JP2017039556A - Equal division planning device of steel material, equal division planning method of steel material, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To create an equal division plan in a practical time regardless of characters of problems to be solved.SOLUTION: The number of representative slab groups is expressed as the total number of divisions in order to solve an optimization problem for minimizing a value of an objective function directed to reduce the total number of divisions and reduce the number of making divisions. Also, a slab group pair is selected from a representative slab group and a slab group represented by the representative slab group. The total number of the slab group pairs in which relationship of the reverse (reverse pair) is established is assumed as the number of reverse, and this is represented as the number of making divisions.SELECTED DRAWING: Figure 2

Description

  The present invention relates to a steel divide plan planning apparatus, a steel divide plan planning method, and a program, and is particularly suitable for use in drafting a steel divide plan in a yard.

  In the steel process, which is an example of a metal manufacturing process, for example, when transporting a steel material from a steel making process to the next rolling process, the steel material is once placed in a temporary storage place called a yard and then the next rolling process. It is carried out of the yard according to the processing time. An example of the yard layout is shown in FIG. As shown in FIG. 8, the yard is storage places 801 to 804 that are partitioned vertically and horizontally as a buffer area for supplying a steel material such as a slab discharged from the upstream process to the downstream process. The vertical division is often referred to as “building” and the horizontal division is referred to as “row”. The cranes (1A, 1B, 2A, 2B) are movable in the building and transfer steel materials between different rows in the same building. In addition, steel materials are transferred between buildings using a transfer table. When creating the transport command, by specifying the “building” and “row”, indicate where the steel material is transported (number (11) in parentheses in the locations 801 to 804 in FIG. 8, (See (12), (21), (22)).

  FIG. 8 shows an example of the basic work flow in the yard. First, the steel material carried out from the continuous casting machine 810 in the steelmaking process which is the previous process is carried into the yard at the receiving table X via the pillar 811 and is partitioned by the cranes 1A, 1B, 2A and 2B. To 804 and stacked and placed. And according to the manufacturing schedule of the rolling process which is the next process, the cranes 1A, 1B, 2A and 2B are again loaded on the dispensing table Z and conveyed to the rolling process. Generally, in the yard, steel materials are placed in a piled state as described above. This is to effectively utilize the limited yard area. On the other hand, when the steel materials are stacked, the steel materials need to be stacked from the top in the processing order of the next process so that the steel materials can be easily supplied to the next process. Furthermore, it is necessary to prevent the steel materials from being stacked in an inverted pyramid shape with an unstable stacking shape. In this way, dividing a steel material into a plurality of optimum mountains (= paid-out mountain: a mountain in the final mountain shape to be paid out to the next process) is called mountain division.

  Here, in order to reduce the fuel consumption rate of the heating furnace in the next rolling process, it is required to discharge (charge) the steel material having the highest possible temperature to the heating furnace. For this reason, recently, a heat insulation facility is installed in the yard, and the steel materials are piled up and stored in the heat insulation facility as described above. Even when using heat insulation equipment in this way, as in the case of stacking steel materials directly in the storage areas 801 to 804, in order to make effective use of the heat insulation equipment, the highest possible payout mountain in the heat insulation equipment. It is necessary to create. Moreover, it is necessary to prevent the steel materials from being stacked in an inverted pyramid shape while allowing the steel materials to be stacked from above in the processing order of the next step.

  As mentioned above, when creating a pile plan that divides a plurality of steel materials with different sizes and processing orders in the next process into a plurality of piles, all the piles that can be generated by the steel material to be planned From the candidates, we will solve the optimization problem that minimizes the number of hills and pile load (steel handling load by transport equipment such as cranes), but if there are a lot of steel materials to be planned, Such a problem becomes a large-scale problem.

  Therefore, Patent Document 1 lists all feasible mountains that are subsets that satisfy the pile constraints for the entire set of steel materials that are targets of planning, and minimizes the number of peaks and the pile load. There is disclosed a method for performing an optimal mountain division plan by obtaining an optimal combination of feasible mountains as a set division problem under an objective function.

  Further, Patent Document 2 discloses a method of formulating a multiple-to-one assignment problem in which a plurality of transport lots (a group of steel materials that can be transported by a transport device at a time) are allocated to an appropriate mountain (optimum mountain = payout mountain). It is disclosed.

JP 2007-137612 A JP 2011-105483 A

M. Campleo, R. Correa, and Y. Frota, "Cliques, holes and the vertex coloring polytope," Information Processing Letters, 89 (2004), pp. 159-164 M. Campelo, V. A. Campos, and R. C. Correa, "On the asymmetric representatives formulation for the vertex coloring problem," Discrete Applied Mathematics, 156 (2008), pp. 1097-1111

However, the methods described in Patent Documents 1 and 2 have the following problems.
First, in the solution method applying the set partitioning problem shown in Patent Document 1, the same pile is obtained because the required stacking order is different from the condition of the size (width / length) of any steel pair and the condition of the payout order. When there are relatively few steel pairs that cannot be achieved, the number of feasible mountains increases. If this number exceeds several millions, it takes time to enumerate the feasible mountains and calculate the optimum mountain, and the calculation is not completed within the requested time (for example, about 3 to 5 minutes). The plan cannot be created. In the case of the mountain division problem, if the number of feasible mountains exceeds tens of millions, it becomes difficult to obtain a feasible solution within a practical time (for example, about 10 minutes). In such a case, there may be a case where it can be solved within an allowable time by a method formulated as a many-to-one assignment problem shown in Patent Document 2. However, the method shown in Patent Document 2 also has the following problems.

  That is, in the method shown in Patent Document 2, calculation time is required when there are many steel pairs (reverse pairs) in which the arrival order at the yard and the stacking order at the yard are reversed, and the calculation is performed within a practical time. May not be completed.

  As described above, according to the conventional method, there are a case where a solution can be obtained within a practical time and a case where it is impossible depending on the nature of the problem. Therefore, there is a need for a technique that can solve a problem stably for any problem. In addition, when creating a grouping plan for a steel group having a high number of feasible peaks exceeding tens of millions and a high ratio of reverse rotation, it cannot be solved within a practical time. Therefore, even in the case of a large-scale problem where the number of feasible mountains exceeds 10 million or when there are many reverse pairs, a method for solving in a practical time is necessary.

  The present invention has been made in view of the above problems, and an object of the present invention is to make it possible to make a divide plan within a practical time regardless of the nature of the problem to be solved.

  The steel material division planning apparatus according to the present invention stacks a plurality of steel materials carried into a yard where steel materials are arranged as a place between processes in the steel process, in such a order that the steel materials with a fast delivery order to the next process are on top. A steel material division planning apparatus for creating a division plan for creating a plurality of payout piles to be paid out to the post-process of the yard, which is a variable to be determined when determining the division plan A decision variable setting means for setting a decision variable, a mountain sorting constraint formula setting means for setting a mountain sorting constraint formula that is a constraint when assigning each of the plurality of steel materials to one of the plurality of payout piles, A stacking shape constraint formula setting means for setting a stacking shape constraint formula, which is a constraint on the stacking shape of the payout mountain, reducing the total number of the payout mountain, and any two of the steel materials stacked on the same payout mountain One The purpose of setting an objective function is to reduce the number of reversal pairs in a reversal relationship in which the steel material with the earlier arrival order to the yard is stacked above the steel material with the later arrival order Satisfying the function setting means, the mountain sorting constraint equation, and the product form constraint equation, and a mountain sorting determination unit for determining the mountain division so as to minimize the objective function, the determination variable includes: When one of the steel materials is stacked on a payout mountain represented by a representative steel material that is one steel material representing the payout mountain, selected for each of the payout piles, the representative steel material is Including the representative relation variable that the representative steel material does not represent the one steel material, when the one steel material is not stacked on the payout mountain represented by the representative steel material, The mountain sorting constraint formula is the representative steel However, in order to violate the first constraint equation that stipulates that the representative steel material itself and the steel material to be loaded on the payout mountain represented by the representative steel material, and the stacking shape constraint equation, Any two of the steel materials that cannot be used are in the same payout pile in order to violate the second constraint equation that the one steel material does not represent the other steel material and the stacking shape constraint equation. Any two steel materials that cannot be stacked are represented by a third constraint formula that specifies that the two steel materials are not represented by the steel materials different from the two steel materials, and all the steel materials are represented by any of the representative steel materials. It is specified that the total number of steel materials represented by each of the representative steel materials is equal to or less than the upper limit value, which is a value indicating the total number of the steel materials stacked on each of the payout hills. 5th constraint equation to be performed and one is the other For any two of the steel materials representing the above, a sixth constraint formula that defines that the reversal relationship occurs when a steel material that arrives early in the yard is stacked on top, and in the objective function, The total number of representative steel materials is defined as the total number of payout peaks, and the number of steel material pairs in the reverse relationship defined by the sixth constraint equation is defined as the number of reverse pairs.

  The method of planning the steel material division according to the present invention is a method of stacking a plurality of steel materials carried into a yard where steel materials are arranged as a place between processes in the steel process, in such a order that the steel materials with a fast delivery order to the next process are on top. A steel material division planning method for creating a division plan for creating a plurality of payout piles to be paid out to the subsequent process of the yard, which is a variable to be determined when determining the division plan A decision variable setting step for setting a decision variable, a mountain sorting constraint equation setting step for setting a mountain sorting constraint equation that is a constraint when assigning each of the plurality of steel materials to one of the plurality of payout piles, A loading form constraint expression setting step for setting a loading form constraint expression that is a restriction on the loading form of the payout mountain, reducing the total number of payout mountains, and any two of the same payout mountain For the steel materials, the objective function is set to reduce the number of reversal pairs in the reversal relationship in which the steel material with the earlier arrival order to the yard is stacked above the steel material with the slower arrival order. Objective function setting step, satisfying the mountain sorting constraint equation and the product form constraint equation, and a mountain sorting determination step for determining the mountain division so as to minimize the objective function, When one of the steel materials is stacked on a payout mountain represented by a representative steel material that is one steel material representing the payout mountain, selected for each of the payout piles, the representative Including a representative relation variable in which the steel material represents the one steel material and the one steel material does not represent the one steel material when the one steel material is not stacked on the payout mountain represented by the representative steel material. , The mountain sorting Because the representative steel material violates the first constraint equation that stipulates that the representative steel material represents the steel material to be loaded on the payout hill represented by the representative steel material, and the stacking shape constraint equation. Any two of the steel materials that cannot be stacked on the same payout pile violate the second constraint formula that defines that one steel product does not represent the other steel product, and the stacking constraint formula Therefore, any of the two steel materials that cannot be stacked on the same payout hill is not represented by the steel material different from the two steel materials, and the third constraint equation and all the steel materials are either The total number of steel materials represented by each of the representative steel materials, which is a value indicating the total number of the steel materials stacked on each of the payout hills, is defined as the upper limit of the fourth constraint formula that stipulates that the representative steel materials are represented Fifth constraint specifying that the value is less than or equal to the value And a sixth constraint formula that defines that the reversal relationship occurs when steel materials that arrive early in the yard are stacked on top of any two of the steel materials, one of which represents the other. Including, in the objective function, the total number of the representative steel materials as the total number of payout hills, and the number of pairs of steel materials in the reverse relationship defined by the sixth constraint equation as the number of the reverse pairs. It is characterized by.

  The program according to the present invention causes a computer to function as each unit of the steel material divide plan planning apparatus.

  According to the present invention, it is possible to make a grouping plan within a practical time regardless of the nature of the problem to be solved.

It is a figure which shows an example of a simple undirected graph. It is a figure which shows an example of a functional structure of the divide plan planning apparatus of steel materials. It is a flowchart explaining an example of operation | movement of the division plan planning apparatus of steel materials. It is a figure which illustrates notionally an example of the method of ordering (numbering) with respect to a slab group. It is a flowchart explaining an example of the method of ordering (numbering) with respect to a slab group. It is a figure which shows the 1st example of the preparation result of a division plan in a table format. It is a figure which shows the 2nd example of the preparation result of a division plan in a table format. It is a figure which shows an example of the layout of a yard.

<Overview of vertex coloring>
As will be described later, in this embodiment, the vertex coloring problem is applied to the divide problem. The vertex coloring problem itself is a known technique, but in order to clarify the difference from the present embodiment when the vertex coloring problem is applied to the divide problem, before explaining the embodiment of the present invention, the general vertex The coloring problem will be described.

FIG. 1 is a diagram illustrating an example of a simple undirected graph.
The vertex coloring problem is one of the prominent problems in graph theory, and is defined on a simple invalid graph G = (V, E) (V: vertex set of graph, E: edge (branch) set of graph) . As shown in FIG. 1, when each vertex of the simple undirected graph G is painted with a certain color and any two adjacent vertices (connected by edges) can be painted with different colors, this coloring is simply undirected. This is called the coloring of the graph G. When the color used for coloring is c color (c is an integer of 2 or more), the simple undirected graph G is said to be c-colorable. The minimum value of c that enables simple undirected graph G to be c-colored is called the number of colors of simple undirected graph G, and is represented by χ (G). The vertex coloring problem is a problem of obtaining the number of colors χ (G) in the simple undirected graph G.

  As a solution to the vertex coloring problem, there are a symmetric representative point method and an asymmetric representative point method described in Non-Patent Documents 1 and 2. By using the symmetric representative point method and the asymmetric representative point method, it can be expected that the problem can be solved at a higher speed than the general solution of the vertex coloring problem.

[Symmetric representative point method]
In the symmetric representative point method, with respect to the coloring of the simple undirected graph G, one vertex from each color is selected as the representative point of that color. The vertex that is the representative point represents another vertex of the same color as the vertex itself. The representative point does not represent a vertex of a different color. For any ordered vertex pair (u, v) εV ² , introduce a 0-1 variable x _uv . The variable x _uv is defined as a 0-1 variable that is “1” when the vertex u represents the vertex v, and “0 (zero)” otherwise.

When x _uv = 1, the ordered vertex pair [u, v] is in a relationship in which one represents the other. If the vertex v is a representative point, x _vv = 1. At this time, the number of colors colored with respect to each vertex of the simple undirected graph G is equal to the number of representative points, and is represented by _ΣvεV × _vv . Since the ordered pair of vertices {u, v} εE that are adjacent in the simple undirected graph G (that is, connected to each other by edges (branches)) cannot be colored to the same color, these two vertices u, v Are not related to each other. Therefore, x _uv = x _vu = 0. Further, the ordered vertex pair {u, v} εE adjacent in the simple undirected graph G cannot have the same vertex t as a representative point. Therefore, x _tu + x _tv ≦ x _tt (∀tεV, ∀ {u, v} εE) must be satisfied. Also, every vertex must be represented by itself or one of the other vertices. Therefore, for all vertices vεV, Σ _uεV x _uv = 1 holds. In addition, when the vertex u represents another vertex, the vertex u itself must be a representative point. That is, x _uv ≦ x _uu must be satisfied for all vertices u and v. Therefore, in the symmetric representative point method, a variable x _vv that minimizes the objective function of the equation (a) is derived within a range that satisfies the constraint equations of the following equations (b) to (f).

[Asymmetric representative point method]
Assume that the vertex set V of the simple undirected graph G is V = {1, 2,..., N}, and that all vertices are given to these vertices with a positive integer magnitude relationship. . In the symmetric representative point method, all vertices can be representative points. On the other hand, in the asymmetric representative point method, the vertex v cannot represent the vertex u with respect to the ordered vertex pair {u, v} ordered by u <v. Therefore, x _vu = 0 must be satisfied for all ordered vertex pairs {u, v} where u <v. Therefore, in the asymmetric representative point method, the variable x _vv that minimizes the objective function of the equation (a) is derived within a range satisfying the constraint equations of the following equations (b) to (f).

As described above, in the asymmetric representative point method, the expression (g) is added to the constraint expression in the symmetric representative point method (otherwise, there is no difference between the asymmetric representative point method and the symmetric representative point method).
Further, since the value of x _{vu at} u <v is defined by the equation (g), the equations (b), (c), and (e) are expressed by the following equations (b ′), (c ′ ) And (e ′) may be used as constraint equations in the asymmetric point method.

In the expression (c) ′, min {u, v} indicates a smaller value of u and v.
As described above, the original vertex coloring problem is that each vertex of the simple undirected graph G is colored with a certain color, and any two adjacent vertices (connected by edges (branches)) are different colors. This is a problem of grouping all the vertices so that the number of colors to be colored is minimized. On the other hand, in the divide problem, it is necessary to obtain a solution in which a trade-off between minimizing the total number of peaks and minimizing the number of hills is taken. As will be described later, the total number of mountains can be formulated in a natural manner by the number of colors. On the other hand, with regard to the number of rounding numbers, there is no formulation for evaluating the number of rounding numbers, not only for the original vertex coloring problem but also for various problems that have been transformed. In response to such problems, the present inventors have found that the vertex coloring problem can be applied to the divide problem as in the embodiment of the present invention described below.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
(First embodiment)
First, the first embodiment will be described.
<Configuration and Processing of Steel Material Dividing Plan Planning Device 200>
FIG. 2 is a diagram illustrating an example of a functional configuration of the steel material division planning apparatus 200. FIG. 3 is a flowchart for explaining an example of the operation of the steel divide plan planning apparatus 200. For example, the hardware of the steel mountain division planning apparatus 200 is an information processing apparatus including a CPU, ROM, RAM, HDD, and various interfaces, a PLC (Programmable Logic Controller), an ASIC (Application Specific Integrated Circuit), or the like. This can be realized by using dedicated hardware. Note that, in the following description, the steel material division planning apparatus 200 is abbreviated as a mountain division planning apparatus 200 as necessary.

[Input unit 201: Target slab group list input step S301]
The input unit 201 acquires a slab group slab group list that is a list of slabs (steel materials) that are targets of the divide plan. It should be noted that the slab group slab group list may be acquired at regular intervals, or may be acquired irregularly triggered by the occurrence of a specific event or the like.
The input unit 201 is realized, for example, when the CPU stores data of the slab group slab group list received from a steel material management computer (not shown) via a communication interface in the HDD or RAM. The steel material management computer is a host computer having a database related to all steel materials arriving at the slab.

  In the present embodiment, an example in which the plurality of slabs arrive at the yard at the same time in units of a plurality of slabs which are the smallest units that are not divided when transported by a transport device such as a crane. Will be described. However, a plurality of slabs may not arrive at the yard at the same time. In that case, after the slab that finally arrives at the yard among the plurality of slabs arrives at the yard, the stacking of the plurality of slabs is started. In the following description, such a plurality of slabs are referred to as “slab groups” as necessary.

In the present embodiment, the slab group slab group list includes, for each slab group, an identification number, an estimated arrival time, a payout order, the number of steel materials, a maximum width, a minimum width, a maximum length, and a minimum length. Information is included.
The identification number is a number that uniquely identifies each slab group.
The estimated arrival time is the estimated arrival time at the yard of each slab group. In the present embodiment, a divide plan is created when no slab is yet placed in the yard. Therefore, the estimated arrival time is given for all the slab groups that are the targets of the divide plan.

The payout order is the order of conveyance to the rolling process of each slab group.
The number of steel materials is the number of slabs constituting each slab group.
The maximum width / minimum width are the maximum width / minimum width of the slabs constituting each slab group.
The maximum length and the minimum length are the maximum length and the minimum length of the slabs constituting each slab group, respectively.

  Here, the case where a list for each slab group is acquired has been described as an example, but a list for each slab may be acquired. In this case, for each slab, the identification number of the slab group to which the slab belongs is included in the list. In addition, instead of the maximum width, the minimum width, the maximum width, and the minimum width, for each slab, the width and length of the slab are included in the list.

[Variable Setting Unit 202: Variable Setting Step S302, Objective Function Setting Unit 203: Objective Function Setting Step S303, Constraint Expression Setting Unit 204: Constraint Expression Setting Step S304]
The variable setting unit 202 sets a variable that is not a fixed value among variables included in an objective function and a constraint expression described later. The objective function setting unit 203 sets an objective variable based on the variable set by the variable setting unit 202. Further, the constraint equation setting unit 204 sets a constraint equation based on the variable set by the variable setting unit 202. Hereinafter, the objective function and the constraint equation formulated in the present embodiment will be described.

[[Decision variable (representative relation variable) x _ij ]]
One representative slab group is selected from a plurality of slab groups belonging to each payout mountain, and the representative slab group includes all slab groups included in the payout mountain to which the representative slab group belongs (including the representative slab group itself). It shall be representative.

In the present embodiment, 0-1 variable x _ij represented by the following equation (1) is used as a decision variable, which is a 0-1 variable for a set {i, j} ∈N ² of any two slab groups. To do. Here, N is a set of slab groups (N = {1, 2,..., N}). As shown in the equation (1), the decision variable x _ij is a variable indicating “1” when the slab group i represents the slab group j, and indicating “0 (zero)” otherwise. Note that variables other than the decision variables x _ij is the dependent variable determined when the decision variable x _ij are determined. As described above, the representative slab group also represents itself. Therefore, i and j of the decision variable x _ij can take the same value.

[[Stacking constraints]]
The stacking shape restriction is a restriction on the loading form of the payout mountain. In the present embodiment, the stacking shape constraint includes the same mountain prohibition constraint.
<Same mountain prohibition restriction>
The same mountain prohibition restriction defines slab groups that cannot be stacked on the same payout mountain. In the present embodiment, it is assumed that slab groups that do not satisfy the following width condition and length condition must not be stacked on the same payout pile.

Width condition If the maximum width of a slab group is narrower than the minimum width of a slab group located below the slab group, the slab group positioned unconditionally Can be placed on top. When the maximum width of a certain slab group is wider than the minimum width of a slab group located below the certain slab group, the difference between the widths of the two is a reference value (for example, 300 [mm]) determined by work constraints. If it is less than (), the certain slab group can be placed on the slab group located below, but cannot be placed beyond that.

  That is, when the width condition is satisfied, the maximum width of a certain slab group is smaller than the minimum width of a slab group located below the certain slab group, and the maximum width of a certain slab group is This is a case where the width is wider than the minimum width of the slab group located under the slab group and the difference between the two widths is less than a reference value (for example, 300 [mm]).

-Length condition If a maximum length of a certain slab group is shorter than a minimum length of a slab group located below the certain slab group, the certain slab group is unconditionally placed in the slab located below the slab group. Can be placed on a group. When the maximum length of a certain slab group is longer than the minimum length of a slab group located below the certain slab group, the difference between the lengths of both is a reference value determined by work constraints (for example, 3000 [mm ]), The certain slab group can be placed on the slab group located immediately below, but cannot be placed beyond that.

  That is, when the length condition is satisfied, the maximum length of a certain slab group is shorter than the minimum length of a slab group located below the certain slab group, and the maximum length of a certain slab group is This is a case where it is longer than the minimum length of a slab group located below a certain slab group and the difference between the lengths of both is less than a reference value (eg, 3000 [mm]).

  Here, a set of two slab groups that cannot be stacked on the same payout pile is referred to as a prohibited pair, and a set of the prohibited pairs is referred to as a prohibited pair set F as necessary. In the following description, a set of two slab groups is referred to as a slab group pair as necessary. The forbidden pair set F is expressed by the following equation (3).

  In the formula (3), i. j is a slab group that does not satisfy at least one of the width condition and the length condition. In this embodiment, as shown in equation (3), slab group pairs (branches) that do not satisfy at least one of the width condition and the length condition (that is, must not be stacked on the same payout hill) Is introduced as a forbidden pair set F.

[[Reverse vs. same mountain variable r _ij ]]
Arbitrary two slab groups {i, j} ⊆ N can be stacked on the same payout pile, but when loading on the same payout pile, the load at the same payout pile in the order of arrival at the yard A slab group pair whose order needs to be changed is defined as a reverse pair. In the following description, this set of reversed pairs is referred to as a reversed pair set R as necessary. The order of arrival at the yard and the stacking order at the same payout mountain are reversed. It means that the arrival order to the yard is early. The reverse pair set R is expressed by the following equation (4).

The expression (4) indicates that the slab groups i and j need to be replaced when the slab groups i and j are stacked on the same payout hill. In the present embodiment, for all slab group pairs {i, j} εR belonging to this reverse pair set R, the 0-1 variable shown in the following equation (5) is introduced as the reverse pair identical mountain variable r _ij . . In the present embodiment, as shown in the equation (4), the reverse pair identical pile variable r _ij indicates “1” when the reverse pair slab groups i and j are piled on the same payout pile, and otherwise. 0-1 variable indicating “0 (zero)”.

[[Mount sorting constraint]]
The mountain sorting constraint equation is a constraint equation generated when each of the plurality of slab groups is sorted into one payout mountain. There is only one slab group representing one slab group in one payout mountain, and the slab group representing the other slab group is a payout mountain other than the payout mountain to which it is sorted. This means that it is not possible to represent other slab groups sorted into In the present embodiment, the mountain sorting constraint equations include first to sixth constraint equations. In the following description, a slab group representing another slab group is referred to as a representative slab group as necessary.

<First constraint expression>
When slab group i represents another slab group j, slab group i itself must be a representative slab group. From this, the first constraint equation shown in the following equation (7) is given. The first constraint equation is a constraint equation that prescribes that the representative slab group represents the representative slab group itself and other slab groups stacked on the same payout mountain as the representative slab group.
x _ij ≦ x _ii (∀i, j∈N, i ≠ j) (7)

<Second constraint expression>
Since the slab group pair {i, j} εF included in the prohibited pair set F cannot be stacked on the same payout mountain, one does not have a relationship representing the other. From this, the second constraint equation shown in the following equation (8) is given. The second constraint formula is a constraint formula that stipulates that any two slab groups that cannot be stacked on the same payout mountain because they violate the stacking shape constraint do not represent one of the other.
x _ij = x _ji = 0 (∀ {i, j} ∈F) (8)

<Third constraint expression>
Since the slab group pair {j, k} εF included in the prohibited pair set F cannot be stacked on the same payout hill, the slab group j and k constituting the slab group pair are different from the same slab group i. There is no representation. From this, the third constraint equation shown in the following equation (9) is given. The third constraint formula is a constraint that stipulates that any two slab groups that cannot be stacked on the same payout mountain because they violate the above-mentioned stacking shape constraint cannot be represented by the same same slab group. It is a formula.
x _ij + x _ik ≦ x _ii (∀i∈N, ∀ {j, k} ∈F) (9)

<Fourth constraint formula>
All slab groups must be represented by themselves or one of the other slab groups. From this, the fourth constraint equation shown in the following equation (10) is given. The fourth constraint equation is a constraint equation that defines that all slab groups are represented by any one slab group.
_{Σ i∈N x ij = 1 (∀j∈N} ) ··· (10)

<Fifth constraint expression>
The height of one payout mountain must be below the reference value.
In the present embodiment, it is assumed that all slabs have the same thickness. Therefore, the condition that the number of slabs loaded on one payout pile is equal to or less than a reference number (for example, 12 [sheets]) is defined as a mountain height constraint. Here, the upper bound of the number of slabs that can be loaded on one payout mountain is represented as h (hεZ ₊ (natural number)).

  Then, for all slab groups iεN, the following peak height constraint equation (fifth constraint equation) must be satisfied.

The left side of the equation (6) is the total number of slab groups in the payout mountain including slab group i. More specifically, the first term (w (i)) on the left side of equation (6) is the slab number (w (i): N → Z ₊ (natural number) of the slab group i (∀i∈N). ). w (i) is, for example, a natural number of 1 or more and 6 or less (1 ≦ w (i) ≦ 6).

Further, the second term (Σ term) on the left side of the equation (6) represents the total number of other slab groups j represented by the slab group i (∈N).
In equation (6), Σ in the second term on the left side of equation (6) represents the sum for slab group j other than slab group i in slab group set N (this also applies to the following equations) The same).

<Sixth constraint expression>
A slab group pair {i, j} ∈R, which is a slab group pair belonging to the reverse pair set R and one of which represents the other, must be stacked on the same payout mountain. A rounding occurs for the group pair i, j. In addition, a slab group pair {j, k} εR that is a slab group pair belonging to the inverted pair set R and one of which is not representative of the other (all represented by the same other slab group i). Is piled up on the same payout hill, slab group pair j, k is piled up. From this, the sixth constraint equation shown in the following equations (11) and (12) is given. The sixth constraint formula is that when an slab group that is in the order of arrival at the yard is stacked on top of an arbitrary slab group pair in which one is representative of the other, a reverse relationship (= sampling) occurs. Is a constraint equation that prescribes
r _ij ≧ x _ij , r _ji ≧ x _ji (∀ {i, j} ∈R) (11)
r _jk ≧ x _ij + x _ik −1 (∀i∈N, ∀ {j, k} ∈R) (12)

[[Metric]]
Next, the evaluation index in the objective function will be described.
In the present embodiment, the objective function is a weighted linear sum of the total number of peaks (mountain height) and the number of hills, that is, the total number of slab group pairs belonging to the reverse pair set R stacked on the same payout mountain. The weighted linear sum means a weighting factor for the total number of peaks (mountain height) and a weighting factor for the number of hills multiplied by a value obtained by multiplying the total number of hills (peak height) and the number of hills. . The weighting coefficient for the total number of mountains (mountain height) is a coefficient representing the balance between the evaluation for the total number of mountains (peak height) and the evaluation for the number of hills. The weight coefficient for the number of hills is a coefficient representing the balance between the evaluation for the number of hills and the evaluation for the total number of peaks (mountain height).

  The total number of mountains (mountain height) is used as an evaluation index because the storage capacity of the thermal insulation equipment is limited, the slab storage space is limited, and the slab is placed directly in the storage space. In some cases, it is required to make the peak height as high as possible and to reduce the total number of peaks as much as possible because the cooling of the uppermost and lowermost slabs is larger than other slabs. It is.

  The reason why the rounding number is used as an evaluation index is as follows. First, when carrying out the mountain division, it is required that the number of carrying operations for carrying out the pile is as small as possible in consideration of the problem of the work space and the ability of the carrying device such as a crane for carrying out the work. In the case of mountain division, it is ideal if slabs can be stacked in the order of arrival at the yard. On the other hand, in order to eliminate the pile-up at the time of payout and perform the payout work quickly, it is fundamental that the payout piles are piled up the ones that are quickly paid to the lower process. Therefore, in reality, the order of arrival at the yard may be different from the order of loading at the payout mountain. In other words, the slab with the earliest arrival order may have to be stacked on the same top of the payout hill than the later slab. In that case, the slabs that arrived at the yard first are temporarily placed in the temporary storage area until the slabs that are loaded at the lower level arrive at the yard, and the slabs that are loaded at the lower level arrive at the yard and are piled up. After that, it is necessary to load the temporary storage slab on the slab. Therefore, it is desirable to divide the mountain so that such work is minimized. The number of occurrences of such temporary placement is mathematically expressed as the number of inversions or the number of falls. The number of inversions (the number of overturns) is the total number of slab group pairs in which the relationship that the order of arrival at the yard and the order of products in the same payout mountain are reversed is established. Thus, the number of rounds is represented by the number of inversions.

[[Objective function]]
Since there is one representative slab group in one payout mountain, the total number of representative groups (= Σ _i ∈ _N x _ii ) is the total number of mountains.
In addition, since the number of reverse rotations (= crest number) is the total number of reverse pairs stacked on the same payout mountain, the total number of reverse pairs stacked on the same payout mountain (= Σ _{[i, j]} ∈ _R r _ij ).
If the weighting coefficient for the total number of mountains (mountain height) is k ₁ and the weighting coefficient for the number of inversions is k ₂ , the objective function is “k ₁ × total number of mountains + k ₂ × number of inversions”.
Therefore, the objective function is expressed by the following equation (13).
k ₁ × Σ _i∈N x _ii + k ₂ × Σ _{[i, j] ∈R} r _ij (13)

[[Objective function and constraint expression]]
As described above, in the present embodiment, the objective function of the equation (13) is satisfied within the range satisfying the constraints of the constraints of the equations (6) to (12), (14), and (15) as follows. The decision variable x _ij that minimizes the value of is derived.

The variable setting unit 202, for example, based on the slab group slab group list and the reference values in the width condition and the length condition, sets F (prohibited pairs) of slab group pairs (branches) that should not be stacked on the same mountain. A set F) is derived. The reference values in the width condition and the length condition may be acquired by the input unit 201 from a steel material management computer, or may be acquired by an operation by an operator on the user interface of the divide plan planning apparatus 200, for example. The variable setting unit 202 sets possible values as i and j of the decision variable x _ij and the reverse-versus-identical mountain variable r _ij based on the target slab group list input by the input unit 201 and The value of the number of slabs w (i) is set. For the decision variable _xij , i and j have the same value and different values.

The objective function setting unit 203 sets the decision variable x _ij and the reverse pair identical mountain variable r _ij set by the variable setting unit 202 in the equation (13). The objective function setting unit 203 sets a weighting factor k ₁ for the total number of peaks (mountain height) and a weighting factor k ₂ for the number of inversions. These weighting factors k ₁ and k ₂ may be acquired by the input unit 201 from the steel material management computer, or may be acquired by an operator's operation on the user interface of the divide plan planning apparatus 200, for example.

The constraint equation setting unit 204 sets the decision variable x _ij and the reverse pair equal mountain variable r _ij set by the variable setting unit 202 to equations (6) to (12), (14), and (15). . In addition, the constraint equation setting unit 204 sets the upper limit h of the number of slabs that can be stacked on one payout hill to the equation (6). The upper limit h of the number of slabs that can be loaded on one payout hill may be acquired by the input unit 201 from a steel material management computer, or may be acquired by an operator's operation on the user interface of the divide plan creation apparatus 200, for example. Good.

[Relationship between the Yaman problem and the vertex coloring problem]
Here, the relationship between the divide problem and the vertex coloring problem will be described.
A set N of slab groups is a set of vertices, and a simple undirected graph G with a prohibited pair set F (a set of slab group pairs that should not be stacked on the same payout mountain) as an edge (branch). In the division problem, slab group pairs that cannot be stacked on the same payout mountain can be regarded as adjacent vertex pairs (connected by edges (branches)) in the simple undirected graph G. In addition, stacking slabs into a plurality of payout mountains in the yard corresponds to painting the vertices of the simple undirected graph G into several colors. That is, slab groups corresponding to vertices of the same color are piled up on the same payout pile, and slab groups corresponding to vertices of different colors are piled up on different payout piles. By doing this, when the peak height constraint is excluded and only the total number of peaks is considered as the objective function, the peaking problem becomes an equivalent problem to the vertex coloring problem. As described above, since the divide problem has properties similar to the vertex coloring problem, it is possible to apply the formulation of the vertex coloring problem.

  On the other hand, the general vertex coloring problem has not been formulated to evaluate the rounding number. Therefore, in the present embodiment, the slab group in which the order of arrival is higher in the slab group in which the product order is lower than the slab group in which the order of arrival is lower than the slab group in which the order of arrival is earlier (the reverse pair). ) Is defined as a reverse pair set R. Then, a constraint equation is provided for determining whether the slab group pair that is an element of the reverse pair R has a representative relationship or whether the slab group pair is represented by the same representative slab group, and the reverse pair R When the slab group pairs that are the elements of the slab group are representatively represented or are represented by the same representative slab group, a term for counting the number of the slab group pairs is included in the objective function. In this way, the vertex coloring problem can be applied to the divide problem.

[Optimum Solution Deriving Unit 205: Optimal Solution Deriving Step S305]
The optimum solution deriving unit 205 minimizes the value of the objective function of equation (13) within a range that satisfies the constraints of the equations (6) to (12), (14), and (15). A decision variable x _ij (that is, an optimal solution of the decision variable x _ij ) is derived.

In the present embodiment, optimization calculation is performed under the following assumptions.
(A) When paying out the slab of the payout hill to the next process, the payout order to the next process of the slab group having a relatively higher stacking order is set so that the slab group on the payout hill can be paid in order. The slabs are piled up so as to be earlier than the delivery order to the next process of the slab group whose order is relatively lower.

(B) When there is a degree of freedom in the order of paying out the slab group to the next process, the earlier the slab group arrives at the yard, the lower the payout pile. For example, for the slab groups having the same lot number, there is no restriction in the order of dispensing the slab groups to the next process. A lot represents a group of processes in the next process (for example, a hot rolling process), and a lot number represents the order of processes in the next process of the group.
(C) The order of arrival at the yard is uniquely determined, and there is no overlap between different slab groups.
With this assumption, the order of stacking is determined uniquely for an arbitrary subset N′⊆N of the slab group.
Note that the optimization calculation by the 0-1 integer programming method is realized by using a known technique, and the detailed description thereof is omitted here.

[Output unit 206: Output step S306]
The output unit 206 outputs information based on the optimal solution of the decision variable x _ij derived by the optimal solution deriving unit 205. For example, the output unit 206 can output the optimal solution of the decision variable x _ij derived by the optimal solution deriving unit 205. In this case, the operator creates the optimal solution for the decision variables x _ij, for each slab groups included in Whack target slab group list, the information including a product order in the payout mountain and the payout mountain which the slab group belongs can do. Further, the output unit 206 can derive and output such information from the optimum solution of the decision variable x _ij derived by the optimum solution deriving unit 205. In addition, the output unit 206 identifies which slab group is transported to which location by which transport device at which timing based on the slab group list to be divided and the optimal solution of the decision variable x _ij , Based on this, it is possible to issue an operation command to the transfer device. In this case, the optimal solution for the decision variable x _ij may or may not be output.

[Summary]
As described above, in the present embodiment, the total number of mountains is reduced, and the number of piles (in order to stack the slab group with the earlier arrival order to the yard on the same payout mountain above the slab group with the later number) The optimization problem that minimizes the value of the objective function for the purpose of reducing the number of temporary placements required for the above is solved by performing an optimization calculation by mathematical programming. At that time, let the vertices correspond to slab groups, and two slab groups corresponding to two vertices connected to each other by edges (branches) should not be stacked on the same payout mountain (restricted pair relationship) It is expressed as two slab groups. A representative slab that is a slab group that represents another slab group and that exists only in one payout mountain and cannot represent another slab group in any other payout mountain. Express the number of groups as the total number of mountains. In addition, it is possible to pile up on the same payout pile, but when stacking on the same payout pile, it is necessary to change the order of arrival at the yard and the order of load at the same payout pile. The total number of reverse pairs stacked on the same payout mountain is defined as the reverse number, and this is expressed as the number of rounds.

  Specifically, in this embodiment, a set of reversed pairs is defined as a reversed pair set R. And a constraint equation that prescribes that slab grouping occurs when an arbitrary slab group pair in which one represents the other is a reverse pair and when the slab group pair is represented by the same representative slab group Is included in the constraint expression.

  Therefore, the mountain separation problem can be applied to the vertex coloring problem. By doing this, if there are many slab groups that are subject to the divide plan, the slab groups that are subject to the divide plan will become larger when piled on the same payout mountain, Even when the number is large, it is possible to create a divide plan in the yard within a practical time. That is, regardless of the nature of the problem to be solved, it is possible to create a yarding plan in a yard within a practical time.

For example, in the present embodiment, it is not necessary to enumerate executable mountains as in the set partitioning problem and prepare variables for that number. Since the number of subsets in the set partitioning problem shown in Patent Document 1 is 2 ^{n when the} number of elements in the set is ⁿ , it is an exponential time algorithm. On the other hand, in the present embodiment, the problem can be formulated by a variable of the order of the polynomial of n ² . Therefore, it is possible to construct an algorithm independent of the number of executable mountains (subsets). In the method of the present embodiment, when the vertex is a representative vertex (slab group i is a representative slab group), the color number χ (G) is set to χ (G) = Σ by promising that the variable x _ii = 1. It can be simply expressed as _i ∈ _V x _ii . Therefore, even if compared with the method of Patent Document 2, the variable indicating whether or not there is a mountain (a variable indicating the existence of a color in the vertex coloring problem) that is necessary in Patent Document 2 is not necessary. Since the number of variables and the search range can be greatly reduced, the solution can be obtained at high speed even when there are many reverse pairs.

<Modification>
[Modification 1]
In the present embodiment, the objective function aimed at minimizing the weighted linear sum of the total number of peaks (mountain height) and the number of peaks (inversion number) has been described as an example. However, the objective function is not limited to a weighted linear sum of the total number of peaks (mountain height) and the number of peaks (number of inversions). For example, the sum of all payout mountains, the total number of mountains (mountain height), and the number of piles (reversed) of the time until one payout mountain is completed (working time of the transport device for making one mountain) The objective function may be a weighted linear sum with (number). Also, in one payout hill, the time required to pay out the slab to be paid out last from the first slab to the next process (from the payout time of the first slab to the payout time of the last slab in one payout hill) It is also possible to use a weighted linear sum of the sum of all payout mountains, the total number of peaks (mountain height), and the number of peaks (number of inversions) as the objective function. With respect to the former, if the time until one payout hill is completed is short, for example, it is possible to shorten the time for keeping the heat insulation facility open for accepting the slab, and to suppress a decrease in the temperature of the slab. Regarding the latter, if the time required to pay out the slab to be paid out from the first slab to the next process is short in one payout hill, the time for the heat insulation equipment to open for the payout from the heat insulation equipment is set. It can shorten and can suppress the fall of the temperature of a slab.

[Modification 2]
In the present embodiment, the case where the optimization problem that minimizes the value of the objective function is solved by mathematical programming has been described as an example. However, for example, an optimization problem that maximizes the value of the objective function may be obtained by multiplying each term of the equation (23) by (−1).

[Modification 3]
In the present embodiment, the case where all the slabs have the same thickness has been described as an example. However, the thickness of the slabs may not be the same. In this case, w (i) may be the sum of the thicknesses of the slabs included in the slab group i.

[Modification 4]
In the present embodiment, the case where the divide plan is created for each slab group has been described as an example. However, a divide plan may be created for each slab. In that case, the “slab group” in the description so far is read as “slab”, and the number of steel materials becomes one (for example, the number of slabs w (i) of the slab group i becomes “1”). The maximum width and the minimum width are the same value as the width of the slab. Similarly, the maximum length and the minimum length have the same value as the length of the slab.

(Second Embodiment)
Next, a second embodiment will be described. In the first embodiment, the case where the divide plan is applied to the vertex coloring problem using the symmetric representative point method as a solution has been described as an example. On the other hand, in this embodiment, the case where a divide plan is applied to the vertex coloring problem using the asymmetric representative point method as a solution will be described as an example. Therefore, the present embodiment and the first embodiment are mainly different in part of the constraint equation. Therefore, in the description of this embodiment, the same parts as those in the first embodiment are denoted by the same reference numerals as those in FIGS.

Each slab group set N (N = {1, 2,..., N}) is ordered in a positive integer magnitude relationship. As described above, in the asymmetric representative point method, for two slab groups i and j, if i <j, the slab group j cannot represent the slab group i. That is, the decision variable x _ji is 0 (x _ji = 0) for all slab groups i, j where i <j. Therefore, the objective function and the constraint equation when the asymmetric representative point method is used as a solution are as follows.

  In the equations (9 ′) and (12 ′), min {j, k} indicates a smaller value of j and k. Further, equation (16) corresponds to the above-described equation (g) and is a seventh constraint equation included in the mountain sorting constraint equation described in the first embodiment. The expressions (8 ′), (9 ′), and (7 ′) are constraint expressions corresponding to the expressions (b ′), (c ′), and (e ′) described above, respectively. This is a constraint equation in which the range of the parameter i of the constraint equation set by the equations (8), (9), and (7) described in the embodiment is reduced using the definition of the equation (16). The expression (6 ′) corresponds to the expression (6) described in the first embodiment, and is a peak height constraint expression (fifth constraint expression).

As described above, in this embodiment, a unique rank is assigned to each slab group (vertex), and a slab group having a relatively low rank cannot represent a slab group having a relatively high rank. To. Even when the asymmetric representative point method is used as a solution method as well as the symmetric representative point method, the division scheme can be applied to the vertex coloring problem. Since the decision variable x _ji is 0 (x _ji = 0) for all slab groups i and j where i <j, the calculation time can be further shortened.
Also in this embodiment, various modifications described in the first embodiment can be employed.

(Third embodiment)
Next, a third embodiment will be described. In the second embodiment, the case where the ordering method for the set N (N = {1, 2,..., N}) of slab groups is arbitrary has been described as an example. On the other hand, in the present embodiment, there is a limit on how to order the set N of slab groups. As described above, the present embodiment and the second embodiment mainly differ in processing due to different ordering methods for the set N of slab groups. Therefore, in the description of the present embodiment, portions different from those in the first and second embodiments are denoted by the same reference numerals as those in FIGS.

  Focusing on the equation (12 ′) among the constraint equations described in the second embodiment, (min {j, k} −1) constraint equations are required for each inversion pair {j, k} ∈R. To do. This means that if the number assigned to the slab group j, k corresponding to the reverse pair {j, k} is small, the number of constraint expressions in the expression (12 ′) can be reduced. That is, in the asymmetric representative point method, it is possible to reduce the constraint formulas related to the reverse pair by changing the order (numbering) to the slab group.

Therefore, in this embodiment, the variable setting unit 202 performs ordering (numbering) on the slab groups as follows.
FIG. 4 is a diagram conceptually illustrating an example of a method for performing ordering (numbering) on slab groups. FIG. 5 is a flowchart for explaining an example of a method for ordering (numbering) slab groups. An example of a method for ordering (numbering) slab groups will be described with reference to FIGS.

  First, in step S501, the variable setting unit 202 sets the slab group set N as the vertex set V, and the inverted pair set R (the slab group with the product order higher than the slab group with the product order lower). In addition, a simple undirected graph Γ (V, R) is created with an edge (branch) as a pair of slab groups (a set of reverse pairs) in which a reverse relationship occurs in the order of arrival at the yard. Note that, for a slab group that is not a reverse pair with any other slab group, the vertex corresponding to the slab group exists in isolation (that is, the vertex has a side ( It will not be connected at the branch)).

  The first diagram from the top in FIG. 4 is an example of this simple undirected graph Γ. At this time, the variable setting unit 202 temporarily assigns numbers 1 to N to the vertices corresponding to the set N of each slab group so as not to overlap each other. In the first diagram from the top of FIG. 4, this number is shown beside each vertex. In addition, the variable setting unit 202 sets the column Q as an empty column. Each column of column Q is given a slab group identification number, and number j is assigned to the jth slab group (j is a positive integer).

  Next, in step S502, the variable setting unit 202 determines whether or not there is a vertex in the simple undirected graph Γ (V, R). If the result of this determination is that there are no vertices in the simple undirected graph Γ (V, R), the ordering (numbering) for each slab group ends, so the processing according to the flowchart of FIG. 5 ends. To do.

On the other hand, if the simple undirected graph Γ (V, R) has at least one vertex, the process proceeds to step S503. In the example of the first figure from the top in FIG. 4, since there is a vertex in the simple undirected graph Γ (V, R), the process proceeds to step S503.
In step S503, the variable setting unit 202 has the highest number of vertices (ie, the number of edges (branches) connected to the vertices) among the vertices of the simple undirected graph Γ (V, R). Select (Vertex). When there are a plurality of vertices having the highest degree, the variable setting unit 202 selects a vertex having the smallest number temporarily assigned in step S501 among the plurality of vertices. In the example of the first figure from the top in FIG. 4, the number of sides (branches) connected to the vertex assigned the temporary number “5” is “4”, and the degree of the vertex is the highest. Therefore, the variable setting unit 202 selects the vertex to which the temporary number “5” is attached.

  Next, in step S504, the variable setting unit 202 deletes the vertex selected in step S503 and the side (branch) connected to the vertex. In the example of the first diagram from the top in FIG. 4, as shown in the second diagram from the top in FIG. 4, the vertex assigned the temporary number “5” and the side (branch) connected to the vertex ). In FIG. 5, the deleted one is indicated by a broken line.

  In step S505, the variable setting unit 202 changes the number for the slab group corresponding to the vertex selected in step S503. By inserting the identification number of the slab group corresponding to the vertex selected in step S503 at the end of the column Q, the number for the slab group corresponding to the vertex selected in step S503 is changed. In the example shown in the second diagram from the top in FIG. 4, the slab group identification number is not yet inserted in the column Q. Therefore, the identification number of the slab group corresponding to the vertex with the temporary number “5” is inserted at the beginning of the column Q. In this way, the number of the slab group corresponding to the vertex with the temporary number “5” is changed from “5” to “1”.

  And it returns to step S502 mentioned above. In step S502, the variable setting unit 202 determines whether or not there is a vertex in the simple undirected graph Γ (V, R). In the example shown in the second diagram from the top in FIG. 4, there are still four vertices with temporary numbers “1”, “2”, “3”, and “4” assigned in step S501. Therefore, in step S503, the variable setting unit 202 selects a vertex assigned with a temporary number “2”, which is the vertex having the highest degree among the vertices.

  Then, in step S504, the variable setting unit 202, as shown in the third diagram from the top in FIG. 4, the vertex assigned with the temporary number “2” and the side (branch) connected to the vertex In step S505, the identification number of the slab group corresponding to the vertex assigned the temporary number “2” is inserted at the end (second column) of the column Q. As a result, as shown in the third diagram from the top in FIG. 4, the number of the slab group corresponding to the vertex assigned the temporary number “2” becomes “2”.

  In the example shown in the third diagram from the top in FIG. 4, there are still three vertices with the temporary numbers “1”, “3”, and “4” assigned in step S501. Therefore, the variable setting unit 202 determines in step S502 that the simple undirected graph Γ (V, R) has a vertex. In the example shown in the third diagram from the top in FIG. 4, there are no vertices connected by edges (branches) among the currently remaining vertices (the order of all vertices is the same). Accordingly, in step S503, the variable setting unit 202 selects the vertex with the smallest temporary number “1” among the three vertices with the temporary numbers “1”, “3”, and “4”.

Then, in step S504, the variable setting unit 202 deletes the vertex assigned the temporary number “1” as shown in the fourth diagram from the top in FIG. In the (third column), the identification number of the slab group corresponding to the vertex assigned the temporary number “1” is inserted. As a result, as shown in the fourth diagram from the top in FIG. 4, the number of the slab group corresponding to the vertex assigned the temporary number “1” becomes “3”.
Thereafter, in the same manner as the processing for the vertices assigned with the temporary number “1”, as shown in the fourth diagram from the top in FIG. 4, the vertices assigned with the temporary numbers “3” and “4” are added. “4” and “5” are set as the corresponding slab group numbers, respectively. When all the vertices disappear as described above, the processing according to the flowchart of FIG. 5 is terminated as described above.

As described above, in the present embodiment, in the simple undirected graph Γ (V, R) in which the set N of slab groups is the vertex set V and the inverted pair set R is the edge (branch), it is connected to other vertices. In order from the vertex with the largest number of edges (branches), the number of the vertex and the edge (branch) connected to the vertex are deleted and the number of the slab group corresponding to the vertex increases from 1 to 1 in ascending order Is attached. Therefore, a relatively smaller number is assigned to a slab group that has a reverse pair relationship with a larger number of other slab groups. Therefore, it is possible to reduce the number of expressions listed as the expression (12 ′) that is a constraint expression related to the reverse pair. Therefore, the calculation time can be further shortened.
Also in this embodiment, various modifications described in the first and second embodiments can be adopted.

(Example)
Next, examples will be described.
<Example 1>
In this example, a divide plan is created by the solution according to the third embodiment (invention example), the solution according to Patent Document 1 (Comparative Example 1), and the solution according to Patent Document 2 (Comparative Example 2). The time required for solution was compared. However, when the calculation time was 3 minutes (180 seconds) or more, the evaluation was made by the dual gap representing the accuracy of the solution obtained at that time.
The dual gap is expressed by the following equation (17).
Dual gap = {(upper bound value−lower bound value) / upper bound value} × 100 (17)

  In equation (17), the upper bound value is the value of the objective function of the best solution among the solutions that can realize the divide plan obtained when 3 minutes have passed since the calculation was started. The lower bound value is the value of the largest (worst) objective function among the optimum solutions obtained when the relaxation problem is solved, which is obtained when 3 minutes have passed since the calculation was started. When the upper bound value and the lower bound value coincide with each other, the solution at that time is the optimal solution. Further, the relaxation problem refers to a problem in which the 0-1 variable condition of the optimization problem is relaxed (allowing the 0-1 variable to take a value between 0 and 1 other than 0 and 1).

In any solution, the total number of slab groups is set to 50, and a divide plan is created for the same slab group (that is, the same divide target slab group list is used).
In any solution, the objective function was k ₁ × total number of peaks + k ₂ × number of inversions. Here, the weighting factor k ₁ for the total number of mountains (mountain height) is set to 5.0 (k ₁ = 5.0), and the weighting factor k ₂ for the number of inversions is set to 1.0 (k ₂ = 1.0). .
FIG. 6 is a diagram showing the creation results of the division plan based on these solutions in a table format.

  In FIG. 6, “prohibited%” is the percentage of the number of slab group pairs (branches) that should not be stacked on the same payout mountain with respect to the total number of slab group pairs. “Reversal%” refers to the slab in which the order of arrival at the yard and the order of product at the payout mountain are reversed relative to the total number of slab group pairs minus the number of slab group pairs that must not be piled up at the same payout pile. The percentage of the number of group pairs is expressed as a percentage. “F.Mt” is the number of realizable mountains (unit: million). “Opt.V” is the value of the objective function or the upper bound value when the optimal solution is obtained. “Number of mountains” is the number of payout mountains obtained as a result of the optimization calculation. “Reversal” is the number of slab group pairs obtained as a result of the optimization calculation, in which the order of arrival at the yard and the order of product at the payout mountain are reversed.

  In FIG. 6, coloring is shown because the best solution among the three solutions is obtained. As shown in FIG. 6, out of the 19 data used, the solution according to the invention example (asymmetric representative point method) in 14 data out of the solution according to the comparative example 1 (set division) and the comparative example 2 A better solution is reached sooner than the solution (many-to-one assignment). Only the three data (data ID 03, 05, 15) have the best solution by the solution method (set division) according to Comparative Example 1. Of the two data (data IDs 03 and 05), the same level of solution is obtained with the solution according to the invention example (asymmetric representative point method) and the solution according to comparative example 1 (set partitioning). In the data (data ID 15), almost the same level of solution is obtained. In addition, in the solution method according to Comparative Example 2 (many-to-one assignment), there is no case where the best solution is obtained.

  In the case where the solution by the comparative example 1 (set division) is better than the solution by the invention example (asymmetric representative point method), the number of feasible mountains is at most about 3 million. When the number approaches 10 million, the solution (set division) according to Comparative Example 1 does not provide a feasible solution within 3 minutes. On the other hand, with the solution according to the invention example (asymmetric representative point method), even if the number of feasible mountains is tens of millions to 100 million, the optimal value or a value close to it can be obtained within 3 minutes. As described above, in the solution according to the invention example (asymmetric representative point method), the optimum solution can be obtained within 3 minutes even when the number of realizable mountains increases.

<Example 2>
In this example, the solution according to the third embodiment (described as an asymmetric representative point method (invention example)) and the solution according to the first embodiment (described as a symmetrical representative point method (invention example)), respectively, We created a divide plan and compared the time required for solution. The data used for the divide plan, the creation condition of the divide plan, and the evaluation method of the divide plan are the same as those in the first embodiment.
FIG. 7 is a table showing the results of creating a mountain division plan based on these solutions in a table format. In FIG. 7, “expression (12 ′)” and “expression (12)” are the numbers of expressions listed as expressions (12 ′) and (12), respectively. “%” Represents a percentage obtained by dividing the number of formulas listed as the formula (12 ′) by the number of formulas listed as the formula (12).
As shown in FIG. 7, out of the 19 data used, in all 14 data,
The solution according to the third embodiment (asymmetric representative point method) reaches a good solution earlier than the solution according to the first embodiment (symmetric representative point method). However, there is no case where a feasible solution is not obtained even with the solution according to the first embodiment (symmetric representative point method), and the solution according to Comparative Example 1 (set division) and the solution according to Comparative Example 2 shown in FIG. Compared to many-to-one allocation, a good solution can be obtained quickly even if the number of realizable mountains increases.

(Other variations)
The embodiment of the present invention described above can be realized by a computer executing a program. Further, a computer-readable recording medium in which the program is recorded and a computer program product such as the program can also be applied as an embodiment of the present invention. As the recording medium, for example, a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a nonvolatile memory card, a ROM, or the like can be used.
In addition, the embodiments of the present invention described above are merely examples of implementation in carrying out the present invention, and the technical scope of the present invention should not be construed as being limited thereto. Is. 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 relationship between a claim and embodiment is shown. Note that the relationship between the claims and the embodiment is not limited to the following relationship, as described in the modification and the like.
<Claim 1>
The decision variable setting means is realized by using the variable setting unit 202, for example.
The mountain division constraint equation setting unit and the stacking shape constraint equation setting unit are realized by using the constraint equation setting unit 204, for example.
The objective function setting means is realized by using the objective function setting unit 203, for example.
The total number of payout hills is realized by using, for example, Σ _i ∈ _N x _ii .
The number of inversions is realized by using, for example, Σ _{[i, j]} ∈ _R r _ij .
The division determination unit is realized by using the optimum solution deriving unit 205, for example.
The representative relationship variable (decision variable) is realized by, for example, x _ij (where i and j include the same and different ones).
The product form constraint equation is realized by using, for example, Equation (3).
The first constraint equation is realized by using, for example, equation (7).
The second constraint equation is realized by using, for example, equation (8).
The third constraint equation is realized, for example, by using equation (9).
The fourth constraint expression is realized by using, for example, Expression (10).
The fifth constraint equation is realized by using, for example, equation (6).
The sixth constraint expression is realized by using, for example, Expression (11) and Expression (12) (or Expression (11) ′ and Expression (12) ′).
<Claim 2>
The seventh constraint expression is realized by using, for example, Expression (16).
<Claim 3>
Claim 3 is realized by using, for example, the variable setting unit 202 (the process according to the flowchart of FIG. 5).
<Claim 4>
The steel material group corresponds to, for example, a slab group.

  200: Steel material division planning device, 201: input unit, 202: variable setting unit, 203: objective function setting unit, 204: constraint equation setting unit, 205: optimal solution derivation unit, 206: output unit

Claims (6)

To pile up multiple steel materials that have been transported to a yard where steel materials are arranged as a place between processes in the steel process in order that the steel materials that are delivered earlier to the next process are on top, and to be delivered to the subsequent process of the yard A steel material division planning device for creating a division plan for creating a plurality of payout mountains,
A decision variable setting means for setting a decision variable which is a variable to be determined when determining the divide plan;
A mountain sorting constraint equation setting means for setting a mountain sorting constraint equation that is a constraint when assigning each of the plurality of steel materials to one of the plurality of payout piles;
A loading figure constraint equation setting means for setting a loading figure constraint equation that is a restriction on the loading figure of the payout mountain;
Reducing the total number of payout hills and, for any two steel members stacked on the same payout hill, the steel material with the earlier arrival order to the yard is stacked above the steel material with the slower arrival. An objective function setting means for setting an objective function for reducing the number of reverse pairs in a reverse relationship;
Satisfying the mountain sorting constraint equation and the product form constraint equation, and having a mountain sorting determination means for determining the mountain division so as to minimize the objective function,
The decision variable includes
When one of the steel materials is stacked on a payout mountain represented by a representative steel material that is one steel material representing the payout mountain, selected for each of the payout piles, the representative steel material is Including the representative relation variable that represents the one steel material, and when the one steel material is not stacked on the payout hill represented by the representative steel material, the representative steel material does not represent the one steel material;
The mountain sorting constraint formula is
A first constraint formula that prescribes that the representative steel material represents the steel material piled up on the payout hill represented by the representative steel material itself and the representative steel material;
Any two of the steel materials that cannot be stacked on the same payout pile because they violate the stacking shape constraint formula are as follows: a second constraint formula that defines that one steel material does not represent the other steel material; ,
A third constraint formula that stipulates that any two steel materials that cannot be stacked on the same payout pile because they violate the stacking shape constraint formula are not represented by the steel materials different from the two steel products;
A fourth constraint formula that specifies that all the steel materials are represented by any representative steel material;
A fifth constraint formula that defines that the total number of steel materials represented by each of the representative steel materials is a value equal to or less than the upper limit value, which is a value indicating the total number of the steel materials stacked on each of the payout piles;
For any two steel products, one representing the other, a sixth constraint formula that specifies that the reversal relationship occurs when steel products that arrive early in the yard are stacked on top of each other;
Including
In the objective function,
The total number of the representative steel materials is the total number of the payout hills, and the number of pairs of steel materials in the reverse relationship defined by the sixth constraint formula is the number of the reverse pairs, Planning device. The steel is given a unique order,
The mountain sorting constraint equation further includes a seventh constraint equation that defines that the steel material having a relatively low order cannot represent a steel material having a relatively high order. Item 1. A steel mountain division planning apparatus according to item 1.   The order given to the steel materials in which the number of the reverse relations is established is relatively higher than the order given to the steel materials in which the number of the reverse relations is established is relatively small. The steel material mountain division planning apparatus according to claim 2, wherein the steel material is divided into parts.   The steel divide plan planning apparatus according to any one of claims 1 to 3, wherein the divide plan is made in units of a steel group composed of a plurality of steel materials. To pile up multiple steel materials that have been transported to a yard where steel materials are arranged as a place between processes in the steel process in order that the steel materials that are delivered earlier to the next process are on top, and to be delivered to the subsequent process of the yard A steel material division planning method for creating a division plan for creating a plurality of payout mountains,
A decision variable setting step for setting a decision variable which is a variable to be determined when determining the divide plan;
A mountain sorting constraint equation setting step for setting a mountain sorting constraint equation that is a constraint when assigning each of the plurality of steel materials to one of the plurality of payout piles;
A loading figure constraint formula setting step for setting a loading figure constraint formula that is a constraint on the loading figure of the payout mountain;
Reducing the total number of payout hills and, for any two steel members stacked on the same payout hill, the steel material with the earlier arrival order to the yard is stacked above the steel material with the slower arrival. An objective function setting step for setting an objective function for reducing the number of inversion pairs in a reverse relationship;
Satisfying the mountain sorting constraint equation and the product form constraint equation, and a mountain sorting determination step for determining the mountain division so as to minimize the objective function,
The decision variable includes
When one of the steel materials is stacked on a payout mountain represented by a representative steel material that is one steel material representing the payout mountain, selected for each of the payout piles, the representative steel material is Including the representative relation variable that represents the one steel material, and when the one steel material is not stacked on the payout hill represented by the representative steel material, the representative steel material does not represent the one steel material;
The mountain sorting constraint formula is
A first constraint formula that prescribes that the representative steel material represents the steel material piled up on the payout hill represented by the representative steel material itself and the representative steel material;
Any two of the steel materials that cannot be stacked on the same payout pile because they violate the stacking shape constraint formula are as follows: a second constraint formula that defines that one steel material does not represent the other steel material; ,
A third constraint formula that stipulates that any two steel materials that cannot be stacked on the same payout pile because they violate the stacking shape constraint formula are not represented by the steel materials different from the two steel products;
A fourth constraint formula that specifies that all the steel materials are represented by any representative steel material;
A fifth constraint formula that defines that the total number of steel materials represented by each of the representative steel materials is a value equal to or less than the upper limit value, which is a value indicating the total number of the steel materials stacked on each of the payout piles;
For any two steel products, one representing the other, a sixth constraint formula that specifies that the reversal relationship occurs when steel products that arrive early in the yard are stacked on top of each other;
Including
In the objective function,
The total number of the representative steel materials is the total number of the payout hills, and the number of pairs of steel materials in the reverse relationship defined by the sixth constraint formula is the number of the reverse pairs, Planning method.   A program that causes a computer to function as each means of the steel material divide plan planning apparatus according to any one of claims 1 to 4.

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