be further incorporated into the optimum lot candidate,
An embedding candidate product selection step in which the embedding candidate product selection means of the planning apparatus selects at least one of the embedding candidate products extracted by the embedding candidate product extraction step.
The second lot candidate derivation means of the planning apparatus includes the embedded candidate product selected by the embedded candidate product selection step and the first by the first optimization step according to the first determination step. Of the first optimum lot candidates derived by the first optimization step when it is determined that the results of the optimization calculation of the above have converged, the first optimum lot candidate that does not include the embedded candidate product The second lot candidate derivation step of deriving the subset satisfying the same lot inclusion condition as the second lot candidate among the subsets of
The second optimization means of the planning apparatus constrains the second optimum lot candidate, which is the optimum lot candidate from the second lot candidate derived by the second lot candidate derivation process, with the second constraint. A second optimization step derived by performing a second optimization calculation that maximizes or minimizes the value of the objective function within a range that satisfies the equation, and
The second determination means of the planning apparatus includes a second determination step of determining whether or not the result of the second optimization calculation by the second optimization step has converged.
When the second redefining means of the planning apparatus is determined by the second determination step that the result of the second optimization calculation has not converged, it is derived by the second optimization step. A second redefinition step of redefining the product group included in the second optimum lot candidate as one product group, and
The second optimization derived by the second optimization step when the output means of the planning apparatus determines that the result of the second optimization calculation has converged by the second determination step. It has an output process in which a lot candidate is set as an optimum lot and information indicating which said product is included in the optimum lot is output.
The objective function is an objective function that includes at least the number of lots as a lot candidate derivation evaluation index.
In the first constraint formula, the number of the product groups included in the first optimum lot candidate and the number of the product groups selected by the product selection step are the same, and the same product. Includes an expression formulated that the group is not included in the first optimal lot candidate with a different group.
The second constraint formula is based on the number of product groups included in the second optimum lot candidate and the result of the first optimization calculation by the first optimization step according to the first determination step. The first product group is the same as the number of products included in the first optimum lot candidate derived by the first optimization step when it is determined that the product has converged, and the same product group is different. Including the formula formulated not to be included in the lot candidates of 2
In the product selection step, when the product group is redefined by the first redefinition step, all of the product groups redefined by the first redefinition step and the unselected product group Select some of our product groups and
In the embedded candidate product selection step, when the product group is redefined by the second redefinition step, the unselected embedded candidate product is selected.
In the incorporation candidate product extraction step, the first optimization step derived by the first optimization step when it is determined that the result of the first optimization calculation by the first optimization step has converged. The set is based on the result of comparing the predetermined attribute of the optimum lot candidate with the threshold value and the result of comparing the predetermined attribute of the product group not included in the first optimum lot candidate with the threshold value. Extract candidate products
The redefinition of the product group by the first redefinition step, the selection of the product group by the product selection step, the derivation of the first lot candidate by the first lot candidate derivation step, and the first. The first optimization calculation by the optimization step of the above is repeated until it is determined by the first determination step that the result of the optimization calculation by the first optimization step has converged.
The product group is redefined by the second redefinition step, the embedded candidate product is selected by the embedded candidate product selection step, and the second lot candidate is derived by the second lot candidate derivation step. In the second optimization calculation by the second optimization step, it is determined by the second determination step that the result of the second optimization calculation by the second optimization step has converged. A planning method characterized by being repeated until the end. A program characterized in that a computer functions as each means of the planning apparatus according to any one of claims 1 to 15.

Images