JP7192382B2 - YARD MANAGEMENT DEVICE, YARD MANAGEMENT METHOD, AND PROGRAM - Google Patents

Description

The present invention relates to a yard management device, a yard management method, and a program, and in a metal manufacturing process, a yard provided for smoothly supplying metal materials such as slabs and coils to the next process. It is suitable for sorting piles of containers in a field or the like.

In the ironmaking process, which is an example of a metal manufacturing process, when conveying steel, which is an example of a metal material, from the steelmaking process to the next rolling process, the steel material is temporarily placed in a temporary storage place called a yard. It is carried out from the yard according to the processing time of the rolling process which is the next process. An example of the layout of the yard is shown in FIG. As shown in FIG. 5, the yards are storage areas 501 to 504 partitioned vertically and horizontally as buffer areas for supplying steel materials such as slabs delivered from upstream processes to downstream processes. Vertical divisions are often called "buildings" and horizontal divisions are called "columns". In other words, the cranes (1A, 1B, 2A, 2B) are movable within the building to transfer steel materials between different rows within the same building. In addition, the transfer table is used to transfer steel materials between buildings. When creating a transport command, specify the "ridge" and "row" to indicate where the steel material is to be transported (number (11) in parentheses in storage areas 501 to 504 in FIG. 5, (12), (21), (22)).

Next, FIG. 5 shows the flow of basic work in the yard as an example. First, the steel material unloaded from the continuous casting machine 510 in the steelmaking process, which is the previous process, is transported to the yard by the receiving table X via the piler 511, and is moved to the storage area 501 by the cranes 1A, 1B, 2A, and 2B. 504 and piled up. Then, according to the manufacturing schedule of the rolling process, which is the post-process, the cranes 1A, 1B, 2A, and 2B again place the wafers on the delivery table Z and transport them to the rolling process. Generally, in the yard, the steel materials are placed in piles as described above. This is to effectively utilize the limited yard area.
In this specification, claims, and drawings, the terms "already-arrived mountain", "virtual mountain", "initial mountain", "final mountain", and "temporary mountain" are used with the following meanings.
Already-arrived pile: A pile that has already been formed in the yard at this time.
Virtual pile: A pile (not a pile that actually exists) when it is assumed that metal materials that have not yet arrived at the yard at the present time are piled up in order of arrival at the yard.
Initial mountain: A general term for already-arrived mountains and virtual mountains.
Final pile: The final pile (also referred to as the payout pile) that is piled up to be delivered to the post-process.
Temporary pile: A pile that is unavoidably placed temporarily when moving from the initial pile to the final pile after the present time.

In the yard, in order to reduce the fuel consumption of the heating furnace in the hot rolling process, which is the next process, it is required that the steel material is charged into the heating furnace while maintaining the highest possible temperature. Therefore, in recent years, there is a case where a heat insulating facility is installed in the yard and the steel materials are stored in a state of being piled up in it. In order to make effective use of the limited thermal insulation facilities, it is necessary to pile up the steel materials as high as possible to the limits of the facilities. On the other hand, when stacking steel materials, in order to facilitate supply to the next process, in the final pile, the steel materials should be stacked from the top in the order of processing in the next process, and the shape of the final pile should not be an unstable inverted pyramid shape. There are restrictions (this is called "stacking restriction") such as In addition, the work load during the pile up (creating the final pile) is also an element that cannot be overlooked. Therefore, in the yard control, it is desirable to formulate a work plan for erecting the final pile as high as possible with the least possible workload under the above-mentioned stacking restrictions.

In addition, when sorting the piles (dividing the steel into multiple piles), which is performed in the yard to smoothly deliver the steel requested to the post-process, the steel that is scheduled to arrive will be demoted. Due to quality problems, etc., the grade may be lowered from the originally planned use and transferred to another use. As a result, steel products often fail to arrive as originally planned. In addition, it is almost impossible to expect that the status of the yard storage will change smoothly as originally planned, and it is a daily occurrence that unplanned steel materials have to be placed in unplanned storage locations.

Furthermore, the rolling order in the hot rolling process, which is the post-process, of the steel materials piled up in the order of delivery from the yard to the hot-rolling process, which is the post-process, changes after the steel materials arrive at the yard. As a result, the pile is no longer stacked in the order of delivery, and there are frequent cases where the steel materials are forced to be reloaded according to the changed rolling order. Here, the steel materials are stacked in a pile in the order of delivery, meaning that one or more steel materials that are relatively higher or a plurality of steel materials that are conveyed at the same time are lower than the steel materials at any stacking position of the pile. It means that a certain steel material is delivered to the post-process earlier than other steel materials.

However, the transshipment work required here must be performed in parallel with the work of receiving steel materials into the yard and the work of unloading steel materials from the yard. Storage space is limited. For this reason, it is required to efficiently and space-savingly carry out the steel material transshipment work.
Therefore, due to various circumstances before and after arrival at the yard, the work of reloading the piles that are not in the order of payout at the time of arrival at the yard can be efficiently (that is, with as few transports as possible) and as few final deliveries as possible. There is an extremely high demand for keeping the number of piles as small as possible and keeping the number of temporary storage areas as small as possible.

There are inventions described in Patent Documents 1 to 3 regarding yard management methods that require these things. The inventions described in Patent Documents 1 to 3 are when all the steel materials to be sorted in the mountains have been received into the yard, or some of the steel materials to be sorted in the mountains are in the process of being received. To provide an invention for efficiently reloading steel materials in a space-saving manner so that the steel materials are stacked in the final pile in the order of dispensation when the received steel materials are not stacked on the pile in the order of dispensation.

First, in Patent Document 1, when reloading the steel materials of the already arrived piles in the yard in the order of delivery, the optimal pile configuration of the final pile is combined and optimized in consideration of the required distribution load and stacking configuration restrictions. A method of formulating the problem as a generalization problem and calculating it using a tab search method is disclosed. However, in the invention described in Patent Document 1, although a method for obtaining the shape of the final mountain is shown, it is clearly shown how to obtain the order of conveyance from the initial mountain to the final mountain. not Also, since the shape of the final mountain is also calculated by a heuristic method, there is no guarantee of its optimality.

Next, in Patent Document 2, under a situation where steel materials that have already arrived at the yard and steel materials that have not yet arrived are mixed, an initial pile state and a final pile state at the time are given. There is a method to formulate the problem of transshipment and transport of steel materials from the state to the final pile state as a mixed integer programming problem using initial transport time variables and final transport time variables on the premise that each steel material is transported at most twice. disclosed. However, in the invention described in Japanese Patent Laid-Open No. 2002-200012, the order of transportation is determined after the final peak is determined. In other words, the final pile and the order of conveying the steel materials are individually optimized. Therefore, there is a possibility that the number of conveyed steel materials, that is, the number of temporarily placed steel materials cannot be minimized.

Finally, the invention described in Patent Document 3 is an invention that optimizes pile sorting and transport order at the same time by reducing it to a mathematical programming problem that satisfies the constraints on stacking and transport. However, the invention described in Patent Document 3 is a two-dimensional assignment problem in which steel materials are assigned to the final pile and in the order of transportation. Therefore, the solution space becomes large, it takes time to find the solution, and when applied to a real-scale problem (for example, a problem in which the number of steel materials to be transported is 30 or more), within an allowable calculation time (for example, about 5 minutes) There is a possibility that the solution cannot be obtained. Furthermore, the invention described in Patent Document 3 does not consider temporary ridges, so the number of temporary ridges cannot be minimized.

Japanese Patent No. 4935032 Japanese Patent No. 5365759 JP 2010-269929 A JP 2016-81186 A

In the mountain transshipment problem, that is, the problem of transshipping metal materials from a given initial pile shape to an unknown appropriate final pile shape, the temporary pile generated in the transshipment process and the temporary pile formed by it are To take this into account, it is necessary to simultaneously optimize the appearance of the final pile, the order of transportation of the metal materials, and the appearance of the temporary pile when reloading the metal materials from the initial pile to the final pile. However, the conventional technology has not solved this problem.
The present invention has been made in view of the above-described problems, and is designed to provide a final pile shape, a conveying order of the metal materials, and a temporary pile when reloading the metal materials from the initial pile to the final pile. The purpose is to realize simultaneous optimization of the shape within the time available for actual operation.

The yard management device of the present invention transports an initial pile of metal materials piled up in a yard, which is a storage site between processes, by a transport device, and stacks the metal materials according to the delivery order to the post-process of the yard. A yard management device for creating a final pile of metal materials piled up in order, which determines the relative order of initial transportation, which is transportation from the initial pile, for any two of the metal materials. An initial transfer order variable that is a binary variable; a final transfer order variable that is a binary variable that determines the relative order of final transfer, which is transfer to the final pile, for any two of the metal materials; A final pile assignment variable representing which final pile the metal material belongs to, and a temporary pile consisting of the metal materials piled up in the temporary storage area of the yard, when the metal material is piled up. A temporary pile assignment variable, which is a variable representing which temporary pile belongs to, is used as a decision variable, the identification information of the initial pile and the identification information of the metal material at each lamination position of the initial pile, and the metal material and a constraint expression setting for setting a constraint expression including a first constraint expression and a second constraint expression based on the metal information. means, an evaluation index for evaluating the number of the final piles, an evaluation index for evaluating the number of the metal materials temporarily placed in the temporary storage site of the yard, and an evaluation index for evaluating the number of the temporary piles. and an objective function setting means for setting an objective function containing based on the metal material information; and an optimization calculation means for executing optimization calculation by mathematical programming, wherein the first constraint expression is, for any two of the metal materials, the distance from the initial mountain When the order of transportation is different from the order of transportation to the final stack, the metal material that is transported first from the initial pile among the two metal materials is temporarily stored in the temporary storage site. It is a constraint expression that expresses using the decision variable that it is necessary to do so, and the second constraint expression is that in order for any two of the metal materials to be piled on the same temporary pile, and a constraint expression that expresses, using the decision variable, that the order of transportation from the initial pile and the order of conveyance to the final pile must be different for the two metal materials. characterized by

In the yard management method apparatus of the present invention, an initial pile of metal materials piled up in a yard, which is a storage site between processes, is transported by a transport device, and the metal materials are delivered to the post-process of the yard according to the order of delivery. A yard management method for creating a final pile consisting of metal materials piled in the order of stacking, wherein the relative order of initial transportation, which is transportation from the initial pile, for any two of the metal materials An initial transport order variable that is a binary variable that defines a final transport order variable that is a binary variable that determines the relative order of final transport, which is transport to the final mountain, for any two of the metal materials, When the metal material is piled up in a temporary pile consisting of a final pile assignment variable that is a variable representing which final pile the metal material belongs to, and a metal material that is piled up in the temporary storage site of the yard, the metal material A temporary pile assignment variable, which is a variable indicating which temporary pile a material belongs to, is used as a decision variable. and a metal material information acquisition step of acquiring metal material information including the identification information of the metal material and the order of dispensing of the metal material ; is set based on the metal material information, and the objective function setting means performs an evaluation index for evaluating the number of the final piles, and the metal material that is temporarily placed in the temporary storage site of the yard. and an evaluation index for evaluating the number of temporary peaks based on the metal material information ; an optimization calculation step of deriving the value of the decision variable when the value of the objective function is the minimum or maximum within the range satisfying and the first constraint expression is such that, for any two of the metal materials, if the order of transportation from the initial pile is different from the order of conveyance to the final pile, the two A constraint expression that expresses, using the decision variable, that the metal material that is first conveyed from the initial pile needs to be temporarily placed in the temporary storage site, and the second In order for any two of the metal materials to be stacked on the same temporary pile, the two metal materials must be transported from the initial pile and to the final pile. is a constraint expression that uses the decision variable to express that the order of transportation of must be different from that of It is characterized by

A program of the present invention is characterized by causing a computer to function as each means of the yard management apparatus.

According to the present invention, it is possible to simultaneously optimize the shape of the final pile, the order of transportation of the metal materials, and the shape of the temporary pile when reloading the metal materials from the initial pile to the final pile. can be achieved within a reasonable amount of time.

FIG. 1 is a diagram illustrating an example of a functional configuration of a yard management device; FIG. 2 is a flow chart illustrating an example of a yard management method. FIG. 3 is a diagram showing an example of the form of conveying the steel material when the initial crest has a fixed portion. FIG. 4 is a diagram showing, in tabular form, the results of optimization calculations according to the invention example and the results of optimization calculations according to the technique of the comparative example. FIG. 5 is a diagram showing an example of a yard layout.

An embodiment of the present invention will be described below with reference to the drawings. In each of the following embodiments, in the iron and steel manufacturing process, given the shape of the initial pile, the shape of the final pile, the number of conveyances of each steel material when conveying from the initial pile to the final pile, and the pile of the temporary pile. A case of simultaneously optimizing (deriving) the shape and shape will be described as an example. It should be noted that the steel materials (slabs) manufactured in the steelmaking process are not stacked in the order of transportation to the rolling process in at least a part of the initial pile. Further, in the following description, the order in which the steel materials are conveyed to the rolling process will be referred to as the delivery order as necessary. In addition, steel materials that have not yet been piled up in the yard are referred to as unarrived materials as necessary, and steel materials that are piled up in the yard are referred to as arrived materials as necessary.

<Background>
First, the process of simultaneously optimizing the shape of the final pile, the order of transportation when reloading steel materials from the initial pile to the final pile, and the shape of the temporary pile will be described.
Patent Literature 4 discloses an invention for a case in which a mountain sorting plan is performed for unarrived materials. The problem of transshipment of already-arrived materials (hereinafter referred to as "arrived materials transshipment problem") is the problem of sorting unarrived materials as disclosed in Patent Document 4 (hereinafter referred to as "unarrived materials sorting problem"). There is an essential difference from ), which is shown below.

When the steel materials have not yet arrived at the yard, the order of receipt and delivery of the two steel materials to the yard are the same (that is, the order of receipt and delivery of one of the two steel materials is higher than the If the two steel materials are to be stacked on the same final pile, it is necessary to temporarily place the steel material received in the yard first and change the stacking order. In other words, it is determined whether or not to be temporarily placed based on the relationship between the order of receipt and the order of delivery. On the other hand, when considering the state of arrival at the yard, the element corresponding to the order of receipt is the order of stacking the steel materials on the initial pile. In other words, since it can be accessed from the steel materials piled up in the initial pile, this corresponds to the order of receipt. Here, when the steel materials have not yet arrived at the yard, the "acceptance order" is uniquely ordered for all the steel materials. On the other hand, in the already-arrived state, if there are multiple initial piles, it is possible to access steel materials on different initial piles, so there is a degree of freedom corresponding to the number of initial piles, and the order of transportation cannot be uniquely determined. Therefore, the "already-arrived material transshipment problem", in which the initial state is the state in which steel materials have already arrived at the yard, is better than the "unarrived material sorting problem," in which the initial state is the state in which all steel materials have not yet arrived at the yard. It can be seen that the difficulty of the problem is high.

The difficulty of this "transshipment problem of materials that have already arrived" appears in the difficulty of counting temporary storage, which is one of the evaluations. In other words, the number of temporary placements can be determined by the order in which the steel materials arrive at the yard in the "unarrived material sorting problem", so if the shape of the final pile is determined, it can be determined individually for each pile (influence of other piles). not). On the other hand, in the "problem of transshipment of already-arrived materials", even if a single final pile was given, the temporary placement necessary to construct it included the steel materials that make up the final pile ( (multiple) initial piles, other (multiple) final piles created from those initial piles, the order of transport of steel materials from the initial piles (the order of decomposition of the initial piles), and the final piles It also depends on the order of transportation of the steel materials (the order of assembly of the final pile).

Therefore, in the "already-arrived material transshipment problem", unlike the case of solving the "unarrived material sorting problem", the number of temporary placements cannot be determined for each pile. In other words, in the problem of transshipment of already-arrived materials, when determining the shape of the final pile, the order of transportation has a degree of freedom equivalent to the number of piles in the initial pile. It is not possible to solve the problem of solving the shape of the final mountain that minimizes the number of placements. Furthermore, even if the number of temporary storages is reduced, it is not preferable that the steel materials to be temporarily stored cannot be grouped into the same temporary pile and the temporary storage space increases because the storage space in the yard is limited. Therefore, when determining which steel materials to temporarily store, it is necessary to simultaneously consider what kind of temporary pile the steel materials to be temporarily stored should be put together.

Based on the above findings, the inventors of the present invention have determined the shape of the final pile, the order of transportation of the steel products when reloading the steel products from a given initial pile to the final pile, and the shape of the temporary pile. We have come up with a method to perform simultaneous optimization within the time available for actual operation. A specific example of the technique will be described below.

<First embodiment>
First, the first embodiment will be described.

(problem setting (given element))
In this embodiment, given the initial pile shape and delivery order (rolling order) of each steel material, the final pile shape and the steel material when reloading the steel material from the given initial pile to the final pile are given. To simultaneously optimize the order of transportation and the appearance of temporary piles generated in the process of transshipment transportation. Here, a set of steel material groups is expressed as N={1, 2, . . . , n}. A steel material group refers to a collection of a plurality of steel materials (as a minimum unit) that are not divided when transported by transport equipment (mainly a crane). Therefore, when a steel material is conveyed in units of one sheet, the steel material group is regarded as a steel material. In this embodiment, it is assumed that the final pile formation, the provisional pile formation, and the transportation are performed in units of steel material groups. Also, the final pile is assumed to be a pile piled up in order of payout from the top.

(Assumption)
In this embodiment, under the following assumptions (1) and (2), the shape of the final pile, the transportation order of the steel products when reloading the steel products from a given initial pile to the final pile, and the provisional To optimize the appearance of mountains at the same time.
(1) The maximum number of transports from the initial stack (initial storage site) to the final stack (final storage site) is two for any steel material. That is, it is assumed that the steel materials to be transported twice are placed temporarily. In addition, the steel materials transported to a temporary pile (temporary storage site) shall always be transported to the final pile (final storage site) the next time they are transported, and shall not be transported between different temporary piles (temporary storage sites). do.
(2) The storage sites for the initial pile and the final pile are different, and it is assumed that all steel materials must be transported from the initial pile (initial storage site) to the final pile (final storage site). be covered).

(Elements to be determined and their evaluation methods)
As described above, in the present embodiment, the shape of the final pile, the shape of the temporary pile, and the order of transport of steel materials when transferring steel materials from a given initial pile to the final pile are optimized at the same time. Specifically, it is as shown in (I) to (III) below.
(I) Configuration of the final pile: Find the shape of all the final piles stacked in order of payout from the top. The appearance of the final pile satisfies the stacking form constraint, and the smaller the total number of final piles, the higher the evaluation.
(II) Configuration of temporary mountain: In the process of creating the final mountain, the shape of the temporary mountain to be created primarily is obtained. It is required that the piles of temporary piles are stacked in order from the top to the final pile. The appearance of the temporary pile satisfies the stacking shape constraint, and the smaller the total number of temporary piles, the higher the evaluation.
(III) Conveyance order: From the initial mountain shape (given) to the final mountain (above (I)) (when temporarily placed, transportation from the initial mountain to the temporary mountain, Find all delivery orders (including delivery order to ). The smaller the total number of transports, the higher the evaluation.

(stacking restrictions)
In addition, in this embodiment, the following width restrictions, length restrictions, height restrictions, restrictions on steel material pairs that are prohibited from being placed on the final mountain (set of steel material pairs that are prohibited from being placed on the same final mountain), and placement on temporary mountains Restrictions on steel material pairs that are prohibited (set of steel material pairs prohibited from stacking up and down the same temporary pile) are set as stacking restrictions.
・Width constraint If the maximum width of a steel group is narrower than the minimum width of the steel group located below the steel group, the steel group is placed above the steel group located below. placed unconditionally. When the maximum width of a certain steel group is wider than the minimum width of the steel group located below the certain steel group, the difference between the two widths is a reference value (for example, 200 [mm]) determined by work constraints. ), then the given steel group can be placed above the lower steel group, but not beyond.

That is, the width constraint is satisfied when the maximum width of a certain steel group is narrower than the minimum width of the steel group located below the certain steel group, and when the maximum width of a certain steel group is less than the is wider than the minimum width of the steel material group located below the steel material group, and the difference between the two widths is less than a reference value (for example, 200 [mm]).

・Length constraint If the maximum length of a steel group is shorter than the minimum length of the steel group located below the steel group, the steel group is placed above the steel group located below. can be placed unconditionally. If the maximum length of a certain steel material group is longer than the minimum length of the steel material group located under the certain steel material group, the difference between the two lengths is a reference value (for example, 2000 [mm ]), then the given steel group can be placed above the lower steel group, but not beyond.

That is, the length constraint is satisfied when the maximum length of a steel group is shorter than the minimum length of the steel group below it, and when the maximum length of a steel group is less than the minimum length of the steel group below it. This is the case where the length is longer than the minimum length of a steel material group positioned below a certain steel material group, and the difference between the two lengths is less than a reference value (for example, 2000 [mm]).

・Height restriction The number of stacking layers h of the final pile must be less than the upper limit h _max of the number of steel materials that can be piled as the final pile. The upper limit h _max of the number of steel materials that can be piled as the final pile is 10, for example.

・Assemblage F of steel pairs prohibited from arranging on the same final pile
Due to the width and length constraints described above, for any pair of steel groups (two steel groups) {s, s'}⊆N, it is unique whether the steel groups s and s' can be stacked on the same final pile. Determined by Therefore, the same final peak placement prohibited steel material pair set F is defined as in the following equations (1) and (2). Here, s and s' are identification information (steel material group ID) that uniquely identifies each steel material group (this also applies to s'' described later). In the present embodiment, the steel material group ID is assumed to match the payout order of the steel material group identified by the steel material group ID.

Here, as explained in (problem setting (given element)), ``the shape of the final mountain is determined in the order of disbursement from the top of the final mountain'', and the ``stacking constraint (width constraint and length Constraint)" uniquely determines whether or not the steel material groups s, s' can be stacked on the same final pile for any pair of steel material groups {s, s'}⊆N. The former condition determines the order of stacking of the steel material groups on the final pile, and when the steel material groups are stacked in this vertical relationship, if the latter condition (at least one of the width and length restrictions) is violated, Those steel groups will not be piled into the same final pile. Therefore, as in equation (2), a set of steel material group pairs (prohibited pairs) that cannot be piled on the same final pile can be defined as the same final pile prohibited steel material pair set F.

・Assembly F' of steel material pairs prohibited from stacking up and down on the same temporary pile
As explained in (Problem setting (given element)), the payout order is given, so in the final pile, this payout order determines the order of stacking of the steel material groups in the final pile. On the other hand, the order of transportation from the temporary pile to the final pile is unknown (decision variable). Therefore, when defining a pair of steel material groups that cannot be piled on the same temporary pile (prohibited pair), it is necessary to specify the order of stacking of the steel material groups s and s' on the temporary pile. Therefore, as shown in the following equation (3), regardless of the payout order, in the same temporary pile, when the steel material group s is stacked below and the steel material group s' is stacked above it, the stacking shape constraint (width constraint and (length constraint) is expressed as (s, s'), and a set having these as elements is defined as a steel material pair set for prohibiting stacking of the same temporary pile F'.

(Constraint)
(i) The final pile shall meet the stacking shape restrictions and shall be stacked in the order of disbursement from top to bottom.
(ii) The steel of each initial pile can only be conveyed from the top of the initial pile.
(iii) When creating the final stack, stacking can only be done from the bottom to the top.
As mentioned above, the number of times of transportation from the initial stack (initial storage site) to the final stack (final storage site) is two at maximum for any steel material (see (1) of the above (assumed)). Minimizing the number of transports is equivalent to minimizing the number of temporary placements.

<Decision variable>
In this embodiment, for any pair of steel material groups, a variable that determines the order in which the steel material groups are removed from the initial pile, a variable that determines the order in which the steel material groups are placed in the final pile, and a variable that determines which temporary pile the arbitrary steel material group A variable indicating whether or not the steel material group belongs to the position t, a variable indicating whether or not to use the temporary crest position t, a variable indicating which final crest position l an arbitrary steel group belongs to, and the final crest position l are used. A variable that indicates whether or not to perform is defined as a decision variable. The position of the final pile indicates the position where the final pile is made in the yard (the position of the final storage place). The temporary pile position refers to the position where the temporary pile is created in the yard (the position of the temporary storage site).

In the following description, a variable that determines the order in which steel material groups are removed from an initial pile for an arbitrary pair of steel material groups will be referred to as an initial transfer order variable y(s, s') as necessary. Also, a variable that determines the order in which the steel material groups are placed on the final pile is called a final transfer order variable z(s, s') as necessary. A variable indicating which temporary pile position t an arbitrary steel material group s belongs to is called a temporary pile position assignment variable p(s, t) as required. A variable indicating whether or not to use the temporary ridge position t will be referred to as a temporary ridge presence/absence variable q(t) as required. A variable representing which final crest position l an arbitrary steel material group s belongs to is referred to as a final crest allocation variable r(s, l) as required. A variable indicating whether or not to use the final peak position l is called a final peak presence/absence variable δ(l) as required.

(a) Initial transfer order variable y(s, s'): Number of variables = _n C ₂
Let G=(N, E) be a fully directed graph in which each element of a set N of steel material groups has one vertex. Then E={(s, s')εN ² |s≠s'). A 0-1 variable y(e) (∀eεE) defined on the directed edge set E is introduced, and an initial transport order variable y(s, s') is defined as in the following equation (4). do. The initial transfer order variable y(s, s') is a variable that defines the relative order of initial transfer of the two steel product groups s, s'. Here, the initial transport means transporting the steel material group in the initial pile to the final pile (final storage site) or temporary pile (temporary storage site).

(b) Final delivery order variable z(s, s'): Number of variables = _n C ₂
In the same way as the initial transfer order variable y(s, s'), a 0-1 variable z(e) (∀eεE) defined on the directed edge set E is introduced, and the following equation (5) Define the final transfer order variable z(s, s') as follows. The final transfer order variable z(s, s') is a variable that defines the relative order of the final transfer of the two steel product groups s, s'. Here, final transport means transporting the steel materials in the initial pile or temporary pile (temporary storage site) to the final pile (final storage site).

(c) Temporary mountain position assignment variable p(s, t): Number of variables = n x t _max
The temporary pile assignment variable p(s, t) is a 0-1 variable representing whether or not the steel material group s (εN) is temporarily placed at the temporary pile position t (εT). Therefore, a temporary ridge position assignment variable p(s, t) is defined as in the following equation (6). t _max is the maximum value of the number assumed as the number of temporary ridge positions. t _max is, for example, the number of steel material groups n.

(d) Temporary mountain presence/absence variable q(t): number of variables = t _max
The temporary ridge presence/absence variable q(t) is a 0-1 variable representing whether or not the temporary ridge position t is used (whether or not there is a temporary ridge at the temporary ridge position t). Therefore, a temporary peak presence/absence variable q(t) is defined as in the following equation (7). t _max is the maximum number assumed as the number of false peaks. t _max is, for example, the number of steel material groups n.

(e) final peak assignment variable r(s, l): number of variables = n x L _max
The final peak assignment variable r(s, l) is a 0-1 variable that specifies the final peak position l (εL) at which the steel material group s (εN) is placed. Therefore, the final peak allocation variable r(s, l) is defined as in the following equation (8). L _max is the maximum number of possible final crests. L _max is, for example, the number of steel material groups n.

(f) final peak presence/absence variable δ(l): number of variables L _max
The final peak presence/absence variable δ(l) is a 0-1 variable representing whether or not the final peak position l is used (whether or not there is a final peak at the final peak position l). Therefore, the final peak presence/absence variable δ(l) is defined as in the following equation (9).

(Functional configuration of yard management device 100)
FIG. 1 is a diagram showing an example of a functional configuration of the yard management device 100. As shown in FIG. The hardware of the yard management device 100 is realized by using, for example, a CPU, ROM, RAM, HDD, and an information processing device having various interfaces, or dedicated hardware. FIG. 2 is a flowchart illustrating an example of a yard management method executed by the yard management device 100. As shown in FIG.
[Steel material information acquisition unit 101, step S201]
The steel material information acquisition unit 101 acquires steel material information about steel materials to be piled up. The steel material information includes steel material group information, information specifying the initial mountain shape of each steel material group, and information specifying the maximum height of the mountain.

The steel group information includes identification information, delivery order, number of steels, and Includes maximum width, minimum width, maximum length, and minimum length information. A steel material group refers to a group of steel materials that are not divided (as a minimum unit) when transported by transport equipment (mainly a crane).
The identification information is identification information (steel material group ID) that uniquely identifies each steel material group.
The delivery order is the delivery order of each steel material group (the order of transportation to the rolling process).

The number of steel materials (w: N→Z+) is the number of steel materials constituting each steel material group. The number w(i) of steel materials included in one steel material group is, for example, 1 or more and 6 or less (∀iεN, 1≤w(i)≤6). In this way, a steel material group may include not only a plurality of steel materials but also only one steel material.
The maximum width and minimum width are respectively the maximum width and minimum width of the steel materials forming each steel material group.
The maximum length and minimum length are respectively the maximum length and minimum length of the steel materials forming each steel material group.

The information specifying the shape of the initial pile includes an initial pile ID, which is identification information that uniquely identifies the initial pile, and a steel material group ID located on each stack of the initial pile identified by the initial pile ID. .
As described above, the initial mountain includes already-arrived mountains and virtual mountains. An already-arrived pile is a pile piled up in the yard at the time when the steel material information is created (that is, when the final pile is created) among the steel materials for which the final pile is to be created. Of the steel materials to be created for the final pile, the virtual pile is the steel material that has not yet been piled in the yard at the time the steel information is created (that is, the time at which the final pile is created). It is a pile when it is assumed that the early ones are piled up. In this embodiment, all the steel materials that have not yet arrived at the yard and have not yet been piled up among the steel materials for which the final pile is to be created are piled up in one virtual pile. As described above, in this embodiment, it is assumed that steel materials that have not yet arrived at the yard and have not yet been piled up are also piled up as virtual piles (that is, all steel materials to be created as the final pile are piled up in the yard). ), given its stack.

The information specifying the maximum height of the pile is information including the upper limit h _max (εZ+) of the number of steel materials that can be piled as the final pile. The upper limit h _max of the number of steel materials that can be piled as temporary piles and final piles is 10, for example. Here, assuming that each steel material has the same thickness, the information specifying the maximum height of the pile is used as the upper limit of the number of steel materials that can be piled up as the final pile. When information on the thickness of each steel material is included in the steel material information, the maximum height of the final crest may be used as the information specifying the maximum height of the crest.
In addition, when all the steel materials to be created for the final pile are transported one by one, the identification information (steel material ID), delivery order, width, and length information for each steel material are used instead of the steel material group information. to be obtained. In addition, as information for specifying the shape of the initial pile, the identification information of the initial pile (initial pile ID) is acquired, and instead of the steel material group ID located on each stack of the initial pile, each pile of the initial pile A steel ID located in the step is obtained.
Examples of the acquisition form of the steel material information include input operation of the user interface of the yard management device 100, transmission from an external device, or reading from a portable storage medium.

[Constraint expression/objective function setting unit 102, steps S202 and S203]
The constraint expression/objective function setting unit 102 sets the constraint expression that expresses the above-mentioned constraint by a mathematical expression and the objective function that expresses the above-mentioned purpose by a mathematical expression.
<<constraint expression>>
First, the constraint formula will be explained.
(a) Definition constraint of initial transfer order variable y(s, s') ) and is transitive (referring to the following binary relationship of the following (11)), the initial transport The forward variable y(s, s') satisfies the perfect law (comparable) represented by the linear equation of the following equation (10) and the transitive law represented by the linear inequality of the following equation (11). Also, an initial transfer order variable y(s, s') that satisfies the following equations (10) and (11) corresponds to the total order of the steel material groups.

Equation (10) indicates that one of the initial transport of the steel group s and the initial transport of the steel group s' always precedes the other. Note that these two steel groups are separate steel groups.
Equation (11) is given by , indicates that the initial transfer of the steel group s precedes the initial transfer of the steel group s''. These three steel material groups are different steel material groups.

Also, the work of removing the steel material group from the initial pile must be done in order from the top of each initial pile. Therefore, when the steel material group s' is lower than the steel material group s in the same initial mountain, the following linear equation (12) holds for the two steel material groups s and s' .

（ｂ）最終山への搬送制約
任意の２つの鋼材グループを最終山に配置（搬送）する順序も、任意の２つの鋼材グループを初期山から取り除く順序と同様に、鋼材グループの集合Ｎの全順序（反対称且つ完全（以下の（１３）式）であり、推移的（以下の（１４）式）な二項関係を言う）となることから、任意の２つの鋼材グループｓ、ｓ'を最終山に配置する相対的な順序を定める最終搬送順変数ｚ（ｓ，ｓ'）は、以下の（１３）式の線形等式で表される完全律（比較可能)および以下の（１４）式の線形不等式で表される推移律を満たす。また、以下の（１３）式および（１４）式を満たす最終搬送順変数ｚ（ｓ，ｓ'）も、鋼材グループの全順序に対応する。

(b) Conveyance Constraints to the Final Mountain Since it is an order (antisymmetric and complete (formula (13) below) and transitive (refers to formula (14) below), any two steel groups s and s' can be The final transport order variable z (s, s'), which determines the relative order of placement on the final mountain, is represented by the following linear equation (13), which is a complete rule (comparable) and (14) below. satisfies the transitive law expressed by the linear inequality of Eq. Also, the final transfer order variable z(s, s') that satisfies the following equations (13) and (14) also corresponds to the total order of the steel material groups.

Equation (13) indicates that the final transport of the steel group s and the final transport of the steel group s' are always preceded by one. Note that these two steel groups s, s' are separate steel groups.
Equation (14) is given by , indicates that the last delivery s of the steel group is prior to the last delivery of the steel group s''. These three steel material groups are different steel material groups.

(c) Constraints on the final transport order associated with transport to the final pile The order in which two arbitrary steel material groups are placed (transported) to the final pile is the order of stacking when counting from the bottom of the final pile for each final pile. handle. For example, for a certain final pile, the order of stacking from the bottom of the steel material group that is first conveyed to the final pile is 1, and the steel material that is secondly conveyed to the final pile. The stacking order is 2 when counting from the bottom of the last mountain of the group. Therefore, when the steel material group s whose payout order is relatively earlier and the steel material group s' whose payout order is relatively later are placed on the same final mountain (that is, s<s', r(s, l )=1 and r(s′, l)=1), those steel material groups s and s′ must be stacked from the top in the order of disbursement on the final pile. Therefore, in this case, the final transportation of the steel material group s' must precede the final transportation of the steel material group s, and the following linear inequality (15) holds. Incidentally, as described above, the steel material group ID is assumed to match the payout order of the steel material group identified by the steel material group ID.

(d) Temporary Placement Constraint For any two steel groups s and s′, the steel group s is initially conveyed before the steel group s′ (that is, y(s, s′)=1) and the steel group If s' is to be final-conveyed before steel group s (i.e., z(s', s) = 1), steel group s is removed from the initial pile, then steel group s' is removed, and the final pile has The steel group s must be placed after the steel group s' is placed. That is, in the two steel material groups s and s', since the order of the initial transportation is different from the order of the final transportation, the steel material group s must be temporarily placed. This is expressed as a linear inequality of the following equation (16) using the temporary peak position assignment variable p(s, t). In equation (16), Σ _t∈T p(s, t) is always 1 for the steel material group s that requires temporary placement.

(e) Constraints on Dividing to the Final Mountain Constraints on dividing the mountains to the final mountain include the following equations (17) to (19).
First, as in the linear equation of equation (17) below, the final pile assignment variable r(s,l) is used to represent that all steel groups must be piled to some final pile. Use constraint expressions.

Moreover, the following (18) Formula is used as a constraint formula showing stacking|stacking restrictions mentioned above. Constraint expressions representing the width constraint and the length constraint are expressed as the following linear inequalities in the following equation (18) using the same final peak arrangement prohibited steel material pair set F defined by the equation (2).

Equation (18) states that when a pair of steel material groups s, s' belongs to the same final pile arrangement prohibited steel material pair set F, the pair of steel material groups s, s' cannot be piled on the same final pile. represents
Also, the constraint expression representing the height constraint is expressed as the following linear inequality in equation (19) using the final peak presence/absence variable δ(l) defined in equation (9). It should be noted that the following linear inequality of formula (20) may be used instead of formula (19). By using either formula (19) or formula (20), it is possible to impose a restriction so that the number of steel materials that can be piled up as the final pile does not exceed the upper limit. In equations (19) and (20), w(s) is the number of steel materials included in the steel material group identified by variable s.

(f) Constraints on the definition of the final peak presence/absence variable δ(l) The final peak presence/absence variable δ(l) is expressed by the linear inequality of the following equation (21) using the final peak assignment variable r(s, l). Defined.

(g) Constraint to Distinguish the Position of the Final Mountain The constraint to distinguish the position of the final crest is a constraint for distinguishing (the position of) the final crest l. In this embodiment, as in the linear inequality of the following equation (22), the final crest position discrimination constraint is such that the smaller the variable l, the higher the final crest (the number of steel materials included in the final crest is increased). It shall be a constraint that expresses

The final peak position discrimination constraint is not necessarily a necessary constraint. However, there is a possibility that the calculation time can be reduced by the final peak position discrimination constraint.

(h) Same Temporary Pile Possibility Constraint In the steel material group pair s, s' temporarily placed at the same temporary pile position t, the permutation represented by the initial transfer order variable y(s, s') and the final transfer order variable It must be in the reverse order of the permutation represented by z(s, s'). After a certain steel material group s is transported from the initial pile to the temporary pile and stacked on the temporary pile, another steel material group s' is transported from the initial pile to the temporary pile and stacked on the certain steel material group s. This is because the other steel material group s' is finally conveyed before the certain steel material group s. That is, if two arbitrary steel material groups s and s' are temporarily placed at the same temporary pile position t (that is, p(s, t)=p(s', t)=1), the steel material group s , s′ are reversed in order of initial transfer and final transfer (ie, y(s, s′)=z(s′, s)). If this is represented by a linear inequality, it becomes like the linear inequality of the following equation (23).

If at least one of the two arbitrary steel material groups s and s' is not temporarily placed at the temporary pile position t (that is, p(s, t) + p(s', t) < 2), (23) p (s, t) + p (s ', t) -2 becomes -2 or -1 (that is, -1 or less), and 2-p (s, t) of formula (23) -p(s',t) will be 2 or 1 (ie, 1 or greater). Therefore, when neither of the steel material groups s, s' is temporarily placed at the temporary pile position t, -2≤y(s, s')-z(s', s)≤2. Further, when one of the steel material groups s and s' is temporarily placed at the temporary pile position t and the other is not temporarily placed at the temporary pile position t, the equation (23) is -1 ≤ y(s, s') - z (s', s)≤1, and either the initial transfer order variable y(s, s') or the final transfer order variable z(s', s) may be set to 0 (zero), or both may be set to 1, Alternatively, both may be set to 0 (zero). Therefore, if at least one of the two arbitrary steel material groups s, s' is not temporarily placed at the temporary pile position t, the initial transfer order variable y(s, s') for the steel material groups s, s' and The value of the final transfer order variable z(s', s) is not subject to any restrictions.

(i) Temporary pile shape constraint The temporary pile shape constraint includes the following formulas (24) to (25).
First, the constraint expression representing the width constraint and the length constraint is expressed as a linear inequality in the following equation (24) using the same temporary pile prohibition steel material pair set F′ defined by equation (3). be done.

Equation (24) becomes a self-explanatory inequality when any one of the three terms on the left side is 0 (zero). Therefore, expression (24) is a constraint expression that prohibits the three terms on the left side from being 1 together. Specifically, formula (24) defines steel groups s and s' that violate stacking constraints (width and length constraints) when steel group s is stacked below and steel group s' is stacked above it. (p(s, t) = p(s', t) = 1), and (z(s , s′)=1) are prohibited from being satisfied at the same time. In other words, the formula (24) applies to steel groups s and s' that violate the stacking constraints (width and length constraints) when the steel group s is stacked below and the steel group s' is stacked above it. When the group s is initially transported before the steel material group s', the steel material groups s and s' are not temporarily placed at the same temporary pile position l.

A constraint expression representing the height constraint is expressed as a linear inequality of the following equation (25) using the temporary peak position assignment variable p(s, t) defined by the equation (6). Instead of the equation (25), the following linear inequality of the equation (26) may be used using the variable q(t) defined by the equation (7). By using either formula (25) or formula (26), it is possible to impose a restriction so that the number of steel materials that can be piled up as a temporary pile does not exceed the upper limit. Similar to the expressions (19) and (20), in the expressions (25) and (26), w(s) is the number of steel members included in the steel member group specified by the variable s.

(j) Temporary ridge position distinction constraint The temporary ridge position distinction constraint is a constraint for distinguishing the temporary ridge position t. In this embodiment, as in the following linear inequality (27), the provisional ridge position discrimination constraint is a constraint indicating that provisional ridge positions are used in ascending order of variable t. In addition, as in the linear inequality of the following equation (28), with regard to the variable q(t) for the presence or absence of temporary ridges, when the steel material group s is arranged at the temporary ridge position t, the temporary ridge position t must be used. Use a constraint expression that expresses

It should be noted that the provisional crest position discrimination constraint of formula (27) is not necessarily a necessary constraint, as is the final crest position discrimination constraint of formula (22) described above. However, there is a possibility that the calculation time can be reduced due to the provisional mountain position distinction constraint of the equation (27). Also, when using the formula (26), the formula (28) may or may not be used.

The constraint expression/objective function setting unit 102 sets variables s, s', By setting s'', k, w(s), h _max , L _max and t _max , equations (10) to (19), equations (21) to (25), and equations (27) to (28) Set the constraint expression of the expression. As described above, the formula (20) may be used instead of the formula (19), and the formula (26) may be used instead of the formula (25).

For the formulas (10), (13), (16) and (23), s and s' are set for each combination of any two steel material groups in the set N of steel material groups. For the formulas (11) and (14), s, s', and s'' are set for each combination of any three steel material groups in the set N of steel material groups.

(12) When setting the formula, from the initial mountain shape identification information, the steel group relatively lower and the steel group higher in the same initial mountain are identified, and the upper of the two steel groups is identified. Let s be the variable set for the steel group below, and s' be the variable set for the steel group below.

Also, when setting the formula (15), the payout order of each steel group is specified from the steel group information, and the variable be s and the variable set for the subsequent steel group is s'.
Also, when setting the equation (18), s and s' are set for each combination of two steel material groups that must not be stacked on the same final pile (that is, the same final pile prohibited steel material pair set F). do.
Also, when setting the formula (24), two steel groups s that must not be stacked on the same temporary pile, with the steel group s below and the steel group s′ above it, out of the combination of the two steel groups , s' (that is, steel material pair set F' for which vertical stacking of the same temporary pile is prohibited) is set.

<<objective function>>
Next, the objective function will be explained.
As described above, in the present embodiment, the purpose is to reduce the number of final piles, the total number of conveying times of steel material groups (that is, the number of temporarily placed steel material groups), and the number of temporary piles. , an objective function J given by the following equation (29) is used.

In equation (29), the weighting factors k ₁ , k ₂ , and k ₃ are set in advance depending on how much weight is given to each evaluation item. It represents the balance of the evaluation between the total number of transports and the number of temporary piles). For example, when the number of crests in the final crest is more important than the total number of conveying times and the _number of temporary crests in _a steel material group _, the magnitude of weighting factor k1 is the magnitude of weighting factors k2 and k3. make it bigger than
For example, the constraint expression/objective function setting unit 102 sets the variables s, N, L, T, k ₁ , k ₂ , and k ₃ to the expression (29) to obtain the objective function J set.

[Optimization calculation unit 103, step S204]
The optimization calculation unit 103 satisfies the constraint equations (10) to (19), (21) to (25), and (27) to (28), and the expression (29) Initial transfer order variable y(s, s'), final transfer order variable z(s, s'), temporary pile position assignment variable p(s, t), presence/absence of temporary pile when the value of the objective function J is minimized A variable q(t), a final mountain assignment variable r(s,l), and a final mountain presence/absence variable δ(l) are calculated as optimal solutions. Also, the calculation of the optimum solution can be realized by using a known algorithm (including use of solver, etc.) for solving the optimization problem by mathematical programming such as mixed integer programming.

[Post-processing unit 104, step S205]
When the initial transfer order variable y(s, s') is derived as described above, it is possible to determine the initial transfer order (the order of removal from the initial pile) of each steel material group included in the set N of steel material groups. can. However, the final transport order (from the temporary _pile (temporary storage place) to the final pile (final storage place) Since the order of transfer to the first transfer) is not determined in relation to the initial order of transfer, it is necessary to determine this. That is, it is necessary to determine where in the initial transfer order determined as described above the final transfer order of the steel material group determined to cause temporary placement should be interrupted. Therefore, in the present embodiment, the post-processing unit 104 determines the final transport order of each steel material group as follows.

A steel material group that is determined to be temporarily placed needs to be transported twice, an initial transport and a final transport. On the other hand, for the steel material group determined that temporary placement does not occur, the initial transportation and the final transportation coincide. Therefore, for a steel material group determined to be temporarily placed, the final transportation from the temporary storage site to the final pile is regarded as the initial transportation of the virtual steel material group. Then, the original steel material ID corresponding to the initial transfer and the steel material ID corresponding to the virtual steel material group corresponding to the final transfer are set as variables s. That is, for the steel group, two variables s are set as if there are two virtual different steel groups. Therefore, the number of steel material groups to be transported here is a value obtained by adding the number of steel material groups determined to be temporarily placed to the number of steel material groups to be actually transported. By changing the information given to the algorithm described above in this way, all the steel material groups to be transported can be reloaded from the initial pile to the final pile by the initial transport, and the final transport order of each steel material group can be obtained. be able to. Specifically, the algorithm described above is modified as follows. In the following description, a steel material group determined to be temporarily placed will be referred to as a temporary placement target steel material group as necessary.

A variable s is a variable that specifies the initial transport, and is set for each steel material group included in the set N of steel material groups. Two variables s are set for the temporary placement target steel material group. In this embodiment, the variable s for each steel group is the steel group ID of that steel group. Therefore, an ID different from the steel material group ID is set as a virtual steel material group ID for each steel material group to be temporarily placed. Then, the steel group ID of the temporary placement target steel group and the virtual steel group ID set for the temporary placement target steel group are set as two variables s for the temporary placement target steel group. Assuming that the number of steel material groups to be temporarily placed is m and the virtual steel material group set is M, the number of variables s is (n+m). In this way, two variables s specifying the initial transport are set for the temporary placement target steel material group. One of these two variables, s, specifies the initial transfer from the initial pile, and the other specifies the final transfer from the false pile (treat this as the initial transfer of the virtual steel group, as described above). A variable to specify. As described above, by regarding a steel material group determined to cause temporary placement as two steel material groups, the steel material group is transported twice (initial transportation from the initial pile to the temporary pile, and from the temporary pile to the final pile). ) can be treated as initial transfers, respectively.

Next, for the temporary placement target steel material group specified by the variable s that specifies the initial transportation from the initial mountain, the initial transportation order variable y (s , s′), the steel group is piled up in order from the top in order of the initial transport order. The number of tiers of this first mountain is n. In addition, to each stack of this first pile, the steel material group ID of the corresponding steel material group is assigned from the top according to the initial transfer order calculated by the optimization calculation unit 103 . On the other hand, for the steel material group determined to be temporarily placed by the optimization calculation unit 103, the virtual initial peak when considering the final transportation is set to the virtual second peak with the number of stacking stages of two. The second row of the second mountain is s, which is the steel material group ID of the steel material group that constitutes the second mountain. ) (the number of first peaks is one, and the number of second peaks is the number of steel groups determined to be temporarily placed by the optimization calculation unit 103). .

Here, as the initial pile, the first pile with the stacking number n is created because the initial transfer order of all the steel material groups determined by the optimization calculation unit 103 (step S204) is applied to the post-processing unit 104 (step This is to maintain the transfer order obtained by S205). The reason why the second pile corresponding to the steel material group to be temporarily placed and which has two stacking levels is formed is to define the order of initial transportation and final transportation for the steel material group to be temporarily placed. By assigning the steel material group ID corresponding to the initial transport of the steel material group to be temporarily placed redundantly to both the first pile with the number of stacks n and the second pile of the number of stacks of 2, the steel material group to be temporarily placed is The post-processing unit 104 (step S205) simultaneously determines the order relationship between the initial transport and the initial transport of the steel material group going straight to the final pile, and the order relationship between the initial transport and the final transport of the steel material group to be temporarily placed. .
Next, the final mountain shape is obtained by replacing the steel material ID of the steel material group to be the temporary storage target steel material group with the virtual steel material group ID given to the temporary storage target steel material group in the final mountain shape identification information. becomes.

The post-processing unit 104 sets variables s, s', and s'' for the constraint equations (10) to (12). However, the set N in equations (10) and (11) shall be replaced with N∪T. Equation (12) is also applied to the first peak and the second peak. Furthermore, in the final mountain obtained in the main processing, the steel group s' to which the initial transfer specified by the variable s' is performed is higher than the steel group s to which the initial transfer specified by the variable s is performed. , the following equation (30) holds for the pair {s, s'}⊆N of the steel group. Here, x(s) is "1" if the initial transport of the steel material group from the initial pile to the final pile is transport to a temporary pile (temporary storage site), otherwise It is a 0-1 variable (temporary placement occurrence/non-occurrence variable) that becomes "0 (zero)" in each case (the number of variables=n).

Then, the post-processing unit 104 performs an initial A transfer order variable y(s, s') is calculated as an optimum solution.

Alternatively, since it is clear that the objective function of equation (31) is "0" in this post-processing, instead of using the objective function of equation (31), the following constraint equation of equation (32) is used. You can add it.

The post-processing unit 104 determines the initial pile of each steel material group included in the steel material group set N and the virtual steel material group set T based on the optimum solution of the initial transfer order variable y(s, s′) calculated in this way. to the final pile.

[Output unit 105, step S206]
The output unit 105 outputs the information derived by the post-processing unit 104 indicating the order in which the steel materials included in the steel material set N and the virtual steel material group set T are conveyed from the initial pile to the final pile. The form of output includes at least one of display on a computer display, storage in a storage medium inside or outside the yard management device 100, and transmission to an external device. External devices include, for example, a crane or a control device that controls the operation of a crane.

(summary)
As described above, in the present embodiment, the yard management device 100 uses the initial transport order variable y (s, s′), which is a binary variable that determines the relative order of the initial transport of any two steel material groups, and the yard The management device 100 includes a final transfer order variable z(s, s'), which is a binary variable that defines the relative order of final transfer of any two steel groups, and a final pile on which the steel group is placed. Using the final peak assignment variable r (s, l), which is a variable representing whether or Therefore, of the two steel groups whose order of initial transportation is different from that of their final transportation, the linear inequality that expresses that the temporary placement of the steel group that is initially transported first is required, and the same temporary pile Constraint expressions including a linear inequality expressing that the order of initial transportation and the order of final transportation of the two steel material groups to be temporarily placed are reversed are set. Then, the yard management device 100 determines that the number of final piles, the occurrence of temporary placement, and the number of piles of temporary piles are minimized according to the balance of these evaluations so as to satisfy the set constraint formula. Initial transfer order variable y (s, s'), final transfer order variable z (s, s'), final peak allocation variable r (s, l), when the value of the objective function J to be aimed at is minimized, Temporary pile position assignment variables p(s, t) are derived, and based on these, the transfer order from the initial pile to the final pile of each steel material group included in the set N of steel material groups is derived. Therefore, it is possible to simultaneously optimize the shape of the final pile when transferring the steel material groups from the initial pile to the final pile, the order of transportation of the steel material groups, and the shape of the temporary pile within the time that can be used in actual operation. can be realized.

(Modification)
In this embodiment, the problem of minimizing the objective function J has been described as an example. However, if an objective function including an evaluation index for evaluating the total number of transports of the steel material group and an evaluation index for evaluating the number of final peaks is used, the problem of minimizing the objective function J does not need to be considered. For example, each term on the right side of equation (29) may be multiplied by (-1) as the objective function, and the problem of maximizing the objective function may be used.

In addition, the inter-process storage area may be the storage area between two manufacturing processes, and the metal material may be semi-finished products, or the inter-process storage area may be the storage area between the manufacturing process and the shipping process. , as a metal material, the final product may be the target. At this time, when a plurality of metal materials are accommodated in a container and transported and arranged, the container in which the metal materials are accommodated may be handled as one metal material. Furthermore, the inter-process storage area is not limited to the storage area in the metal manufacturing process, and general inter-process physical distribution and transportation may be used. In the physical distribution field, it can be applied not only to the contents but also to the transportation and arrangement of containers. Therefore, in the present invention, metal materials include any one of final products, semi-finished products, and containers.

<Second embodiment>
Next, a second embodiment will be described. In the first embodiment, the initial pile and the final pile are placed in different places, and it is assumed that all steel material groups must be transported from the initial pile (initial pile) to the final pile (final pile). was described as an example. However, there is a case where the order of stacking from the bottom of the initial mountain is already the order of payout (the order of payout is descending from the bottom to the top). In such a case, there is no need to reload parts of the initial pile whose stacking order from the bottom is in the payout order (the payout order is descending from the bottom to the top). Therefore, in this embodiment, for such a portion, the case where the initial pile and the final pile are allowed to be placed in the same place (that is, the initial pile is not moved) will be described. As described above, the main difference between the present embodiment and the first embodiment is the processing due to the difference in (2) of the (assumed) explained in the first embodiment. 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. 1 and 2, and detailed description thereof is omitted.

In this embodiment, the following assumption (3) is adopted instead of (2) of the (hypothesis) described in the first embodiment.
(3) It is permissible for the initial pile and the final pile to be placed in the same place, and the portion of the initial pile whose stacking order from the bottom is in the payout order (the payout order is descending from the bottom to the top) is transported. (That is, some steel material groups of the initial pile (one or a plurality of steel material groups continuing from the bottom stage) may not be transported).

The difference between (2) of (hypothesis) described in the first embodiment and (3) is that under (3), the same place (mountain) cannot occur under (3) of (hypothesis) (2). ) allows the replacement of the upper steel group. In order to replace the steel group in this way, the steel group that was on the top of the initial pile is transported to the temporary pile or the final pile, and another steel group is placed on the remaining part (lower part) of the initial pile. will be transported. The steel groups to be transported to the remaining lower part of the initial pile include the steel groups on the initial pile different from the initial pile, and the steel groups temporarily placed on the temporary pile among the steel groups on the upper part of the initial pile. and the steel group.

Therefore, the "initial transfer order" of the steel group to be moved that was originally on the initial pile must precede the "final transfer order" of the steel group that is transferred from another pile onto the remaining part of the initial pile. (In the following description, this will be referred to as a constraint condition for replacement as needed). In order to strictly set the constraint conditions for this replacement, it is necessary to define the order relationship between the initial and final transfer order between any two steel material groups. Instead of setting a large-scale problem, a constraint condition for replacement is expressed as a sufficient condition in the variable system of the algorithm described in the first embodiment. In the following explanation, the order of stacking from the bottom of the initial pile is the order of delivery (the order of delivery is descending from the bottom to the top). A fixed portion is called, and a portion of the initial mountain above the fixed portion that carries out transportation for transshipment is called a moving portion as necessary.

This algorithm can be realized by making the following changes to the constraint equations (10) to (28) of the first embodiment.
First, constraint equations added to the constraint equations (10) to (28) described in the first embodiment will be described.
If all the steel material groups are not transported and part of the initial pile is used as the final pile as it is, the following cases that are not possible when all steel materials are transported are assumed. additional constraints must be added.
FIG. 3 is a diagram showing an example of the form of conveying the steel material when the initial crest has a fixed portion.
In the initial peak shown in FIG. 3, it is assumed that the steel material groups I and II in the two lowest stages are fixed parts, and the steel material groups III, IV and V above them are moving parts. In this case, at the final crest, steel groups I and II of the fixed portion remain as they are. In addition, among the steel groups III, IV, and V of the moving portion of the initial pile, the steel groups III and V are conveyed to another final pile, and the steel group IV is conveyed to the temporary pile and then again to the initial pile (that is, On top of the steel material group IV, steel material groups VI and VII are transported from another initial mountain. In order to properly calculate the transfer order even in such a case, it is necessary to set a constraint on the initial transfer order.

When conveying a steel group from another initial pile or temporary pile to an initial pile having a fixed part (that is, the final pile), the steel groups III, IV, V of the moving part above the fixed part are initially transferred. Only after this can the final transfer of steel groups IV, VI and VII be allowed. Therefore, it is necessary to impose a constraint that the final transfer of steel groups IV, VI, VII must be after the initial transfer of steel groups III, IV, V. Thus, the initial transfer order of the steel groups above the fixed part, such as steel groups III, IV, V, is transferred to the upper part of the fixed part from another initial pile or temporary pile, such as steel groups IV, VI, VII. It is a necessary and sufficient condition that it precedes the final transport order of the steel group that However, with the algorithm described in the first embodiment, the order relationship between the initial transport order and the final transport order cannot be explicitly given. Therefore, in this embodiment, a constraint expression that provides a sufficient condition is added as follows.
That is, the variable that specifies the initial transport of the steel material group in the moving portion of the initial pile l is _iU , and the initial value of the steel material group that is transported to the initial pile l from a different pile (initial pile or temporary pile) from the initial pile l. Let i _T be a variable that specifies transportation, and add the following constraint expression (33).

If the initial transport specified by the variable i _T is transport to the final pile, the equation (33) satisfies the above-mentioned necessary and sufficient condition, but the initial transport specified by the variable i _T is transport to the temporary pile. , the equation (33) becomes a sufficient condition and an excessive restriction. If the following formula (34) holds, then the following formula (35) is unconditional and only a necessary condition.

Also, in the case of a group of steel materials that is initially transported from the initial mountain _l and returns to the initial mountain _l again, such as the steel group IV in the example of FIG. becomes meaningless, the following equation (36) is set for such a steel material group.

Next, a description will be given of portions that are changed from the constraint equations (10) to (28) described in the first embodiment.
If at least one of the variables s, s', and s'' specifying the initial transport is a variable set for the steel material group of the fixed portion of the initial pile, those variables s and s For the initial transfer order variables y(s, s'), y(s', s), y(s', s''), y(s, s'') by ', s'', (10) It is assumed that the constraint expressions of the equations and (11) are not set. Alternatively, by expanding the formula (12) as follows, all the constraint expressions other than the formula (12) can be set in the same way as the steel group of the moving part (non-fixed part) for the steel material of the fixed part. .

In other words, the above formula (12) is for the moving part (non-fixed part) steel material, but when one steel group is the fixed part and the other steel material group is the non-fixed part, the following (37) is set, and if both steel material groups are fixed parts and they are on the same initial crest, the following constraint expression (38) is set.

In this embodiment, the constraint expression/objective function setting unit 102, for example, formulas (10) to (19), formulas (21) to (25), and formulas (27) to (28) as described above. , (33), and (36) are set. Incidentally, as described above, the constraint equations (37) and (38) may be set. Then, the optimization calculation unit 103 calculates the formulas (10) to (19), (21) to (25), (27) to (28), (33), (36) (or , (10) to (19), (21) to (25), (27) to (28), (33), (36) to (38)) , the initial transfer order variable y (s, s'), the final transfer order variable z (s, s'), and the temporary pile position assignment variable p ( s, t), temporary peak presence/absence variable q(t), final peak assignment variable r(s, l), and final peak presence/absence variable δ(l).

As described above, in this embodiment, when at least one of the steel groups is the steel group of the fixed portion of the initial pile, the constraint expression (12) representing the constraint when conveying the steel group is not set. Alternatively, the constraint equations (34) and (35) are set. Also, using the initial transfer order variable y(s, s'), the initial transfer of the steel material group on the moving portion of the initial pile is earlier than the initial transfer of the steel material group that is transferred to the initial pile having the moving portion. A constraint expression (equation (32)) is added. Therefore, in addition to the effects described in the first embodiment, it is possible to convey the steel materials when transferring the metal materials from the initial pile to the final pile so as not to convey the steel material group of the fixed portion of the initial pile that does not need to be conveyed. order can be requested.

As described above, the expression (12) expresses the constraint condition for the replacement as a sufficient condition, so the solution obtained in this way is not guaranteed to be the optimal solution, and the feasible solution space is narrowed. In extreme cases, an optimal solution may be calculated as infeasible (no solution). Therefore, instead of the expression (12), the constraint expression of the following expression (39), which expresses the constraint condition for the replacement as a necessary condition, may be used.

Equation (39) states that when a steel material group to be transported to an initial pile having a moving part of the initial pile is temporarily placed, the order of the initial transport of the steel material group and the initial transport of the steel material group of the moving part is Regardless, otherwise, as in equation (12), the initial transport of the steel material group on the moving portion of the initial pile precedes the initial transport of the steel material group transported on the initial pile having the moving portion. show that In equation (39), if the steel material group to be transported to the initial pile having a moving part is temporarily placed, it is only a necessary condition because there is no restriction, and since the feasible solution space is expanded, the solution obtained is It is possible to have an infeasible solution (ie, the solution obtained cannot be conveyed).

For example, if you want to reliably prevent an unrealizable solution from being found, use equation (12). (39) can be used to select the constraint equation to be adopted. If a feasible solution is obtained using equation (39), it is a true optimal solution.
Also, the modified example described in the first embodiment can be employed in this embodiment as well.

<Example>
Next, an example will be described.
In the following examples, calculations were performed in the following computing environment.
(i) Processor: Intel (registered trademark) Xeon (registered trademark) CPU E5-2687W @ 3.1.GHz (2 processors)
(ii) Mounted memory (RAM): 128GB
(iii) OS: Windows (registered trademark) 7 Professional 64-bit operating system (iv) Optimal calculation software: ILOG CPLEX Cplex11.0 Concert25 (registered trademark)

In this embodiment, the shape and order of delivery of all the steel materials (slabs) to be created as the final pile are given, and on the premise that all the steel materials are moved, each of the initial piles is delivered from the top. It shall be transshipped to the final pile, which is piled up in order. At this time, steel materials shall be conveyed one by one. It is an object of the transshipment to transport the steel materials with as few transports as possible and to minimize the number of final piles and temporary piles as much as possible. Here, since it is assumed that all the steel materials are moved, reducing the number of transports is equivalent to reducing the number of temporary placements. The weighting factors in equation (29) are k ₁ (weighting factor for the number of final ridges)=10, k ₂ (weighting factor for the number of temporary ridges)=1, and k ₃ (weighting factor for the number of temporary ridges)=5. did. Also, the upper limit h _max of the number of steel materials that can be piled up as the final pile was set to 10.

Further, the method described in Patent Document 3 is a method of optimizing the final pile and the transfer order at the same time, like the methods of the first and second embodiments. Therefore, as a comparative example with respect to the method (invention example) of the first embodiment, the method described in Patent Document 3 was used to compare the two. Note that the method described in Patent Document 3 is a method for obtaining the shape of the final mountain and the order of transportation for creating the final mountain, and does not consider the shape of the temporary mountain. Therefore, here, the arrival order in Patent Document 4 is used as the transport order obtained in Patent Document 3, and the method described in Patent Document 4 is applied as the problem of obtaining the realizable final peak as the realizable peak. Then, I asked for the shape of the temporary mountain. Also, in the comparative example, k ₁ (weighting factor for the number of final piles)=10 and k ₂ (weighting factor for the temporary placement number)=1, as in the invention example.

FIG. 4 is a diagram showing, in tabular form, the results of optimization calculations according to the invention example and the results of optimization calculations according to the technique of the comparative example.
In FIG. 4, the data of the calculation conditions identifies the steel material information, and indicates that the invention example and the comparative example are compared with respect to 13 types of steel material information. Also, SL in the calculation condition is the number of steel materials for which the final pile is to be created. Also, the initial number of peaks in the calculation condition is the number of initial peaks. The final ridge, the number of temporary ridges, and the number of temporary ridges in the comparative example and the inventive example are the number of final ridges, the number of temporary ridges, and the number of temporary ridges, respectively, obtained as a result of the optimization calculation. Moreover, the time in the comparative example and the invention example is the time required for the optimization calculation.

Here, for Data 1 to 5, even in the comparative example, the calculation was continued until the optimum solution was obtained. On the other hand, for Data 6 to 13, if a solution cannot be obtained within 10 minutes, which is assumed to be the practically allowable calculation time limit, the calculation is terminated at that stage, and the feasibility obtained at that stage is The solutions are described in the columns of the final number of ridges, the number of temporary placements, and the number of temporary ridges. If even an executable solution cannot be obtained even after 10 minutes, it is described in the relevant column as not being able to obtain an executable solution.

First, for a small-scale problem (n<20), we confirmed that both solutions agree. The results are shown in Data 1 and 2 in FIG. It can be seen that the final number of ridges, the number of temporary placements, and the number of temporary ridges are the same in both solutions. In addition, even for a relatively large-scale problem, it was confirmed that the two solutions match (see Data 5 in FIG. 4).

Next, we verified the problem that there are multiple steel materials to be temporarily placed, and multiple temporary piles may be required. The results are shown in Data 3 and 4. In Data 3, 5 steel materials were temporarily placed, and in the comparative example, these 5 steel materials could only be put together into 4 temporary piles. On the other hand, in the invention example, the temporary pile is taken into consideration at the same time as the determination of the steel material to be temporarily placed, so it can be seen that the five steel materials to be temporarily placed can be combined into one temporary pile. Similarly, in Data 4, the number of steel materials to be temporarily placed is 3 in both the comparative example and the inventive example, but these three steel materials can only be combined into two temporary piles in the comparative example, whereas in the inventive example , are grouped into one false mountain.

Finally, Data 6 to 13 in FIG. 4 show the results of comparing the calculation times for problems of the same scale as the actual operation. As described above, here, if a solution cannot be obtained within 10 minutes, which is assumed to be the practically allowable calculation time limit, the calculation is terminated at that stage, and the feasibility obtained at that stage is It describes the solution. When the optimal solution is not reached, the dual gap at that time is described (see Data 9 and 11). Of the 8 cases in Data 6 to 13, there are 6 cases in which even a feasible solution cannot be obtained even after 10 minutes (see Data 6, 7, 8, 10, 12, 13), and the remaining 2 cases Cases (Data 9, 11) also did not yield optimal solutions. On the other hand, it can be seen that the invention example provides the optimum solution within 5 minutes in any case.

<Other Modifications>
The embodiments of the present invention described above can be implemented by a computer executing a program. A computer-readable recording medium recording the program and a computer program product such as the program can also be applied as embodiments of the present invention. Examples of recording media that can be used include flexible disks, hard disks, optical disks, magneto-optical disks, CD-ROMs, magnetic tapes, nonvolatile memory cards, and ROMs.
In addition, the embodiments of the present invention described above are merely examples of specific implementations of the present invention, and the technical scope of the present invention should not be construed to be limited by these. It is. That is, the present invention can be embodied in various forms without departing from its technical concept or main features.

<Relationship with claims>
An example of the relationship between claims and embodiments is shown below. It should be noted that the description of the claims is not limited to the description of the embodiment, as shown in the modifications and the like.
(Claims 1 and 7)
The initial transfer order variable is realized by using the initial transfer order variable y(s, s'), for example. The final transfer order variable is realized by using, for example, the final transfer order variable z(s, s'). The final peak assignment variable is implemented, for example, by using the final peak assignment variable r(s, l). Temporary allocation variables are implemented, for example, by using temporary allocation variables p(s, t).
The metal material information acquisition means is realized by using the steel material information acquisition unit 101, for example. Steel material information is realized by using, for example, steel material group information. The identification information of the initial pile and the identification information of the metal material at each lamination position of the initial pile are, for example, information specifying the appearance of the initial pile of each steel material group (identified by the initial pile ID and the initial pile ID). It is realized by using the steel material group ID) located at each stack of the initial pile. The delivery order of the metal materials is realized, for example, by using the delivery order (conveyance order to the rolling process) of each steel material group.
The constraint expression setting means is implemented by using the constraint expression/objective function setting unit 102, for example. The first constraint expression is realized by using, for example, expression (16). The second constraint expression is realized by using the expression (23), for example.
The objective function setting means is realized by using the constraint expression/objective function setting unit 102, for example. The objective function is realized, for example, by using equation (29).
The optimization calculation means is realized by using the optimization calculation unit 103, for example.
(Claim 2)
The third constraint expression is realized by using, for example, expression (24).
Stacking constraints are implemented, for example, by using width and length constraints.
(Claim 3)
The fourth constraint expression is realized by using, for example, expression (10).
The fifth constraint expression is realized by using, for example, expression (11).
(Claim 4)
The sixth constraint expression is realized by using, for example, expression (13).
The seventh constraint expression is realized by using, for example, expression (14).
(Claim 5)
The eighth constraint expression is realized, for example, by using expression (12).
(Claim 6)
The ninth constraint expression is realized, for example, by using expression (15).

100: Yard management device, 101: Steel product information acquisition unit, 102: Constraint expression/objective function setting unit, 103: Optimization calculation unit, 104: Post-processing unit, 105: Output unit

Claims (12)

The initial pile of metal materials piled up in the yard, which is a storage site between processes, is transported by a transport device, and the metal materials piled up in the order of delivery to the post-process of the yard. A yard management device for creating a final pile of
An initial transport order variable that is a binary variable that determines the relative order of initial transport, which is transport from the initial mountain, for any two of the metal materials, and the final transport order variable for any two of the metal materials. A final transfer order variable that is a binary variable that determines the relative order of the final transfer that is transfer to a mountain, a final transfer order variable that is a variable that indicates which final transfer mountain the metal material belongs to, and A temporary pile assignment variable, which is a variable indicating to which temporary pile the metal material belongs when the metal material is piled up in a temporary pile made up of metal materials piled up in a temporary storage area of a yard, is used as a decision variable. ,
metal material information acquisition means for acquiring metal material information including the identification information of the initial pile, the identification information of the metal material at each piling position of the initial pile, and the order of dispensing of the metal material;
Constraint expression setting means for setting a constraint expression including a first constraint expression and a second constraint expression based on the metal material information;
Purpose including an evaluation index for evaluating the number of the final piles, an evaluation index for evaluating the number of the metal materials temporarily placed in the temporary storage site of the yard, and an evaluation index for evaluating the number of the temporary piles objective function setting means for setting a function based on the metal material information;
Optimization that derives the value of the decision variable when the value of the objective function is the minimum or maximum within the range that satisfies the constraint expression as the optimum solution by performing optimization calculation using mathematical programming. calculating means;
The first constraint expression is such that, for any two of the metal materials, when the order of transportation from the initial pile is different from the order of transportation to the final pile, the two metal materials , a constraint expression that expresses, using the decision variable, that the metal material that is first conveyed from the initial pile needs to be temporarily placed in the temporary storage site,
In order for any two of the metal materials to be piled on the same temporary pile, the second constraint expression is such that the two metal materials are first and next in the order of transportation from the initial pile, and the A yard management apparatus characterized by a constraint expression that expresses, using the decision variable, that the order of transportation to the final pile must be different. The constraint formula is such that when one of the metal materials is stacked on the bottom and the other metal material is stacked on the top of the same temporary pile, the two metal materials that do not satisfy the stacking shape constraint, the one metal A third constraint expression that uses the decision variable to express that the two metal materials should not be temporarily placed on the same temporary pile when the material is initially conveyed before the other metal material is conveyed. further includes
2. The yard management according to claim 1, wherein the stacking restriction is a restriction determined based on the size of the metal materials, and is a restriction regarding the stacking order of a plurality of the metal materials on the same pile. Device. The initial transfer order variable is a binary term that defines the relative order of the initial transfer of any two metal materials from the initial pile by regarding the initial transfer order of the metal materials from the initial pile as the total order. is a variable and
The constraint expression is a fourth constraint expression, which is a linear equation expressed using the initial transfer order variable, that the initial transfer order variable is comparable, and the initial transfer order variable is transitive. 3. The yard management apparatus according to claim 1, further comprising a fifth constraint expression that is a linear inequality expressed using the initial transport order variable. The final transport order variable is a binary term that determines the relative order of the final transport of any two metal materials to the final stack, considering the final transport order of the metal materials to the final pile as the total order. is a variable and
The constraint expression is a sixth constraint expression that is a linear equation expressed using the final transfer order variable that the final transfer order variable is comparable, and that the final transfer order variable is transitive. The yard management apparatus according to any one of claims 1 to 3, further comprising a seventh constraint expression that is a linear inequality expressed using the final transport order variable. The constraint expression uses the initial transfer order variable to indicate that, in the same initial pile, the metal material above the metal material below must be initially conveyed from the initial pile. A yard management device according to any one of claims 1 to 4, further comprising an eighth constraint equation which is a linear equation expressed. The constraint expression is such that when the metal material that is relatively earlier in the payout order and the metal material that is relatively later in the payout order are arranged on the same final mountain, the payout order is relatively The final transport of the later metal material to the final pile needs to precede the final transport of the metal material that is relatively earlier to the final pile. The yard management apparatus according to any one of claims 1 to 5, further comprising a ninth constraint expression, which is a linear inequality expressed using a transfer order variable and the final pile assignment variable. The first constraint expression is a linear inequality expressed using the temporary pile assignment variable, the initial transfer order variable, and the final transfer order variable,
7. The second constraint expression is a linear inequality expressed using the temporary pile assignment variable, the initial transfer order variable, and the final transfer order variable. The yard management device according to item 1. the initial mountain includes an already-arrived mountain and a virtual mountain;
The already-arrived pile is a pile piled up in the yard when the final pile is created,
The virtual mountain is a metal material that has not arrived at the yard at the time of creating the final mountain, and the metal material that is the target of creating the final mountain is higher in order of scheduled arrival at the yard. The yard management device according to any one of claims 1 to 7, characterized in that it is one pile when it is assumed that the piles are piled up so as to be equal to each other. The metal material is a metal material group,
The yard according to any one of claims 1 to 8, wherein the metal material group is composed of a plurality of the metal materials that are not divided when the metal material is transported by a transport device. management device. The yard is a storage place between the steelmaking process and the rolling process in the steel manufacturing process,
The yard management device according to any one of claims 1 to 9, wherein the metal material is steel material. The initial pile of metal materials piled up in the yard, which is a storage site between processes, is transported by a transport device, and the metal materials piled up in the order of delivery to the post-process of the yard. A yardage management method for creating a final pile of
An initial transport order variable that is a binary variable that determines the relative order of initial transport, which is transport from the initial mountain, for any two of the metal materials, and the final transport order variable for any two of the metal materials. A final transfer order variable that is a binary variable that determines the relative order of the final transfer that is transfer to a mountain, a final transfer order variable that is a variable that indicates which final transfer mountain the metal material belongs to, and A temporary pile assignment variable, which is a variable indicating to which temporary pile the metal material belongs when the metal material is piled up in a temporary pile made up of metal materials piled up in a temporary storage area of a yard, is used as a decision variable. ,
Metal material information acquisition for acquiring metal material information including the identification information of the initial pile, the identification information of the metal material at each piling position of the initial pile, and the payout order of the metal material by the metal material information acquisition means. a step;
a constraint expression setting step of setting a constraint expression including a first constraint expression and a second constraint expression by a constraint expression setting means based on the metal material information;
An evaluation index for evaluating the number of the final piles, an evaluation index for evaluating the number of the metal materials temporarily placed in the temporary storage site of the yard, and the number of the temporary piles are evaluated by the objective function setting means . an objective function setting step of setting an objective function including an evaluation index based on the metal material information;
The optimization calculation means performs optimization calculation by mathematical programming to derive the value of the decision variable when the value of the objective function is the minimum or maximum within the range satisfying the constraint expression as the optimum solution. and an optimization calculation step performed by
The first constraint expression is such that, for any two of the metal materials, when the order of transportation from the initial pile is different from the order of transportation to the final pile, the two metal materials , a constraint expression that expresses, using the decision variable, that the metal material that is first conveyed from the initial pile needs to be temporarily placed in the temporary storage site,
In order for any two of the metal materials to be piled on the same temporary pile, the second constraint expression is such that the two metal materials are first and next in the order of transportation from the initial pile, and the A yard management method, comprising: a constraint expression that expresses, using the decision variable, that the order of transportation to the final pile must be different. A program that causes a computer to function as each means of the yard management apparatus according to any one of claims 1 to 10.

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