JP6642273B2 - Plan creation device, plan creation method, and program - Google Patents

Description

  The present invention relates to a plan creation device, a plan creation method, and a program, and in particular, is suitable for using a plurality of products in a lot to produce or process a plurality of products in lot units.

When a production plan of a product is made in the manufacturing industry, a production plan is often made so that a plurality of products are assembled into an appropriate number of lots in an appropriate scale and manufactured in lot units.
Here, as an example of a 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.

  In a steelmaking plant, 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 poured into a container called a ladle and transported to a secondary refining process. This molten steel for one ladle is called charge. As the secondary refining process, for example, there is a RH (Ruhrstahl Heraeus) process, in which molten steel is circulated in a vacuum tube to remove impure gas in the molten steel in a vacuum to adjust the components 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, molten steel is poured into a mold from a ladle and cooled at the same time to produce a semi-finished cast slab. In a continuous casting machine, a plurality of charges can be continuously cast, and a group of a plurality of charges continuously cast is called a cast. Continuously casting molten steel of a plurality of charges is called successive casting. If the number of continuous castings is too large, the components of the continuous casting machine (such as refractories of tundishes and molds, immersion nozzles, etc.) will be eroded. The number of charges to be performed must be determined appropriately.

The slab produced in the continuous casting machine is called a slab and is conveyed to a 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 in a high temperature state, and wound into a coil. There is a limit to the number of slabs that can be continuously rolled by a rolling mill depending on the shape and hardness of the slab. A group of slabs that are continuously rolled by a rolling mill is called a chance.
Each slab is provided with information such as a component, a shape, and a desired hot rolling date from the order information, and lots such as casts and chances are formed in consideration of constraints in the steel making process and the rolling process.

  In recent years, attempts have been made to reduce the lead time and the heat loss by making the cast that is the lot of the steelmaking process the same as the chance that is the lot that is the roll process. In performing such operations, it is necessary to determine cast knitting (slabs to be included in each cast) that simultaneously satisfy the constraints in the steel making process and the rolling process.

  In cast knitting, large numbers of slabs are taken into the cast to increase the number of castings, reducing the number of defective slabs at the start and end of continuous casting and preparing time for starting recasting. It can be expected that the production volume will increase due to the reduction of the volume. On the other hand, there are restrictions on slabs that can be taken into the same cast depending on conditions such as components, shape, and desired date of hot rolling. Therefore, it is required to perform a cast knitting as large as possible within a range satisfying the constraint conditions.

In the cast knitting work, generally, hundreds or thousands of slabs are handled, so that the number of slab combinations increases. Therefore, it takes a long time for the planner to perform the cast knitting satisfying 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 formed by tying the charges that can be tied together and represented by a directed branch, and the longest cast route is searched on the network. Have been.

JP 2012-11451 A

  However, in the technique described in Patent Literature 1, there is no description on a method of combining slabs into charges, and cast knitting is performed based on information on a given charge. Therefore, if the charge is not knitted properly, there is a possibility that an optimal cast knitting result cannot be obtained. As described above, since there are many combinations of slabs, if the charge described in Patent Document 1 is appropriately included in the cast, the problem scale becomes too large, and the calculation time may be lengthened.

As described above, according to the conventional technology, a plurality of slabs (products) are put together in a cast (lot) and a casting (production) plan for casting (producing) a slab (product) in cast (lot) units is considered. However, it has not been easy to shorten the planning time without greatly reducing the accuracy of the planning result.
The present invention has been made in view of the above problems, and enables a plan for producing or processing a product in a lot unit to be planned in a short time without greatly reducing the accuracy of the plan result. The purpose is to:

  The plan creation device of the present invention is a plan creation device that creates a plan for collectively producing or processing a plurality of products in units of lots, wherein the information on the plurality of products includes a manufacturing condition of the products. Acquisition means for acquiring product information including: a selection means for selecting a part of the plurality of products; and a product among the subsets of the products selected by the selection means can be included in the same lot. A lot candidate deriving unit that derives a subset satisfying the condition represented by using the manufacturing condition as a lot candidate as a lot candidate, and an optimal lot candidate from the lot candidate derived by the lot candidate deriving unit, a constraint formula. Optimizing means derived by performing an optimization calculation for maximizing or minimizing the value of the objective function within a satisfying range, and determining whether or not the result of the optimization calculation has converged If the result of the optimization calculation is not converged by the determination means and the determination means, the product included in the optimal lot candidate derived by the optimization means is redefined as one product The re-defining means, and the determining means, when it is determined that the result of the optimization calculation has converged, the optimal lot candidate derived by the optimizing means as the optimal lot, the optimal lot Output means for outputting information indicating which product is included, wherein the objective function is an objective function including at least the number of the lots as an evaluation index, and the constraint expression is the optimal lot. It is formulated that the number of the products included in the candidate is the same as the number of the products selected by the selection means, and the same product is not included in the different lot candidates. Formula, wherein the selecting means, when the product is redefined by the redefining means, all of the products redefined by the redefining means, and some of the unselected products Selecting a product, selecting the product by the selecting means, deriving the lot candidate by the lot candidate deriving means, and determining the optimum value until the determining means determines that the result of the optimization calculation has converged. And the optimization calculation by the optimization means.

  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, wherein the information on the plurality of products includes a manufacturing condition of the products. An obtaining step of obtaining product information including: a selecting step of selecting a part of the plurality of products; and a subset of the products selected by the selecting step, wherein the products can be included in the same lot. A lot candidate derivation step of deriving a subset satisfying the condition represented by using the manufacturing condition as a condition as a lot candidate, and an optimal lot candidate from the lot candidates derived by the lot candidate derivation step, a constraint formula. An optimization step derived by performing an optimization calculation that maximizes or minimizes the value of the objective function within a satisfying range, and determining whether or not the result of the optimization calculation has converged If the result of the optimization calculation is determined not to converge in the determination step and the determination step, the product included in the optimal lot candidate derived in the optimization step is redefined as one product The re-defining step, and the determining step, when it is determined that the result of the optimization calculation has converged, the optimal lot candidate derived by the optimization step as the optimal lot, the optimal lot, An output step of outputting information indicating which product is included, wherein the objective function is an objective function including at least the number of the lots as an evaluation index, and the constraint equation is the optimal lot. It is formulated that the number of the products included in the candidate is the same as the number of the products selected in the selection step, and the same product is not included in the different lot candidates. Wherein the selecting step includes, when the product is redefined by the redefining step, all of the products redefined by the redefining step and some of the unselected products. Selecting a product, selecting the product by the selection step, deriving the lot candidate by the lot candidate derivation step, and determining the optimality until the determination step determines that the result of the optimization calculation has converged. And performing the optimization calculation in the optimization step.

  A program according to the present invention causes a computer to function as each unit of the plan creation device.

  According to the present invention, a part of a plurality of products is selected, and a subset of the selected products is set as a lot candidate. Then, an optimal lot candidate is derived from the lot candidates by performing an optimization calculation. If the result of the optimization calculation does not converge, the lot candidate is redefined as one product, and all of the redefined products and a part of unselected products are selected. Such processing is repeated until the result of the optimization calculation converges. Therefore, a plan for producing or processing a product in lot units can be drafted in a short time without greatly deteriorating the accuracy of the drafting result, as compared with a case in which lots are collectively derived from products.

It is a figure explaining an example of the outline of the technique of creating a cast plan. It is a figure showing an example of functional composition of a cast organization device. It is a figure showing the 1st example of slab information. It is a figure showing an example of slab information after rearranging. It is a figure showing an example of slab group information. It is a figure showing an example of slab group information after rearranging. It is a figure which shows notionally an example of the method of solving a set division problem. FIG. 3 is a diagram conceptually illustrating a matrix. It is a figure showing an example of slab group information after redefinition. It is a flow chart explaining an example of processing of a cast organization device. It is a flow chart explaining an example of processing of Step S1002. It is a figure which shows the 1st example of the result of an invention example and a comparative example in a table format. It is a figure which shows the relationship between the number of slabs and calculation time in an invention example and a comparative example. It is a figure which shows the evaluation value in an invention example and a comparative example. It is a figure explaining an example of the relation between the steel type of a slab, and charge. It is a figure showing the 2nd example of slab information. It is a flow chart explaining an example of processing of a cast candidate derivation part. It is a figure which shows the 2nd example of the result of an invention example and a comparative example in a table format.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. In each of the following embodiments, a case where a cast plan in a continuous casting machine is created (that is, cast knitting is performed) will be described as an example of a production plan. In this case, “slab” corresponds to “product”, “cast” corresponds to “lot”, and “casting” corresponds to “manufacturing”. Further, the “product” refers to a product obtained by modifying a raw material, and is not limited to a final product or the like on the market. For example, intermediate products (semi-finished products) are also included in “products”.

[First Embodiment]
(Overview)
An outline of the present embodiment will be described.
FIG. 1 is a diagram illustrating an example of an outline of a method for creating a cast plan according to the present embodiment.
Each of the plurality of slabs to be manufactured during the planning period is linked with slab information including manufacturing conditions of the slab. Based on the slab information, each of the plurality of slabs is grouped such that slabs whose manufacturing conditions match within a predetermined range belong to the same slab group.

  In FIG. 1, the slab group No. for identifying the slab group obtained in this way. And the slab group No. The number of slabs belonging to the slab group (the number of slabs) and the slab group No. The earliest day (earliest day) of the desired hot-rolling days given as one of the manufacturing conditions of the slab belonging to the slab group of. The slab manufactured by the continuous casting machine is placed in a yard and then hot-rolled in the next hot-rolling process. The date desired by the factory as the date for performing the hot rolling is the desired hot rolling date. That is, the desired hot rolling date is the delivery date of the slab to the hot rolling mill. The desired date of hot rolling 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 operation status of the hot rolling line equipment, and the like.

In the example shown in FIG. 1, the slab groups are sorted in ascending order of the desired hot rolling date (earliest date). In FIG. 1, for convenience of explanation, the slab group No. and the slab group No. are arranged in the case where the slab groups are arranged in ascending order of the desired hot rolling date (earliest date). And the same.
Next, a part of the plurality of slab groups is selected, and a subset of the selected slab groups is created. In the example shown in FIG. 1, ten slab groups are selected from the 27 slab groups having the earliest desired hot rolling date (earliest date), and a subset of these 10 slab groups is created. It is determined whether or not each of these subsets satisfies a condition (restriction condition) that can be manufactured by the same cast, and a subset that satisfies this condition is set as a cast candidate.

Next, the optimal combination of the cast candidates is derived from the cast candidates by solving the optimization problem. Details of the optimization problem will be described later. In the following description, the optimal cast candidate obtained in this manner is referred to as a “cast piece” as necessary.
FIG. 1 shows that the cast pieces 101a to 101d are obtained as a result of the calculation of the optimization problem (the result of the “first division optimization”). In FIG. 1, one square shown in the cast pieces 101a to 101r indicates a slab group constituting the cast piece. Is shown.

  Next, each of the cast pieces 101a to 101d is redefined as a new slab group, all the new slab groups and some slab groups among the unselected slab groups are selected, and the selected slab group is selected. Create a subset of. In the example shown in FIG. 1, six slab groups are selected from the seventeen unselected slab groups from the earliest hot rolling desired date (earliest day), and four new slab groups and six new slab groups are selected. Create a subset of slab groups. As described above, among these subsets, a subset that satisfies the conditions (constraint conditions) that can be included in the same cast is defined as a cast candidate, and the optimal combination of cast candidates (cast piece) is selected from the cast candidates. , By solving the optimization problem.

FIG. 1 shows that the cast pieces 101e to 101h are obtained as a result of the calculation of the optimization problem (the result of the “second division optimization”). In FIG. 1, a portion that has already been derived as a cast piece and is a new slab group is shown in gray.
Next, each of the cast pieces 101e to 101h thus obtained is redefined as a new slab group. Then, cast pieces 101i to 101m and 101n to 101r are derived in this order by the same procedure as described above. In this way, while maintaining the already derived cast piece, a slab group is gradually added to the cast piece, and the size of the cast piece is enlarged. In practice, the order of the slab groups included in the cast is determined based on the widths of the slabs belonging to the slab group. In order to clearly show the situation, a newly added slab group is shown connected to the end of the already created cast piece without rearrangement 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 determination 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 casts obtained in this way, the cast to which each slab belongs is output as the result of planning the cast plan.
FIG. 1 shows the concept of the present embodiment, and does not always correspond to the contents described below. For example, the number of slabs included in the slab group shown in FIG. 1 and the content of the desired hot rolling date (earliest date) are different from those shown in FIGS.

(Cast knitting device 200)
FIG. 2 is a diagram illustrating an example of a functional configuration of the cast knitting apparatus 200. The hardware of the cast knitting apparatus 200 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 unit 201>
The slab information acquisition unit 201 acquires and stores slab information. The slab information acquisition unit 201 acquires slab information by, for example, operating the cast knitting apparatus 200 by an operator, receiving slab information transmitted from an external device, or reading slab information stored in a portable storage medium. I do.

FIG. 3 is a diagram illustrating an example of the slab information 300.
3, the slab information 300 includes the slab No. , Material, slab weight, slab width, slab thickness, coil width, coil thickness, coil length, and desired hot rolling date. Slab information is provided individually for each slab to be drafted.

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

  The coil width, coil thickness, and coil length are respectively the slab No. Are the width, thickness and length of the coil obtained by hot rolling the slab identified by. The coil width, the coil thickness, the coil length, and the desired hot rolling date are manufacturing conditions in a process (hot rolling process) subsequent to the process of manufacturing the slab. As described above, the desired hot rolling date is a date desired by the factory as a date for performing hot rolling.

<Slab group creation unit 202>
The slab group creation unit 202 is included in the slab information 300 based on the slab information 300 acquired by the slab information acquisition unit 201 so that slabs whose manufacturing conditions match within a predetermined range belong to the same slab group. 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 the present embodiment, the slabs (records) of the slab information 300 are sorted in order from the slab having the earliest desired hot rolling date. 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. In order to clearly show the relationship between FIGS. 3 and 4, in FIGS. Is attached. However, in FIG. Is set to “1”, and thereafter, the slab Nos. May be added again. Further, slabs may be sorted based on the item to be emphasized next to the desired hot rolling date in the slab (record) having the same hot rolling desired date.

  Next, the slab group creation unit 202 selects one of the highest-order slabs among unselected slabs (records) included in the slab information 400 sorted as described above. 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 rolling date.

Next, the slab group creation unit 202 determines whether 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 whose slab production conditions match within a predetermined range are included in the same slab group.
Specifically, in the present embodiment, when all of the following determination conditions (A1) to (D1) are satisfied, the slab group creation unit 202 selects a slab group that has already been created from the slab information 400. It is determined that there is a slab group to which the added slab can be added.

(A1) The maximum value of the difference between the slab width (slab width) included in the slab group already created 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 slab group already created 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 hot rolling date of the slab included in the slab group already created and the desired hot rolling date of the slab selected from the slab information 400 is 2 days or less.
(D1) The slab material included in the slab group that has already been created is the same as the slab material selected from the slab information 400.

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

The slab group creation unit 202 creates a new slab group when the sum of the 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 equal to or less than the upper limit, The selected slab is included in the created new slab group.
On the other hand, when the total number of the 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 determines the selected slab as the relevant slab. Include in slab group.

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

FIG. 5 is a diagram showing an example of the 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, slab group information 500 includes slab group No. , Material, slab width (maximum value, minimum value), slab thickness (maximum value, minimum value), slab weight, coil length, desired hot rolling date (earliest date, latest date), and number of slabs are correlated Information.

Slab group No. Is a number for identifying a slab group.
The material is a material of the slab belonging to the slab group. In the present embodiment, slabs of the same material belong to one slab group under the condition (D1) described above.
The maximum value of the slab width refers to the maximum value of the width (slab width) of the slab included in the slab group. The minimum value of the slab width refers to the minimum value of the width (slab width) of the slab included in the slab group.

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

The coil length is a total value of the coil lengths of the slabs included in the slab group.
The earliest date of the desired hot rolling date is the earliest date of the hot rolling desired dates of the slabs included in the slab group. The latest date of the desired hot rolling date is the latest date among the desired hot rolling 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 the present embodiment, a cast is configured by combining a plurality of slab groups. For this reason, when the manufacturing conditions (for example, at least one of the slab thickness, the slab width, and the desired rolling date) of the slab belonging to one slab group vary, the slab manufacturing conditions are also obtained in the cast combining these. Becomes large. Therefore, in the present embodiment, the slab group creation unit 202 creates a record (slab) of the slab information 300 according to at least one value of the slab manufacturing conditions included in the slab information 300 (desired hot rolling date in the present embodiment). The slab group to which the slab belongs is determined in the rearranged order. In this way, it is possible to suppress slabs having significantly different manufacturing conditions from belonging to the same slab group.

<Slab group selector 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 date of the desired hot rolling date. FIG. 6 is a diagram showing an example of the slab group information 600 in which the slab groups (records) of the slab group information 500 shown in FIG. 5 and 6, the same slab group is assigned to the same slab group No. in FIG. 5 and FIG. Is attached. However, in FIG. Is set to “1”, and the slab group Nos. May be added again.

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

  When the number of slab group selections per one time (the predetermined number) is “5”, when the slab group selection unit 203 performs the first slab group selection, the slab group information 600 shown in FIG. The slab groups on the first to fifth rows are selected. The case where the second and subsequent slab groups are selected will be described later. Since the calculation time required for the optimization calculation increases as the number of slab groups to be selected increases, the number of slab groups to be selected is determined as at least two or more based on the time allowed for the main calculation.

<Cast candidate derivation unit 204>
The cast candidate deriving unit 204 derives a cast candidate from the slab group selected by the slab group selecting 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. If the number of slab group selections performed by the slab group selection unit 203 at one time is “5”, the cast candidate derivation unit 204 determines 32 (= 2 ⁵ ) combinations (subsets) as slab group combinations (subsets). Subsets).

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

(A2) Material Constraint There is no mixture of slab materials included in the slab group combination (subset) 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 restrictions. So it is not adopted as a cast candidate.

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

  In the present embodiment, it is necessary to derive a cast that satisfies the restrictions that occur during hot rolling in order to hot-roll the slabs included in the same cast as the same lot (chance) in the hot rolling process. There is. Thus, in the present embodiment, the following constraint conditions (C2) to (E2) are adopted.

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

(D2) Width transition restriction The difference between the widths of two slabs that are adjacent to each other when rearranged in the rolling order is equal to or less than the upper limit.
In the hot rolling process, there is a case where a restriction is imposed that so-called narrow down must be performed by hot rolling in order from a slab having a large width. In this case, when the slabs included in the combination (subset) of the slab groups are sorted in ascending order of the slab width, the difference between the widths (slab widths) of two successive slabs must be equal to or less than the upper limit value. is there. For example, when the upper limit is 150 [mm], the slab group No. Consider whether the slab 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]. The maximum value of the slab width of the slab group with “5” is 1400 [mm]. Therefore, when the slabs included in these slab groups are rearranged so as to be narrowed down, a difference in slab width of 200 [mm] or more occurs between any of the slabs. Therefore, combinations (subsets) of these slab groups are not adopted as cast candidates.

(E2) Number of slabs with the same width The number of slabs whose difference in width is equal to or less than a certain value is equal to or less than the upper limit.
If a large number of slabs having a difference in width equal to or smaller than a certain value are included in the same chance, the shape of the coil may be deteriorated due to 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 whose width difference is equal to or less than a certain value is equal to or less than an upper limit value. For example, when the number of slabs having a width difference of 100 [mm] or less is limited to 40 [sheets] or less, the slab group No. In the slab groups (subsets) of “2” and “4”, the number of slabs in the range of 1600 [mm] to 1700 [mm] is 49 [slabs]. Therefore, combinations (subsets) of these slab groups are not adopted as cast candidates.

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

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

Next, n subsets are derived as subsets of the set M. For example, all possible combinations of the elements are set as a subset. However, all combinations that can be taken as combinations of elements may not be subsets, and some combinations may be subsets. FIG. 7 shows only subsets 701a to 701g for convenience of notation. In the present embodiment, one subset corresponds to one cast candidate.
Next, an evaluation index (cost) is derived for each of these n subsets.

Next, a combination of subsets in which the sum of the values of the evaluation index (cost) is optimal is determined as an optimal solution. In the case of a problem setting with a smaller evaluation index value, the minimum value is optimal. Conversely, in the case of a problem setting with a larger evaluation index value, the maximum value is optimal. FIG. 7 shows that the subsets 701a, 701d, and 701f are optimal solutions. In the present embodiment, each of such subsets corresponds to a cast piece.
In the set partitioning problem, an optimal solution is generally derived under a constraint that the same element is not included in a plurality of subsets. As shown in FIG. 7, the ten elements are included in only one of the subsets.
Since the set partitioning problem itself can be realized by a known technique, a detailed description thereof is omitted here.

Based on the above, an example of a process performed by the optimization unit 205 will be described.
In the present embodiment, an optimization problem (set division problem) for deriving an optimal cast (cast piece) is formulated by the following equations (1) to (3). That is, in the present embodiment, the optimizing unit 205 determines when the value of the objective function f in the following equation (1) is minimized within a range that satisfies the following constraints (2) and (3). A decision variable x _j is derived. Note that the optimization problem (set partitioning problem) can be solved by, for example, a known mixed integer programming method, and in that case, a commercial solver (such as a cplex) can be used.

Here, a set of slab groups i included in the cast candidate j is set as i∈N _I , and a set of the cast candidate j is set as j∈N _J. Also, 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 a cast piece and becomes “0” when it is not adopted. I do. Also, c _j represents the evaluation value of the cast candidate j. In the present embodiment, the evaluation value c _j is represented by the following equation (4).
c _j = C _W × W + C _T × T + C _D × D + C _N −C _S × S (4)

In the expression (4), W is a difference between the maximum value and the minimum value of the width (slab width) of the slab 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 and the earliest date of the desired hot rolling date of the slab included in the cast candidate j. C _D is a weighting factor for D.

C _N is a weight coefficient 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 a cast piece and becomes “0” when it is not adopted. Thus, (1) in the calculation of the equation, the integrated value of the decision variable x _j is the number of casts. Therefore, by multiplying the value obtained by multiplying the decision variable x _j by the weight coefficient C _N , the number of casts can be evaluated.
S is the number of slabs included in the cast candidate j. C _S is a weighting factor for S. Since the yield improves as the number of slabs included in one cast increases, the evaluation value c _j of the cast candidate j becomes a value indicating high evaluation (the value is small in the expression (4)). ).
The weighting factors C _W , C _T , C _D , C _N , and C _S are set in advance depending on how much importance is placed on each evaluation item, and represent the balance of evaluation between the evaluation items.

For example, the slab group Nos. Of the slab group information 500 and 600 shown in FIGS. The evaluation value c _j of the cast candidate j including the slab groups “1” and “2” is as follows. First, W is 200 (= 1700-1500). T is 0 (= 250−250). D is 0.4 (= 1.4-1). Here, when obtaining D, the slab group No. It is assumed that the average value of the desired hot rolling days of the slabs included in the slab groups “1” and “2” is June 1.4. S is 37 (= 9 + 28).
From the above, for example, when C _W = 1, C _T = 1, C _D = 200, C _N = 1000, and 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. _{(2) i∈N I andM i ≧} H MAX of expression for each slab group i contained in the cast candidates j, if the number M _i of slabs belonging to the slab group i is equal to or greater than the upper limit value H _MAX Means that equation (2) is applied. _{Further, (3) i∈N I andM i} <H MAX of expression for each slab group i contained in the cast candidate j, the number M _i of slabs belonging to the slab group i is less than the upper limit value H _MAX In this case, it means that the equation (3) is applied.

A _ij in the expressions (2) and (3) is a matrix having the slab group i as a row and the cast candidate j as a column, and is a matrix having “0” or “1” as an element.
FIG. 8 is a diagram conceptually illustrating the matrix A _ij .
In FIG. 8, each column indicates a slab group i included in one cast candidate j. “1” is assigned to the row corresponding to the slab group i included in the cast candidate j, and “0” is assigned 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 and 2) and does not include other slab groups.

For each of the cast candidates j derived by the cast candidate deriving unit 204, the result of such assignment of “1” or “0” is a matrix A _ij . The portion below the arrow line in FIG. 8 indicates that the evaluation value c _j and the decision variable x _j are 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, (2) the constraints slab group i number M _i belonging slab is not less than the upper limit value H _MAX represents be employed exactly once as a slab group including 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 adoptions is 0 (zero)).
Optimization unit 205, the deriving the decision variable x _j as described above, performed by casting the candidate deriving unit 204 every time the cast candidate is derived. The cast candidate j corresponding to the decision variable x _j given “1” becomes a cast piece.

<Determination unit 206>
The determination unit 206 determines whether the result of the optimization calculation in the optimization unit 205 satisfies the convergence determination condition.
In the present embodiment, the slab group creation unit 202 or the slab group redefinition unit 207 described later creates one of the cast candidates j (cast pieces) corresponding to the decision variable x _j to which “1” is given. When all (latest) slab groups are included one by one, the result of the optimization calculation in the optimization unit 205 determines that the convergence determination condition is satisfied. It is assumed that the result of the optimization calculation does not satisfy the convergence determination condition.

As a result of this determination, when the result of the optimization calculation in the optimization unit 205 satisfies the convergence determination condition, the determination unit 206 determines that the decision variable given “1” in the result of the optimization calculation in the optimization unit 205 A cast candidate j (cast piece) corresponding to x _j is determined 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 determination condition, the determination unit 206 activates the slab group redefinition unit 207.

<Slab group redefinition unit 207>
The slab group redefinition unit 207 generates a plurality of slabs included in the cast candidate j (cast piece) corresponding to the decision variable x _j to which “1” is given as the (latest) result of the optimization calculation in the optimization unit 205. Redefining the group as one slab group is individually performed for each of the cast candidates j (cast pieces).
FIG. 9 is a diagram illustrating 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. Are included in the first cast piece, and the slab group Nos. “1” and “2” are included in the first cast piece. The slab groups of “3” and “4” are included in the second cast piece, and slab group Nos. An example is shown in which the slab group of “5” is included in the third cast piece.

  Slab group No. included in the first cast piece. In this example, 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. Will be described.

The slab group redefinition unit 207 stores the slab group No. From the maximum value and the minimum value of the slab width of the slab groups of “1” and “2”, 1700 and 1500 are derived as the maximum value and the minimum value of the slab width of the new slab group, respectively.
The slab group redefinition unit 207 stores the slab group No. Are derived as the maximum and minimum values of the slab thickness of the new slab group from the maximum and minimum values of the slab thickness of the slab groups "1" and "2", respectively.

The slab group redefinition unit 207 stores the slab group No. Add 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 stores the 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 stores the slab group No. From the earliest day and the latest day of the desired rolling date of the slab groups of “1” and “2” to the earliest and latest days of the desired rolling date of the new slab group, respectively, on June 1 and June 2 respectively. Derive the day.
The slab group redefinition unit 207 stores the slab group No. Is added to the number of slabs of the slab groups of “1” and “2” to derive 37 (= 9 + 28) as the number of slabs of the new slab group.
The slab group No. Is “A” and the material of the slab group of “1” and “2” is not changed.

  The slab group redefinition unit 207 stores the slab group No. in the slab group information 500 shown in FIG. The slab group consisting of the material, slab width, slab thickness, slab weight, coil length, hot rolling desired date, and the number of slabs derived as described above is deleted. Record) and a slab group No. for identifying the slab group (record). Is given to the slab group (record). In FIG. Is a new slab group redefined from the slab groups “1” and “2”. The case where “1” is given as an example will be described.

  Slab group No. included in the second cast piece. Similarly, new slab groups are obtained for the slab groups of “3” and “4”. 9, the slab group No. of the slab group information 500 shown in FIG. Is a new slab group redefined from the slab groups “3” and “4”. Is given as an example.

  The slab group included in the third cast piece is the slab group No. Is only the slab group of “5”. Therefore, the slab group No. Is “5”, the slab group no. Only changes are made. 9, the slab group No. of the slab group information 500 shown in FIG. Is a new slab group redefined from the slab group of “5”. The case where “3” is given as an example will be described.

  The slab group No. of the slab group information 500 shown in FIG. Are also “6” to “10”, the slab group Nos. Only changes are made. 9, the slab group No. of the slab group information 500 shown in FIG. Is a new slab group redefined from the slab groups "6" to "10". As an example, a case where “4” to “8” are assigned is shown.

  Then, the slab group selection unit 203 selects some slab groups from the slab group information 900 including the slab groups redefined as described above, and the cast candidate derivation unit 204 determines from the selected slab groups. , The cast candidate is derived, the optimization unit 205 derives a 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 result of the optimization calculation by the optimization unit 205 does not satisfy the convergence determination condition, the slab group redefinition unit 207 determines whether the 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 until the determination unit 206 determines that the result of the optimization calculation in the optimization unit 205 satisfies the convergence determination condition. Here, when the number of slab group selections per time is “5”, when the slab group selection unit 203 performs the second or subsequent slab group selection, one line of the slab group information 900 shown in FIG. Select the slab group in the first to fifth rows.

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

  If it is attempted to derive casts at once from all the slab groups included in the slab group information 500, the number of combinations of slab groups becomes enormous (that is, the problem scale becomes large), and the casts are cast within a practical calculation time. It is not easy to derive. In contrast, in the present 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 enlarged by repeating the process of taking in the unselected slab group and deriving the cast piece. Therefore, even for a large-scale problem, it is possible to derive a cast plan in a practical calculation time. In addition, since the slab groups are sorted in advance by operationally important items and the generation of cast pieces and the redefinition of slab groups are repeated in the sorted order, the variation in the emphasized items in the generated cast pieces is suppressed. As described above, it is possible to minimize a decrease in accuracy due to dividing a problem to obtain a solution.

<Output unit 208>
When the determination unit 206 determines that the result of the optimization calculation in the optimization unit 205 satisfies the convergence determination condition, and the cast is determined, the output unit 208 outputs slab information included in each cast to the cast plan. Output as a planning result. The output unit 208 performs information on a slab included in each cast by performing at least one of display on a computer display, transmission to an external device, and storage in an internal or external storage medium, for example. Is output. For example, the output unit 208 outputs, as an item of the slab information 300 shown in FIG. Can be output as slab information included in each cast.

  As shown in equation (3), in the present embodiment, there may be slab groups that are not included in the cast. The output unit 208 can output such slab group information together. Accordingly, the operator can instruct the cast knitting apparatus 200 to which cast of the cast plan derived as described above (the slab included in the slab group) is to be incorporated. Thereby, the cast knitting apparatus 200 can include the slab group in the specified cast. Instead of doing so, the slab group may be included in the cast plan in the next planning period.

(flowchart)
An example of the process of the cast knitting apparatus 200 will be described with reference to the flowchart of FIG.
First, in step S1001, the slab information acquisition unit 201 acquires the slab information 300 (see FIG. 3).
Next, in step S1002, 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 S1001, and derives the slab group information 500 (see FIG. 5). reference). Details of step S1002 will be described later with reference to FIG.

Next, in step S1003, the slab group selection unit 203 sorts the slab groups (records) of the slab group information 500 created in step S1002 in order from the slab group with the earliest date of the desired hot rolling date. From 600 (see FIG. 6), a predetermined number of slab groups are selected in order from the earliest date of the desired hot rolling date.
Next, in step S1004, the cast candidate deriving unit 204 derives, from the slab group selected in step S1003, a cast candidate that satisfies all the above-described constraints (A2) to (E2) as a cast candidate.

Next, in step S1005, the optimizing unit 205 determines the value of the objective function f in equation (1) as a minimum variable x _j when minimizing the value within the range satisfying the constraint equations in equations (2) and (3). Is derived to derive a cast piece.
Next, in step S1006, the determination unit 206 determines whether the result of the optimization calculation in step S1005 satisfies the convergence determination condition.

As a result of this determination, if the result of the optimization calculation does not satisfy the convergence determination condition, the process proceeds to step S1007. In step S1007, the slab group redefinition section 207, a plurality of slabs contained in the cast candidate j (cast piece) corresponding to the decision variables x _j to "1" is given as a result of the optimization calculation in step S1005 The group is redefined as one slab group 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 S1003, and the process of step S1003 is performed using the slab group information 900 of the redefined slab group.

  In step S1006, when it is determined that the result of the optimization calculation satisfies the convergence determination condition and the cast is determined, the process proceeds to step S1008. In step S1008, the output unit 208 outputs information on the slabs included in each cast as a result of the casting plan. Then, the processing according to the flowchart in FIG. 10 ends.

FIG. 11 is a flowchart illustrating an example of the process of step S1002 in FIG.
First, in step S1101, the slab group creation unit 202 sorts the slabs (records) included in the slab information 300 obtained in step S1001 of FIG. 10 in order from the slab having the earliest desired hot rolling date (shown in FIG. 4). (See slab information 400).
Next, in step S1102, the slab group creation unit 202 sets “0 (zero)” to a variable k that specifies a line of the rearranged slab information 400.

Next, in step S1103, the slab group creation unit 202 adds “1” to a variable k specifying a line of the rearranged slab information 400.
Next, in step S1104, the slab group creation unit 202 sets the slab registered in the k-th line of the sorted slab information 400 in the slab group that has already been created. It is determined whether there is a slab group that can be added. As described above, in the present embodiment, when all the determination conditions (A1) to (D1) are satisfied, it is determined that there is a slab group to which the selected slab can be added, among the already created slab groups. .

  As a result of this determination, if there is no slab group to which the slab registered in the k-th row of the rearranged slab information 400 can be added among the already created slab groups, the process proceeds to step S1105. In step S1105, the slab group creation unit 202 creates a new slab group, and includes the slab registered in the k-th row of the sorted slab information 400 in the created new slab group. Then, the process proceeds to step S1108 described below.

  On the other hand, if the result of determination in step S1104 is that there is a slab group to which a slab registered in the k-th row of the sorted slab information 400 can be added, the flow proceeds to step S1106. In step S1106, the slab group creation unit 202 determines the number of slabs included in the slab group determined to be added in step S1104 and the number of slabs registered in the k-th row of the sorted slab information 400. It is determined whether the sum is equal to or less than the upper limit.

  If the result of this determination is that the total number of slabs is less than or equal to the upper limit, processing proceeds to step S1107. In step S1107, the slab group creation unit 202 includes the slab registered on the k-th line of the rearranged slab information 400 in the slab group determined to be able to add the slab in step S1104. Then, the process proceeds to step S1108 described below.

  On the other hand, if it is determined in step S1106 that the total number of slabs is not less than or equal to the upper limit, the process proceeds to step S1105 described above. As described above, in step S1105, the slab group creation unit 202 creates a new slab group, and assigns the slab registered on the k-th line of the sorted slab information 400 to the created new slab group. include. Then, the process proceeds to step S1108.

  In step S1108, the slab group creation unit 202 determines whether all the slabs included in the rearranged slab information 400 have been assigned to any of the slab groups. As a result of this determination, if all the slabs included in the rearranged slab information 400 have not been assigned to any slab group, the process returns to step S1103. Then, the processes of steps S1103 to S1108 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 rearranged as described above are assigned to any slab group, slab group information 500 is obtained (see FIG. 5). Then, in step S1109, 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 S1003 in FIG.

(Example)
Next, examples will be described.
In the present embodiment, cast plans were created for each of the six cases in which the number of slabs was “50”, “100”, “150”, “200”, “250”, and “300”. In the invention example, a cast plan was created by repeatedly selecting a part of the slab group by 15 parts, deriving a cast candidate, performing an optimization calculation to derive an optimal cast candidate (cast piece). . On the other hand, in the comparative example, in step S1003 of FIG. 10, a method is used in which all the slab groups created in step S1002 are selected. Created a new cast plan. In both the invention example and the comparative example, the set partitioning problem was adopted as the optimization problem, and the expression (1) was used as the objective function, and the expressions (2) and (3) were used as the constraint expressions. In addition, the evaluation value c _j is represented by Expression (4). Here, the values of the weighting factors C _W , C _T , C _D , C _N , and C _S are respectively set to “0”, “0”, “1”, “100”, and “10” (C _W = 0, C _T = 0, C _D = 1, C _N = 100, C _S = 10).

FIG. 12 is a diagram showing the results of the invention example and the comparative example in a table format. FIG. 13 is a diagram showing the relationship between the number of slabs shown in FIG. 12 and the calculation time. FIG. 14 is a diagram showing evaluation values in each of the six cases described above.
In FIG. Is a number for identifying the six cases described above. Case No. shown in FIG. And case No. shown in FIG. Are the same.
The number of slabs to be drafted is the number of slabs to be drafted for the cast plan. As described above, in the present embodiment, since six cases of “50”, “100”, “150”, “200”, “250”, and “300” are considered, these become the number of slabs to be planned. .
The number of slab groups is the number of slab groups obtained by grouping slabs for which a cast plan is to be prepared by the processing of the slab group creation unit 202.

  The cast number is the number of casts finally obtained. The number of slabs is the number of slabs included in any of the finally obtained casts. In the present embodiment, as described in the present embodiment, the optimization calculation is terminated when the entire slab group is included in any one of the casts (cast pieces). Therefore, in FIG. 12, the original number of slabs for planning and the number of slabs are the same.

The number of repetitions is the number of repetitions of the optimization calculation. The number of repetitions of the optimization calculation is the same as the number of times of execution of step S1006 in FIG. In the comparative example, the number of times of the optimization calculation is “1” in each case (that is, the optimization calculation is performed only once).
The calculation time is the time required until a cast plan is obtained.

As shown in FIGS. 12 and 13, in the example of the invention, the calculation time can be reduced to about 1 second. On the other hand, in the comparative example, the calculation time is several tens seconds to several hundred seconds. Further, as shown in FIG. 14, in the invention example, the evaluation value is not significantly deteriorated as compared with the comparative example. In this embodiment, since the value of the objective function f in the equation (1) is minimized, the smaller the evaluation value, the better the result.
As described above, the invention example can obtain a cast plan in a calculation time of about 1 second without significantly deteriorating the evaluation value as compared with the comparative example. About several minutes are allowed as the waiting time for the optimization calculation time in the operator. Therefore, according to the method described in the present embodiment, a cast plan having practically sufficient accuracy can be created and output within such a waiting time.

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

In the present embodiment, a part of the plurality of slab groups is selected in order from the earliest date of the desired hot rolling date. Then, among the selected slab groups, those that satisfy the conditions that can be included in the same cast (all of the constraint conditions (A2) to (E2)) are derived as cast candidates. An objective function f having, as variables, a decision variable x _j that 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 variables x _j that minimizes, derived by performing optimization calculation. As a constraint in the optimization calculation, the number of slab groups included in the optimal cast candidate and the number of slab groups selected before deriving the cast candidate are the same, and the same slab group is The condition that it is not included in different cast candidates is adopted. The slab groups included in the cast candidates adopted by such optimization calculation are combined into one new slab group (that is, the slab group is redefined). The above processing is repeated until the result of the optimization calculation converges.

  In this way, since 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, 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 for creating the cast plan can be reduced. In addition, since the slab groups are sorted in advance by items important in operation, such as the earliest date of the desired hot rolling, the generation of cast pieces and the redefinition of slab groups are repeated in the sorted order. Variations in the emphasized items can be suppressed, and it is possible to minimize a decrease in accuracy due to dividing a cast knitting problem and finding a solution.

Further, in the present embodiment, the constraint conditions for the optimization calculation, the number of slabs contained in the slab group varied depending whether the upper limit value or more H _MAX.
That is, for the slab group number of the slab is not less than the upper limit value H _MAX contained imposes the following constraints. That is, for a slab group having the same contents, a constraint is imposed on the number of slab groups included in the optimal cast candidate and the number of lab groups selected prior to deriving the cast candidate. Therefore, a slab group to which many slabs belong is easily adopted as a cast piece. Therefore, the calculation time can be further reduced.

On the other hand, with respect to the slab group number of the slab is not more than the upper limit value H _MAX contained imposes the following constraints. That is, for a slab group having the same contents, a restriction is imposed on the number of slab groups included in the optimum cast candidate to be equal to or less than the number of slab groups selected prior to deriving the cast candidate. This allows the slab group selected prior to deriving the cast candidate not to be included in the optimal cast candidate. Therefore, it is possible to suppress a slab group to which a small number of slabs belong from being included in an undesirable cast piece.

  In the present embodiment, among the slab groups, those that satisfy the constraint conditions of (C2) the coil length, (D2) the width shift constraint, and (E2) the same width number constraint are adopted as cast candidates. Therefore, a cast that is a lot in the steel making process can be made the same as a chance that 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 hot rolling in the hot rolling process. Thus, for example, it is possible to realize a reduction in the manufacturing period and a reduction in the fuel consumption rate of the heating furnace in the hot rolling process due to a decrease in the temperature of the slab.

[Second embodiment]
Next, a second embodiment will be described. In the first embodiment, a case has been described as an example in which it is assumed that all slabs for which a cast plan is created are of the same steel type. On the other hand, in the present embodiment, a case will be described in which at least one of the slabs for which a cast plan is created has a degree of freedom in selecting a steel type (a steel type can be selected from a plurality of steel types). As described above, the present embodiment differs from the first embodiment mainly in the configuration and processing due to the degree of freedom in selecting the steel type of the slab. Therefore, in the description of the present embodiment, the same portions as those of the first embodiment are denoted by the same reference numerals as those shown in FIGS.

  As described in the background art, in the primary refining (converter) and the secondary refining process (RH etc.) of the steelmaking plant, components are adjusted in ladle units, so that one charge (one ladle) is required. A collection of slabs of corresponding weight must be manufactured as slabs of the same steel grade. Since a group of multiple charges to be cast continuously becomes a cast, in the problem of determining the composition of the slabs included in the cast and the steel type of each slab, when selecting the slabs that make up the cast, manufacture them as the same steel type It is necessary to collect possible slabs and determine the steel type on a charge basis. Here, the steel type that can be manufactured is determined according to the component standard (component of molten steel) specified for each charge.

  FIG. 15 is a diagram illustrating an example of the relationship between the steel type of the slab and the charge. As shown in FIG. 15, it is assumed that the ranges of the double-headed arrows shown in FIG. 15 are defined for the steel types I, II, and III, respectively, as the range of the component a. In this case, Charge 1 can be manufactured as Steel Type I or Steel Type II falling within the range of component a included in Charge 1, but Charge 1 cannot be manufactured as Steel Type III that does not fall within this range.

As described above, the type of steel that can be manufactured is determined according to the component standard defined for each charge. Further, depending on the component standard, a plurality of steel types that can be manufactured for one slab may be set. In addition, for example, when the component range of the molten steel is narrow and the type of the steel is difficult to adjust, or when it is necessary to adjust the component value of the molten steel by adding an alloy to the molten steel, the manufacturing cost is increased. . As described above, since the manufacturing cost varies depending on the type of steel to be manufactured, there is a demand to manufacture the steel as cheaply as possible within a range satisfying the component standard.
Based on the above, an example of the cast knitting apparatus of the present embodiment will be described below.

<Slab information acquisition unit 201>
The slab information acquisition unit 201 acquires and stores, as slab information, information on steel types that can produce each slab, in addition to the information included in the slab information 300 shown in FIG. FIG. 16 is a diagram illustrating an example of the slab information 1600 acquired by the slab information acquisition unit 201 according to the present embodiment.

As shown in FIG. 16, slab information 1600 contains slab No. In addition to the material, slab weight, slab width, slab thickness, coil width, coil thickness, coil length, and the desired date of hot rolling, the steel types (steel types I, II, and III) that can manufacture the slab are correlated. Information. In the example shown in FIG. 16, each slab indicates that it can be manufactured with the steel type indicated by “」 ”. For example, the slab No. Slab No. 1 can be manufactured using only steel type I, whereas slab No. 1 can be manufactured. However, the slab having a value of “2” can be manufactured with either steel type I or steel type II. As described above, the given slab information 1600 has no flexibility in selecting the material, slab weight, slab width, slab thickness, coil width, coil thickness, coil length, and desired hot rolling date. On the other hand, a manufacturable steel type may or may not have a degree of freedom for the given slab information 1600.
In addition, the slab information 1600 includes, in addition to the steel types that can be manufactured (steel types I, II, and III), a manufacturing cost (not shown) when manufacturing a slab of the steel type.

<Slab group creation unit 202>
The slab group creation unit 202 is included in the slab information 1600 based on the slab information 1600 acquired by the slab information acquisition unit 201 such that slabs whose manufacturing conditions match within a predetermined range belong to the same slab group. A slab group is created by grouping each of the slabs. In the present embodiment, the slab group creation unit 202 is already created when the following criterion (E1) is satisfied in addition to the criterion (A1) to (D1) described in the first embodiment. It is determined that there is a slab group to which the slab selected from the slab information can be added among the existing slab groups. As described in the first embodiment, this slab information is obtained by rearranging the slabs (records) of the slab information 1600 shown in FIG. 16 in ascending order of the desired hot rolling date (FIG. 4). Slab information 400).

(E1) At least one of the slab manufacturable steel types included in the already created slab group and the slab manufacturable steel types selected from the slab information overlap.
For example, the slab No. of FIG. Slab No. 1 and slab No. Is included in the same slab group as the slab of “4”, the steel type that is duplicated as the steel type that can be manufactured is steel type I. Therefore, the slab No. The slab having the slab No. “5” can be added to the slab group. The slab with “6” cannot be added to the slab group.
The other processes of the slab group creation unit 202 are the same as the processes described in the first embodiment. Note that the slab group creation unit 202 may create a slab group in the same manner as in the first embodiment (that is, considering the determination conditions of (A1) to (D1), the determination condition of (E1) Need not be considered).

<Cast candidate derivation unit 204>
The cast candidate deriving unit 204 derives a cast candidate from the slab group selected by the slab group selecting unit 203.
FIG. 17 is a flowchart illustrating an example of the process of the cast candidate derivation unit 204. The processing in the flowchart in FIG. 17 is, for example, processing that replaces the processing in step S1004 in FIG. 10 described in the first embodiment. An example of the process of the cast candidate derivation unit 204 of the present embodiment will be described with reference to the flowchart of FIG.

In step S1701, the cast candidate derivation unit 204 lists all possible slab group combinations (subsets) from the set of slab groups selected by the slab group selection unit 203. This processing is the same as in the first embodiment.
Next, in step S1702, the cast candidate derivation unit 204 satisfies all the constraints (A2) to (E2) described in the first embodiment among the combinations (subsets) of the slab groups listed. Is extracted.

  In the first embodiment, a candidate that satisfies all of the constraints (A2) to (E2) is a cast candidate. In the present embodiment, in addition to the constraints of (A2) to (E2), A candidate that satisfies the constraint condition (F2) is set as a cast candidate.

(F2) Width transition restriction within steel type When the slabs included in the combination (subset) of the slab group are divided for each steel type, and the slabs divided for each steel type are sorted so that the slab width is in ascending or descending order. The difference in width between adjacent slabs in each steel type is equal to or less than the upper limit.
For example, 100 [mm] can be adopted as the upper limit.

  The “(D2) width transition constraint” described in the first embodiment is a constraint relating to the transition of the slab width during rolling, whereas the “(F2) width transition constraint within a steel type” is a condition during casting. This is a restriction on the transition of the slab width for each steel type. “(F2) Width transition restriction within steel type” is a restriction required because the width of the mold in the continuous casting machine cannot be changed rapidly.

  In order to determine whether or not “(F2) width transition constraint within steel type” is satisfied, an appropriate steel type must be determined from the manufacturable steel types for each slab included in the slab group combination (subset). Must. However, as shown in FIG. 16, there is a slab in which a steel type that can be manufactured is not uniquely determined (for example, a slab having a slab No. of “2”). The problem of determining a steel type so as to satisfy “(F2) Width transition within steel type” can be regarded as an optimization problem. Therefore, in the present embodiment, an appropriate steel type is determined from the steel types that can be manufactured as in the processing after step S1703, and the steel type of each slab is determined to be “(F2 ) Satisfaction of “width transition constraint within steel type” is determined.

First, in step S1703, the cast candidate derivation unit 204 selects one unselected one of the combinations (subsets) of the slab groups extracted in step S1702.
Next, in step S1704, the cast candidate derivation unit 204 determines that the production cost of the slab included in the combination (subset) of the slab group selected in step S1703 is the lowest among the steel types capable of producing the slab. Tentatively determine the appropriate steel type. For example, in FIG. 16, when the production cost of steel type I is lower than that of steel type II, slab No. Is tentatively determined for the slab having the value “2”. For a slab having one steel type option, the steel type is provisionally determined for the slab. For example, in FIG. However, for the slab with the “6”, the steel type II is provisionally determined.

Next, in step S1705, the cast candidate deriving unit 204 sets, in the slab information 1600, a plurality of steel types among the slabs included in the combination (subset) of the slab groups selected in step S1703 as the manufacturable steel types. Extract the slab that is. In the example shown in FIG. Are extracted as “2”, “3”, “5”, “8”, and “10” to “12”. The number of slabs is extracted in step S1705 and N _s.
Next, in step S1706, cast candidate deriving unit 204, the N _s number of slab extracted in step S1705, sorted in ascending or descending order by the production cost. The production cost for the steel type provisionally determined in step S1704 is used as the production cost at this time.

Next, in step S1707, cast candidate derivation unit 204, among the N _s number of slab extracted in step S1705, the slab s unselected, select one in the order sorted in step S1706.
Next, in step S1708, cast candidate derivation unit 204, a steel type k slab s selected in step S1707, calculates an evaluation value c _k for steels k provisionally determined in step S1704.

Here, the evaluation value _ck will be described.
In the present embodiment, the steel type of each slab is determined using the following four evaluation indexes (A3) to (D3).
(A3) Number of Steel Types When a plurality of different steel types coexist in the same cast, a mixed portion of molten steel is generated in the tundish between charges where the steel types are switched. For this reason, if the components of the mixing section do not satisfy the requirements required for the slab, a part of the slab is cut and discarded. Therefore, when the operation is carried out by successive casting of different steel types (the same applies hereinafter), the yield is reduced. Therefore, it is desirable that the number of successive different steel types in the same cast is as small as possible. It should be noted that “different steel types” means that different steel types are continuously and continuously cast. Therefore, it is desirable that the number of steel types of the slabs included in the combination (subset) of the slab groups is small.

(B3) Surplus material The surplus material is a product that is produced in the lot when the order is allocated to the lot for which the production volume is determined but the production volume is less than the production volume. It is a product for which it is undecided whether it is linked to an order. Surplus material refers to the amount of such products.
Since the production of the components of the molten steel is performed in the converter and the secondary refining process, the steel type is manufactured in charge units. Therefore, a portion where the total weight of the slab to which a certain steel type is assigned is less than the charge weight (the weight of one charge) is manufactured as surplus material that is not linked to the order. The surplus material stays in the yard as a slab until it is linked to the order, which causes an increase in the in-process inventory. For this reason, it is desired that the total weight of the slab to which a certain steel type is assigned approaches (preferably coincides with) the charge weight so that the surplus material is reduced as much as possible.

(C3) Manufacturing Cost As described above, since it is necessary to accurately adjust the range of components and to input an alloy, a steel type having a narrow component range or a steel type requiring an alloy or the like is manufactured in a larger number. Costly. For this reason, if there is a choice of steel type for a certain slab, it is desirable to manufacture it as a steel type that is as inexpensive as possible.
However, it is possible to consolidate steel types by manufacturing low-grade steel types with low manufacturing costs as more expensive steel types, and in some cases, it is possible to reduce the number of steel types and the amount of surplus material. On the other hand, consolidating low-grade steel grades with low production costs into expensive steel grades worsens production costs. Therefore, “(A3) Number of steel types” and “(B3) Surplus material amount” and “(C3) Manufacturing cost” have a trade-off relationship.

(D3) Amount of Improvement of Width Transition Constraint in Steel Type As described above, in order to enable continuous casting in a continuous casting machine, violation of the above-mentioned “(F2) Width transition constraint in steel type” is eliminated in each steel type. It is desirable to change the steel type.

In the present embodiment, by using an evaluation index of the above (A3) ~ (D3), the evaluation value c _k for steels k, expressed by the following equation (6).
c _k = W _W -W _N -W _Y -W _P (6)
(6) In the formula, W _W is the steel grade in width transition constraint violations improvement amount. When changing the steel type k of the slab s eliminates the violation of the width transition constraint in the steel type k (the above-mentioned “(F2) Width transition constraint in the steel type”), the improvement amount W _W in the steel type width transition constraint is eliminated. Is a number C _W having a predetermined positive value (W _W = C _W (> 0)). If there is no width transition constraint violation within the steel type k both before and after the change of the steel type k of the slab s, or if the width transition constraint violation within the steel type k is not resolved even if the steel type k of the slab s is changed, It is assumed that the improvement amount W _W for violation of the width transition constraint within the steel type is 0 (W _W = 0).

W _N is the number cost of steel grade. When the steel type of the slab s is steel type k, the number of steel types of the slabs included in the combination (subset) of the slab groups selected in step S1703 is N _k, and the weighting factor for N _k is C _N. The number cost W _N is represented by the product of these (W _N = N _k × C _N ).
W _Y is the surplus material cost. When the steel type of slab s is steel type k, the total weight of the slab of steel type k included in the combination (subset) of the slab group selected in step S1703 is Q _k , and the charge weight is Q _ch , the total weight is In order to manufacture a slab of Q _k , n _ch (= Q _k整数 the integer part of the value of Q _ch +1) charges are required. Then excess material amount Q _Y will n _ch × Q _ch -Q _k. Then, excess material amount cost W _Y is a surplus material amount Q _Y, represented by the product of the weight coefficient C _Y for _{Q Y (W Y = Q Y} × C Y).

W _P is the manufacturing cost. Assuming that the integrated value of the manufacturing cost for each steel type is E _k and the weighting factor for E _k is C _P , the manufacturing cost W _P when the steel type of the slab s is steel type k is the product of these (W _P = E _k × C _P ).
The weighting factors C _N , C _Y , and C _P are set in advance depending on how much importance is placed on each evaluation item, and represent the balance of evaluation among the evaluation items.

In step S1708, the cast candidate deriving unit 204, the slab s selected in step S1707, the evaluation value c _k for steels k provisionally determined in step S1704, calculates the above equation (6).

  Next, in step S1709, the cast candidate deriving unit 204 determines, as the steel type k of the slab s selected in step S1707, a steel type that can manufacture the slab s and an unselected steel type other than the steel type provisionally determined in step S1704. Select one steel type. For example, the cast candidate derivation unit 204 can select one steel type from such unselected steel types according to some predetermined order (for example, the steel type whose manufacturing cost is the lowest or the most expensive). The type of steel from which the slab s can be manufactured can be specified from the slab information 1600.

Next, in step S1710, cast candidate derivation unit 204, a steel type k slab s selected in step S1707, the evaluation value c _k for steels k selected in step S1709, is calculated by equation (6).
Next, in step S1711, the cast candidate derivation unit 204 determines, as the steel type k of the slab s selected in step S1707, all steel types other than the steel type that can be manufactured in the slab s and the steel type provisionally determined in step S1704. It is determined whether or not it has been selected. If it is determined that all the steel types have not been selected, the process returns to step S1709. Then, as the steel type k of the slab s selected in step S1707, the processing of steps S1709 to S1711 is repeated until the evaluation values _ck for all the steel types capable of manufacturing the slab s are calculated.

Then, when the evaluation values _ck for all the steel types capable of manufacturing the slab s are calculated as the steel type k of the slab s selected in step S1707, the process proceeds to step S1712.
In step S1712, the cast candidate derivation unit 204, among the evaluation values c _k for each steel type k slab s selected in step S1707, extracts the evaluation value c _k largest values. Then, the cast candidate deriving unit 204 determines the steel type k used when obtaining the extracted evaluation value _ck as the steel type k of the slab s selected in step S1707.

Next, in step S1713, cast candidate deriving unit 204 determines whether to select all N _s number of slab s extracted in step S1705. If it is determined that not all slabs have been selected, the process returns to step S1707. Until determining the steel grade k of N _s number of slab s extracted in step S1705, repeating the process of step S1707～S1713.

When determining the steel grade k of N _s number of slab s extracted in step S1705, the process proceeds to step S1714.
In step S1714, the cast candidate derivation unit 204 determines whether or not each slab included in the combination (subset) of the slab groups selected in step S1703 satisfies the above-described “(F2) Width transition constraint within steel type”. Is determined. For this determination, the steel type k determined in step S1712 for each slab s included in the combination (subset) of the slab groups selected in step S1703 is used.

  If the result of this determination is that “(F2) the width transition constraint within the steel type” is satisfied, the process proceeds to step S1715, where the cast candidate derivation unit 204 determines the combination (subset) of the slab groups selected in step S1703 as a cast candidate. To be adopted. Then, the process proceeds to step S1717. On the other hand, if the “(F2) width transition constraint within the steel type” is not satisfied, the process proceeds to step S1716, where the cast candidate derivation unit 204 adopts the combination (subset) of the slab groups selected in step S1703 as the cast candidate. do not do. Then, the process proceeds to step S1717.

  In step S1717, the cast candidate derivation unit 204 determines whether all combinations (subsets) of the slab groups extracted in step S1702 have been selected. If the result of this determination is that a combination (subset) of all slab groups has not been selected, processing returns to step S1703. Then, the processes of steps S1703 to S1717 are repeated for all combinations (subsets) of slab groups until it is determined whether or not to be adopted as a cast candidate. When it is determined whether or not all combinations (subsets) of slab groups are to be adopted as cast candidates, the processing in the flowchart of FIG. 17 ends, and the process proceeds to step S1005 of FIG.

<Optimizer 205>
The optimization unit 205 derives an optimal combination of cast candidates (cast pieces) from the cast candidates derived by the cast candidate derivation unit 204 by solving an optimization problem.
In the present embodiment, the evaluation value c _j of the cast candidate _j is expressed by the following expression (7) instead of the expression (4) described in the first embodiment.
_{c j = C W × W +} C T × T + C D × D + C N -C S × S-C n × n-C y × y-C p × p ··· (7)

The first to fifth terms on the right side of equation (7) are the same as equation (4).
n is the total number of steel types of the slab included in the cast candidate j. C _n is a weighting factor for n.
y is the total sum of the surplus materials in the cast candidate j. C _y is a weighting factor for y.

p is the sum of the manufacturing costs of the slabs included in the cast candidate j. C _p is a weighting factor for p.
The weighting factors C _W , C _T , C _D , C _N , C _S , C _n , C _y , and C _p are set in advance depending on how much importance is placed on each evaluation item. Represents the balance of evaluation.
The other processing of the optimization unit 205 is the same as the processing described in the first embodiment.

(Example)
Next, examples will be described.
In the present embodiment, each of the nine cases in which the number of slabs is “50”, “100”, “150”, “200”, “250”, “300”, “350”, “400”, and “450” Created a cast plan. In any case, a slab in which any of a plurality of steel types can be selected and a slab in which only one steel type is designated are included. The steel type was determined as described in the embodiment. In the example of the invention, a cast plan was created by repeatedly selecting a part of the slab group by 20 and deriving a cast candidate, performing an optimization calculation to derive an optimal cast candidate (cast piece). . On the other hand, in the comparative example, in step S1003 of FIG. 10, a method is used in which all the slab groups created in step S1002 are selected. Created a new cast plan.

In both the invention example and the comparative example, the set partitioning problem was adopted as the optimization problem, and the expression (1) was used as the objective function, and the expressions (2) and (3) were used as the constraint expressions. In addition, the evaluation value c _j is represented by Expression (7). Here, the values of the weighting factors C _W , C _T , C _D , C _N , C _S , C _n , C _y , and C _p are respectively set to “0”, “0”, “1”, “100”, “10”. , "1", "1", and "1" (C _W = 0, C _T = 0, C _D = 1, C _N = 100, C _S = 10, C _n = 1, C _y = 1 , C _p = 1).

FIG. 18 is a diagram showing the results of the invention example and the comparative example in a table format.
In FIG. 18, in the comparative example, when the number of slabs is 200 or more, the calculation time exceeds one hour, and the cast knitting result was not obtained within a practical calculation time. Therefore, the optimization calculation was terminated. On the other hand, in the invention examples, the cast knitting results were obtained within a practical calculation time of 10 minutes or less in all cases.

Therefore, the waiting time of the optimization calculation time for the operator is allowed to be about several minutes, so that the calculation method described in the present embodiment can obtain an optimum cast composition result with a sufficiently long waiting time.
In addition, as a result of assigning steel types to each slab, only combinations (subsets) of slab groups that satisfy the above-mentioned “(F2) Width transition constraint within steel types” are registered as cast candidates, thereby obtaining (A2) to (A2) to ( It is possible to obtain a cast knitting result satisfying all the constraints of F2).

(Summary)
As described above, in the present embodiment, each of the slabs included in the slab information 1600 is grouped so that the slabs satisfying the determination condition of (E1) in addition to (A1) to (D1) belong to the same slab group. . Further, a part of the plurality of slab groups is selected in order from the earliest date of the desired hot rolling date, and in addition to the constraints (A2) to (E2), (F2) Are derived as cast candidates. And, in addition to the difference between the maximum value and the minimum value of the width of the slab, the difference between the maximum value and the minimum value of the thickness of the slab, the difference between the average value of the desired hot rolling date of the slab and the re-early day, and the number of casts, The evaluation value of the cast candidate j is derived using the number of steel types, the surplus material, and the manufacturing cost as evaluation indexes. Therefore, in addition to the effects described in the first embodiment, the optimum casting plan including the number of successive different types of steel, the surplus material, and the manufacturing cost is kept within a practical time in addition to the constraints on casting. Can be created.

Further, in the present embodiment, for slabs that can be manufactured with a plurality of steel types, the width transition constraint violation amount within the same steel type, the total number of slab steel types included in the combination (subset) of the slab groups, and the slab group One of the plurality of steel types is determined using the total amount of surplus materials in the combination (subset) and the manufacturing cost as evaluation indexes. Therefore, the steel type of each slab can be appropriately determined according to these evaluation indices.
In the present embodiment, a combination (subset) of slab groups satisfying the constraint condition (F2) is searched from combinations (subsets) of slab groups satisfying the constraint conditions (A2) to (E2). . Therefore, the calculation time can be reduced as compared with the case where it is determined at a time whether or not the constraints (A2) to (F2) are satisfied.

  Further, in the present embodiment, as the steel type of each slab included in the combination (subset) of the slab groups, a steel type having the lowest manufacturing cost among the steel types that can manufacture the slab is temporarily determined. Therefore, also in the method of the present embodiment that satisfies “(F2) width transition restriction within steel type”, it is possible to easily select a steel type having a low manufacturing cost as a steel type of each slab.

[Modification]
<Modification 1>
In the first and second embodiments described above, the case where the slabs (records) of the slab information 300 are rearranged in order from the slab having the earliest desired hot rolling date 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, an operation of rolling from a wide slab to a narrow slab is generally performed, but the operation tends to be more stable as the change amount of the slab width to be rolled back and forth is smaller. Therefore, for example, the slabs (records) having a smaller slab width may be sorted in order. By doing so, variation in the slab width within the same cast is suppressed, and the operation is stabilized. For slabs represented by numerical values such as slab width, slab thickness, and slab weight, the slabs (records) are rearranged so that the numerical values are in descending or ascending order. On the other hand, for materials represented by symbols such as materials, the slabs (records) are rearranged in ascending or descending order according to, for example, dictionary order (alphabetical order or alphabetical order).
The same applies to the case where the slab group selection unit 203 rearranges the slab groups (records) of the slab group information 500.

<Modification 2>
In the first and second embodiments described above, when all of the above-described determination conditions (A1) to (D1) are satisfied, the slab selected from the slab information 400 is included in the slab group that has already been created. The case of inclusion has been described as an example. However, it is determined whether or not the slab selected from the slab information 400 is to be included 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 necessary to do so. For example, the condition (D1) may be omitted.

<Modification 3>
In the first and second embodiments described above, for each of the combinations (subsets) of the slab groups listed, only those that satisfy all the above-described constraints (A2) to (E2) are adopted as cast candidates. The case has been described as an example. However, this is not always necessary as long as a condition that can be included in the same cast (a constraint condition) is adopted as a cast candidate. For example, at least one of (B2) to (E2) may be employed.

<Modification 4>
In the first and second embodiments described above, 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 S1003 to S1006 shown in FIG. 10 are repeated, the number of slabs belonging to the slab group increases due to the redefinition of the slab group. Then, cast candidates that do not satisfy the above-described constraint conditions (A2) to (E2) are likely to occur, so that the number of cast candidates is reduced, and the time required for one processing in steps S1003 to S1006 is reduced. It becomes a tendency. Therefore, the processing of steps S1003 to S1007 shown in FIG. 10 may be repeated, and the number of slab groups selected by slab group selecting section 203 may be increased as the number of slabs included in the slab group increases. This suppresses a decrease in the number of cast candidates derived in step S1004, obtains a cast piece from a larger number of combinations as an optimization result, and reduces the number of repetitive calculations in steps S1003 to S1007 required for convergence. It can be suppressed.

<Modification 5>
In the above-described first and second embodiments, (C2) to (C2) to (C2) to (C2) The constraint condition of E2) has been described as an example. However, the constraints for allowing the slabs included in the same cast to be hot-rolled in the hot rolling process as the same lot (chance) include at least one of the constraints (C2) to (E2). You only need to include it. For example, it is possible to determine which of the constraints (C2) to (E2) is to be adopted, depending on the slab or equipment to be hot-rolled.

<Modification 6>
In the first and second embodiments described above, 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 maximum value and the minimum value of the slab thickness of the slab included in the cast candidate j, and The difference T, the difference D between the average value and the earliest date of the desired hot rolling date of the slab included in the cast candidate j, and the number of casts are used as an example of the evaluation of the cast candidate j. However, when creating a production plan for a product produced in lot units, other evaluation indices may be determined as appropriate as long as the number of lots is evaluated. That is, in the example of the present embodiment, the evaluation index only needs to include at least the number of casts. Further, in addition to or instead of the difference D between the average value and the earliest date of the desired hot rolling date of the slab included in the cast candidate j, the latest date and the earliest date of the desired hot rolling date of the slab included in the cast candidate j May be used as an evaluation index. Further, the material may be included in the evaluation index.

<Variation 7>
In the first and second embodiments described above, since it is assumed that there is no plurality of slab groups i having the same contents (that is, slab groups i having the same combination of constituent slabs), equations (2) and (3) are used. The value on the right-hand side of the constraint expression in equation (1) is set to “1”. However, for example, when there are a plurality of slab groups i having the same content, the value on the right side of the constraint expressions of Expressions (2) and (3) is the number. For example, when there are two slab groups i having the same content, a constraint equation in which the value on the right side of the constraint equation of equations (2) and (3) is set to “2” is given as a constraint equation for the slab group i. . In this way, even when 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 group belongs.

<Modification 8>
In the first and second embodiments described above, the determination unit 206 assigns the slab group creation unit 202 or the slab group creation unit 202 to one of the cast candidates j (cast pieces) corresponding to the decision variable x _j given “1”. When it is determined that the result of the optimization calculation in the optimization unit 205 satisfies the convergence determination condition when all of the (latest) slab groups created in the slab group redefinition unit 207 are included one by one Has been described as an example. However, the convergence determination condition is not limited to such.

  In order to determine the convergence of calculation even when a so-called extra combination occurs, in which it is impossible to incorporate a slab into any cast piece, for example, in order to determine calculation convergence, for example, the slab included in any of the cast pieces with respect to the total number of slab groups i If the ratio of the total number of groups i (ie, the ratio of adoption of the slab group i to cast pieces) is equal to or greater than a predetermined ratio, it may be determined that the convergence determination condition is satisfied. Further, when the ratio of the total number of slabs in slab group i included in any of the cast pieces to the total number of slabs in slab group i (that is, the adoption rate of slabs to cast pieces) is equal to or greater than a predetermined ratio. Alternatively, it may be determined that the convergence determination condition is satisfied.

  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 equal to or less than a predetermined value, or If the value of the objective function f obtained as a result of the calculation is the same as the value of the objective function f obtained as a result of the current optimization calculation, it may be determined that the convergence determination condition is satisfied.

<Modification 9>
When the number of slabs to be cast is large, it is preferable to create a slab group as described in the first and second embodiments. This is because the calculation time can be reduced as described above. However, for example, when the number of slabs to be cast is not large, the slab group need not be created.

<Variation 10>
In the first and second embodiments described above, an upper limit value of the calculation time in one optimization calculation is provided, and when the calculation time in one optimization calculation reaches the upper limit value, The obtained solution may be regarded as an optimal cast candidate.

<Modification 11>
In the second embodiment described above, steels within the width transition constraint violations improvement amount W _W, steel grade number cost W _N, excess material amount cost W _Y, and the evaluation value c _k for steels k by using the manufacturing cost W _P This has been described by taking the case of representing as an example (see equation (6)). However, the evaluation value _ck for the steel type _k is expressed using at least one of the steel type internal width transition constraint violation improvement amount W _W , the steel type number cost W _N , the surplus material cost W _Y , and the production cost W _P. Just do it. For example, it is possible to determine which of these is to be adopted according to the plan policy of the cast plan.

<Modification 12>
In the above-described first and second embodiments, the case where a cast plan is created has been described as an example. However, the method described in the present embodiment can be applied to a production plan for a plurality of products that are produced in a lot by combining a plurality of products into lots, other than the cast plan.

  For example, the method described in the present embodiment may be applied to a thick plate production plan (board removal problem). After rolling the slab to a target thickness, the rolled slab is sheared as required to obtain a thick plate. Therefore, it is necessary to determine which plank to cut out from which slab. Such a content is created as a thick plate production plan. In this case, "thick plate" corresponds to "product", "slab" corresponds to "lot", "shearing (cutting)" corresponds to "manufacturing", and "refinement process" "Corresponds to" manufacturing conditions having a degree of freedom of selection ", and the" excess portion "of the cut-out slab corresponds to" surplus material amount ".

  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 conditions corresponding to (A2) to (E2), conditions (constraint conditions) that allow a thick plate to be cut from the same slab are given. This constraint includes, for example, that the same slab does not include a thick plate different from the predetermined material, that the total weight of the thick plate does not exceed the upper limit, that the thickness of the thick plate included in the same slab is Is within a predetermined range. A slab satisfying this constraint is a slab candidate. Note that thick plates can be grouped. For example, 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, a thick plate group can be created. The evaluation index at the time of optimization may include, for example, a surplus portion of the slab, in addition to the number of slabs. The surplus portion of the slab is a portion of the slab that does not become any thick plate after cutting from the slab. The smaller the surplus portion of the slab, the higher the evaluation value indicates the higher the evaluation. In addition, as described in the present embodiment, an evaluation index using the size and delivery date of a product (thick plate) can be adopted. In addition, the constraint equation for 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 the equation (2), for a thick plate (or thick plate group) having the same contents, the number of thick plates (or thick plate groups) included in the optimal slab candidate and a slab candidate are derived. Prior to this, it is possible to adopt a constraint formula formulated that the number of planks (or plank groups) selected is the same. In addition, since the sheared thick plate is sent to a different refining process such as painting, care, and slow cooling, in the plate removing problem, the “steel type” described in the second embodiment is replaced with the “refinement process”. A thick plate that is sheared from the same slab may be allocated to the refining process so as to maximize the processing efficiency under the constraints on the processing in each refining process.

  The method described in the present embodiment may be applied to a hot rolling plan (chance composition problem). It is necessary to determine a plurality of slabs to be continuously hot-rolled. The unit of the plurality of slabs is called a chance. In this case, “hot rolled sheet (coil)” corresponds to “product”, “chance” corresponds to “lot”, “rolling” corresponds to “manufacturing”, and “selection of furnace number of heating furnace” Corresponds to "manufacturing conditions with freedom of choice". The hot rolled sheet information corresponding to the slab information includes, for example, manufacturing conditions such as the material of the hot rolled sheet (coil), the size of the slab, the size of the hot rolled sheet (coil), and the desired date of hot rolling. As the conditions corresponding to (A2) to (E2), for example, (C2) to (E2) can be used. A chance that satisfies this constraint is a chance candidate. Incidentally, the hot rolled sheets can be grouped. For example, a hot-rolled sheet group can be created by performing the processing 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 a product (hot-rolled sheet) or a desired hot-rolling date can be adopted. In addition, the constraint equation for 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 expression corresponding to the expression (2), for a hot rolled sheet (or hot rolled sheet group) having the same contents, the number of hot rolled sheets (or hot rolled sheet groups) included in the optimal chance candidate and the chance It is possible to employ a constraint formula formulated that the number of hot rolled sheets (or hot rolled sheet groups) selected prior to deriving a candidate is the same. When the slab constituting the chance is distributed and heated to a plurality of heating furnaces, the “steel type” described in the second embodiment is replaced with the “heating furnace”, and the heating furnace determined according to the capability of the heating furnace is used. The slab may be assigned to each heating furnace so that the heating efficiency is maximized under the restrictions.

Further, the application target of the method described in the present embodiment is not limited to a plan for producing a plurality of products collectively in lot units, but is a plan for processing a plurality of products collectively in lot units. Is also good.
For example, the method described in the present embodiment may be applied to a hill formation plan (hill hill problem). When a plurality of slabs are divided into a plurality of piles and piled up in a steel material storage yard (yard) using a transfer device such as a crane, it is necessary to determine the hills to which the slabs belong and the position (stacking stage) of each slab in each hill. There is. Such a content is created as a hill plan. In this case, "slab" corresponds to "product", "mountain" corresponds to "lot", and "mountain (conveyance of slab by conveyance device)" corresponds to "processing". As the slab information, the slab information 300 described in the present embodiment can be used. Conditions (constraint conditions) corresponding to (A2) to (E2) may include conditions in which “cast” in (A2) to (E2) is replaced with “mountain”. A mountain satisfying this constraint is a mountain candidate. Note that slabs can be grouped to create a slab group, as in the present embodiment. The evaluation index at the time of optimization can include, for example, the number of hill-turning in addition to the number of hills. Mountain turning refers to temporarily placing a slab in a location different from the final location when making a mountain. The smaller the number of times of mountain hopping, the higher the evaluation value indicates the higher the evaluation. In addition, as described in the present embodiment, an evaluation index using a slab size and a desired hot rolling date can be adopted. In addition, the constraint equation for the optimization calculation can be set in the same manner as the constraint equation in the cast plan (see equations (2) and (3)).

<Other modifications>
The embodiments of the present invention described above can be realized by a computer executing a program. 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 nonvolatile memory card, a ROM, and the like can be used.
Further, the embodiments of the present invention described above are merely examples of specific embodiments for carrying out the present invention, and the technical scope of the present invention should not be interpreted in a limited manner. Things. That is, the present invention can be implemented in various forms without departing from the technical idea or the main features.

(Relation with claims)
The relationship between the items described in the present embodiment and the claims is enumerated below. It should be noted that the present invention is not limited to the following, as described in the modified examples.
The plan creation device corresponds to, for example, the cast knitting device 200.
The acquisition unit is realized by using, for example, the slab information acquisition unit 201.
The product information corresponds to, for example, the slab information 300.
The selection unit is realized by using, for example, the slab group selection unit 203.
The lot candidate deriving unit is realized by using the cast candidate deriving unit 204, for example.
The first lot inclusion condition is realized by, for example, the constraint conditions (A2) to (E2), and the second lot inclusion condition is realized by, for example, the constraint condition of (F2) (see FIG. 17). (See also steps S1702 and S1714).
The optimizing unit is realized, for example, by using the optimizing unit 205.
The objective function is realized by, for example, equation (1).
The lot candidate derivation evaluation index is realized by, for example, each term of Expression (4).
The first constraint expression is realized by, for example, Expression (2), and the second constraint expression is realized by, for example, Expression (3).
The determination unit is realized by using the determination unit 206, for example.
The redefining means is realized by using the slab group redefining unit 207, for example.
The output unit is realized by using the output unit 208, for example.
The group creation unit is realized by using, for example, the slab group creation unit 202.
The product group corresponds to the slab group.
The determination condition is realized by, for example, the determination conditions (A1) to (D1).
The manufacturing condition selection evaluation index is realized, for example, by the evaluation indexes (A3) to (D3) (the second to fourth terms on the right side of the equation (6)).

  200: cast knitting apparatus, 201: slab information acquisition unit, 202: slab group creation unit, 203: slab group selection unit, 204: cast candidate derivation unit, 205: optimization unit, 206: determination unit, 207: slab group rebuilding unit Definition unit, 208: 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

Claims (16)

A plan creation device for creating a plan for collectively producing or processing a plurality of products in lot units,
Acquisition means for acquiring information on the plurality of products, the product information including manufacturing conditions of the products,
Selecting means for selecting a part of the plurality of products,
Among the subsets of the products selected by the selection unit, a subset satisfying a first lot inclusion condition expressed by using the manufacturing condition as a condition that the products can be included in the same lot is a lot candidate Lot candidate deriving means derived as
Optimizing means for deriving an optimal lot candidate from the lot candidates derived by the lot candidate deriving means by performing an optimization calculation to maximize or minimize the value of the objective function within a range satisfying the constraint equation,
Determining means for determining whether the result of the optimization calculation has converged,
A redefining means for redefining the product included in the optimal lot candidate derived by the optimizing means as one product when the deciding means determines that the result of the optimization calculation is not converged; When,
When the determination unit determines that the result of the optimization calculation has converged, the optimum lot candidate derived by the optimization unit is determined as an optimum lot, and the product is included in the optimum lot. Output means for outputting information indicating whether the
The objective function is an objective function including at least the number of lots as a lot candidate derivation evaluation index,
In the constraint formula, the number of the products included in the optimal lot candidate is the same as the number of the products selected by the selection unit, and the same product is not included in the different lot candidates. Contains a formalized expression,
When the product is redefined by the redefining means, the selecting means selects all of the products redefined by the redefining means and some of the unselected products,
Until the determination means determines that the result of the optimization calculation has converged, the selection of the product by the selection means, the derivation of the lot candidate by the lot candidate derivation means, and the optimization by the optimization means. A plan creation device characterized by performing a conversion calculation. A group creation unit that creates a plurality of product groups by grouping the plurality of products based on manufacturing conditions of the products included in the product information acquired by the acquisition unit,
The selecting means selects a part of the product group created by the group creating means,
The lot candidate deriving unit, among the subsets of the product group selected by the selecting unit, derives a subset that satisfies a condition that a product group can be included in the same lot as a lot candidate,
In the constraint formula, the number of the product groups included in the optimal lot candidate is the same as the number of the product groups selected by the selection unit, and the same product group is included in different lot candidates. Not including the formulated formula,
The redefining means, when the determination means determines that the result of the optimization calculation has not converged, converts the product group included in the optimal lot candidate derived by the optimization means into one product Redefined as a group,
Until it is determined by the determination unit that the result of the optimization calculation has converged, the selection of the product group by the selection unit, the derivation of the lot candidate by the lot candidate derivation unit, and the determination by the optimization unit The plan creation device according to claim 1, wherein optimization calculation is performed. The constraint equation is a first constraint equation for the product group in which the number of included products is equal to or greater than a predetermined value, and a second constraint equation for the product group in which the number of included products is less than the predetermined value. Including
In the first constraint formula, the number of the product groups included in the optimal lot candidate is the same as the number of the product groups selected by the selection unit, and the same product group is different from the lot. It is a formula that is not included in the candidate,
The second constraint formula is that the number of the product groups included in the optimal lot candidate is equal to or less than the number of the product groups selected by the selection unit, and the same product group is assigned to different lot candidates. The plan creation device according to claim 2, wherein a formula that is not included is a formalized formula.   The group creating unit sorts the plurality of products based on manufacturing conditions of the products included in the product information acquired by the acquiring unit, and sorts the sorted products in ascending order in the sorting order. Or selecting one by one in descending order, and determining whether to include the selected product in an already created product group according to a determination condition determined based on manufacturing conditions of the product. The plan creation device according to 2 or 3. The group creating unit rearranges the plurality of product groups based on manufacturing conditions of the products included in the product information acquired by the acquiring unit,
3. The method according to claim 2, wherein the selection unit selects a part of the plurality of product groups rearranged by the group creation unit in a predetermined number in ascending or descending order in the arrangement order. 5. The plan creation device according to any one of 4.   The plan according to any one of claims 2 to 5, wherein the group creation unit is configured to prevent the number of the products included in one product group from exceeding an upper limit specified in advance. Creating device. The lot candidate derivation unit has a degree of freedom in the selection of the products included in the subset of the products selected by the selection unit and having the manufacturing conditions with the degree of freedom in selection. For each of the plurality of different options of the manufacturing condition, a manufacturing condition selection evaluation index is derived based on the manufacturing condition of the product included in the subset of the product selected by the selecting unit, and the derived manufacturing condition is derived. First manufacturing condition selecting means for determining selection of a manufacturing condition having a degree of freedom based on a selection evaluation index;
Assuming that the selection of the manufacturing condition having the degree of freedom of selection is determined by the first manufacturing condition selecting means, the subset of the products selected by the selecting means includes the products in the same lot. It is determined whether or not a second lot inclusion condition expressed using the manufacturing conditions is satisfied as a condition that can be performed, and based on a result of the determination, a subset of the product selected by the selection unit is determined. And a second manufacturing condition selecting means for deriving the lot candidate from among the above,
The manufacturing condition selection evaluation index is a manufacturing condition of the product included in the subset of the product selected by the selection unit, and is selected from among the manufacturing condition options having the degree of freedom of selection. An evaluation index relating to the number of different options, an evaluation index relating to a surplus amount generated when producing the product included in the subset of the product selected by the selection unit, and an evaluation index of the product selected by the selection unit. At least one of an evaluation index relating to a manufacturing cost when producing the product included in the subset, and an evaluation index relating to improvement of a violation of the second lot inclusion condition realized by selecting the manufacturing conditions. The plan creation device according to any one of claims 1 to 6, further comprising:   The first manufacturing condition selecting means in the lot candidate deriving means is a manufacturing condition of the product included in the subset of the product selected by the selecting means, the manufacturing condition having a degree of freedom of the selection. The selection is tentatively determined to be the one with the lowest manufacturing cost when producing the product, and the manufacturing condition selection evaluation is performed by sequentially changing the selection of the manufacturing conditions having the degree of freedom from the tentatively determined contents. The plan creation device according to claim 7, wherein the index is derived. The manufacturing conditions include at least one of material, size, weight, and delivery date of the product,
9. The method according to claim 1, wherein the lot candidate derivation evaluation index further includes an evaluation index for evaluating at least one of a material, a size, a weight, and a delivery date of the product. 10. Planning equipment.   The determination means is configured to determine, when the optimum lot includes a product of a predetermined ratio or more of the plurality of products, and when the optimization calculation is performed before or after the optimization calculation of the objective function maximized or minimized by the optimization calculation. And the case where the difference between the value of the optimization calculation and the value in the current optimization calculation is equal to or smaller than a predetermined value is determined to be that the result of the optimization calculation has converged. Item 10. The plan creation device according to any one of items 1 to 9. The product is a slab cast by a continuous casting machine,
The lot is a cast, which is a unit of a plurality of charges to be continuously cast,
The plan creation device according to claim 1, wherein the plan is a cast plan indicating the cast to which the slab belongs. The product is a slab cast by a continuous casting machine,
The lot is a cast, which is a unit of a plurality of charges to be continuously cast,
The plan is a cast plan indicating the cast to which the slab belongs,
The conditions under which the product can be included in the same lot are that the total weight of the slab does not exceed an upper limit specified in advance, and the sum of the lengths of the coils manufactured by rolling the slab is determined in advance. That the specified upper limit is not exceeded, that the difference in width of the slabs that precedes and succeeds when the slabs are sorted in the rolling order is equal to or less than the upper limit specified in advance, and that the difference in width is a fixed value The plan creation device according to any one of claims 1 to 6, including at least one of the following numbers of slabs being equal to or less than a predetermined upper limit value. The product is a slab cast by a continuous casting machine,
The lot is a cast, which is a unit of a plurality of charges to be continuously cast,
The plan is a cast plan indicating the cast to which the slab belongs,
The manufacturing conditions having the degree of freedom of selection are steel types specified in advance based on the components of molten steel,
The first lot inclusion condition includes a constraint in manufacturing the slab, which is determined independently of the steel type,
The second lot inclusion condition includes a constraint upon manufacturing the slab, which is determined depending on the steel type,
The first manufacturing condition selecting means in the lot candidate deriving means extracts a subset of the products satisfying the first lot inclusion condition from a subset of the products selected by the selecting means, Among the products included in the extracted subset of the products, for the product having a degree of freedom in selecting the steel type, the extraction is performed for each of a plurality of different options of manufacturing conditions having a degree of freedom in the selection. The production condition selection evaluation index is derived based on the production conditions of the product included in the subset of the products, and one of the steel types is determined based on the derived production condition selection evaluation index. ,
The second manufacturing condition selecting means in the lot candidate deriving means determines that the steel type having the degree of freedom of selection is the determined steel type, and the extracted subset of the products includes the second lot. Determining whether a possible condition is satisfied, and deriving, as the lot candidate, a subset that satisfies the second lot inclusion possibility condition among the extracted subsets of the product. The planning device according to claim 7 or 8, wherein the plan is created. The first lot inclusion condition is that, among the materials of the slabs included in the combination of the slab groups, which are subsets of the slabs, the materials prohibited from being included in the same cast are not mixed. The total weight of the slabs included in the combination of slab groups, which is a subset of the slabs, does not exceed the upper limit of the weight of the cast, and the sum of the lengths of the coils manufactured by rolling the slabs That does not exceed the upper limit specified in advance, and that the difference in width of the slab before and after when the slabs are rearranged in rolling order is equal to or less than the upper limit specified in advance, and the difference in width is That the number of slabs equal to or less than a certain value is equal to or less than an upper limit value specified in advance, including at least one of:
The second lot inclusion condition is a difference between widths of adjacent slabs when the slabs included in the subset of the slabs selected by the selection unit are rearranged in casting order for each steel type. 14. The plan creation device according to claim 13, which includes a condition that is equal to or less than an upper limit value specified in advance. A plan creation method for creating a plan for producing or processing a plurality of products collectively in units of lots,
An acquisition step of acquiring information of the plurality of products, the product information including manufacturing conditions of the products,
A selecting step of selecting a part of the plurality of products,
Among the subsets of the products selected in the selection step, a subset satisfying a first lot inclusion condition expressed using the manufacturing conditions as a condition that the products can be included in the same lot is a lot candidate A lot candidate derivation process derived as
An optimization step of deriving an optimal lot candidate from the lot candidate derived in the lot candidate derivation step by performing an optimization calculation that maximizes or minimizes the value of the objective function within a range satisfying the constraint equation;
A determining step of determining whether or not the result of the optimization calculation has converged;
A redefining step of redefining the product included in the optimal lot candidate derived in the optimizing step as one product when it is determined in the determining step that the result of the optimization calculation does not converge; When,
In the determination step, when it is determined that the result of the optimization calculation has converged, the optimum lot candidate derived in the optimization step is determined as an optimum lot, and the product is included in the optimum lot. Output step of outputting information indicating whether the
The objective function is an objective function including at least the number of lots as a lot candidate derivation evaluation index,
The constraint formula is that the number of the products included in the optimal lot candidate is the same as the number of the products selected in the selection step, and the same product is not included in different lot candidates. Contains a formalized expression,
The selecting step, when the product is redefined by the redefining step, select all of the products redefined by the redefining step, and select some of the unselected products,
Until it is determined by the determination step that the result of the optimization calculation has converged, the selection of the product by the selection step, the derivation of the lot candidate by the lot candidate derivation step, and the optimization by the optimization step A plan creation method characterized by performing a conversion calculation.   A non-transitory computer-readable storage medium storing a program that causes a computer to function as each unit of the plan creation device according to any one of claims 1 to 14.

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