JP2020107277A - Plan creation device, plan creation method, and program - Google Patents

Abstract

To enable planning for producing or processing products in units of lots in a short time without greatly deteriorating the accuracy of planning results.SOLUTION: A cast organization device 100 derives a duality solution (an optimum solution of a duality variable λi) as an optimum solution of a duality problem DLP when a linear alleviation problem LP linearly alleviating an aggregate division problem MP is a main subject. Then, the cast organization device 100 uses the duality solution to derive an optimum solution of a string generator problem SP. Specifically, within a range where a new executable lot (a) satisfies restriction conditions for establishment as a lot (=cast), the cast organization device 100 derives, as an optimum solution of the new executable lot (a), the new executable lot (a) when a value obtained by subtracting a duality cost (=Σiincluded in NIλi×ai) for the new executable lot (a) from a cost (c) of the new executable lot (a) becomes minimum.SELECTED DRAWING: Figure 1

Description

The present invention relates to a plan creating apparatus, a plan creating method, and a program, and is particularly suitable for use in collecting a plurality of products in a lot and producing or processing a plurality of products in a lot unit.

When making a production plan of a product in the manufacturing industry, it is often the case that a production plan is made so that a plurality of products are put together in an appropriate number and in an appropriate number of lots and manufactured in lot units.
Here, as an example in which 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, molten iron supplied from a blast furnace is charged into a converter and carbon is removed from the molten iron by blowing oxygen to produce molten steel. This is called primary refining. Next, the molten steel is poured into a container called a ladle and conveyed to the secondary refining process. This molten steel for one ladle is called a charge. As a secondary refining process, for example, there is a RH (Ruhrstahl Heraeus) process. By circulating molten steel in a vacuum tube, impure gas in the molten steel is removed in vacuum to adjust the composition of the molten steel. When the secondary refining process is completed, the ladle is transported to the continuous casting machine. In a continuous casting machine, molten steel is poured from a ladle into a mold and cooled at the same time to produce a semi-finished slab. In a continuous casting machine, it is possible to continuously cast a plurality of charges, and a group of a plurality of charges cast continuously is called a cast. Further, continuous casting of molten steel having a plurality of charges is called continuous casting. If the number of consecutive castings is increased too much, the components of the continuous casting machine (such as the tundish and the refractory of the mold, the immersion nozzle, etc.) will be melted. The number of charges to be implemented must be set appropriately.

The slab produced by the continuous casting machine is called a slab and is conveyed to the rolling process. In the rolling process, the slab is reheated by a heating furnace, rolled at a high temperature by a rolling mill to a thickness of several millimeters, and wound into a coil. Depending on the shape and hardness of the slab, there is a limit to the number of slabs that can be continuously rolled by the rolling mill. A group of slabs that are continuously rolled by a rolling mill is called an opportunity.
Each slab is given information such as composition, shape, desired hot rolling date, etc. from the order information, and lots such as casts and chances are knitted in consideration of constraint conditions in the steel making process and rolling process.

Further, in recent years, attempts have been made to shorten the lead time and heat loss by making the cast, which is a lot in the steelmaking process, the same as the chance, which is a lot in the rolling process. In the case of performing such an operation, it is necessary to determine a cast formation (slab included in each cast) that simultaneously satisfies the constraint conditions in the steel making process and the rolling process.

In the cast knitting, by incorporating a large number of slabs into the cast and making them into a large lot, the number of castings in succession is increased, and preparations for reducing slab defects at the start and end of continuous casting and starting recasting are made. It is expected that the production amount will increase due to the reduction of time. On the other hand, there are restrictions on the slab that can be incorporated into the same cast depending on the conditions such as composition, shape, and desired hot rolling date. For this reason, it is required to perform the cast knitting in which the lot is as large as possible within the range satisfying the constraint condition.

In the cast organization work, since the number of slabs such as hundreds or thousands is generally handled, the number of slab combinations increases. Therefore, it takes a long time for the planner to perform the cast formation that satisfies all the constraint conditions.
Therefore, there is a technique described in Patent Document 1 as a technique for automatically performing cast formation.
Patent Document 1 discloses that each charge is represented by a node, a network in which the charges that can be bundled together and cast are represented by a directional branch is created, and the longest cast route is searched on the network. Has been done.

JP2012-11451A

Kubo Mikio, Tamura Akihisa, Matsui Tomoki, "Applied Mathematical Planning Handbook", Asakura Shoten Co., Ltd., May 2002, p.133, 337, 621, 634

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

As described above, according to the conventional technology, when a plurality of slabs (products) are collected in a cast (lot) and a slab (product) is cast (produced) in units of cast (lot), a casting (production) plan is prepared. , It was not easy to shorten the planning time without significantly lowering 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 lot units to be planned in a short time without significantly lowering the accuracy of the planning result. The purpose is to

The plan creation apparatus of the present invention sets a problem of creating a plan for producing or processing a plurality of products in batch units so as to satisfy a predetermined lot formation constraint, and sets the set partition problem. Is a plan creation device that creates a plan by solving a product using a column generation method, and is an information acquisition unit that acquires product information that includes information about the plurality of products and that includes manufacturing conditions of the products; For each of a plurality of feasible lots that are combined so as to satisfy the lot formation constraint, the realizable lot is determined using a binary variable that determines whether or not to adopt the feasible lot as a solution. Based on the evaluation index for lot grouping of the products with respect to, a set division problem for finding an optimal combination of the feasible lots that includes the plurality of products without duplication and without omission is used as an original problem, and an optimal solution of the original problem is obtained. A column generating means for deriving an optimal solution of the column generator problem for generating a candidate lot that is a candidate for a feasible lot that constitutes the candidate lot, and a candidate lot satisfying the column addition requirement for the candidate lot derived by the column generating means are If included, a column adding unit that adds the candidate lot generated by the column generating unit to the set of feasible lots, a candidate lot derived by the column generating unit, and an addition by the column adding unit An optimal solution deriving means for deriving a combination of the feasible lots as an optimum solution of the original problem based on the set of the feasible lots including the selected candidate lots.

In the plan creating method of the present invention, a problem of creating a plan for producing or processing a plurality of products in batch units so as to satisfy a predetermined lot formation constraint is a set partition problem. Is a plan creating method for creating a plan by solving using a column generation method, and an acquiring step of acquiring product information including information on the plurality of products, including manufacturing conditions of the products; For each of a plurality of feasible lots that are combined so as to satisfy the lot formation constraint, the realizable lot is determined using a binary variable that determines whether or not to adopt the feasible lot as a solution. Based on the evaluation index for lot grouping of the products with respect to, a set division problem for finding an optimal combination of the feasible lots that includes the plurality of products without duplication and without omission is used as an original problem, and an optimal solution of the original problem is obtained. A column generation step of deriving an optimal solution of the column generator problem that generates a candidate lot that is a candidate for a feasible lot that constitutes a candidate lot that satisfies the column addition requirement in the candidate lot derived by the column generation step. If included, a column addition step of adding the candidate lot generated by the column generation step to the set of feasible lots, a candidate lot derived by the column generation step, and an addition by the column addition step An optimal solution derivation step of deriving a combination of the feasible lots as an optimal solution of the original problem based on the set of the feasible lots including the selected candidate lots.

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

According to the present invention, a plan for producing or processing products in lot units can be planned in a short time without significantly lowering the accuracy of the planning result.

It is a figure which shows an example of a functional structure of a cast knitting apparatus. It is a flow chart explaining an example of a cast organization method (plan creation method) by a cast organization device. It is a figure which shows an example of slab information. It is a figure which shows an example of slab group information. It is a figure explaining an example of manufacturing order restrictions. It is a figure which shows an example of the planning time of a cast plan in a table format. It is a figure explaining the cost coefficient at the time of continuously casting the molten steel of two different steel types. It is a figure which shows the actual number of times used in this calculation example. It is a figure which shows the calculation result of the cost coefficient at the time of continuously casting the molten steel of two different steel types. It is a figure which shows the number of different steel types in a cast candidate for every combination of steel types.

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

[First Embodiment]
First, the first embodiment will be described.
FIG. 1 is a diagram showing an example of a functional configuration of the cast knitting apparatus 100. FIG. 2 is a flowchart for explaining an example of a cast organization method (plan creation method) by the cast organization apparatus 100. The hardware of the cast knitting apparatus 100 is realized by using, for example, an information processing apparatus including a CPU, ROM, RAM, HDD, and various interfaces, or dedicated hardware.

<Slab information acquisition unit 101, slab information acquisition step S201>
The slab information acquisition unit 101 acquires and stores slab information. The slab information acquisition unit 101 acquires the slab information by, for example, an operator operating the cast knitting apparatus 100, receiving the slab information transmitted from an external device, or reading the slab information stored in the portable storage medium. To do.

FIG. 3 is a diagram showing an example of the slab information 300.
3, the slab information 300 is the slab number. , Steel type, slab weight, slab width, slab thickness, coil width, coil thickness, and coil length are information associated with each other. Slab information is individually given for each slab to be planned.

Slab No. Is a number that identifies the slab.
The steel type refers to the type of slab that is determined according to the components of the slab. Here, the steel type is represented by a symbol for identifying the steel type.
The slab weight, the slab width, and the slab thickness are the slab weight, width, and thickness, respectively. The steel type, the slab weight, the slab width, and the slab thickness are manufacturing conditions in the process of manufacturing the slab (continuous casting process).

The coil width, the coil thickness, and the coil length are respectively the slab No. The width, thickness, and length of the coil obtained by hot rolling the slab identified by. The coil width, the coil thickness, and the coil length are manufacturing conditions in a step (hot rolling step) after the step of manufacturing the slab.

<Slab Group Creation Unit 102, Slab Group Creation Step S202>
Based on the slab information 300 acquired by the slab information acquisition unit 101, the slab group creation unit 102 includes the slab information 300 such 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 102 selects one unselected slab from the unselected slabs (records) included in the slab information 300.

Next, the slab group creation unit 102 determines whether or not there is a slab group to which the slab selected from the slab information 300 can be added, among the already created slab groups. The slab group creation unit 102 includes slabs whose slab manufacturing conditions match within a predetermined range in the same slab group.
Specifically, in the present embodiment, the slab group creation unit 102 selects from the slab information 300 among the already created slab groups when all the following determination conditions (A1) to (C1) are satisfied. It is determined that there is a slab group to which added slabs can be added.

(A1) The maximum value of the difference between the width (slab width) of the slab included in the already created slab group and the width (slab width) of the slab selected from the slab information 300 is 100 [mm] or less.
(B1) The maximum value of the difference between the slab thickness (slab thickness) included in the already created slab group and the slab thickness (slab thickness) selected from the slab information 300 is 2 [mm] or less.
(C1) At least one of the manufacturable steel type of the slab included in the already created slab group and the manufacturable steel type of the slab selected from the slab information overlap.

Although FIG. 3 shows only one type of steel for each slab, some slabs can be manufactured from any of a plurality of steel types. Therefore, the determination condition (C1) is imposed. As described above, the steel grade has a freedom in selection (one steel grade can be selected from a plurality of steel grades in one slab).

When the slab group creation unit 102 determines that there is no slab group to which the slab selected from the slab information 300 can be added among the already created slab groups, a new slab group is created and the selected slab group is selected. Include the slab in the new slab group created.
On the other hand, when there is a slab group to which the slab selected from the slab information 300 can be added in the slab groups that have already been created, the slab group creation unit 102 determines the slabs included in the slab group and the selected slab. It is determined whether the total number of sheets is less than or equal to the upper limit value. Since the rolling rolls are worn in the hot rolling process, there is a limit to the number of slabs of the same width band that are continuously hot rolled at the same chance. Therefore, in this embodiment, an upper limit is set for the number of slabs included in one slab group. In this embodiment, the upper limit value is set to 40 [sheets] or less.

The slab group creation unit 102 creates a new slab group if the total of the slabs included in the slab group to which the slab selected from the slab information 300 can be added and the total number of the selected slabs is not less than or equal to the upper limit value, Include the selected slab in the new slab group created.
On the other hand, when the total of the slabs included in the slab group to which the slab selected from the slab information 300 and the number of the selected slabs is equal to or less than the upper limit value, the slab group creation unit 102 sets the selected slab to the relevant slab. Include in slab group.

The slab group creation unit 102 selects unselected slabs (records) included in the slab information 300 one by one, and repeats the above processing to set the slabs included in the slab information 300 to any slab group. include. The same slab does not belong to multiple slab groups.

FIG. 4 is a diagram showing an example of the slab group information 400 created from the slab information 300 shown in FIG. The slab group information 400 is a list of slab groups.
4, the slab group information 400 is the slab group number. , Steel type, slab width (maximum value, minimum value), slab thickness (maximum value, minimum value), slab weight, coil length, and the number of slabs are associated with each other.

Slab group No. Is a number that identifies the slab group.
The steel type is a slab steel type that belongs to the slab group. Although FIG. 4 shows a case where each slab group is composed of one steel type slab, one slab group may include a plurality of steel type slabs.
The maximum value of the slab width refers to the maximum value of the width (slab width) of the slabs included in the slab group. The minimum value of the slab width means the minimum value of the width (slab width) of the slabs included in the slab group.

The maximum value of the slab thickness refers to the maximum value of the thickness of the slabs included in the slab group (slab thickness). The minimum value of the slab thickness means the minimum value of the thickness (slab thickness) of the slabs included in the slab group.
The slab weight is a total value of the weights (slab weights) of the slabs included in the slab group.
The coil length is the total value of the coil lengths of the slabs included in the slab group.
The slab group creation unit 102 creates the slab group information 400 as described above.

A set of slab groups created by the slab group creation unit 102 is denoted by N _I, and a slab group (element of N _I ) is denoted by i. In the present embodiment, a plurality of slab groups (slabs created by the slab group creating unit 102) satisfying constraint conditions (see expressions (8) to (22)) to be satisfied as a lot (=cast) described later. A single cast is constructed by combining (a subset of the entire set of groups). In the following description, a group of a plurality of slab groups that are candidates for this cast (a subset of the entire set of slab groups created by the slab group creation unit 102) will be referred to as a feasible lot as necessary. A set of feasible lots is denoted by N _J, and a feasible lot (element of N _J ) is denoted by j. By thus grouping a plurality of slabs included in the same cast into one slab group, it is possible to reduce the number of feasible lots that can be selected, and thus the calculation load can be reduced.

<Initial Column Set Setting Unit 103, Initial Column Set Setting Step S203>
The initial column set setting unit 103 creates a set N _I (={1,2,...,i,...,n}) of the slab group i created by the slab group creation unit 102, that is, a slab group creation. The initial value of the matrix (two-dimensional array) A _i,j is set from the slab group i created by the unit 102. The element in the i-th row and the j-th column of the matrix A _i,j has a value of “1” when the slab group i is included in the feasible lot j, and has a value of “0” when not included. At this time, the initial column set setting unit 103 includes the slab group i created by the slab group creation unit 102 without duplication and without omission, and further, the constraint condition (Equation (8) to ((8) The initial value of the matrix A _i,j is set so as to satisfy the expression (22)). As an example, in the present embodiment, the initial column set setting unit 103 sets the matrix A _i,j having “1” only to the element _{j for} which i=j and “0” for the other elements as initial values. And That is, the initial values of the matrix A _i,j are set so that each feasible lot j has only one arbitrary slab group i different from each other as an element. Therefore, the number of slab group i created in the slab group creation unit 102 | and the number of possible lot j (matrix A _i, the number of columns of _{j) | | N I N J} | is the matrix A _i, the _j The initial values match (|N _I |=|N _J |). Thus matrix A _i, line number _j becomes the number to identify the slab group i, a matrix A _{i, j} column number will number identifying the feasibility lots j. That is, one column of the matrix A _i,j corresponds to one feasible lot j, and a slab group i corresponding to a row having a value of “1” in the column is included in the feasible lot j. Become a slab group.

The user inputs the information of the initial value of the matrix A _i,j by operating the user interface of the cast knitting apparatus 100, and the initial column set setting unit 103 stores the information in the storage medium in the cast knitting apparatus 100. By storing _, the initial value of the matrix A _i,j can be set. However, this is not necessarily the case, and for example, the initial column set setting unit 103 may derive the initial value of the matrix A _i,j by a predetermined logic.

<Set division problem construction unit 104, set division problem construction step S204>
In the present embodiment, by solving the set division problem MP (original problem), the feasible lot j to be adopted as a cast is determined from the feasible lot j shown in each column of the matrix A _i,j . The set partitioning problem MP is a subset that includes exactly one element each (that is, includes each element without omission and without duplication), given a subset of elements and the cost of the element. Is a problem of deciding the combination of the above so as to minimize the total sum of the costs. In the present embodiment, the set division problem MP includes exactly one slab group i (that is, each slab group i when given a feasible lot j and a cost for the feasible lot j). There is a problem of determining a combination of feasible lots j that includes all the leaks and does not overlap each other so that the total sum of the costs is minimized.

The set division problem MP in this embodiment is expressed as follows.
<<set>>
・_I ∈ N _I : Slab group ・j ∈ N _J : Realizable lot
<<Decision variable>>
・Z _j ={0, 1}
The decision variable z _j is a 0-1 variable that becomes “1” when the feasible lot j is adopted as a cast and “0” otherwise.
<<constant>>
・Matrix A _i,j
As described above, the matrix A _i,j is composed of elements that are “1” when the slab group i is included in the feasible lot j and “0” otherwise.
・Cost c _j
The cost c _j is determined according to the slabs forming the slab group i included in the feasible lot j.

<< constraint >>
As described above, in the set division problem MP, a combination of feasible lots j including exactly one slab group i is obtained. Therefore, in the matrix A _i,j , only one feasible lot j has to be selected from the set of feasible lots j to which an arbitrary slab group i belongs. This constraint condition is expressed by the following equation (1).

<< Objective function >>
As described above, in the set division problem MP, the total sum of the costs c _j for the feasible lot j is set to be the minimum. Therefore, the objective function is expressed by the following equation (2).

<<Specific example of cost c _j >>
In this embodiment, the case where the cost c _j in the equation (2) is set as follows is given as an example.
-Number of casts The total sum of costs c _j is basically represented by the total number of casts. One feasible lot j corresponds to one cast. Therefore, in order to evaluate the number of casts, it is assumed that the manufacturing cost C _CAST occurs for each feasible lot j. The manufacturing cost C _CAST of each feasible lot j is the same value.

Further, a cost other than the manufacturing cost C _CAST may be added to the cost c _j . In this embodiment, the case where the following surplus material amount and the number of steel types are added to the cost c _j will be taken as an example.
-Amount of surplus material A surplus material is a product that is produced in a lot when the production quantity is less than the production quantity even if the order is assigned to the lot. It is a product for which it is unclear whether or not it will be tied. The amount of surplus material means the amount of such a product.
Since the components of molten steel are produced in the converter and the secondary refining process, steel types are produced 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 (weight of one charge) is manufactured as a surplus material that is not tied to the order. The surplus material stays in the yard as a slab until it is tied to the order, resulting in an increase in the amount of work-in-process inventory. For this reason, it is desired that the total weight of slabs assigned the same steel type approaches (preferably coincide with) the charge weight so that the amount of surplus material is reduced as much as possible.

In this way, since the composition adjustment of molten steel is carried out in charge units in the steelmaking plant, the total weight of slabs manufactured as the same steel type in a certain cast approaches a multiple of the charge weight (weight constituting one charge). Doing so (preferably matching) is desired. For example, if the charge weight is 200 tons and the weight of the slab manufactured in a certain steel grade is 500 tons among the slabs included in the feasible lot j, the slab for three charges is used as the slab of the steel grade. Will be manufactured. Therefore, the amount of surplus material is 100 (=3×200−500) tons.

When the number of charges required to manufacture the total weight of the slabs included in the feasible lot j is n _j ^CH , the charge weight is W ^CH, and the weight of the slab group belonging to the feasible lot j is W _j ^SG , The surplus material amount W _j ^Y is expressed by the following equation (3).

The feasible lot j may include slab groups of different steel types. In this way, when the slab group of different steel types is included in the feasible lot j, the calculation of equation (3) is performed for each steel type, and the sum of them is used as the surplus material amount W _j ^Y for the feasible lot j. ..

-Number of steel types When a plurality of different steel types coexist in the same feasible lot j, a molten steel mixing part occurs in the tundish between the charges at which the steel types are switched. The connecting portion of different steel types in such a feasible lot is called a different steel type seam. When the composition of the joint portion of this different steel type does not satisfy the requirements required for the slab, a part of the slab is cut and discarded. Therefore, when the operation by continuous casting of different steel types (that is, continuous casting of different steel types) is performed, the yield decreases. Therefore, it is desirable that the number of different steel type seams in the same feasible lot j is as small as possible. That is, it is desirable that the number N _j ^G of steel types contained in the feasible lot j is small.
From the above, the cost c _j for feasibility lots j is expressed by the following equation (4).

In the equation (4), C ^Y and C ^G are cost coefficients (weighting coefficients) for the amount of surplus material and the number of steel types, respectively. The cost coefficients C ^Y and C ^G are preset depending on how much importance is attached to each evaluation item, and represent the balance of evaluation among the evaluation items. It should be noted that the value obtained by integrating the formula (2) with respect to the manufacturing cost C _CAST of the first term on the right side of the formula (4) is equal to the total manufacturing cost of the feasible lots j adopted as the optimum solution of the set partitioning problem MP. It is the value multiplied by C _CAST . Therefore, the manufacturing cost C _CAST serves as a cost coefficient for the number of feasible lots j. When the manufacturing cost C _{CAST is set} to “1”, the value obtained by integrating the manufacturing cost C _CAST of the first term on the right side of the formula (4) in the formula (2) is adopted as the optimum solution of the set partitioning problem MP. It becomes the total number of feasible lots j.
The set partitioning problem construction unit 104 calculates the equation (4) from the current value of the matrix A _i,j to calculate the cost c of each column (each feasible lot j) included in the matrix A _{i,j. Derive j} . As described above, in the process of the first step S204 _, the current value of the matrix A _i,j becomes the initial value. In the processing of step S204 after the second time, the set division problem construction unit 104 derives the cost c _j of the column (feasible lot j) newly added by the column addition unit 109 described later.

<Linear Relaxation Problem Constructing Unit 105, Linear Relaxation Problem Constructing Step S205>
The linear relaxation problem construction unit 105 forms a linear relaxation problem LP by linearly relaxing the set division problem MP. That is, the linear relaxation problem configuration unit 105 redefines the decision variable z _j so that it can take a value in the range of 0≦z _j ≦1 in the expressions (1) and (2).

<Dual Solution Derivation Unit 106>
The dual solution derivation unit 106 derives a dual solution which is an optimal solution of the dual problem DLP when the linear relaxation problem LP of the set division problem MP (original problem) is used as a main problem.
The set partitioning problem MP (original problem) itself is a 0-1 integer programming problem, but the dual problem DLP is a linear relaxation problem (linear programming problem). The dual problem DLP in the case where the linear relaxation problem of the set partitioning problem MP (original problem), which is a 0-1 integer programming problem, is used as a dual problem DLP, if the symbols used in the original set partitioning problem MP are used. ) Is represented by the objective function and the constraint equation of the following equation (6).

As described above, the dual variable λ _i is a decision variable of the dual problem DLP and is a continuous variable (−∞<λ _i <∞) defined for each slab group i. Row j of A _{j,i in} the equation (6) corresponds to the feasible lot j. The (one) row j of A _{j,i in} the equation (6) becomes “1” when the feasible lot j corresponding to the row j includes the slab group i, and becomes “0” otherwise. Includes 0-1 variables as elements. This element is a variable having the same meaning as the decision variable a _i of the column generator problem SP described in the section <Column generator 107, step S207>. Dual variable lambda _i Since the corresponding improvement of the value of the set partitioning problem MP objective function (original problem) ((2)), by obtaining the largest possible Shigumaramuda _i, more of the objective function set partitioning problem MP A good lower limit will be obtained. Therefore, the objective function (equation (5)) of the dual problem DLP becomes a maximization problem.

The dual solution derivation unit 106 performs the optimization calculation by the linear programming method using a known solver such as CPLEX (registered trademark) so that the objective of the expression (5) is satisfied within a range satisfying the constraint expression of the expression (6). The dual variable λ _i that maximizes the value of the function is derived as the optimum solution (that is, dual solution) of the dual variable λ _i . Since the dual problem itself, which is mainly the linear relaxation problem of the set partitioning problem, can be realized by a known technique as described in Non-Patent Document 1, its detailed description is omitted here.

<Column Generation Unit 107, Column Generation Step S207>
In the set partitioning problem MP, it is difficult to list all feasible lots j. Therefore, in the present embodiment, the set partitioning problem MP is configured by limiting the feasible lot j included in the matrix A _i,j . The column generation unit 107 uses the dual solution (that is, the optimum solution of the dual variable λ _i ) derived by the dual solution derivation unit 106 to add a new addition to the set partitioning problem MP (that is, the matrix A _i,j ). A feasible lot j (column) is generated.

The new feasible lot j is not necessarily a collection of any slab group i. That is, the new feasible lot j satisfies the constraint condition for being established as a lot (=cast) and improves the value of the objective function (equation (2)) of the set division problem MP (original problem). It must be a feasible lot j that satisfies both contributing and contributing. Here, the candidate new feasible lot j added as a column of the matrix A _i,j is a={a ₁ , a ₂ ,..., A _N }. N is the number of slab groups created by the slab group creation unit 102. It is premised that the new feasible lot a is established as a cast, and if the new feasible lot a is established as a cast, the cost c for the new feasible lot a can be calculated. Then, if the cost c for the new feasible lot a satisfies the following expression (7), improvement in the value of the objective function (expression (2)) of the set partitioning problem MP (original problem) can be expected. This is because the amount of improvement in the value of the objective function (equation (2)) of the set partitioning problem MP (original problem) is larger than the cost c for the new feasible lot a.

Therefore, in the present embodiment, a column generator problem SP for obtaining an optimal solution candidate of the set division problem MP (original problem), that is, a column to be newly added (new feasible lot a) is formulated as follows. ..
<<set>>
_I i N _I : Slab group k i N _K : Steel type As described above, N _I is a set of slab groups created by the slab group creation unit 102, and i is a slab group (element of N _I ). N _K is a set of steel types of the slab group created by the slab group creating unit 102, and k is a steel type (element of N _K ).

<<Decision variable>>
The decision variable a _i is an element of the new feasible lot a, and is a 0-1 variable that is “1” when the new feasible lot a includes the slab group i, and “0” otherwise. is there. In the following description, this decision variable a _i will be referred to as a lot constituent product presence/absence variable as necessary. The element of A _{j,i in} the equation (6) described in the section <Dual solution deriving unit 106> is a variable having the same meaning as the lot constituent product presence/absence variable a _i .
Further, a variable x _i,k that is a 0-1 variable that becomes “1” when the slab group i is manufactured as the steel type k and becomes “0” otherwise is defined. Further, "1" in the production of slabs of steel grade k in the cast defines a variable g _k is a 0-1 variable becomes "0" otherwise. Further, a variable r _i,i′ that is a 0-1 variable that becomes “1” when the slab group i′ is manufactured next to the slab group i and becomes “0” otherwise is defined.

<< constraint >>
[Lot component product existence variable definition constraint]
First, as the constraint equation defining the lot constituent product presence/absence variable a _i , the constraint equation of the following equation (8) is used.

When the slab group i is included in the new feasible lot a, the formula (8) is used to manufacture the slab group i with any steel type k, and if not, with the slab group i with any steel type k. Indicates that i is not manufactured.

[Manufacturing constraint]
Next, since the slab group i is either included or not included in the new feasible lot a, the constraint formula of the following formula (9) is used as the constraint formula representing this.

As shown in the equations (8) and (9), in the slab group i included in the new feasible lot a, even if the steel type k has a degree of freedom in selection, the slab group i has only one steel type k. Determined.

[Restrictions on steel types that cannot be manufactured]
Next, the set of steel types that can be manufactured for the slab group i is denoted by N′ _K (i). Then, as a constraint expression indicating that the slab group i of the steel type kε{N _K −N′ _K (i)} cannot be included in the new feasible lot a, the constraint expression of the following expression (10) To use.

[Weight constraint]
Next, assuming that the weight of the slab group i is SW _i , the total weight w _k of the slab of the steel type k included in the new feasible lot a is expressed by the constraint equation (11) below.

[Charge number constraint]
Next, let the maximum weight of the slab that can be included in one charge be maxChW. Then, the number of charges m _k required to manufacture the slab of the steel type k by the weight w _k is represented by the following constraint equations (12-1) and (12-2). That is, the number of charges m _k required to manufacture the slab of the steel type k by the weight w _k is within the range determined by the following formulas (12-1) and (12-2).

[Maximum consecutive casting count constraint]
Next, the maximum number of consecutive castings in one cast (maximum number of consecutive castings) is defined as maxchWRen. Then, the maximum number of consecutive castings maxchWRen in one cast must be greater than or equal to the sum of all the steel types k of the charge number m _k determined by the equations (12-1) and (12-2). Is expressed by the following equation (13).

[Remaining material amount restriction]
Next, of the total weight of the charges manufactured as one cast, the weight exceeding the total weight of the slabs manufactured from the cast is manufactured as surplus material that cannot be assigned to the order, and until the order is assigned. In stock at the yard (temporary storage). When the weight of the steel type of such excess material to y _k, the weight y _k of the steel type of the surplus material is represented by the constraint equation of the following equation (14).

[Coil length constraint]
Next, assuming that one cast corresponds to one chance, the following restrictions are imposed on the total length of the coil manufactured from the continuously rollable casts on the same rolling roll. Here, the total length of the coil when the slabs included in the slab group i are rolled is CL _i, and the maximum rolling distance on the same rolling roll is maxCoLen. Then, as a constraint expression indicating that the total length of the coil manufactured from the slab rolled in one chance must be equal to or less than the maximum value of the rolling distance in the same rolling roll, the constraint expression of the following equation (15) To use. The following expression (15) may be expressed by the lot constituent product presence/absence variable a _i using the expression (8).

[Variable relation constraint]
Next, the constraint equation of the following equation (16) is used as the constraint equation that defines the relationship between the variables x _i,k and g _k . As described above, the variable x _i,k is a 0-1 variable that becomes “1” when the slab group i is manufactured as the steel type k, and “0” otherwise. The variable g _k is a 0-1 variable that becomes “1” when a slab of steel type k is manufactured in the cast and “0” otherwise.

Equation (16) indicates that when the slab group i is manufactured as the steel type k, a slab of the steel type k must be manufactured in the cast. Even if the steel type of a certain slab group i is not the steel type k, the steel type of another slab group i may be the steel type k. Therefore, in the equation (16), even if the variable x _i,k is “0”, the variable g _k can take “1”.

[Manufacturing order constraint]
FIG. 5 is a diagram illustrating an example of manufacturing order constraints. One node (indicated by a circle) shown in FIG. 5 corresponds to one slab group i. The branch indicated by the broken line indicates that the nodes (slab group i) at both ends of the broken line are slab groups i that have not been selected as cast among the slab groups i that can be continuously manufactured. The branch indicated by the solid arrow line indicates that it is the slab group i selected as a cast among the slab groups i that can be continuously manufactured. For the slab group i selected as these casts, the node (slab group i) at the base end of the arrow line and then the node (slab group i) at the tip end of the arrow line are manufactured.

Further, the variables r _i,i′ for the two nodes (slab groups i, i′) connected by the branch indicated by the solid arrow line are “1”, and are connected by the branch indicated by the solid arrow line. The variable r _i,i′ for the nonexistent node (slab group i, i′) becomes “0”. As described above, the variable r _i,i′ is a 0-1 variable that becomes “1” when the slab group i′ is manufactured next to the slab group i, and “0” otherwise.

In FIG. 5, for example, a part of the region 501 showing the steel type A and a part of the region 502 showing the steel type B overlap, and a part of the region 502 showing the steel type B and the region 503 showing the steel type C are shown. The case where the parts overlap will be shown as an example. The node (slab group i) located in the overlapping range of the region 501 indicating the steel type A and the region 502 indicating the steel type B indicates that either of the steel types A and B can be manufactured. Similarly, the node (slab group i) located in the overlapping range of the region 502 indicating the steel type B and the region 503 indicating the steel type C indicates that either of the steel types B and C can be manufactured. Further, in FIG. 5, for convenience of notation, only the steel types A to C are shown in the region 504 indicating the slab group set N _I , but in reality, all the steel types included in the slab information 300 are of the slab group. It is included in the region 504 indicating the set N _I.

As shown in FIG. 5, in addition to the slab group set N _I created by the slab group creation unit 102, a dummy slab group n _S indicating the start of manufacturing and a dummy slab group n _E indicating the end of manufacturing are prepared. .. The dummy slab groups n _S and n _E are virtual slab groups, not slab groups included in the cast. Next to the dummy slab group n _S , any slab group i included in the slab group set N _I can be manufactured. Further, it is assumed that any slab group i included in the slab group set N _I can manufacture the dummy slab group n _E next to the slab group i. Only one node (slab group i) is connected to the dummy slab groups n _S and n _E. On the other hand, two nodes (slab group i) are connected to the slab group i included in the slab group set N _I.

Here, the starting point set of the slab group i is N _S (=N _I +n _S ). The starting point set is a set of nodes (slab group i) that can be the base end of the arrow line, that is, a set of two slab groups i that are consecutive in the manufacturing order and that can be the slab group i that is manufactured first. .. Further, the end point set of the slab group i is N _E (=N _I +n _E ). The end point set is a set of nodes (slab group i) that can be the tip of the arrow line, that is, a set of two slab groups i that are consecutive in the manufacturing order and that can be the slab group i that is manufactured later.

Given the above, an example of a constraint (manufacturing order constraint) on the manufacturing order of the slab group i included in one cast will be described.
First, after the dummy slab group n _S, the constraint expression of the following expression (17) is used as a constraint expression indicating that any slab group i included in the end point set is manufactured.

Next, in the set N _I of the slab group i, if the slab group i is included in the new feasible lot a as a slab group that is manufactured first among the two slab groups that are consecutive in the manufacturing order, The constraint equation of the following equation (18) is used as the constraint equation indicating that the slab group i must be manufactured.

Next, in the set N _I of the slab group i, if the slab group i′ is included in the new feasible lot a as a slab group to be manufactured later out of the two slab groups consecutive in the manufacturing order, The constraint equation of the following equation (19) is used as the constraint equation indicating that the slab group i'must be manufactured.

Next, the constraint equation of the following equation (20) is used as a constraint equation indicating that the dummy slab group n _E must be manufactured next to any one slab group i included in the starting point set.

Next, a set of ^{unmanufacturable} slab groups next to the slab group i is defined as N _i ^Inf . As a constraint equation indicating two slab groups i and i′ that cannot be continuously manufactured, the constraint equation of the following equation (21) is used.

For example, the set condition N _i ^Inf of the next unmanufacturable slab group after the slab group i can be determined under the same determination conditions as those of the above-mentioned (A1) and (B1). That is, for a certain slab group, the maximum value of the difference between the width (slab width) of the slabs included in the slab group and the width (slab width) of the slabs included in other slab groups exceeds 100 [mm]. In this case, the other slab group is included as a set N _i ^Inf of ^{unmanufacturable} slab groups next to the certain slab group i. In addition, for a certain slab group, the maximum difference between the thickness of the slab included in the slab group (slab thickness) and the thickness of the slab included in the other slab group (slab thickness) exceeds 2 [mm]. In this case, the other slab group is included as a set N _i ^Inf of ^{unmanufacturable} slab groups next to the certain slab group i.

Next, in order for the plurality of slab groups i included in the new feasible lot a to form one cast, the first manufactured slab group i and the last manufactured slab group i among the plurality of slab groups i are manufactured. Must be specified. This corresponds to that the number of arrow lines in FIG. 5 must be a value obtained by subtracting “1” from the number of nodes (slab group i) connected by the arrow lines. That is, for any subset of slab groups i, the sum of the variables r _i,i′ for the two slab groups i, i′ included in the subset is calculated from the total number of slab groups included in the subset. Corresponds to being equal to the number minus "1". Therefore, if an arbitrary subset of the slab group set N _I is set to N _I ^S , the following constraint equation (22) is established.

<<Cost c for new feasible lot a>>
In the present embodiment, the cost c for the new realizable lot a is represented by the following equation (23).

The first term on the right side of the equation (23) represents the cost related to the total amount of surplus material of each steel type k manufactured in casting. y _k is calculated by the above equation (14). Since the slab that is the surplus material is stored in the yard until an order is assigned, it is desirable to reduce the surplus material amount as much as possible from the viewpoint of reducing inventory. The second term on the right side of the equation (23) represents the cost related to the total number of steel types manufactured in casting. g _k is defined by the equation (16). When producing multiple steel grades in a cast, mixed parts of different molten steels occur in the tundish. For this reason, it is desirable to reduce the number of steel grade changes (the number of different steel grade joints) as much as possible. The third term on the right side of the equation (23) represents the manufacturing cost necessary for manufacturing the cast. This term is added for the purpose of reducing the number of casts as much as possible when solving the set division problem MP. Here, C ^Y and C ^G are cost coefficients (weighting coefficients) with respect to the amount of surplus material and the number of steel types, respectively, and are the same as those described in the equation (4). Also, the manufacturing cost C _CAST is the same as that described in the equation (4). However, the cost coefficient and the manufacturing cost C _CAST may be the same as or different from the values shown in the equation (4).

<< Objective function >>
From the relationship between the main problem and the dual problem (weak dual theorem), the value of the objective function of the main problem is greater than or equal to the value of the objective function of the dual problem DLP when the main problem is the minimization problem. In this embodiment, the objective function of the main problem is equation (2), and the objective function of the dual problem DLP is equation (5). Therefore, originally, the cost c of the new feasible lot a is not less than the dual cost (=Σ _i ∈ _NI λ _i ×a _i ) of the new feasible lot a (c≧Σ _i ∈ _NI λ _i ×a _i ). Further, the cost c of the new feasible lot a and the dual cost (=Σ _{i εNI} λ _i ×a _i ) for the new feasible lot a are equal (c=Σ _{i εNI} λ _i ×a _{i ).} ) When the main problem and the dual problem DLP are true optimal solutions. Therefore, if there is a feasible lot a that satisfies c<Σ _i ∈ _NI λ _i ×a _i , such a feasible lot a is a set partitioning problem MP (that is, matrix A _i,j ). Must be added to.
Therefore, the objective function of the column generator problem SP is defined by the following equation (24).

The column generation unit 107 performs optimization calculation by the 0-1 integer programming method using a known solver such as CPLEX (registered trademark), and thus a range satisfying the constraint expressions (8) to (22). Then, a new feasible lot a (a lot constituent product presence/absence variable a _i that constitutes the subset) that is a subset that minimizes the value of the objective function of the equation (24) is set as an optimal solution of the new feasible lot a. Derive.

<Determination Unit 108, Step S208>
When the cost c of the new feasible lot a is _less than the dual cost (=Σ _i ∈ _NI λ _i ×a _i ) for the new feasible lot a (c<Σ _i ∈ _NI λ _i ×a _i ). , The dual solution of the dual problem DLP is not a true optimal solution of the dual problem DLP. That is, in this case, the feasible lot j (column) is not sufficiently added to the matrix A _i,j . Therefore, the cost c of the new feasible lot a is _less than the dual cost (=Σ _i ∈ _NI λ _i ×a _i ) for the new feasible lot a (c<Σ _i ∈ _NI λ _i ×a _i ). In this case, the new feasible lot a becomes a candidate for the optimal solution of the set division problem MP that is the original problem, and needs to be added to the matrix A _i,j .

Therefore, the determination unit 108 determines the dual cost (=Σ _i ∈ _NI λ _i ×a _i) for the new feasible lot a from the cost c of the new feasible lot a obtained as the optimum solution by the column generation unit 107. ) Is subtracted, it is determined whether the value is less than "0". That is, the determination unit 108 determines whether the following expression (25) is satisfied. In the following description, the determination formula (25) will be referred to as a column addition requirement as necessary.

If the result of this determination is that the column addition requirement is satisfied, it is necessary to add the new feasible lot a found as the optimum solution by the column generation unit 107 to the matrix A _i,j . On the other hand, if the column addition requirement is not satisfied, even if a new feasible lot a is added to the matrix A _i,j , the new feasible lot a is not affected by the set division problem MP that is the original problem. It can be considered that it will never be a candidate for the optimum solution.

<Column adding unit 109, step S209>
When the determination unit 108 determines that the column addition requirement is satisfied, the column addition unit 109 adds the new feasible lot a derived by the column generation unit 107 to the matrix A _i,j . For example, the column addition unit 109 adds the new feasible lot a derived by the column generation unit 107 to the column next to the last column of the current matrix A _i,j . As a result, the matrix A _i,j (that is, the subset in the set division problem MP) is updated.

<Repeated calculation after adding a new feasible lot a>
The new feasible lot a is added to the matrix A _i,j by the column adding unit 109 as described above, so that the current value of the matrix A _i,j is updated. In this case, the process returns to step S205, and the set division problem construction unit 104 derives the cost c _j of the newly added feasible lot a (see equation (4)). Then, in step S206, the dual solution derivation unit 106 uses the updated matrix A _i,j to maximize the value of the objective function of expression (5) within a range satisfying the constraint expression of expression (6). The dual variable λ _i is derived as a dual solution.

Further, in step S207, the column generation unit 107 uses the dual variables λ _i derived in this way within the range of satisfying the constraint expressions of Expressions (8) to (22), and the purpose of Expression (24). A new feasible lot a that minimizes the value of the function is derived.
Then, in step 208, the determination unit 108 determines the dual cost (=Σ _i ∈ _NI λ _i ×a _i) for the new feasible lot a from the cost c of the new feasible lot a thus derived. ) Is less than "0" (whether the column addition requirement is satisfied) is determined. If the result of this determination is that the column addition requirement is satisfied, then in step S209 the new feasible lot a derived by the column generation unit 107 is added to the matrix A _i,j .

The above processing is repeated until the determination unit 108 determines that the column addition requirement is not satisfied. In the above description, the determination unit 108 determines that the column generation requirement is not satisfied even when the new feasible lot a derived by the column generation unit 107 is already included in the matrix A _i,j. It shall be.

<Optimal Solution Derivation Unit 110, Step S210>
When the determining unit 108 determines that the column addition requirement is not satisfied, the optimal solution deriving unit 110 solves the set partitioning problem MP described above. More specifically, the optimum solution derivation unit 110 uses the (latest) matrix A _i,j obtained at the time when the determination unit 108 determines that the column addition requirement is not satisfied, using CPLEX (registered trademark). ) And other known solvers are used to perform optimization calculation by 0-1 integer programming, thereby minimizing the value of the objective function J of equation (2) within a range satisfying the constraint equation of equation (1). The decision variable z _j is derived and the optimal solution of the feasible lot j group is derived.

In the present embodiment, a set partitioning problem MP is realized rather than solving the set division problem MP, with a set of all feasible lots j generated from the whole set N _I of the slab group i to be cast-organized as a set of feasible lots j. The set division problem MP is solved with the initial value of the feasible lot j and the new feasible lot a added by the column addition unit 109 as a set of the feasible lot j. As described above, in the present embodiment, it can be considered that the set of feasible lots j (matrix A _i,j ) converges and the new feasible lot a does not become a candidate for the optimum solution of the set partitioning problem MP. In this case, the column adder 109 does not add a new realizable lot a. Therefore, the number of feasible lots j listed can be reduced without significantly reducing the calculation accuracy. As a result, the cast plan is created mainly because the feasible lot j cannot be enumerated because the main memory of the computer is insufficient, or even if the enumerable lot j can be enumerated, the subsequent set partitioning problem cannot be solved. It is possible to prevent a situation in which it is not possible.

<Output unit 111, step S211>
Each feasible lot j corresponds to a cast. The output unit 111 uses the information of the slabs forming the slab group i included in each feasible lot j as the casting plan drafting result based on the optimal solution of the feasible lot j group derived by the optimal solution deriving unit 110. Output. The output unit 111 performs, for example, at least one of a display on a computer display, a transmission to an external device, and a storage in an internal or external storage medium, to thereby obtain information on slabs included in each cast. Is output. For example, the output unit 111 uses, as the item of the slab information 300 shown in FIG. The information added with can be output as the information of the slab included in each cast.

(Summary)
As described above, in the present embodiment, the cast knitting apparatus 100 is a dual solution (a dual variable λ _i of an optimal solution of the dual problem DLP when the linear relaxation problem LP obtained by linearly relaxing the set partitioning problem MP is used as the main problem). Derive an optimal solution). Then, the cast knitting apparatus 100 uses the dual solution to derive an optimal solution for the column generator problem SP. That is, the cast knitting apparatus 100 changes the cost c of the new feasible lot a to the new feasible lot a within the range of satisfying the constraint condition for establishing the new feasible lot a as a lot (=cast). A new feasible lot a when the value obtained by subtracting the dual cost (=Σ _{i εNI} λ _i ×a _i ) is minimized is derived as an optimal solution of the new feasible lot a. Then, in the cast knitting apparatus 100, the value obtained by subtracting the dual cost (=Σ _i ∈ _NI λ _i ×a _i ) for the new feasible lot a from the cost c of the new feasible lot a is “0” or less. (That is, the column addition requirement is satisfied), the new feasible lot a is added to the matrix A _i,j indicating the subset in the set division problem MP. The cast knitting apparatus 100 repeats the addition of the new feasible lot a until the column addition requirement is not satisfied. The cast organization device 100 solves the set partitioning problem MP by using the matrix A _i,j thus obtained to derive the decision variable z _j, and optimizes the slab group i included in each feasible lot j. Derive the solution.

Therefore, it becomes possible to apply the column generation method to the cast organization problem, and it is possible to enumerate the candidates of feasible lots without excess or deficiency as much as possible (that is, it is necessary to enumerate all feasible lots. Lost). Therefore, the casting plan can be planned in a short time without significantly lowering the accuracy of the planning result. Also, by imposing a coil length constraint (a constraint that the total length of the coil rolled in one chance is less than or equal to the maximum rolling distance on the same rolling roll), the slab group generated by casting corresponds to the chance. As described above, the cast can be knitted in consideration of the constraint conditions in the continuous casting process and the hot rolling process.

(Modification)
<Modification 1>
In this embodiment, the case where the column adding unit 109 adds only the optimum solution of the column generator problem SP to the matrix A _i,j in step S209 has been described as an example. However, this need not always be the case. For example, in step S207, the column generation unit 107 stores all feasible solutions obtained in the calculation process of the column generator problem SP, and in step S208, the determination unit 108 stores each feasible solution stored therein. Alternatively, the column addition requirement may be determined, and in step S209, the column addition unit 109 may add all feasible solutions that satisfy the column addition requirement to the matrix A _i,j . Further, for example, in step S207, the column generation unit 107 stores all the feasible solutions obtained in the calculation process of the column generator problem SP, and in step S208, the determination unit 108 executes each of the feasible solutions stored above. The column addition requirement is determined for the solution, and in step S209, the column addition unit 109 selects a plurality of feasible solutions randomly selected from all feasible solutions that satisfy the column addition requirement, or a predetermined number of feasible solutions. A plurality of feasible solutions selected according to conditions may be added to the matrix A _i,j .

<Modification 2>
In the present embodiment, the case of creating a cast plan for a plurality of steel grade slabs has been described as an example. However, a cast plan for a single grade slab may be created. In this case, the steel type k may be one type (that is, in the description of the row generation unit 107 (step S207), the steel type set N _K may be N _K ={1}).

<Modification 3>
In this embodiment, the case where the slabs included in the slab information 300 are aggregated into the slab group i has been described as an example. However, this is not always necessary. For example, when the number of slabs included in the slab information 300 is small, the slabs forming the feasible lot may be directly obtained without creating the slab group i. In this case, the variable i is not a slab group but a variable indicating an individual slab.

<Modification 4>
In the present embodiment, the case of creating a cast plan has been described as an example. However, the method described in the present embodiment can be applied to a production plan for a plurality of products that are produced in a lot unit by collecting a plurality of products in a lot, other than the casting plan.
For example, the method described in the present embodiment may be applied to a plank production plan (planing problem). After rolling the slab to a target plate thickness, the rolled slab is sheared according to an order to obtain a thick plate. Therefore, it is necessary to decide which slab to cut out which plank. Such contents are prepared as a plank production plan. In this case, “thick plate” corresponds to “product”, “slab” corresponds to “lot”, “shear (cut out)” corresponds to “manufacture”, and the next step after shearing is the “refining process”. "Corresponds to "manufacturing conditions with a degree of freedom in selection", and "surplus portion" of the cut slab corresponds to "surplus material amount". Moreover, you may apply the method demonstrated in this embodiment to a hot rolling plan (chance formation problem). It is necessary to determine a plurality of slabs that are continuously hot rolled. The unit of this plurality of slabs is called a chance. In this case, "hot rolled plate (coil)" corresponds to "product", "chance" corresponds to "lot", and "rolling" corresponds to "manufacture".
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 a lot unit, but a plan for processing a plurality of products in a lot unit. It may be.

(Calculation example)
Next, a calculation example of the cast plan will be described.
In order to detect the usefulness of the method of this embodiment, a numerical experiment was performed to create cast plans for a plurality of cases in which the number of slabs was changed. FIG. 6 is a diagram showing the result. In FIG. 6, the calculation time (minutes) until the cast plan is created for each slab number is shown for each of the comparative example, invention example 1 and invention example 2. In FIG. 6, "-" indicates that the calculation time is 1 hour or more.

In the comparative example, the slabs included in the slab information are aggregated into slab groups as described in the section of <Slab Group Creating Unit 102, Step S202>, and all the feasible lots j for the slab groups are listed and listed. This is a method for deriving an optimal solution for a feasible lot by a set division problem in which all feasible lots j are subsets.
Inventive Example 1 is the method of the present embodiment. In the invention example 2, in the method described in <Modification 1>, in addition to the method of the present embodiment, in step S209, the column addition unit 109 satisfies all the column addition requirements of the column generator problem SP. _Is a method of adding the feasible solution of the above to the matrix A _i,j .
Except for the above, there is no difference between Invention Example 1, Invention Example 2, and Comparative Example.

In each of Inventive Example 1, Inventive Example 2, and Comparative Example, a feasible cast plan that satisfies all the constraints described in this embodiment (when the solution can be found) is created. It was
However, in the comparative example, the feasible lot j to be listed increases exponentially with the number of slab groups i. Therefore, when the number of slabs is “150”, the calculation time is 9.38 minutes. Further, if the number of slabs is “200” or more, the calculation does not end even if it takes 1 hour or more. On the other hand, in Invention Example 1, the calculation time is 2.76 minutes even when the number of slabs is “350”, which is an allowable calculation time even for a problem of practical scale. In addition, the invention example 2 can be expected to be applied to a larger-scale problem because the calculation is completed faster than the invention example 1.

[Second Embodiment]
Next, a second embodiment will be described.
In the first embodiment, the cost c _j for feasibility lots j, a cost c for a new feasible lot a added by add column 109, respectively (4), when expressed by (23) Was explained as an example. That is, the cost (objective function) for the feasible lot is represented by the sum of the costs of each evaluation index (design variable), and the cost of each evaluation index is the value of the evaluation index and the cost coefficient (weight) for the evaluation index. Coefficient) and is represented by the sum of products. In the example shown in the equation (4), C ^Y and C ^G are cost coefficients with respect to the amount of spare material W _j ^Y (which is the value of the evaluation index) and the number N _j ^G of steel types, respectively. Further, in the example shown in the equation (23), C ^Y and C ^G are the sum Σy _k of the surplus materials of all steel types and the total number of steel types Σg _k (g _k is a slab of steel type k in a certain cast, respectively). Is a 0-1 variable that becomes “1” when manufacturing the product and “0” otherwise. Further, C _CAST becomes a cost coefficient for the number of feasible lots j.

As described in the first embodiment, the cost coefficients C ^Y and C ^G are preset depending on how much importance is attached to the respective evaluation indexes, and represent the balance of evaluations among the evaluation indexes. The cost factors C ^Y and C ^G allow the evaluation indices to be balanced. For example, in the minimization problem, if the cost coefficient for an evaluation index having a high degree of importance is increased, the value of the evaluation index becomes a value (small value) that gives a higher evaluation than other evaluation indexes.

In the first embodiment, the cost coefficients C ^Y and C ^G are assumed to be predetermined constant values. However, even with the same evaluation index, the cast plan may not be close to the cast formation performed by the planner unless the importance (weight) is made different according to the manufacturing conditions.
For example, regarding the amount of surplus material, if it is a steel type that receives orders frequently, even if a slab that is not tied to the order as a surplus material is manufactured, it can be expected to be tied to the newly ordered order of the steel type early. .. Therefore, the planner knits the cast while considering whether or not there is a high possibility that the surplus material is tied to the order for each steel type. Therefore, for example, when the amount of surplus material is used as an evaluation index, it is desirable to determine the cost coefficient for the amount of surplus material for each steel type.

Regarding continuous casting of different steel types, the planner does not evaluate only the number of different steel types one by one, but rather a combination of two different steel types that are continuously cast, which has no problem in operation and quality. Select with priority. Therefore, for example, when the number of different steel types is used as an evaluation index, it is desirable to determine the cost coefficient for the number of different steel types for each combination of two different steel types that are continuously cast. The consecutive number of different steel types is the number of different steel type seams described in the section "Number of steel types" of the first embodiment.

Therefore, in order to classify (one) evaluation index according to the steel type and realize evaluation by each of the classified evaluation indexes, a cost coefficient must be set for each classified evaluation index. For example, the cost coefficient for the amount of surplus material must be set for each steel type, and the cost coefficient for the number of different steel types must be determined according to the combination of two different steel types that are continuously cast. There are generally 100 or more types of steel in steelmaking plants. Therefore, it takes a lot of time and effort for the planner to set the cost coefficient for each steel type. Even if the cost coefficient is set for each steel type at a certain point in time, a large amount of time is required to maintain a large number of cost coefficients so as to correspond to the operating conditions at each time.

Therefore, in the present embodiment, it is possible to determine the cost coefficient for making the evaluation based on the evaluation index different according to the steel type by the cast knitting device without imposing a large amount of labor on the planner. .. As described above, the present embodiment differs from the first embodiment in the method of deriving the cost for the feasible lot. Therefore, in the description of the present embodiment, the same parts as those in the first embodiment will be denoted by the same reference numerals as those in FIGS. 1 to 6, and detailed description thereof will be omitted.

Here, in the present embodiment, a case will be described as an example in which the number of different steel grades among a plurality of evaluation indexes is classified according to the steel grade and the cost coefficient for each of the classified number of different steel grades is derived. The cost coefficient for the evaluation index other than the number of different steel types is set to a predetermined constant value as in the first embodiment.

Therefore, in the present embodiment, the following formula (26) is used instead of the formula (4).

In the formula (26), C _CAST is the manufacturing cost, C ^Y is the cost coefficient for the amount of surplus material, and C ^G is the cost coefficient for the number of steel grades. Is the same. In Expression (26), W _j ^Y is the amount of surplus material and is the same as that shown in Expression (4). The cost coefficients C ^Y and C ^G represent the evaluation balance with other evaluation indexes, and do not represent the evaluation balance between steel types in the same evaluation index. Therefore, the cost coefficients C ^Y and C ^G can be determined by the relative importance of the amount of surplus material, the number of different steel types in series, and the number of feasible lots j. Can be set.

C ^G _k,k′ is a cost coefficient in the case of continuously casting molten steel of steel types k and k′ (continuous casting of different steel types), and is represented by the following equation (27). _nk,k' is the number of different steel types in the feasible lot j.

The cost coefficient C ^G _k,k′ in the case of continuously casting the molten steel of the steel types k and k′ (when continuously casting different steel types) will be described with reference to FIG. 7. FIG. 7 is a diagram illustrating an example of the cost coefficient C ^G _{k,k′ in} the case of continuously casting the molten steel of the steel types k and k′. In the following description, the steel type k, the cost factor C ^G _k in the case of continuously cast molten steel _k', the _k', cost factor optionally C ^G _k, abbreviated as _k'.
When molten steels of two different steel types are continuously cast, the molten steels of the two steel types are mixed in the tundish. When the mixed portion becomes a slab, the slab may be a valuable product or a non-valued product that cannot be a product. In the following description, this valuable product will be referred to as a product steel product as necessary, and the non-value product will be referred to as a non-product steel product as needed.

In general, planners believe that it is better to manufacture product steel than non-product steel. That is, the planner considers that, when performing continuous casting of different steel types, it is preferable that a combination of two mutually different steel types becomes a product steel material. In the original problem and the sequence generator problem described in the first embodiment, the decision variables z _j and a _i when the value of the objective function is minimized are derived as shown in the formulas (2) and (24). To do. Therefore, in order to make it easier to select the feasible lot j that includes more sets of steel types that become product steels than sets of steel types that become non-product steels, the steel types k and k′ that become product steels are selected. cost factor in the case of continuously cast molten steel C ^G _k, weighting factor for _k'is, steels k as a non-product steel material, the cost factor C ^G _k in the case of continuously cast molten steel _{k', k'} It should be below. The steel types k and k'which are the product steel materials and the steel types k and k'which are the non-product steel materials are known and are preset in the cast knitting apparatus.

Therefore, the cost factor C ^G _k, as a cost factor for determining the minimum value of the _k', the cost factor for the product steel as C _G1, the cost factor C ^G _k, as a cost factor for determining the maximum value of the _k', for non-product steel material Let the cost coefficient be C _G2 (C _G1 <C _G2 ).
In FIG. 7, a graph 701 represents the cost coefficient C _G2 for the non-product steel material. Further, NP _k,k′ is the actual number of times that the molten steel of the steel type k′ has been continuously cast after the molten steel of the steel type k in the past fixed period (for example, one year). As shown in FIG. 7, the cost coefficient C _G2 for the non-product steel material has a constant value. In the following description, in a past predetermined period, result count NP k was continuously cast molten steel grades k'followed after molten steel grades _k, the _k', if necessary, result count NP _{k, k'and} Abbreviated.

On the other hand, from the viewpoints of operation and quality, there are a set of two steel types that are different from each other and a set that becomes a product steel material. Generally, the planner considers that it is preferable to increase the number of sets of two steel types that are different from each other and that have a high occurrence frequency for the sets that are product steel materials. Therefore, as shown in the graphs 702a and 702b of FIG. 7, the maximum value is taken when the actual performance number NP _k,k′ is “0”, and the smaller value is taken as the actual performance number NP _k,k′ is increased. Further, the cost coefficient C ^G _k,k′ is expressed so that the minimum value becomes the cost coefficient C _G1 for the product steel material.

As described above, it is necessary to make it easier to select a feasible lot j that includes more sets of steel types that become product steels than sets of steel types that become non-product steels. Therefore, when the actual number of times NP _k,k′ is “0”, the cost coefficient C ^G _k,k′ is set to be lower than the cost coefficient C _G2 for the non-product steel material. Therefore, in the equation (27), the constant L is set to a value (L>1) exceeding “1”. By doing so, the cost coefficient C ^G _k,k′ can be made lower than the cost coefficient C _G2 for the non-product steel material regardless of the combination of the steel types k and k′. The graph 702a shows the cost coefficient C ^G _k,k′ when the constant L is relatively small, and the graph 702b shows the cost coefficient C ^G _k,k′ when the constant L is relatively large. Further, when the constant L is “1” (L=1), when the actual number of times NP _k,k′ is “0”, the cost coefficient C ^G _k,k′ is the cost coefficient C _G2 for the non-product steel material. (C ^G _k,k′ =C _G2 ).

Cost factor C ^G _k As described _{above, k'is,} result count NP _k, by taking the smaller the value _k'increases, among the steels of sets of the product steel material, result count NP _k, often _k' It becomes easy to select a feasible lot j that includes many sets of steel types. Therefore, it is possible to approach the cast formation performed by the planner.

The cost coefficients C _G1 and C _G2 determine the minimum value and the maximum value of the cost coefficient C ^G _k,k′ , respectively, and are set in advance. The constant L is for adjusting the value of the cost coefficient C ^G _k,k′ when the actual number of times NP _k,k′ is “0”, and is set in advance.

The cast knitting apparatus 100 produces manufacturing record data that can specify the record count NP _k,k′ of continuous casting of molten steel of steel type k′ after molten steel of steel type k in a certain past period (for example, one year). , All steel types k manufactured by the continuous casting machine are acquired and stored in advance. In addition, the cast knitting apparatus 100 acquires and stores in advance a combination of steel types that are product steel materials and a combination of steel types that are non-product steel materials. The cast knitting apparatus 100, for example, operates the cast knitting apparatus 100 by an operator, receives the slab information transmitted from an external device, or reads the slab information stored in the portable storage medium, so that these information ( It is possible to acquire manufacturing record data) that can specify the record count NP _k,k′ . For example, the cast knitting apparatus 100 can obtain the actual number of times NP _k,k ′ for the combination of the steel types k and k _′ from the manufacturing actual result data.

In the calculation of the equation (26), first, the set division problem construction unit 104 specifies the feasible lot j from the current value of the matrix A _i,j . Then, the set division problem construction unit 104 derives the spare material amount W _j ^Y for the feasible lot j by the formula (3) and gives it to the formula (26). Since the cost coefficient C ^Y for the amount of surplus material, the cost coefficient C ^G for the number of steel types, and the manufacturing cost C _CAST are determined in advance, the set division problem construction unit 104 gives them to the equation (26).

Further, since the cost coefficients C _G1 and C _G2 and the constant L are predetermined, the set division problem construction unit 104 gives them to the equation (27). Further, the set division problem construction unit 104 derives the actual number of times NP _k,k′ from the actual production data and gives it to the equation (27). As a result, the cost coefficient C ^G _k,k′ in the case of continuously casting the molten steel of the steel types k and k′ to be the product steel material is derived. On the other hand, the set division problem construction unit 104 regards the cost coefficient C ^G _k,k′ in the case of continuously casting the molten steel of the steel types k and k′, which are non-product steel materials, regardless of the actual number of times NP _k,k′ . First, the weighting factor C _G2 for the non-product steel is used. Further, the set division problem construction unit 104 derives the number of sets of steel types k and k′ as consecutive numbers n _k,k of different steel types based on the steel types of the slab group included in the feasible lot j.

The set partitioning problem construction unit 104 gives the cost coefficient C ^G _k,k′ and the number of different steel types n _k,k derived as described above to the equation (26). As described above, the cost c _j of each feasible lot _j is derived.
In the first embodiment, the initial value of the matrix A _i,j is a matrix having “1” only in the element _j where i=j, and is “0” in the other elements. Therefore, the number of different steel types n _k,k becomes “0”.

As described above, in the present embodiment, the cost c _j of each feasible lot _j is derived by using the equation (26) instead of the equation (4).
Further, in the present embodiment, the following equations (28) to (30) are used instead of the equation (23).

In the formula (28), C _CAST is a manufacturing cost, C ^Y is a cost coefficient with respect to the amount of surplus material, and C ^G is a cost coefficient with respect to the number of steel types, which are respectively shown in the formula (23). It is the same as the one. Note that, as described above, the cost coefficients C ^Y and C ^G represent the balance of evaluation with other evaluation indexes, and do not represent the balance of evaluation between steel types in the same evaluation index. Further, in the expression (28), y _k is the weight of the surplus material for each steel type, and is the same as that shown in the expression (23).

In the equation (28), g is an evaluation value for the number of consecutive different steel types and is represented by the equation (29). In the equation (29), cr _i,i′ is an evaluation value (cost) when continuously casting the slab groups i and i′ (when continuously casting different steel types) (note that the slab group i, i'is a different slab group).

In the equation (30), C ^G _k,k′ is the cost coefficient C ^G _k,k′ in the case of continuously casting molten steel of the steel types k and k _′, which is the same as that shown in the equation (26). And is determined as described with reference to FIG. 7 (given to equation (30) in the same manner as when given to equation (26)). r _i, i′ is a 0-1 variable that becomes “1” when continuously casting the slab groups i, i′, and “0” otherwise. M is a sufficiently large positive value and is predetermined. x _i,k is a 0-1 variable that becomes “1” when the slab group i is cast as the steel type k, and “0” otherwise, x _i′,k′ is the slab group i′. Is a 0-1 variable that is "1" when steel is cast as steel type k'and otherwise "0".

Equation (30) is a slab group when casting slab group i as steel type k, casting slab group i′ as steel type k′, and casting slab groups i and i′ continuously. The evaluation value cr _i,i ′ when continuously casting _{i and i ′} must be equal to or higher than the cost coefficient C ^G _k,k′ when continuously casting molten steel of steel types k and k′. Represents.

As described with reference to FIG. 7, the cost coefficient C ^G _k,k′ in the case of continuously casting molten steels of steel types k and k _′ is a feasible lot that includes many sets of steel types that are product steel materials. It is set so that j is easy to be selected, and steel types k and k _′ having a large number of actual results NP _k,k′ are easy to be selected. Since it is preferable that the cost c for the new feasible lot a is smaller, the evaluation value cr _i,i ′ in the case of continuously casting the slab groups i, i′ is provided by providing the constraint expression of the expression (30). The evaluation value g for the number of consecutive different steel types defined by the equation (29) is restricted so that the cost coefficient C ^G _k,k′ when continuously casting molten steels of steel types k and k _′ is close to a value. .. Therefore, it becomes easy to select a feasible lot j that includes a large number of sets of steel types having a large number of actual performance times NP _k,k′ among the sets of steel types that become product steel materials.

The column generation unit 107 is a new realization that is a subset that minimizes the value of the objective function of Expression (24) within a range that satisfies the constraint expressions of Expressions (8) to (22) and (30). The lot a is derived as the optimum solution of the new feasible lot a. At this time, the cost c of the new feasible lot a of the equation (24) is determined as shown in the equations (28) and (29). The cost coefficient C ^G _k,k′ in the case of continuously casting the molten steel of the steel types k and k′ can be obtained by the same method as the calculation of the equation (26). Further, M is predetermined. (Evaluation value cr _i,i' (evaluation value g for the number of different steel types), 0-1 variables r _i,i' , x _i,k when the slab groups i, i'are continuously cast are optimal It is a dependent variable determined in the process of deriving a solution.

When solving the equation (26), the feasible lot j is determined. On the other hand, when solving the equation (28), a new feasible lot a is derived, and therefore the feasible lot is not determined. If the feasible lot is not determined, the cost coefficient C ^G _k,k′ for continuous casting of molten steel of steel types k and k′ cannot be determined. Therefore, here, the cost coefficient C ^G _k,k′ is to be multiplied by the value of the evaluation index (the number of different steel types n _k,k′ in the feasible lot j) as in the equation (26). I can't. Therefore, slab group i to be different steel grades, evaluation value cr i in the case of continuously cast the _i', the _i', cost factor C ^G _k, by providing the constraint equation closer to _k', metrics The value of can be set to a value that makes it easy to select a feasible lot close to the feasible lot selected by the planner when performing cast formation.

The cost coefficients C ^Y , C ^G , and C ^G _k,k′ are preset depending on how much importance is attached to each evaluation index, and represent the balance of evaluation among the evaluation indices. .. One or more of the cost factors C ^Y , C ^G , and C ^G _k,k′ may be “1”.

(Calculation example)
Next, a calculation example will be described.
In the present calculation example, the cast plan is created assuming that the steel type included in the cast candidate j is one of the steel types A, B, C, D, and E.
FIG. 8 is a diagram showing, in a tabular form _, the actual number of times NP _k,k′ used in this calculation example. In FIG. 8, the steel type shown in the row element is the front steel type k, and the steel type shown in the column element is the rear steel type k′. The rear steel type k′ is a steel type that is a product steel material with respect to the front steel type k and is a steel type k′ different from the front steel type k (when the molten steel of the rear steel type k is cast after the molten steel of the front steel type k is cast). , The product steel material is the slab where the molten steel is mixed). Further, when the front steel type k and the rear steel type k′ are the same, the cost coefficient C ^G _k,k′ in the case of continuously casting the molten steel of the steel types k and k _′ shall be “0”. In such a case, the actual number of times NP _k,k′ is unnecessary, so that the corresponding element is indicated by “−” in FIG.

In this calculation example, the weight coefficient C _G1 for the product steel material is set to “10”, and the weight coefficient C _G2 for the non-product steel material is set to “100”. Further, the constant L is set to "1.0". Then, according to the equation (27), the cost coefficient C ^G _k,k′ when continuously casting the molten steel of the steel types k and k _′ is as shown in FIG. 9( a ). As described above, when the front steel type k and the rear steel type k′ are the same, the cost coefficient C ^G _k,k′ in the case of continuously casting the molten steel of the steel types k and k _′ is “0”. Become.

On the other hand, in FIG. 9B, the molten steel of the steel types k and k′, which does not have the formula (27) and has two values depending on whether or not the steel type is the product steel, is continuously obtained. The cost coefficient C ^G _k,k′ for casting is shown. That is, in FIG. 9B, for steel types k and k′ that are product steel materials, the cost coefficient C ^G _k,k′ when continuously casting molten steel of steel types k and k _′ is the same as the product steel materials. a cost factor C _G1 (= 10) with respect to, the steel grade k as a non-product steel material, for k', steels k, the cost factor C ^G _k in the case of continuously cast molten steel _k', the _k', uniform Shows the cost coefficient C ^G _k,k′ when continuously casting the molten steel of the steel types k and k′ when the cost coefficient C _G2 (=100) for the non-product steel material is set.

FIG. 10 is a diagram showing the number of different steel types in the cast candidate j derived by the cast knitting apparatus 100 in a table format for each combination of steel types. “1” shown in FIG. 10 indicates that the number of consecutive different steel types is “1” (for example, in FIG. 10A, the number of continuous castings of the steel type E after the steel type C is “1”). 1" and that the number of continuous castings of the steel type A after the steel type E is "1"). 10A shows an example of the invention, and FIG. 10B shows a comparative example. In the invention example, as shown in FIG. 9A, the cost coefficient C ^G _k,k′ in the case of continuously casting the molten steel of the steel types k and k _′ is derived by the equation (27), and the different steel types are successively connected. The evaluation value g for the number was derived, and the number of different steel types was derived from the finally obtained optimal solution of the feasible lot group. On the other hand, in the comparative example, as shown in FIG. 9B, the cost coefficient C _G2 for the non-product steel material is set to “100”, and the cost coefficient C ^G _k in the case of continuously casting the molten steel of the steel types k and k′ _,k' are all cost factors C _G1 for product steel, and the evaluation value g for the number of different steel types is derived, and the number of different steel types is derived from the finally obtained optimal solution of the feasible lot group. did.

As shown in FIG. 10A, as in the present embodiment, molten steels of steel types k and k′ are continuously provided in a range of cost coefficient C _G1 or more for product steel materials and cost coefficient C _G2 or less for non-product steel materials. By making the cost coefficient C ^G _k,k′ in the case of casting smaller as the actual number NP _k,k′ is larger and evaluating the different steel grades in detail, the total number of different steel grades is reduced, and A combination of steel types k and k′ is selected so that the cost coefficient C ^G _k,k′ in the case of continuously casting molten steel of k and k′ is selected. That is, since the combination of the steel types k and k _′ having the large number of track records NP _k,k′ is selected, the cast plan derived by the cast knitting apparatus 100 can be brought close to the cast plan intended by the planner. On the other hand, when the cost coefficient C ^G _k,k′ in the case of continuously casting molten steels of the steel types k and k _′ is set to a constant value, the total number of different steel types is consecutive as shown in FIG. 10(b). It will increase. Therefore, the cast plan intended by the planner cannot be obtained. In the example of the invention shown in FIG. 10(a), the evaluation value g for the number of consecutive different steel types is equal to the integrated value of the cost coefficient C ^G _k,k′ when continuously casting molten steel of the steel types k and k′. From this (that is, the left side is determined so as to be equal to the right side of Expression (30)), “110.5 (=100+10.5)” is obtained. On the other hand, the evaluation value g for the consecutive number of different steel types in the comparative example shown in FIG. 10B is “210 (=100+100+10)”. Therefore, it can be seen that the evaluation value g with respect to the number of different steel types is significantly improved in the invention example compared to the comparative example.

(Summary)
As described above, in the present embodiment, the cost coefficient C ^G _k,k′ in the case of continuously casting the molten steel of the steel types k and k _′ to be the product steel, the cost coefficient C _G1 or more for the product steel, the non-product steel In the range below the cost coefficient C _{G2 with} respect to, the larger the actual number NP _{k,k′, the} smaller the value. The cost coefficient C ^G _k,k′ when continuously casting molten steels of steel types k and k _{′ that} are non-product steel materials is a constant value with a weighting coefficient C _G2 for non-product steel materials. Therefore, as the combination of the steel types k and k′ included in the optimum feasible lot j, the combination of the steel types k and k′ to be the product steel materials is more likely to be included than the combination of the steel types k and k′ to be the non-product steel materials. Become. Further, regarding the combination of the steel types k and k′ that are the product steel materials, the combination of the steel types k and k _′ with the large number of actual times NP _k,k′ is included in the combination of the steel types k and k′ included in the optimum cast candidate j. It becomes easy to be damaged. It is not realistic for the planner to manually set the cost coefficient C _Gk,k′ for this purpose. As described above, in the present embodiment, in addition to the effects described in the first embodiment, it is a great effort to bring the cast plan derived by the cast knitting apparatus 100 closer to the cast plan intended by the planner. The effect is that it can be realized without calling.

(Modification)
<Modification 5>
In the present embodiment, the case where there are combinations of the steel types k and k′ that are product steels and the steel types k and k′ that are non-product steels has been described as an example. However, this need not always be the case. For example, the product steel materials may be further classified into high quality product steel materials and low quality product steel materials. In this case, the cost coefficient C ^G _k,k′ in the case of continuously casting the steel types k and k _′ is represented by the following equations (31) and (32), for example.

Here, C _G3 is a cost coefficient for low quality product steel, and is a value less than the cost coefficient C _G2 for non-product steel (C _G3 <C _G2 ). C _G4 is a cost coefficient for high quality product steel, and is a value less than the cost coefficient C _G3 for low quality product steel (C _G4 <C _G3 ). The cost coefficient C _G3 for low quality product steel and the cost coefficient C _G4 for high quality product steel are set in advance. The constants L1 and L2 are values (L1, L2>1) exceeding “1”, respectively, and are set in advance. The constants L1 and L2 are the cost coefficients C ^GL _k when continuously casting the steel types k and k′, which are low-quality product steel materials, when the actual number of times NP _k,k′ is 0 (zero). _,k′ , for adjusting the cost coefficient C ^GH _k,k′ in the case of continuously casting the steel types k, k′ which are high-quality product steel materials. As described above, for the steel types k and k′ that are low quality product steels, the formula (31) (the cost coefficient C ^GL when continuously casting the steel types k and k′ that are low quality product steels) is used. _k,k' ) is given to the equations (26) and (30), and for the steel types k and k'which are high quality product steels, the equation (32) (the steel type k which is a high quality product steel is k , K′ are continuously cast, the cost coefficient C ^GH _k,k′ ) is given to the equations (26) and (30). As for the cost coefficient C ^GL _k,k′ in the case of continuously casting the steel types k and k _′ which are non-product steel materials, the weight coefficient C _G2 for the non-product steel material is (26 ) And (30).

<Modification 6>
In the present embodiment, the case where the evaluation index that is classified according to the classification condition represented by using the steel type k is the number of steel types (the number of different steel types consecutively) has been described as an example. However, the evaluation index that is classified according to the classification condition represented by using the steel type k is not limited to the number of steel types (the number of different steel types one after another).
For example, the cost coefficient for each weight y _k of the steel type of the surplus material may be derived. In this case, the cost coefficient is derived for each steel type k. The cost coefficient for each steel type k is represented by, for example, a function in which the value decreases as the amount of surplus material increases within a preset maximum value and minimum value. The cast knitting apparatus 100 acquires the total of the surplus material amounts (actual results) for each steel type k in a certain past period (for example, one year), and calculates the cost coefficient corresponding to the total surplus material amount of the acquired steel type k. , Using the above-mentioned function, it is derived as a cost coefficient for the surplus material amount of the steel type k. The planner determines that the steel type k having a large amount of surplus material in the past may be included in the cast. Therefore, with the above configuration, the cast plan derived by the cast knitting apparatus 100 can be brought closer to the cast plan intended by the planner. In this case, for example, “C ^Y ×W _j ^Y ”in the second term on the right side of the equation (4) and ““C ^Y ×Σ _k ∈ _{Nky k} ” in the first term on the right side of the equation (23). "and it may be respectively" ^{_{C Y × Σ k∈Nk (C Y}} k × W j Y) "," ^{_{C Y × Σ k∈Nk (C Y}} k × y k) ". Here, C ^Y _k is a cost coefficient for the amount of surplus material of the steel type k derived as described above.
Further, two or more evaluation indexes may be classified (for example, the second term on the right side of the equation (26) and the first term on the right side of the equation (28) may be modified as described in this modification. ).

<Modification 7>
In the present embodiment, the cost coefficient C ^G _k,k′ in the case of continuously casting molten steel of the steel types k and k _′ is in the range of the cost coefficient C _G1 or more for the product steel material and the cost coefficient C _G2 or less for the non-product steel material. The case has been described as an example in which the larger the actual number of times NP _{k,k′, the} smaller the value. However, if the cost coefficient for the evaluation index classified according to the classification condition represented using a certain manufacturing condition is changed according to the manufacturing performance value derived from the manufacturing performance data classified according to the classification condition, _However , it does not necessarily have to change according to the actual number of times NP _k,k′ , and changes according to, for example, the surplus material amount (the actual result), the manufacturing cost (the actual result), and the delivery difference (the actual result). Good. Here, the delivery date difference is, for example, the difference between the average value of the desired hot rolling days of the slab and the earliest day.

In addition to this, for example, the cost coefficient for the evaluation index may be changed according to the value indicating the quality of the product, which is an example of the above-described manufacturing actual value. In this case, for example, for the manufactured slab, the number of defects is aggregated for each manufacturing condition (for example, steel type), and the cost coefficient for the evaluation index is within a range between a maximum value and a minimum value set in advance. The smaller the number, the smaller the number may be. The case where the value of the evaluation index is the number of consecutive different steel types will be described as an example. It is manufactured by continuously casting molten steel of the steel type k'(continuous casting of different steel types) after the molten steel of the steel type k. Assuming that the number of flaws in the slab is ND _k and _k′ , the weighting coefficient C _G for the number g of different steel types in succession is expressed by the following equation (33), for example.

(33) In the formula, C _ND is flaws number of slabs ND _j, a cost coefficient for _j', are set in advance. Flaws number ND _j slabs cost factor C _ND for _j'are flaws number ND _j slabs is determined depending on how much importance to assess _j'.
In the example shown in Expression (33), the smaller the combination of steel types k and k′ having a smaller number of slab defects, the smaller the value in the parentheses in Expression (33) becomes. Then, such a combination of steel types k and k′ is likely to be included in the optimum feasible lot.

<Modification 8>
In the present embodiment, the case where the minimization problem is solved by the expressions (2) and (24) has been described as an example, but the maximization problem may be used. In such a case, for example, the one obtained by multiplying the entire right sides of the expressions (2) and (4) by (-1) is used as the objective function. Further, the equation (5) poses a maximization problem. Further, the cost coefficient for the product steel material is set to C _G5 (instead of C _G1 ), and the cost coefficient C _G5 for the product steel material is set to a value (C _G5 >C _G2 ) exceeding the cost coefficient C _G2 for the non-product steel material. Then, the cost coefficient C ^G _k,k′ in the case of continuously casting molten steel of the steel types k and k′ exceeds the weighting coefficient C _G2 for the non-product steel material and is within a range of the weighting coefficient C _G5 or less for the product steel material, The larger the actual number of times NP _{k,k′, the} larger the value.

<Other modifications>
The embodiment of the present invention described above can be realized by a computer executing a program. Also, a computer-readable recording medium recording the program and a computer program product such as the program can be applied as an embodiment of the present invention. As the recording medium, for example, a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a non-volatile memory card, a ROM or the like can be used.
Further, all the embodiments of the present invention described above are merely examples of embodying the present invention, and the technical scope of the present invention should not be limitedly interpreted by these. It is a thing. That is, the present invention can be implemented in various forms without departing from the technical idea or the main features thereof.

(Relationship with claims)
Below, an example of the correspondence between the description of the claims and the description of the embodiments will be described. Note that the description of the claims is not limited to the description of the embodiment, as described in the modified examples and the like.
<Claim 1>
The lot establishment constraint is realized by using, for example, equations (8) to (22).
The acquisition unit is realized by using the slab information acquisition unit 101, for example. The product information is realized by using the slab information 300, for example.
The binary variable for determining whether or not to adopt the feasible lot as a solution is realized by using the decision variable z _j , for example. The evaluation index for lot grouping of the products with respect to the feasible lot is realized by using the cost c _j (equation (4)) for the feasible lot j, for example.
The column generation unit is realized by using the column generation unit 107, for example. The candidate lot is realized, for example, by using the optimum solution of the new feasible lot a.
The column adding unit is realized by using the column adding unit 109, for example.
The optimum solution deriving unit is realized by using the optimum solution deriving unit 110, for example.
<Claim 2>
The dual solution derivation means is realized by using the dual solution derivation unit 106, for example.
The determination unit is realized by using the determination unit 108, for example.
<Claim 3>
The constraint equation of the original problem is realized by using the equation (1), for example.
The objective function of the original problem is realized, for example, by using the equation (2).
The total number of the feasible lots adopted as the solution of the set division problem, which is obtained as the addition value of the decision variable, is, for example, about the manufacturing cost C _CAST of the first term on the right side of the equation (4) in the equation (2). It corresponds to a value obtained by dividing the integrated value by the manufacturing cost C _CAST .
<Claim 4>
The constraint equation of the dual problem is realized by using, for example, equation (6).
The cost of the realizable lot is realized by using the cost c _j for the realizable lot j, for example. The lot constituent product presence/absence variable corresponding to the feasible lot is realized by using the lot constituent product presence/absence variable a _i which is an element of the matrix A _j,i . The dual variable is realized, for example, by using the dual variable λ _i .
The dual cost for the feasible lot is realized, for example, by using the dual cost (=Σ _{i εNI} λ _i ×a _i ).
<Claim 5>
The weight constraint equation is realized, for example, by using the equation (13).
The dimension constraint equation is realized by using, for example, equation (21).
The objective function of the column generator problem is realized, for example, by using the equation (24).
<Claim 6>
The total number of product types included in the feasible lot is realized by using, for example, the number N _j ^G of steel types included in the feasible lot j of the formula (4).
<Claim 7>
The objective function of the original problem is realized, for example, by using the equation (2).
The objective function of the column generator problem is realized by using, for example, equation (24).
The cost of the feasible lot is realized by using, for example, formulas (26) and (28).
The value of the evaluation index is realized, for example, by using the evaluation value g for the number of different steel types.
The cost coefficient for the evaluation index is realized, for example, by using the cost coefficient C ^G _k,k′ in the case of continuously casting molten steel of the steel types k and k′.
The cost coefficient for each of the evaluation indexes classified according to the classification condition represented by using the manufacturing condition of the product is, for example, the cost coefficient C ^G _k, when casting molten steel of steel types k and k′ continuously _. It is realized by using _k' .
The production performance data classified according to the classification condition is realized by using the performance count NP _k,k′ .
<Claim 8>
Of the cost coefficients for each of the evaluation indexes that are classified according to the classification conditions that are expressed using the manufacturing conditions for the product, the cost coefficient that is classified to a predetermined classification destination is, for example, the steel type k or k that is the product steel material. It is realized by using the cost coefficient C ^G _k,k′ in the case of continuously casting the molten steel of ‘′.
The relational expression is realized, for example, by using the expression (27).
<Claim 9>
Of the cost coefficients for each of the evaluation indexes that are classified according to the classification conditions that are expressed using the manufacturing conditions of the product, the cost coefficient that is classified to a predetermined classification destination is, for example, a steel grade k that is a non-product steel material, It is realized by using the cost coefficient C ^G _k,k′ when continuously casting molten steel of _k′ .
The constant value is realized, for example, by using C _G2 as a weighting coefficient for non-product steel.
<Claim 10>
The possible range of the cost coefficient for each of the evaluation indexes classified according to the classification condition represented by using the manufacturing condition of the product is, for example, that the weight coefficient C _G1 for the product steel material is the minimum value and the weight for the non-product steel material is It is realized by using the range in which the coefficient C _G2 is the maximum value (the cost coefficients C _G1 and C _G2 are the cost coefficients C ^G _k,k when continuously casting molten steels of steel types k and k′, respectively). _It defines the minimum and maximum values of _´ ).
<Claim 11>
Derivation of the cost of the feasible lot using the product of the value of the evaluation index and the cost coefficient for the evaluation index corresponds to, for example, <Modification 6>.
<Claim 12>
The index relating to the difference between the lot amount and the product amount contained in the lot is realized by using, for example, a surplus material amount.
<Claim 13>
The cost of the feasible lot is determined so that the value of the evaluation index satisfies the constraint expression expressed by using the cost coefficient for the evaluation index. The evaluation value g for is derived by using the evaluation value cr _i,i ′ in the case of continuously casting the slab groups i, i′ as shown in Expression (29), and the slab groups i, i′ are continuously formed. _So that the evaluation value cr _i,i ' in the case of continuous casting is equal to or higher than the cost coefficient C ^G _k,k' in the case of continuously casting molten steel of steel types k _{and k'as} shown in equation (30). It is realized by being set.
The constraint equation is realized by using, for example, equation (30).
<Claim 14>
The index relating to the number of the different types of products contained in the lot is realized by using, for example, the number of different steel types.
<Claim 15>
The group creating means is realized by using the slab group creating unit 102, for example. The product group is realized by using the slab group i, for example.
<Claim 16>
Adding the plurality of candidate lots to the set of feasible lots corresponds to, for example, <Modification 1>.

100: Cast organization device, 101: Slab information acquisition unit, 102: Slab group creation unit, 103: Initial column set setting unit, 104: Set division problem construction unit, 105: Linear relaxation problem construction unit, 106: Dual solution derivation unit , 107: column generation unit, 108: determination unit, 109: column addition unit, 110: optimum solution derivation unit, 111: output unit

Claims (19)

A problem of grouping a plurality of products in units of lots so as to satisfy a predetermined lot formation constraint and creating a plan for production or processing is a set partitioning problem. A plan making device for making a plan by solving,
An acquisition unit that acquires product information including the manufacturing conditions of the products, which is information about the plurality of products,
For each of a plurality of feasible lots, which are lots of the above products that are combined so as to satisfy the lot formation constraint, the realization is performed using a binary variable that determines whether or not to adopt the feasible lot as a solution. Based on an evaluation index for lot grouping of the products with respect to possible lots, the set division problem for obtaining an optimal combination of the feasible lots that does not overlap and includes the plurality of products without omission is the original problem,
Column generating means for deriving an optimal solution of a column generator problem for generating a candidate lot that is a candidate for a feasible lot that constitutes the optimal solution of the original problem,
When the candidate lot derived by the column generation unit includes a candidate lot that satisfies the column addition requirement, the column addition unit that adds the candidate lot generated by the column generation unit to the set of feasible lots. When,
A combination of the feasible lots is derived as an optimum solution of the original problem based on a set of the feasible lots including the candidate lots derived by the column generating means and the candidate lots added by the column adding means. And an optimal solution deriving means for
A plan preparation device characterized by the above. A dual solution deriving means for deriving a dual solution which is an optimum solution of the dual problem when the linear relaxation problem of the original problem is the main problem;
The candidate lot derived by the column generation means, further comprises a determination means for determining whether or not to meet the column addition requirements,
When the determination unit determines that the candidate lot derived by the column generation unit satisfies the column addition requirement, the column addition unit realizes the candidate lot generated by the column generation unit. Add to the set of possible lots,
The optimum solution derivation means, when the determination means determines that the candidate lot derived by the column generation means does not satisfy the column addition requirement, the feasible lot obtained at that time is determined. Based on the set, as the optimal solution of the original problem, derive the combination of the feasible lot,
The determining means repeats the derivation of the dual solution by the dual solution deriving means, the optimal solution of the column generator problem by the column generating means, and the determination by the determining means to perform convergence calculation, Execute until it is determined that the additional requirements are not satisfied,
2. The plan according to claim 1, wherein the column generator problem is a problem of finding the candidate lot to be added to the set of feasible lots using the dual solution and the lot establishment constraint. Creation device. For each of the plurality of feasible lots, the decision variable is “1” when the feasible lot is adopted as a solution, and is “0” when the feasible lot is not adopted as a solution 0-1 Is a variable
The original problem is a constraint expression representing a constraint that, for each of the plurality of products, one feasible lot including the product is always selected from the set of the feasible lots. A constraint expression expressed using variables and an objective function for obtaining the sum of the costs of the feasible lots included in the set of the feasible lots, which is expressed by using the decision variables and the costs of the feasible lots. And an objective function that is set to 0, the objective variable is a 0-1 integer programming problem in which the value of the objective function is minimized in a range that satisfies the constraint equation.
The cost of the feasible lot is the total number of the feasible lots adopted as the solution of the set division problem, which is obtained as an addition value of the decision variable as an evaluation index for the lot grouping of the products with respect to the feasible lot. The planning apparatus according to claim 2, further comprising: The dual problem is a constraint expression representing a constraint that each cost of the feasible lots included in the set of feasible lots is equal to or more than the dual cost for the feasible lots, and the cost of the feasible lots. , A constraint expression represented by using a lot constituent product presence/absence variable corresponding to the feasible lot and a dual variable, and an objective function for obtaining the sum of the dual variables for the plurality of products, wherein the dual variable is An objective function represented by using, and a linear programming problem for determining, as the dual solution, the value of the dual variable that maximizes the value of the objective function in a range satisfying the constraint equation,
The dual variable is a variable defined for each product,
The dual cost for the feasible lot is a value of the dual variable for the product, and the product of the product and the lot constituent product presence/absence variable corresponding to the feasible lot is represented by a sum total for the plurality of products,
The lot constituent product presence/absence variable is a 0-1 variable defined for each product, and is “1” when the product is included in the feasible lot, and is “0” otherwise. The plan creation device according to claim 3, wherein the plan creation device is one variable. The column generator problem is a constraint expression expressing the lot establishment constraint, and for the feasible lot, a weight constraint expression that a total weight of products constituting the feasible lot is equal to or less than an upper limit value, and the realization constraint A value obtained by subtracting the dual cost for the feasible lot from the dimensional constraint expression that the dimensional difference between products adjacently produced or processed in the feasible lot is less than or equal to the upper limit value, and the cost of the feasible lot. An objective function to be obtained, wherein the objective function represented by using the dual variable and the lot constituent product presence/absence variable is used, and the value of the objective function is minimized in a range satisfying the constraint equation. The planning apparatus according to claim 4, which is a 0-1 integer programming problem that determines a constituent product presence/absence variable. The manufacturing conditions include varieties that are manufacturing conditions that have flexibility in selection,
The column generation means allocates the product type to each of the products,
6. The plan creation device according to claim 3, wherein the cost of the feasible lot further includes the total number of product types of the products included in the feasible lot. In the original problem and the column generator problem, the value of the objective function is derived using the cost of the feasible lot,
The cost of the feasible lot is derived using the value of the evaluation index and a cost coefficient for the evaluation index,
The cost coefficient for the evaluation index includes a cost coefficient for each of the evaluation indexes classified according to the classification condition represented by using the manufacturing condition of the product,
The cost coefficient for each of the evaluation indexes classified according to the classification condition represented by using the manufacturing condition of the product should change according to the manufacturing performance value derived from the manufacturing performance data classified according to the classification condition. The plan making device according to claim 1. Of the cost coefficients for each of the evaluation indexes that are classified according to the classification conditions represented by using the manufacturing conditions of the product, the cost coefficient for the evaluation indexes that are classified to a predetermined classification destination is classified according to the classification conditions. The cost coefficient with respect to the evaluation index according to the above, and the manufacturing performance value derived from the manufacturing performance data classified according to the classification condition are derived using a relational expression. Planning equipment. Of the cost coefficients for each of the evaluation indexes that are classified according to the classification conditions represented by using the manufacturing conditions of the product, the cost coefficient for the evaluation indexes that are classified to a predetermined classification destination is a constant value, At least one of the cost coefficients for the evaluation index classified into a classification destination different from the predetermined classification destination changes according to a manufacturing performance value derived from manufacturing performance data classified according to the classification condition. The plan creation device according to claim 7 or 8. 10. The possible range of the cost coefficient for each of the evaluation indices classified according to the classification condition represented by using the manufacturing condition of the product is set in advance. The planning device described in. The plan creation according to claim 7, wherein the cost of the feasible lot is derived using a product of the value of the evaluation index and a cost coefficient for the evaluation index. apparatus. The plan creating apparatus according to claim 11, wherein the evaluation index includes an index related to a difference between the amount of the lot and the amount of the product included in the lot. 13. The cost of the feasible lot is defined such that the value of the evaluation index satisfies a constraint expression represented by using a cost coefficient for the evaluation index. The plan preparation device described in the item. 14. The plan creating apparatus according to claim 13, wherein the evaluation index includes an index relating to the number of different types of products included in the lot. Further comprising group creating means for creating a plurality of product groups by grouping the plurality of products based on the manufacturing conditions of the products included in the product information acquired by the acquiring means,
15. The process according to claim 1, wherein at least the column generation unit, the column addition unit, and the optimum solution derivation unit are executed with the product as the product group. Planning device. The column generation means generates a plurality of the candidate lots,
15. The column adding unit adds the plurality of candidate lots to the set of feasible lots when there are a plurality of candidate lots that satisfy the column addition requirement. The plan preparation device according to item 1. The product is a slab cast by a continuous casting machine,
The lot is a cast that is a group of multiple charges that are cast continuously.
17. The plan creating apparatus according to claim 1, wherein the plan is a cast plan showing the cast to which the slab belongs. A problem of grouping a plurality of products in units of lots so as to satisfy a predetermined lot formation constraint and creating a plan for production or processing is a set partitioning problem. A method for creating a plan by solving,
An acquisition step of acquiring product information including the manufacturing conditions of the products, which is information of the plurality of products;
For each of a plurality of feasible lots, which are lots of the above products that are combined so as to satisfy the lot formation constraint, the realization is performed using a binary variable that determines whether or not to adopt the feasible lot as a solution. Based on an evaluation index for lot grouping of the products with respect to possible lots, the set division problem for obtaining an optimal combination of the feasible lots that does not overlap and includes the plurality of products without omission is the original problem,
A column generation step of deriving an optimal solution of a column generator problem for generating a candidate lot that is a candidate for a feasible lot that constitutes the optimal solution of the original problem;
When the candidate lot derived by the column generating step includes a candidate lot that satisfies the column addition requirement, a column adding step of adding the candidate lot generated by the column generating step to the set of feasible lots When,
A combination of the feasible lots is derived as an optimal solution of the original problem based on a set of the feasible lots including the candidate lots derived by the column generation step and the candidate lots added by the column addition step. And an optimal solution derivation step of
A plan making method characterized by the following. A program that causes a computer to function as each unit of the plan creating apparatus according to claim 1.

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