JP7506310B2 - 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, which are suitable for use in sorting piles of metal materials in yards set up to smoothly supply metal materials such as slabs and coils to the next process in a metal manufacturing process.

In a steelmaking process, which is an example of a metal manufacturing process, when steel, which is an example of a metal material, is transported from a steelmaking process to a rolling process, which is the next process, the steel is first placed in a temporary storage location called a yard, and then removed from the yard in time for the processing time of the rolling process, which is the next process. An example of the layout of the yard is shown in Figure 7. As shown in Figure 7, the yard is a storage area 701-704 divided vertically and horizontally as a buffer area for supplying steel materials such as slabs discharged from an upstream process to a downstream process. The vertical divisions are often called "buildings" and the horizontal divisions are often called "rows." In other words, cranes (1A, 1B, 2A, 2B) can move within the building and transport steel materials between different rows within the same building. In addition, transport tables X and Y transport steel materials between buildings. When creating a transport command, you indicate where to transport the steel by specifying the "building" and "row" (see the numbers (11), (12), (21), and (22) in parentheses next to storage areas 701 to 704 in Figure 7).

Next, the basic work flow in the yard is shown using Figure 7 as an example. First, the steel material removed from the continuous caster 710 in the preceding steelmaking process is transported to the yard on transport (receiving) table X via piler 711, and then transported by cranes 1A, 1B, 2A, and 2B to one of the partitioned storage areas 701-704 where it is piled up. Then, in accordance with the production schedule for the following rolling process, it is again placed on discharge table Z by cranes 1A, 1B, 2A, and 2B and transported to the rolling process. Generally, steel materials are piled up in the yard as described above. This is to make effective use of the limited yard area.

In the following, the terms "original mountain", "virtual mountain", "initial mountain", "final mountain", "fixed mountain" and "new mountain" are used with the following meanings.
Original Mountain: A mountain that currently consists of at least a portion of a mountain that has already formed in the Yard and does not change location from that mountain.
Virtual pile: A pile that hypothetically represents the steel products that have not yet arrived at the yard, with the products that arrived at the yard earlier being piled on top (this pile does not actually exist).
Initial mountain: A general term for the original mountain at the current point in time (the mountain as it is already formed in the yard) and the virtual mountain.
Final pile: The final pile that is piled up to be sent to the next process (also called the discharge pile).
Fixed pile: The final pile that contains steel that will not be moved (non-moving steel). Note that non-moving steel also includes steel that will not be moved as a result (steel that is temporarily stored from the original pile and then returned to the original pile).
New pile: A pile consisting of steel moved from the initial pile and containing no non-moved steel (only moved steel).
The original mountain and the new mountain are candidates for the final mountain, and the mountain that remains as the fixed mountain or the new mountain among the candidates will be the final mountain.

In the yard, in order to reduce the fuel consumption of the heating furnace in the next process, hot rolling, it is required that the steel be charged into the heating furnace while maintaining the highest possible temperature. For this reason, recently, thermal insulation equipment has been installed in the yard, and steel is sometimes stored in a pile in it. In order to make effective use of the limited thermal insulation equipment, it is necessary to stack the steel as high as possible to the equipment limit. On the other hand, when stacking steel, there are constraints (called "piling shape constraints") such as the steel being stacked from the top in the order of processing in the next process in the final pile so that it can be easily supplied to the next process, and the stacking shape of the final pile not being an unstable inverted pyramid shape. Furthermore, the workload when stacking (creating the final pile) is also an important factor. Therefore, it is desirable for the yard control to formulate a work plan for stacking so that the final pile is as high as possible with as little workload as possible under the stacking shape constraints mentioned above.

In addition, when sorting (splitting steel into multiple piles) in the yard to smoothly send the requested steel to the next process, it is common for the steel that is scheduled to arrive to be downgraded (downgraded from the originally planned use and reassigned to a different use due to quality issues that arise during the manufacturing of the steel), or for the steel that is scheduled to arrive to require unplanned finishing processing or change in size, and as a result, the steel does not arrive as originally planned. Furthermore, it is almost impossible to expect the state of the yard's storage area to transition smoothly as originally planned, and it is common for unexpected steel to have to be stored in an unexpected storage area.

Furthermore, there are frequent cases where steel products that have been piled in the order they will be discharged from the yard to the hot rolling process are changed in the rolling order of the subsequent hot rolling process after the steel products arrive at the yard, causing the pile to be no longer stacked in the order they were discharged, and the steel products must be re-stacked in the changed rolling order. Here, "steel products are stacked in the order they will be discharged" means that, at any stacking position in the pile, a piece of steel product that is relatively higher up, or multiple pieces of steel product that are transported simultaneously, are discharged to the subsequent process earlier than the pieces of steel product that are lower down.

However, since the required transshipment work needs to be performed in parallel with the receiving and unloading of steel materials into and from the yard, the time periods during which the steel materials can be transshipped and the storage space available are limited. Therefore, it is required to perform the transshipment work of steel materials efficiently and in a space-saving manner.
Therefore, there is a great need to efficiently (i.e., with as few transports as possible) and ultimately to minimize the number of piles, when piles that are no longer in the order they were intended to be stacked upon arrival at the yard due to various circumstances before and after arrival at the yard can be stacked in the order they were intended to be stacked upon arrival at the yard.

As prior art for addressing the problem of transferring steel materials from an initial pile to a final pile as described above, there are the inventions described in Patent Documents 1 to 3.
First, Patent Document 1 discloses a method for calculating the optimal stacking shape of the final pile when steel products from an original pile already in a yard are reloaded in the order of shipment, by formulating the optimal stacking shape of the final pile as a combinatorial optimization problem, taking into consideration the required reloading load and stacking shape constraints, and using a tabu search method.

Next, Patent Document 2 discloses a method for formulating the problem of transshipping steel products from the initial pile state to the final pile state when the initial pile state and the final pile state at that time are given in a situation where steel products that have already arrived at the yard and products that have not yet arrived are mixed, as a mixed integer programming problem using an initial transportation time variable and a final transportation time variable, on the assumption that each steel product is transported at most two times.
Next, Patent Document 3 discloses a method for simultaneously optimizing pile sorting and the transport sequence by reducing the problem to a mathematical programming problem that satisfies constraints related to pile formation and transport.

Finally, Patent Document 4 addresses the problem of the time required to find a solution in the invention described in Patent Document 3 by disclosing a method for simultaneously optimizing the number of final piles and the number of steel products that require temporary storage (the number of steel products transported when transferring) within a time that can be used in actual operations.

Japanese Patent No. 4935032 Patent No. 5365759 Japanese Patent No. 5434267 JP 2018-150135 A JP 2018-100166 A

However, in the techniques described in Patent Documents 1 to 4, when transferring a pile, the problem is set on the assumption that either all steel materials will be moved or that the steel materials that will not be moved (fixed) are given in advance. Therefore, it is not possible to consider which steel materials that make up the initial pile will be moved and which will not be moved.

The present invention was made in consideration of the above problems, and aims to achieve a balance between minimizing the total number of final piles and minimizing the number of metal materials to be transported, while determining which metal materials constituting the initial pile should be moved and which should not be moved, when creating a metal material transportation plan for transferring metal materials from an initial pile to a final pile.

The yard management device of the present invention is a yard management device for transporting metal materials from an initial pile of metal materials piled up in a yard, which is a storage area between processes, using a transport device to create a final pile of metal materials piled up in a stacking order that corresponds to the order in which the metal materials are discharged to subsequent processes in the yard, and has a metal material information acquisition means for acquiring metal material information about the metal materials to be piled up, and an optimization calculation means for using the metal material information to solve a mathematical programming problem aimed at minimizing the total number of times the metal materials are transported and the total number of the final piles, thereby classifying the metal materials that make up the initial piles into either moved metal materials that are moved from the initial pile or non-moved metal materials that are not moved from the initial pile, and determining at least the transport order of the moved metal materials and whether or not temporary storage will occur when the moved metal materials are moved , and is characterized in that the total number of times the metal materials are transported is expressed as the sum of the total number of moved metal materials, which are metal materials transported from the initial pile to the final pile in the storage area, and the total number of temporary stored metal materials, which are metal materials that are temporarily stored .

The yard management method of the present invention is a yard management method for transporting metal materials from an initial pile of metal materials piled up in a yard, which is a storage area between processes, by a transport device to create a final pile of metal materials piled up in a stacking order according to the order of discharging to subsequent processes in the yard, and includes a metal material information acquisition step for acquiring metal material information about the metal materials to be piled up, and an optimization calculation step for using the metal material information to solve a mathematical programming problem aimed at minimizing the total number of transports of the metal materials and the total number of the final piles, thereby classifying the metal materials that make up the initial pile into either moved metal materials that are moved from the initial pile or non-moved metal materials that are not moved from the initial pile, and determining at least the transport order of the moved metal materials and whether or not temporary storage will occur when the moved metal materials are moved , and is characterized in that the total number of transports of the metal materials is expressed as the sum of the total number of moved metal materials, which are metal materials transported from the initial pile to the final pile in the storage area, and the total number of temporary stored metal materials, which are metal materials that are temporarily stored .

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

According to the present invention, when creating a metal material transportation plan for transferring metal materials from an initial pile to a final pile, it is possible to determine which metal materials constituting the initial pile will be moved and which will not be moved, while achieving a balance between minimizing the total number of final piles and minimizing the number of metal materials to be transported.

FIG. 2 is a diagram illustrating a first example of a functional configuration of a yard management device. FIG. 13 is a diagram showing an example of replacement of movable steel material. 1 is a flowchart illustrating a first example of a yard management method. FIG. 2 is a diagram illustrating a first example of a functional configuration of a yard management device. 13 is a flowchart illustrating a second example of a yard management method. FIG. 13 is a diagram showing calculation results in an example of the invention and a comparative example. FIG. 2 is a diagram showing an example of a yard layout.

Below, an embodiment of the present invention will be described with reference to the drawings. In the following embodiment, in a steel manufacturing process, the stacking form of the initial piles is given, and the decision variables include a variable indicating the relative transport order of two steel products, a variable indicating whether or not temporary placement of each steel product will occur, and a variable specifying the final pile to which each steel product will be transported, and at least the total number of final piles and the total number of transports of steel products are determined. Furthermore, in the following embodiment, when determining the total number of final piles and the total number of transports of steel products, the steel products that should be moved and the steel products that should not be moved, the transport order of each steel product, and whether or not temporary placement of each steel product will occur are simultaneously determined.

In addition, in at least a portion of the initial pile, the steel materials (slabs) manufactured in the steelmaking process are not stacked in the order in which they are transported to the rolling process. In the following explanation, the order in which each steel material is transported to the rolling process is referred to as the discharge order as necessary. Steel materials that are determined by the present invention to be moved are referred to as moving steel materials as necessary, and steel materials that are determined not to be moved are referred to as non-moving steel materials as necessary. Furthermore, in the following explanation, "moving steel materials" and "non-moving steel materials" may also be referred to as "moving steel materials" and "non-moving steel materials", respectively.

((First embodiment))
First, the first embodiment will be described.
(Problem formulation)
(A) Assumptions (Premise)
(a) In this embodiment, the stacking shape and the withdrawal order (rolling order) of the initial piles of steel materials are assumed to be given. Here, a set of steel materials is represented as N={1, 2, ..., n}.

(b) The initial pile includes an original pile and a virtual pile. The original pile as the initial pile is the pile formed in the yard at the time when the steel information is created (i.e., at the time when the final pile is created) among the steel materials to be created as the final pile. Even if some of the steel materials constituting the initial pile are subsequently piled in another pile, the pile of steel materials remaining in the initial pile is also considered to be the original pile. In this way, the original pile is composed of at least a part of the pile formed in the yard at the time when the steel information is created (i.e., at the time when the final pile is created), and is a pile that does not change location from the original pile. The virtual pile is a pile when it is assumed that the steel materials to be created as the final pile are piled up such that the earlier the scheduled arrival order at the yard, the higher they are. In this embodiment, all the steel materials to be created as the final pile, which have not yet arrived at the yard and have not yet been piled up, are piled up in one virtual pile. In this embodiment, steel materials that have not yet arrived at the yard and are not yet piled up are also considered to be piled up as virtual piles (i.e., all steel materials to be used for creating the final piles are considered to be piled up in the yard), and the stacking state is considered to be given. Note that, with regard to the steel materials (materials that have not yet arrived) that make up the virtual piles, there is no non-moving steel material, and all are considered to be moving steel material. Therefore, when deciding whether the steel materials that make up the virtual piles are moving steel material or non-moving steel material, they are treated as moving steel material.

(c) The shape of the initial pile is known, but the shape of the final pile is unknown. The final pile is assumed to be a pile stacked in the order of removal from the top, and the total number of final piles is also unknown. The total number of final piles is one element of the objective function to be minimized.
(d) The steel materials to be temporarily placed are determined by the method of this embodiment described later. However, the pile shape of the temporarily placed steel materials (the pile shape of the temporary mountain: in which temporary mountain the steel materials to be temporarily placed are located and in which stacking order) is not determined, but is derived by a known method (for example, solving the vertex coloring problem described in Patent Document 5). Note that a method for simultaneously determining the pile shape of the temporary mountain is shown in the third and fourth embodiments.

(e) The number of transports from the initial pile (initial storage area) to the final pile (final storage area) for any steel product will be a maximum of two times. In other words, steel products that are transported twice will be temporarily stored, but steel products that have been transported to a temporary pile (temporary storage area) will always be transported to the final pile (final storage area) on the next transport, and will not be transported between different temporary piles (temporary storage areas).

(f) In this embodiment, the following width constraint, length constraint, and height constraint are set as stacking shape constraints for the final mountain.
Width constraints If the width of a certain steel material is narrower than the width of any steel material located below it, the certain steel material can be placed unconditionally on top of the steel material located below it. If the width of a certain steel material is wider than the width of any steel material located below it, the certain steel material can be placed on top of the steel material located below it if the difference in width between the two (the certain steel material and all the steel materials located below it) is less than a standard value (e.g. 200 mm) determined by the work constraints, but it cannot be placed on top of the steel material located below it if the difference is greater than the standard value.

In other words, the width constraint is met when the width of a certain steel material is narrower than the width of the steel material located below it, or when the width of a certain steel material is wider than the width of the steel material located below it and the difference between the width of the certain steel material and each of the widths of all the steel materials located below it is less than a reference value (e.g., 200 mm).

Length constraints If the length of a certain steel material is shorter than the length of any steel material located below it, it can be placed unconditionally on top of the steel material located below it. If the length of a certain steel material is longer than the length of any steel material located below it, it can be placed on top of the steel material located below it if the difference in length between the two (the certain steel material and all the steel materials located below it) is less than a reference value (e.g., 2000 mm) determined by the work constraints, but it cannot be placed on top of the steel material located below it if the difference is greater than the reference value.

In other words, the length constraint is satisfied when the length of a certain steel material is shorter than the length of the steel material located below it, or when the length of a certain steel material is longer than the length of the steel material located below it and the difference in length between the certain steel material and each of the steel materials located below it is less than a reference value (e.g., 2000 mm).

Height constraint: The number of steel products that can be piled up as one final pile must be equal to or less than the upper limit h of the height of the final pile. The upper limit h of the height of the final pile is, for example, 10.

(g) The location of the initial pile (original pile) containing the non-movable steel materials becomes the location of the final pile. The final pile consisting only of movable steel materials is the new pile. As mentioned above, the location of the new pile is different from the location of the initial pile.

(B) Constraints other than stacking form constraints The following constraints are assumed to exist as constraints other than stacking form constraints.
(h) The final pile satisfies the stacking shape constraints and is stacked in order of removal from the top (the upper steel materials are removed earlier than the lower steel materials).
(i) In each pile, steel materials can only be transported in order from the top of the pile initially stacked.
(j) When creating the final pile, steel may only be stacked from the bottom up.
(k) The number of steel materials that can be transported simultaneously depends on the number of cranes available and the capacity of the cranes. Note that, for the sake of simplicity, a case in which one steel material can be transported simultaneously is illustrated here, but as described in Patent Document 4 and the like, a plurality of steel materials may be transported simultaneously.

(C) Objective The objective is to balance minimizing the total number of final piles and minimizing the total number of transports of steel material. The total number of transports of steel material is expressed as the sum of the total number of transported steel materials and the total number of temporarily stored steel materials, because, according to (d) and (e) above, steel materials that require temporary storage among the moving steel materials will be transported one extra time.

(Decision variable)
In this embodiment, for any steel material i, a non-moving topmost steel material discrimination variable x _i and a movement/non-moving discrimination variable y _i are set as decision variables. The non-moving topmost steel material discrimination variable x _i is defined as in the following formula (1), and the movement/non-moving discrimination variable y _i is defined as in the following formula (2). Note that variable i is numbered in the order in which the steel materials are dispensed (the earlier the steel material is dispensed, the smaller the value of variable i).

The non-moving top-level steel discrimination variable x _i is a 0-1 variable that is 1 when a steel material i constituting a certain initial pile is a non-moving steel material at the top of the non-moving steel materials, and is 0 (zero) otherwise. In this way, if there is no non-moving steel material in the initial pile, the non-moving top-level steel discrimination variable x _i for all steel materials i constituting the initial pile is 0 (zero). On the other hand, if there is one or more non-moving steel materials in the initial pile, only the non-moving top-level steel discrimination variable x _i for the non-moving steel material i at the top of the non-moving steel materials is 1. In this case, the non-moving top-level steel discrimination variable x _i for the other steel materials i constituting the initial pile is 0 (zero) even if the steel material i is a non-moving steel material. That is, for one initial pile, the number of steel materials for which the non-moving top-level steel discrimination variable x _i is 1 is 1 at most.
The movement presence/absence discrimination variable y _i is a 0-1 variable that is 1 if the steel material i is a moving steel material and is 0 (zero) if not.

Furthermore, in this embodiment, the moving steel final pile allocation variable z _ij and the assigned pile identification variable q _j are used as decision variables. The moving steel final pile allocation variable z _ij is defined as in the following formula (3), and the assigned pile identification variable q _j is defined as in the following formula (4). Note that j is identification information (ID) that uniquely identifies each pile. For example, the identification number of the steel storage location in the yard can be used as j.

The movable steel final pile allocation variable z _ij is a 0-1 variable which is 1 when movable steel material i is placed in original pile j (=1, ..., p (p≧1)) or new pile j (=p+1, ..., p+m (m=n)) and is 0 (zero) otherwise. If steel material i is a non-movable steel material (i.e., steel material i for which the movement/non-movement discrimination variable y _i is 0 (zero)), the movable steel final pile allocation variable z _ij is set to 0 (zero) for any final pile j. The movable steel final pile allocation variable z _ij is a variable which indicates whether or not the movable steel material is moved to the final pile, distinguishing between steel material i and final pile j (original pile j and new pile j).
The assigned mountain identification variable q _j (j = 1, ..., p, p+1, ..., p+m) is a 0-1 variable that is 1 if original mountain j (= 1, ..., p) or new mountain j (= p+1, ..., p+m) is assigned as the final mountain, and is 0 (zero) otherwise. As mentioned above, original mountain j and new mountain j are candidates for the final mountain.

Furthermore, in this embodiment, the initial transport order variable t _ii' is set as the decision variable. Let G = (N, E ₁ ) be a complete directed graph in which each element of the set N of steel materials has one vertex. In this case, E ₁ = {(i, i') ∈ N ² | i ≠ i'}. Introducing a 0-1 variable t(e) (∀e ∈ E ₁ ) defined on the directed edge set E, the following formula (5) is defined.

The initial transport order variable t _ii' is a 0-1 variable which is 1 when steel material i is initially transported from the initial pile before steel material i', and is 0 (zero) otherwise. However, the initial transport order variable t _ii' is defined as follows: when steel materials i and i' are both moving steel materials, either t _ii' or t _i'i is 1 according to formula (5), and when at least one of steel materials i and i' is a non-moving steel material, t _ii' = t _i'i = 0. Initial transport refers to transport from the initial pile.

Furthermore, in this embodiment, a temporary storage occurrence variable r _i is used as a decision variable. The temporary storage occurrence variable r _i is defined as in the following equation (6). The temporary storage occurrence variable r _i is a 0-1 variable that is 1 if, when steel material i is initially transported from the initial pile, the initial transport is to a temporary pile (temporary storage site), and is 0 (zero) otherwise (transport to the final pile (final storage site)). Final transport refers to transport to the final pile.

(Functional configuration of the yard management device 100)
1 is a diagram showing an example of the functional configuration of the yard management device 100. The hardware of the yard management device 100 is realized by using, for example, an information processing device including a CPU, a ROM, a RAM, a HDD, and various interfaces, or dedicated hardware.
[Steel material information acquisition unit 101]
The steel material information acquisition unit 101 acquires steel material information on the steel materials to be piled up. The steel material information includes basic steel material information, information specifying the stacking form of the initial pile of each steel material, information specifying the upper limit value h of the height of the final pile, and weighting coefficients _k1 and _k2 .

The basic steel information includes the identification information, the order of dispensing, the number of steel materials, and the size (width, length) of each steel material (set of steel materials N={1, 2, ..., n}) for which the final pile is to be created. Note that, for simplicity of explanation, it is assumed here that all steel materials have the same thickness.
The identification information is a steel material ID that uniquely identifies each steel material.
The delivery order is the delivery order of each steel material (the order of transport to the rolling process). In this embodiment, since the identification information is the delivery order, the delivery order does not need to be included in the steel material basic information.

The information specifying the stacking shape of the initial pile includes an initial pile ID, which is identification information that uniquely identifies the initial pile, and the steel material IDs located in each stack layer of the initial pile identified by the initial pile ID.

The steel information can be acquired, for example, by inputting data into the user interface of the yard management device 100, by transmission from an external device, or by reading from a portable storage medium.

[Constraint equation/objective function setting unit 102]
The constraint equation/objective function setting unit 102 sets a constraint equation that expresses the above-mentioned constraints in mathematical expressions, and an objective function that expresses the above-mentioned objectives in mathematical expressions.
<<Constraint expression>>
First, the constraint equation will be described.

(a) Constraints on moving steel materials The set of steel materials divided into a set N, that is, a set of steel material subsets S _k (⊂N), is denoted as S = {S ₁ , S ₂ , ..., S _r }. Each of these steel material subsets S _k becomes an initial pile. As described above, the variable i for identifying the steel materials is numbered in the order in which the steel materials are dispensed (the earlier the steel material is dispensed, the smaller the value of the variable i). Therefore, the following formulas (7) and (8) hold.

In each initial pile S _k , the partial pile consisting of steel materials from the bottommost steel material to the steel materials in the stacking order in the dispensing order (dispensing order is descending from bottom to top) is defined as max(S _k ). In this case, steel materials not included in max(S _k ) are always moving steel materials (moving part shown in FIG. 2 ). This is expressed by the following formulas (9) and (10).

Formula (9) indicates that steel materials i in the portion excluding max(S _k ) from the initial pile S _k will move (become a moving steel material). Formula (10) indicates that steel materials i in the portion excluding max(S _k ) from the initial _pile S k will not become the steel materials in the top row of non-moving steel materials in the initial pile S _k . Formulas (9) and (10) indicate that steel materials i in each initial pile S _k that are not stacked in the dispensing order from the bottom row (dispensing order is descending from bottom to top) will move.

(b) Restriction on non-moving topmost steel product discrimination variable x _i In each initial pile S _k , the maximum value of the number of steel products i for which the non-moving topmost steel product discrimination variable x _i is 1 (x _i = 1) is 1. Therefore, the following formula (11) holds.

(c) Restriction on Movement/No Movement Discrimination Variable _yi In each initial pile S _k , all steel products above the moving steel product i are moved. Therefore, if the order of removal (=i (steel product identification number)) in each initial pile S _k viewed from the bottom up is k ₁ , k ₂ , ..., the following formula (12) is established.

(d) Constraints that stipulate the relationship between the non-moving top-level steel discrimination variable x _i and the movement/non-moving discrimination variable y _i All steel materials i are uniquely identified as either moving steel materials or non-moving steel materials. In the initial pile S _k , if the number of stacked levels (including the steel material in question and the number of steel materials below it, which is the number of stacked levels when the number of stacked levels of the bottom level is 1) is b _i , the total number of non-moving steel materials can be expressed as Σ _i∈N b _i ·x _i using the non-moving top-level steel discrimination variable x _i . In addition, the total number of moving steel materials can be expressed as Σ _i∈N y _i using the movement/non-moving discrimination variable y _i . Therefore, the following formula (13) is established, which shows that the sum of the total number of non-moving steel materials and the total number of moving steel materials is the total number n of steel materials that make up the initial pile (original pile and virtual pile).

If the movement presence/absence discrimination variable y _i for steel material i is 1 (y _i = 1), then in the initial pile S _k , the non-moving topmost steel material discrimination variable x _i for that steel material i and all of the steel materials i above it will be 0 (zero, x _i = 0). Conversely, if the movement presence/absence discrimination variable y _i for steel material i is 0 (zero, y _i = 0), then in the initial pile S _k , among the steel material i and the steel materials i above it, only the non-moving topmost steel material discrimination variable x _i for one steel material i will be 1 (x _i = 1). Therefore, for steel material i∈S _k , if the set of the steel material i and the steel materials i above it in the initial pile S _k is defined as S _k ^↑ (i) (see equation (14') below), then the following equation (14-1) holds.

Equation (14-1) expresses that for any steel material i in the initial pile S _k , if that steel material i is a moving steel material, there is no non-moving steel material above it, and if that steel material i is not a moving steel material, that steel material i or one of the steel materials above that steel material i will be the non-moving steel material located at the topmost level among the non-moving steel materials (i.e., there is only one non-moving steel material for which x _i = 1).

Equation (14-1) specifies the relationship between the non-moving topmost steel product discrimination variable x _i and the movement presence/absence discrimination variable y _i for each steel product i. For each initial peak S _k , the relationship between the non-moving topmost steel product discrimination variable x _i and the movement presence/absence discrimination variable y _i can be specified as in the following equation (14-2).

|S _k | on the left side of equation (14-2) is the number of steel products i belonging to the initial peak S _k . The first term on the right side of equation (14-2) is the number of moved steel products belonging to the initial peak S _k . The second term on the right side of equation (14-2) is the number of non-moved steel products belonging to the initial peak S _k .
In this embodiment, both the formulas (14-1) and (14-2) are used, but only one of them may be used.

(e) Constraints prescribing the relationship between the movable steel final pile allocation variable z _ij and the movement/non-movement discrimination variable y _i Any steel material i must be allocated to an original pile j (=1, ..., p (p≧1)) or a new pile j (=p+1, ..., p+m (m=n)). Also, as mentioned above, the movable steel final pile allocation variable z _ij for steel material i that is a non-moving steel material (i.e., steel material i for which the movement/non-movement discrimination variable y _i is 0 (zero)) is defined as 0 (zero, z _ij = 0) for any pile j. Therefore, the following equations (15-1), (15-2), and (15-3) hold.

Formula (15-1) indicates that whether or not steel material i is moved to either original pile j or new pile j is equivalent to whether or not steel material i is a non-movable steel material. Formula (15-2) indicates that steel material i in the portion excluding max(S _k ) from initial pile S _k is a steel material that must be moved (y _i = 1), and therefore is a steel material that will be moved to either original pile j or new pile j. Formula (15-3) indicates that steel material i in the portion of max(S _k ) in initial pile S _k is a steel material for which whether or not it can be moved is a determining factor, and therefore it may be moved to either original pile j or new pile j, or it may not be moved to either original pile j or new pile j (i.e., it may be a moved steel material or a non-movable steel material).

(f) Constraints for transferring to the original mountain (constraints for defining the moving steel product final mountain allocation variable z _ij , constraints for specifying the relationship between the non-moving topmost steel product discrimination variable x _i and the moving steel product final mountain allocation variable z _ij and the allocation mountain identification variable q _j )
For steel materials i _k (∈max(S _k )) constituting original pile (initial pile) k (=1, ..., p), the set of steel materials i that can be placed on steel material i _k is defined as U(i _k ). If steel material i _k is a non-movable steel material that is at the top of the non-movable steel materials in original pile k (i.e., if non-movable topmost steel material discrimination variable x _i is 1 (x _i = 1)), steel material i that cannot be placed on steel material i _k cannot be placed in the original pile k to which steel material i _k belongs. This is expressed by the following equation (16). Equation (16) makes it possible to prohibit an unrealizable final pile from being obtained.

Here, in this embodiment, the set U(i _k ) of steel materials i that can be placed on steel material i _k is specified by the same-peak prohibited steel material pair set F. The same-peak prohibited steel material pair set F is a set of pairs of two steel materials {i, j} ⊆ N of any two steel materials, as shown in the following formula (17), and is a set of pairs of two steel materials that do not satisfy at least one of the width condition and the length condition described above. In addition, the set U(i _k ) of steel materials i that can be placed on steel material i _k is determined taking into consideration not only the relationship with steel material i _k but also with all steel materials below it in the initial peak. In other words, when each pair of steel material i _k and all steel materials below it, and a candidate steel material to be placed on steel material i _k is not included in the same-peak prohibited steel material pair set F, the candidate steel material to be placed on the steel material i _k is included in the set U(i _k ) of steel materials i that can be placed on steel material i _k .

Furthermore, the number of steel materials that can be placed above steel material i _k in the final pile is limited by the height constraint described above. If the number of stacked tiers of steel materials i _k belonging to original pile k, counted from the bottom tier (the number of stacked tiers including the steel material in question and below it, and the number of stacked tiers when the number of stacked tiers of the bottom tier is 1), is designated as b _ik , the height of original pile k can be limited by the following formula (18-1). Note that in formula (18-1), k in b _ik is written as a subscript of i.

Equation (18-1) indicates that the total number of steel materials i to be moved to original pile k must be equal to or less than the upper limit of the number of steel materials that can be placed above the topmost non-movable steel material belonging to that original pile k (initial pile). The right-hand side of equation (18-1) indicates the free space (number of steel materials) that can be created above steel material i _k in original pile k. Equation (18-1) makes it possible to prevent an unrealizable final pile from being obtained.

The formula (18-1) is a constraint formula set for each steel material i belonging to max(S _k ). It can also be set for each original mine k, as in the following formula (18-2).

The first term on the left side of equation (18-2) is the total number of steel products i to be moved to original pile k. The second term on the left side of equation (18-2) is the number of non-moved steel products belonging to max(S _k ). The right side of equation (18-2) represents the upper limit h of the height of original pile k, which will be the final pile. Note that equation (18-1) is a more specific constraint than equation (18-2), so when equation (18-2), which has a wider range of application, is used, equation (18-1) does not need to be used.

Furthermore, if the steel material i _k belonging to the initial mountain k (=1, ..., p) is the non-moving steel material at the top of the non-moving steel materials (the non-moving topmost steel material discrimination variable x _i is 1 (x _i = 1)), the initial mountain (original mountain) k becomes the final mountain, and the following equation (19) holds.

Furthermore, the condition for an original pile (initial pile) k (=1, ..., p) to become a final pile (q _k = 1) is that among the steel materials i _k (∈max(S _k )) that make up the original pile k, there exists a steel material whose non-moving topmost steel material discrimination variable x _ik is 1 (x _ik = 1), and therefore the following equation (19') holds.

It is possible to define a feasible solution without using equation (19'), but using equation (19') can reduce the calculation time.

(g) Mountain Height Constraint for Final Mountain (New Mountain) Other Than the Original Mountain The constraint on the height of the new mountain j (=p+1, . . . , p+m), which is the final mountain other than the original mountain, is expressed by the following equation (20).

Equation (20) expresses that the total number of moving steel products moving from the initial peak to peak j is equal to or less than the upper limit value h of the height of peak j that will become the final peak. Equation (20) makes it possible to prevent an unrealizable final peak from being obtained.
(h) Other constraints on the final pile assignment variable z _ij and the assigned pile identification variable q _j If there is a steel material i being moved to any of the new piles j (=p+1, ..., p+m (m=n)) (z _ij = 1), that pile exists as the final pile, and the following equation (21) holds.

For Niiyama j, it is preferable to restrict the solution space by giving priority to solutions with smaller identification information, as shown in the following equation (22).

Incidentally, equation (22) does not apply to Motoyama (∀j∈{1, . . . , p}).
(i) No same final mountain constraint (width, length constraint)
When the moving steel material is placed in the final pile, the final pile satisfies the stacking shape constraints (width constraint, length constraint), so a constraint that prohibits two pairs of steel materials i1, i2 belonging to the same pile prohibited steel material pair set F from being placed in the same final pile j is defined as shown in the following equation (23).

The constraint in equation (23) is a stack shape constraint between moving steel members, and the stack shape constraint between non-moving steel members and moving steel members is defined by the above-mentioned equation (16). Equation (23) makes it possible to prohibit the attainment of an unrealizable final peak.

(j) Formulation of the transfer transport order In the following explanation, the portion of the initial pile where the non-moving steel products are transported will be referred to as the fixed portion as necessary. Also, the portion of the initial pile above the fixed portion where the transport for transfer is performed will be referred to as the moving portion as necessary. The steel products belonging to the fixed portion of the initial pile are the steel products in each layer from the bottom of the initial pile to the stacking layer number of the steel product i where the non-moving topmost steel product discrimination variable x _i is 1 (x _i = 1).

In strictly formulating the order of transport of steel materials when replacing the steel materials at the top of the fixed part of the initial pile, it is necessary to determine not only the initial transport order when transporting steel materials from the initial pile (disassembling the initial pile), but also the order relationship for all transports, including the final transport order from the temporary pile (temporary storage area) to the final pile (final storage area) for steel materials that will be temporarily stored. The steel materials that will replace the steel materials at the top of the fixed part of the initial pile are steel materials from a pile other than the initial pile (initial pile or temporary pile), or steel materials that will be returned from the initial pile to the initial pile.

On the other hand, by determining the order relationship only for the initial transport order of the steel materials when replacing the steel materials located above the fixed part of the initial ridge, it is possible to make a simple formulation that restricts the transport order of the steel materials when replacing the steel materials located above the fixed part of the initial ridge as a necessary or sufficient condition. In this embodiment, an example of such a simple formulation will be described. Note that a strict formulation will be described in the second embodiment described later.

(j-1) Constraint on initial transport order variable t _ii' The steel material (steel material in the moving part) located at the top of the fixed part of the initial pile S _k is required to be initially transported. If a set I _m of such steel materials is defined as in the following formula (24), the following formulas (25-1) to (25-3) and (26) are obtained. I _m is referred to as a set of steel materials that are required to be moved, as necessary. In addition, t _ii' is a variable that is 1 when steel material i is earlier than steel material i' in the initial transport order, as shown in formula (5), and is 0 otherwise.

Equation (25-1) expresses that when steel materials i, i' located at the top of the fixed portion of the initial mountain S _k are both included in the steel material set I _m that requires movement, and are different steel materials, the initial transport order of one of steel materials i, i' will be first and the initial transport order of the other will be later (only one of t _ii' or t _i'i will be 1).

In formula (25-2), the symbol with a - sign above I _m indicates the set of steel materials i that are not included in the set of steel materials I _m for which movement is mandatory (the complement of I _m ). The meaning of this symbol is the same in other formulas. Steel materials i that are not included in the set of steel materials I _m for which movement is mandatory are steel materials for which it has not been determined whether they are movable steel materials (whether initial transportation is mandatory) or not.

Equation (25-2) expresses that, in the case where steel material i' at the top of the fixed portion of initial pile S _k is included in the steel material set I _m for which movement is essential, and steel material i is not included in the steel material set I _m for which movement is essential, and steel materials i and i' are different steel materials, when steel material i is a moving steel material (movement presence/absence discrimination variable y _i is 1 (y _i = 1)), the initial transportation order of one of steel materials i and i' comes first and the initial transportation order of the other comes later (only one of t _ii' or t _i'i is 1). On the other hand, when steel material i is a non-moving steel material (movement presence/absence discrimination variable y _i is 0 (zero) (y _i = 0)), the order relationship of the initial transportation order of steel materials i and i' is not determined (t _ii' and t _i'i are 0).

Equation (25-3) expresses that when steel materials i, i' are not included in the steel material set I _m for which movement is required, and steel materials i, i' are different steel materials, then when steel materials i, i' are moved steel materials (movement presence/absence discrimination variables y _i , y _i' are 1 (y _i = 1, y _i' = 1)), the initial transport order of one of steel materials i, i' will be first and the initial transport order of the other will be later (only one of t _ii' or t _i'i will be 1).

Equation (26) indicates that when steel materials i, i', and i'' are different steel materials, if steel material i is initially transported before steel material i', and if steel material i' is initially transported before steel material i'', then steel material i is initially transported before steel material i''.

(j-2) Initial pile disassembly order constraint When transporting steel products from the initial pile S _k (disassembling the initial pile), it is necessary to transport the steel products from the top of the initial pile S _k first. Therefore, the following formulas (27-1) to (27-3) hold.

Equation (27-1) expresses that when steel materials i and i' are included in a set of steel materials I _m that requires movement, and when steel material i is on top and steel material i' is below, steel material i will be initially transported before steel material i'.
Equation (27-2) represents that when steel material i is included in a set of steel materials I _m for which movement is mandatory, and steel material i' is included in a set (complement of I _m ) of steel materials i that are not included in a set of steel materials I _m for which movement is mandatory, and when steel material i is on top and steel material i' is on the bottom, if steel material i' is a moving steel material (movement or non-movement discrimination variable y _i is 1 (y _{i '} = 1)), steel material i will be transported before steel material i'. On the other hand, if steel material i' is a non-moving steel material (movement or non-movement discrimination variable y _{i '} is 0 (zero) (y _{i '} = 0)), the order relationship of the initial transport order of steel materials i and i' cannot be determined (t _{ii '} is 0).

Equation (27-3) expresses that in the case where steel materials i, i' are included in a set (complement of I _{m) of steel materials i that are not included in the set I m of} steel materials for which movement is mandatory, and where steel material i is on top and steel material i' is on the bottom, if steel material i' is a moving steel material (movement or non-movement discrimination variable y _i is 1 (y _{i '} = 1)), steel material i will be transported before steel material i'. On the other hand, if steel material i' is a non-moving steel material (movement or non-movement discrimination variable y _{i '} is 0 (zero) (y _{i '} = 0)), the order relationship of the initial transport order of steel materials i, i' cannot be determined (t _{ii '} is 0).

(j-3) Temporary placement occurrence condition constraint When transferring steel materials from the initial pile S _k to the final pile, if the order of initial transportation from the initial pile S _k differs from the dispensing order between two steel materials (if the steel material that is initially transported first among the two steel materials is dispensing first (i.e., if the order of initial transportation and the order of dispensing are the same)), the steel material that is initially transported first needs to be temporarily placed. Therefore, the following formula (28) holds.

Equation (28) indicates that when steel material i is discharged before steel material i', steel material i and i' are placed in the same final pile j, and when steel material i is initially transported before steel material i', steel material i needs to be temporarily placed.

(j-4) Fixed Section Upper Part (Moving Section) Replacement Constraint In an initial mountain S _k where both a fixed section and a moving section exist, replacement of steel materials (moving steel materials) belonging to the moving section is performed.
Fig. 2 is a diagram showing an example of the replacement of a movable steel material. The left side of Fig. 2 shows an example of the shape of an initial peak S _k , and the right side of Fig. 2 shows an example of the shape of a final peak obtained by replacing the movable steel material.

In the example shown in FIG. 2, steel materials 201 and 202 belong to the fixed portion of initial peak S _k . Steel materials 203 to 205 belong to the moving portion of initial peak S _k . In initial peak S _k (k=1, ..., p), the set of steel materials i that belong to the moving portion is defined as S _k ^↑ (this S _k ^↑ is a different symbol from the above-mentioned S _k ^↑ (i)). In the example shown in FIG. 2, steel materials 203 to 205 are the set S _k ^↑ of steel materials i that belong to the moving portion. The set S _k ^↑ of steel materials i that belong to the moving portion will be referred to as the moving portion steel material set S _k ^↑ as necessary.

In addition, in the initial pile S _k , a set of steel materials newly piled on the fixed part is defined as E _k ^↓ . In the example shown in FIG. 2, steel materials 204, 206, and 207 are the set of steel materials E _k ↓ newly piled on the fixed part of the initial pile S _k . The set of steel materials E _k ^↓ newly piled on the fixed part of the initial pile S _k is referred to ^as a set of steel materials E _k ^↓ loaded on the fixed part as necessary. In FIG. 2, steel material 204 is a steel material that is initially transported from the initial pile S _k shown in FIG. 2 to a temporary mountain (temporary storage site) and then re-transported (finally transported) to the initial pile S _k . Steel materials 206 and 207 are steel materials that are finally transported to the initial pile S _k shown in FIG. 2 from a mountain (initial mountain or temporary mountain) different from the initial pile S _k shown in FIG. 2.

When replacing steel materials (movable steel materials) belonging to the moving part of the initial pile S _k , the steel materials belonging to the moving part of the initial pile S _k must be initially transported before the steel materials that are finally transported to the initial pile S _k . In the example shown in FIG. 2, the initial transport of the steel materials 203-205 must be earlier than the final transport of the steel materials 204-207. Therefore, in an initial pile S _k in which both a fixed part and a moving part exist, the condition for replacing the steel materials (movable steel materials) belonging to the moving part with the steel materials that are finally transported onto the fixed part after the initial transport of the steel materials belonging to the moving part is that the initial transport of the moving part steel material set S _k ^↑ (steel materials included in the moving part steel material set E k ↓) must be performed before the final transport of the fixed part loaded steel material set E _k ^↓ (steel materials included in the moving part steel material set). This condition is referred to as a replacement condition as necessary, and the constraint indicating the replacement condition is referred to as a fixed part upper part replacement constraint as necessary.

The replacement condition (fixed section upper replacement constraint) can be imposed on the entire movable section steel material set S _k ^↑ (the steel materials contained therein) and the entire steel material set E _k ^↓ loaded on the fixed section (the steel materials contained therein), but it is only necessary to ensure that it is satisfied between the steel materials at the bottommost levels of each of the movable section steel material set S _k ^↑ and the steel material set E _k ^↓ loaded on the fixed section.

The steel material at the bottom of the movable section steel material collection S _k ^↑ is designated as i _Sb , and the steel material at the bottom of the fixed section steel material collection E _k ^↓ is designated as i _Eb . In the example shown in Fig. 2, steel material 203 is i _Sb , and steel material 204 is steel material i _Eb . A necessary and sufficient condition for replacement is that the initial transport of steel material i _Sb precedes the final transport of steel material i _Eb ("initial transport order of steel material i _Sb < final transport order of steel material i _Eb ").

The steel material immediately below the steel material i _Sb at the bottom of the movable steel material collection S _k ^↑ (the steel material at the top of the fixed part) is designated as i _Sf . Steel material i _Sf is within max(S _k ). In the example shown in FIG. 2, steel material 202 is i _Sf . On the other hand, steel material i _Eb at the bottom of the fixed steel material collection E _k ^↓ can be any steel material that is earlier in the withdrawal order than steel material i _Sf at the top of the fixed part, and cannot be specified. Therefore, the replacement condition (fixed part upper part replacement constraint) is "initial transport order of steel material i _Sb < final transport order of any steel material i _E in the fixed steel material collection E _k ^↓ ".

Furthermore, in this embodiment, since the final conveying order is not specified, the order relationship between the initial conveying order and the final conveying order cannot be specified. Therefore, the sufficient condition for replacement is set as the upper-fixed-part replacement constraint, and "initial conveying order of steel material i _Sb < initial conveying order of any steel material i _E in the steel material ^set E _k loaded on the fixed part (≦ final conveying order of any steel material i _E in the steel material ^set E _k loaded on the fixed part)" is specified as in the following formula (29-1). Furthermore, by adding a temporary placement occurrence variable r _iE for steel material i _E to the right side of formula (29-1), a constraint indicating a necessary condition for replacement can be specified as the upper-fixed-part replacement constraint, as in the following formula (29-2). In formula (29-2), E in r _iE is expressed as a subscript of i. In formula (29-2), a temporary placement occurrence variable r _iSf for steel material i _Sf may be used instead of r _iE . The constraint indicating the necessary condition for replacement (fixed portion upper replacement constraint) can be expressed by an equation other than equation (29-2). For example, the following equation (29-3) may be used instead of equation (29-2).

Formula (29-1) indicates that when steel material i _Sf is within max(S _k ), the steel material i _Sf is the non-moving steel material at the top of the non-moving steel materials (x _iSf =1), and when steel material i _E is placed in the initial pile S _k (z _iEk =1), the initial transport of steel material i _Sb at the bottom of the moving steel material set S _k ^↑ must precede the initial transport of steel material i _E (t _iSbiE =1). However, if steel material i _E is temporarily placed and its final transport order is later than the initial transport order of steel material i _Sb , the replacement is established even if steel material i _E is first in the initial transport order, so this condition is a sufficient condition. In formula (29-1), Sf of x _iSf is expressed as a subscript of i. E of z _iEk is expressed as a subscript of i. In t _iSbiE , Sb is written as a subscript symbol of i, and E is written as a subscript symbol of i.

When the steel material _iE is temporarily placed (r _iE = 1), the formula (29-2) becomes a self-evident formula and is not a constraint. Therefore, it is a necessary condition. The formula (29-2) indicates that the constraint explained in the formula (29-1) is imposed when the steel material _iE is not temporarily placed.

Equation (29-3) indicates that when steel material i _Sk is in initial pile S _k , steel material i _C is placed in initial pile S _k (z _iCk =1), and when the initial transport of steel material i _C precedes the initial transport of steel material i _Sk (t _iCiSk =1), steel material i _C must be temporarily placed (r _iC =1). If the initial transport of steel material i _C precedes the final transport of steel material i _Sk , the replacement condition (necessary and sufficient condition) is satisfied, so equation (29-3) becomes a constraint indicating the necessary condition for replacement. Equation (29-3) requests that when the initial transport of steel material in steel material set E _k ^↓ loaded on the fixed part is performed before the initial transport of steel material in steel material set S _k ^↑ , the steel material in steel material set E _k ^↓ loaded on the fixed part is temporarily placed.
In addition, in the formula (29-3), C in z _iCk , t _iCiSk , and r _iC is written as a subscript symbol of i, and Sk in t _iCiSk is written as a subscript symbol of i.

The constraint equation/objective function setting unit 102 sets the constraint equations by setting i, j, S, S k , p, n, N, F, h, b i , and m for, for example, equations (9) to (13), equations (14-1) to (14-2), equations (15-1) to (15-3), equations (16) to (17), equations (18-1) or (18-2), equation (19), equation (19′), equations (20) to (23), equations (25-1) to (25-3), equation (26), equations (27-1) to (27-3), equation ( _{28 )} , equation (29-1), and equation (29-2) or (29-3).

<<Objective function>>
Next, the objective function will be described.
As described above, the objective of this embodiment is to minimize the total number of steel material conveyances and the total number of final piles. The total number of steel material conveyances is expressed as the sum of the total number of moving steel materials and the total number of temporarily placed steel materials. Therefore, the objective function J shown in the following equation (30) is used.

In this embodiment, as shown in equation (30), the total number of conveyances of steel materials (Σ(y _i
The objective function is a weighted linear sum of the total number of conveyances of steel material (Σq _j in equation (30)) and the total number of final peaks (Σq j in equation (30 ₎ ). The weighted linear sum refers to the sum of the values obtained by multiplying the weighting coefficient k ₁ for the total number of conveyances of steel material and the weighting coefficient k ₂ for the total number of final peaks by the total number of conveyances of steel material and the total number of final peaks, respectively. The weighting coefficient k ₁ for the total number of conveyances of steel material is a coefficient that represents the balance between the evaluation of the total number of conveyances of steel material and the evaluation of the total number of final peaks. The weighting coefficient k ₂ for the total number of final peaks is a coefficient that represents the balance between the evaluation of the total number of final peaks and the evaluation of the total number of conveyances of steel material. If the weighting coefficient k ₁ for the total number of conveyances of steel material is set to a value larger than the weighting coefficient k ₂ for the total number of final peaks, for example, the amount of decrease in the value of the objective function J is greater when the total number of conveyances of steel material is reduced by one than when the total number of final peaks is reduced by one. Therefore, the objective function J in this case is an objective function that places more importance on the evaluation of the total number of conveyances of steel materials than on the evaluation of the total number of final peaks. Conversely, if the weighting coefficient _k2 for the total number of final peaks is set to a value greater than the weighting coefficient _k1 for the total number of conveyances of steel materials, for example, the reduction in the value of the objective function J is greater when the total number of final peaks is reduced by one than when the total number of conveyances of steel materials is reduced by one. Therefore, the objective function J in this case is an objective function that places more importance on the evaluation of the total number of final peaks than on the evaluation of the total number of conveyances of steel materials. In this way, the objective function J in formula ( ₃₀ ) can balance the evaluation of the total number of conveyances of steel materials and the evaluation of the total number of final peaks by the weighting coefficients _k1 and k2. In other words, formula (30) is an objective function that finds the minimum value of the total number of conveyances of steel materials and the minimum value of the total number of final peaks after balancing such evaluations (under the conditions of such balance of evaluations). In this way, by using equation (30) as the objective function J, which has the total number of steel transports (total number of steel materials to be moved and total number of steel materials to be temporarily stored) and the total number of final piles as decision variables, a balance can be achieved between minimizing the total number of steel transports and minimizing the total number of final piles.

The constraint equation/objective function setting unit 102 sets the objective function J by setting i, j, k ₁ , and k ₂ for equation (30), for example.

[Optimization calculation unit 103]
The optimization calculation unit 103 performs a first optimization calculation and a second optimization calculation. The second optimization calculation is performed when the result (optimal solution) of the first optimization calculation does not satisfy the replacement condition. On the other hand, when the result (optimal solution) of the first optimization calculation satisfies the replacement condition, the second optimization calculation is not performed.

In the first optimization calculation, of the constraint equations (equations (29-1) to (29-3)) for the fixed part upper (moving part) replacement constraint, the constraint equation (equation (29-2) or (29-3)) indicating the necessary condition for replacement is used. In the second optimization calculation, of the constraint equations (equations (29-1) to (29-3)) for the fixed part upper (moving part) replacement constraint, the constraint equation (equation (29-1)) indicating the sufficient condition for replacement is used.

Therefore, the optimization calculation unit 103 calculates the decision variables (non-moved topmost steel material discrimination variable x j , movement/non-movement discrimination variable y i , moved steel material final mountain allocation variable z ij , allocated mountain identification variable q j ) when the value of the objective function J in equation (30) is minimized within the range satisfying the constraint equations of equations (9) to (13), (14-1) to (14-2), (15-1) to (15-3), (16) to (17), (18-1) or (18-2), (19), (19'), (20) to (23), (25-1) to ( _25-3 ) _, (26), (27-1) to (27-3), ( ₂₈₎ , and (29-2) or ( _29-3) . , temporary placement occurrence variable r _i , and initial transport order variable t _ii′ ) as an optimal solution, thereby executing a first optimization calculation. Note that the calculation of the optimal solution can be realized by using a known algorithm (including the use of a solver, etc.) for solving an optimization problem by mathematical programming such as mixed integer programming.

The optimization calculation unit 103 also calculates the decision variables (non-moved topmost steel material discrimination variable x j , movement/non-movement discrimination variable y i , moved steel material final mountain allocation variable z ij , allocated mountain identification variable q j , provisional placement occurrence/non-occurrence variable r i ) when the value of the objective function J in the equation (30) is minimized within a range satisfying the constraint equations of the equations (9) to (13), (14-1) to (14-2), (15-1) to (15-3), (16) to (17), (18-1) or (18-2), (19), (19'), (20) to ( ₂₃ ), (25-1) to (25-3), (26), (27-1) to (27-3 _{) ,} ( ₂₈₎ , and ( _29-1 ) , and the initial transport order variable t _ii′ ) as an optimal solution, thereby executing a second optimization calculation.

[Determination unit 104]
As described above, in the first optimization calculation, among the constraint equations (equations (29-1) to (29-3)) for the fixed section upper (movable section) replacement constraint, the constraint equation (equation (29-2) or (29-3)) indicating the necessary conditions for replacement is used. Therefore, there is a possibility that the result of the first optimization calculation (optimum solution) does not satisfy the replacement condition ("initial transport order of steel material i _Sb < final transport order of any steel material i _E in the set of steel materials E _k loaded on the fixed section ^↓ ")). For this reason, the determination unit 104 determines whether the result of the first optimization calculation by the optimization calculation unit 103 (optimum solution) satisfies the replacement condition. This determination can be automatically made by the determination unit 104 based on the result of the first optimization calculation. In addition, the optimization calculation unit 103 may display information indicating the result of the first optimization calculation (optimum solution) on the display device. In this case, the operator checks whether the replacement condition is satisfied based on the display, and inputs the confirmed result to the yard management device 100. The determination unit 104 determines, based on the input result, whether or not the result of the first optimization calculation (optimum solution) satisfies the replacement condition.

If the result of this determination is that the result (optimal solution) of the first optimization calculation by the optimization calculation unit 103 does not satisfy the replacement condition, the optimization calculation unit 103 executes a second optimization calculation. As described above, in the second optimization calculation, among the constraint equations (equations (29-1) to (29-3)) for the fixed section upper (movable section) replacement constraint, the constraint equation (equation (29-1)) indicating the sufficient condition for replacement is used. Therefore, the result (optimal solution) of the second optimization calculation will not fail to satisfy the replacement condition ("initial transport order of steel material i _Sb < final transport order of any steel material i _E in steel material set E _k loaded on the fixed section ^↓ ").

[Output unit 105]
When the judgment unit 104 judges that the result (optimal solution) of the first optimization calculation by the optimization calculation unit 103 satisfies the replacement condition, the output unit 105 outputs information indicating the transportation order of each steel material included in the steel material set N from the initial pile to the final pile, as identified from the result (optimal solution) of the first optimization calculation.
When the judgment unit 104 judges that the result (optimal solution) of the first optimization calculation by the optimization calculation unit 103 does not satisfy the replacement condition, the output unit 105 outputs information indicating the transportation order of each steel material included in the steel material set N from the initial pile to the final pile, which is identified from the result (optimal solution) of the second optimization calculation.

In addition to or instead of this information, the output unit 105 may output at least one of the following: identification information of the movable steel and non-movable steel, the total number of final piles, the stacking shape of the final piles, and identification information of the steel to be temporarily stored. 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. Examples of external devices include a crane or a control device that controls the operation of the crane.

(flowchart)
FIG. 3 is a flowchart illustrating an example of a yard management method performed by the yard management device 100. As shown in FIG.
In step S301, the steel material information acquisition unit 101 acquires steel material information.

Next, in step S302, the constraint equation/objective function setting unit 102 sets the constraint equations ((9) to (13), (14-1) to (14-2), (15-1) to (15-3), (16) to (17), (18-1) or (18-2), (19), (19'), (20) to (23), (25-1) to (25-3), (26), (27-1) to (27-3), (28), (29-1), and (29-2) or (29-3).

Next, in step S303, the constraint equation/objective function setting unit 102 sets the objective function J (equation (30)).
Next, in step S304, the optimization calculation unit 103 executes a first optimization calculation, in which equation (29-2) or equation (29-3) is used, and equation (29-1) is not used.

Next, in step S305, the determination unit 104 determines whether or not the result (optimal solution) of the first optimization calculation in step S304 satisfies the replacement condition. If the result of this determination indicates that the result (optimal solution) of the first optimization calculation in step S304 satisfies the replacement condition (YES in step S305), the process of step S306 is executed.
In step S306, the output unit 105 outputs information indicating the transportation order of each steel material contained in the steel material collection N, from the initial pile to the final pile, identified from the result (optimal solution) of the first optimization calculation in step S304.

On the other hand, in step S305, if the result (optimal solution) of the first optimization calculation in step S304 does not satisfy the replacement condition (NO in step S305), the process proceeds to step S307.
In step S307, the optimization calculation unit 103 executes a second optimization calculation, in which equation (29-1) is used, but equations (29-2) and (29-3) are not used.

When the processing of step S307 is completed, in step S306, the output unit 105 outputs information indicating the transport order of each steel material contained in the steel material collection N from the initial pile to the final pile, which is identified from the result (optimal solution) of the second optimization calculation in step S307.

(summary)
As described above, in this embodiment, the yard management device 100 solves a mathematical programming problem aimed at minimizing the total number of steel material transports and the total number of final piles, thereby classifying the steel material constituting the initial piles into either movable steel material or non-movable steel material, and at least determining the order of transport of movable steel material and whether or not temporary storage occurs when the movable steel material is moved. Therefore, when creating a metal material transport plan for transferring metal material from the initial pile to the final pile, it is possible to balance minimizing the total number of final piles and minimizing the number of transports of metal material while determining which steel material constituting the initial pile is to be moved and which metal material is to be moved. In addition, when determining the total number of final piles and the total number of steel material transports, movable steel material and non-movable steel material, the order of transport of each steel material, and whether or not temporary storage occurs for each steel material are simultaneously determined. In this way, by considering the order of transport of each steel material and whether or not temporary storage occurs for each steel material, it is possible to create a transport plan in which the total number of steel material transports is reduced compared to, for example, a case in which only the total number of movable steel materials is considered.

In this embodiment, variables including the initial conveying order variable t _ii' , the temporary placement occurrence variable r _i , the movement presence/absence discrimination variable y _i , and the moved steel material final pile allocation variable z _ij are used as decision variables, and the decision variables are derived when the value of the objective function J, which aims to minimize the total number of steel material conveyances and the total number of final piles, is minimized. Therefore, the mathematical programming problem can be formulated and solved.

In this embodiment, a decision variable is derived when the value of the objective function J is minimized within a range satisfying a constraint equation including a first constraint affecting the total number of times steel materials are transported and a second constraint affecting the total number of final piles. Here, the first constraint includes a constraint equation (equations (25-1) to (26)) expressing the relationship between the relative orders of transport of two steel materials using decision variables (movement presence/absence discrimination variable y _i and initial transport order variable t _ii' ), and a constraint equation (equation (28)) expressing that the metal materials in the same initial pile must be transported from the metal materials on the initial pile using decision variables (temporary placement occurrence presence/absence variable r _i and moved steel material final pile allocation variable z _ij ). The second constraint includes a constraint equation (equation (16)) expressing a constraint on steel materials that cannot be placed on steel materials that are not moved from the initial pile using decision variables (non-moved topmost steel material discrimination variable x _i , movable steel material final pile allocation variable z _ij ), constraint equations (equations (18-2) and (20)) expressing a constraint on the upper limit value of the mountain height of the final pile using decision variables (non-moved topmost steel material discrimination variable x _i , assigned mountain identification variable q _j , movable steel material final pile allocation variable z _ij ), and a constraint equation (equation (23)) expressing a constraint on the two metal materials that are prohibited from being placed in the same final pile using decision variables (assigned mountain identification variable q _j , movable steel material final pile allocation variable z _ij ). Therefore, it is possible to prevent the creation of a transportation plan that cannot actually be transported.

In this embodiment, the constraint equations expressing the relationship between the relative orders of transport of two steel materials include constraint equations (equations (25-2) to (25-3)) which indicate that the order relationship of the initial transport order of steel materials including steel materials which are uncertain as to whether they are moving steel materials is determined by the value of the movement presence/absence discrimination variable y _i . Therefore, even when steel materials which are uncertain as to whether they are moving steel materials are included, the initial transport order of steel materials can be determined.

Furthermore, in this embodiment, when steel material i _k is the non-movable steel material that is at the top of the non-movable steel materials in original pile _k , a constraint equation (equation (16)) is further used that expresses, using decision variables (non-movable topmost steel material discrimination variable x _i and movable steel material final pile allocation variable z _ij ), that a steel material i that cannot be loaded on the steel material i _k cannot be placed in the original pile k to which the steel material i k belongs. Therefore, it is possible to prevent the creation of a transportation plan in which a steel material that cannot be placed on top of a non-movable steel material is placed on top of a non-movable steel material.

Furthermore, in this embodiment, when the initial transportation of steel material in the fixed-section-loaded steel material collection E _k ^↓ occurs before the initial transportation of steel material in the movable-section steel material collection S _k ^↑ , constraint equations ( _equations (29-1) to (29-3)) are further used that express, using decision variables (movable steel material final pile allocation variable z _ij and initial transportation order variable t _ii' ), that the steel material in the fixed-section ^- loaded steel material collection E k ↓ will be temporarily stored. Therefore, it is possible to prevent the creation of a transportation plan that makes it impossible to replace the movable section steel material in the initial pile S _k .

In addition, in this embodiment, a constraint equation (equation (9)) is further used to restrict steel materials that are not in the partial pile max(S _k ) consisting of steel materials from the bottommost steel material to those in the payout order (the payout order is descending from bottom to top) to be mobile steel materials, and non-moving steel materials (non-moving topmost steel material discrimination variable x _i ) are determined from the steel materials in max(S _k ). Therefore, the number of steel materials to be determined as moving and non-moving steel materials can be reduced.
(Modification)
In each embodiment, a minimization problem for minimizing the value of the objective function J in equation (30) has been described as an example. However, for example, the problem may be a maximization problem by multiplying each term on the right side of equation (30) by (-1).

In addition, in each embodiment, the case where the steel materials are moved (transported) one by one has been described as an example. However, the method of this embodiment can also be applied when the steel materials are moved (transported) in units of steel material groups. A steel material group refers to a collection of one or more steel materials that is not divided (the smallest unit) when transported by a transport device (mainly a crane). In this case, the width constraint is satisfied, for example, when the maximum width of a certain steel material group is narrower than the minimum width of any steel material group located below the certain steel material group, or when the maximum width of a certain steel material group is wider than the minimum width of any steel material group located below the certain steel material group, and the difference between the respective widths is less than a reference value (for example, 200 [mm]). The length constraint is satisfied, for example, when the maximum length of a certain steel group is shorter than the minimum length of any steel group located below the certain steel group, or when the maximum length of a certain steel group is longer than the minimum length of any steel group located below the certain steel group and the difference between the lengths is less than a reference value (for example, 2000 mm). For example, the number of steel materials can be expressed using the number w _i of steel materials included in (one) steel group i.

In addition, using the movement presence/absence discrimination variable y _i as in this embodiment is preferable because it allows the algorithm (constraint equation and objective function) to be described in an intuitively easy-to-understand manner. However, as shown in equation (15-1), the movement presence/absence discrimination variable y _i can be expressed using the movement steel-material final pile allocation variable z _ij . Therefore, it is not always necessary to use the movement presence/absence discrimination variable y _i .
In addition, in this embodiment, an example has been described in which the second optimization calculation is executed when the result (optimum solution) of the first optimization calculation does not satisfy the replacement condition. This is preferable because it is possible to more appropriately balance the minimization of the total number of final peaks and the minimization of the total number of conveyances of steel materials. However, this is not necessarily required. For example, only one of the result of the first optimization calculation and the second optimization calculation may be executed. In this case, the judgment unit 104 is not necessary.

The storage area between processes may be a storage area between two manufacturing processes, and the metal material may be a semi-finished product, or the storage area between processes may be a storage area between a manufacturing process and a shipping process, and the metal material may be a final product. In this case, if multiple metal materials are stored in a container and transported and placed, the container in which the metal materials are stored may be treated as one metal material. Furthermore, the storage area between processes is not limited to storage areas in metal manufacturing processes, but may also be general logistics and transportation between processes. In the field of logistics, it is not limited to the contents, and can also be applied to the transportation and placement of containers. Therefore, in the present invention, the metal material includes any one of a final product, a semi-finished product, and a container.

((Second embodiment))
Next, the second embodiment will be described. In the first embodiment, as described in the section "(i-4) Fixed-part upper (moving part) replacement constraint", the initial transport order variable t _ii' is used as a decision variable, only the initial transport order of the steel material is considered, and a constraint indicating a necessary or sufficient condition for replacement is used as the fixed-part upper replacement constraint. In contrast, in this embodiment, a case in which a constraint indicating a necessary and sufficient condition for replacement is used as the fixed-part upper replacement constraint will be described. Thus, the main difference between this embodiment and the first embodiment is the content of the fixed-part upper replacement constraint. Therefore, in the description of this embodiment, the same parts as those in the first embodiment are given the same reference numerals as those in FIGS. 1 to 3, and detailed description thereof will be omitted.

(Decision variable)
In this embodiment, instead of the initial transport order variable t _{ii '} , a total transport order variable v _s,s' defined by the following equation (31) is used as a decision variable.

The total transport order variable v _s,s' is a 0-1 variable that is 1 if transport s precedes transport s' and is 0 (zero) otherwise.
Since the total transportation order of steel materials when transferring the steel materials from the initial pile S _k to the final pile is a total order of the set N + N' (transitive, antisymmetric and complete binary relation), the total transportation order variable v _s,s' that determines the total transportation order of steel materials (initial transportation order and final transportation order) satisfies the antisymmetric law, the perfect law (comparable) and the transitive law (see equations (33-1) to (34)).

The variable s for identifying the transport is used as the parameter of the total transport order variable v _s,s' . As described in the first embodiment, the variable i is numbered in the order of dispensing of the steel materials (the earlier the dispensing order, the smaller the value of the variable i). The value of the variable s indicating the initial transport of the steel material i is i (s = i). The value of the variable s indicating the final transport of the steel material i is i + n (s = i + n). Therefore, by expressing the parameter s of the total transport order variable v _s,s' using i (for example, v _i,i' , v _{i,i + n} ), it is possible to distinguish between the initial transport and the final transport, so this will be expressed in the following. On the other hand, when the initial transport and the final transport are not distinguished, the parameter s of the total transport order variable v _s,s' is expressed as s (for example, v _s,s' ).

When steel material i is not temporarily placed, the initial and final transports of steel material i are the same transport, so the order relationship between the initial and final transports of steel material i cannot be determined. Therefore, when steel material i is not temporarily placed, v _i,i+n = v _i+n,i = 0 is defined. In addition, when at least one of steel materials i and i' is a non-moving steel material, v _i,i' = v _i'i = 0 is defined.
The other decision variables are the same as those described in the first embodiment.

(Functional configuration of the yard management device 400)
Fig. 4 is a diagram showing an example of the functional configuration of yard management device 400. The hardware of yard management device 400 is realized by using, for example, an information processing device including a CPU, ROM, RAM, HDD, and various interfaces, or dedicated hardware. Fig. 5 is a flowchart explaining an example of a yard management method by yard management device 400.

[Steel material information acquisition unit 401, steel material information acquisition step S501]
The steel material information acquisition unit 401 acquires steel material information on the steel materials to be piled up. The steel material information acquisition unit 401 is the same as the steel material information acquisition unit 101 of the first embodiment.

[Constraint equation/objective function setting unit 402, constraint equation setting step S502, objective function setting step S503]
In this embodiment, the content of "(j) Formulation of the transshipment transport order" described in the first embodiment is changed as follows.
(j-1) Constraint on all conveying order variables v _i,i' The relationship between the initial conveying i and the final conveying i+n of the same steel material i is expressed by the following formula (32). As described above, when steel material i is not temporarily placed, v _i,i+n = v _i+n,i = 0. Therefore, when steel material i is temporarily placed, the following formula (32') holds.

When transporting different steel materials i and i', the order is fixed, so the following equations (33-1) to (33-9) hold. The transition law is expressed by the following equation (34).

Equations (33-1) to (33-9) are extensions of equations (25-1) to (25-3) to initial transfers, final transfers, and initial and final transfers. Equation (34) corresponds to equation (26).

(j-2) Initial pile disassembly order/final pile construction order constraints When transporting steel products from the initial pile S _k (disassembling the initial pile), it is necessary to transport the steel products from the top of the initial pile S _k first. Therefore, the following formulas (35-1) to (35-3) hold true.

Equation (35-1) expresses that when steel materials i and i' are both included in a set of steel materials I _m that must be moved, and when steel material i is on top of an initial pile S _k and steel material i' is on the bottom, steel material i will be initially transported before steel material i' (v _i,i' = 1, v _i',i = 0).

Equation (35-2) expresses that when steel material i is included in the set of steel materials I _m for which movement is essential, steel material i' is not included in the set of steel materials I _m for which movement is essential, and there is steel material i on the top and steel material i' on the bottom in the initial pile S _k , if steel material i' is a moving material (y _i' =1), then steel material i will be initially transported before steel material i' (v _i,i' =y _i' , v _i',i =0). If steel material i' is not a moving material, the order relationship between steel materials i and i' cannot be determined, so v _i,i' =v _i',i =0.

Equation (35-3) expresses that when neither steel material i nor i' is included in the steel material set I _m that requires movement, and when steel material i is at the top and steel material i' is at the bottom in the initial pile S _k , if steel material i' is a moving steel material (y _i' =1), then steel material i will be initially transported before steel material i' (v _i,i' =y _i' , v _i',i =0). If steel material i' is not a moving steel material, the order relationship between steel materials i and i' cannot be determined, so v _i,i' =v _i',i =0.

Transportation to the final mountain (final transport i+n∈N') must be performed in order starting from the bottom of the final mountain. Therefore, the following equations (36-1) to (36-4) hold true.

Equation (36-1) indicates that when the ejection order of steel material i is later than the ejection order of steel material i', and both steel materials i and i' located at the top of the fixed part of the initial pile S _k are included in the steel material set I _m that requires movement, when steel materials i and i' are placed in the same final pile j, the final transportation of steel material i will come before the final transportation of steel material i' (v _i+n,i'+n = 1) (which indicates that steel material i' is stacked on top of steel material i in the final pile j).

Equation (36-2) expresses that when the discharge order of steel material i is later than the discharge order of steel material i', steel material i is not included in the steel material set I _m for which movement is required, and steel material i' is included in the steel material set I _m for which movement is required, when steel materials i and i' are placed in the same final pile j, and steel material i is a moving steel material (y _i = 1), the final transportation of steel material i will be before the final transportation of steel material i' (v _i+n,i'+n = 1).

Equation (36-3) expresses that when the discharge order of steel material i is later than the discharge order of steel material i', steel material i is included in the steel material set I _m where movement is required, and steel material i' is not included in the steel material set I _m where movement is required, when steel materials i and i' are placed in the same final pile j, and steel material i' is a moving steel material (y _i' = 1), the final transportation of steel material i will be before the final transportation of steel material i' (v _i+n,i'+n = 1).

Equation (36-4) expresses that when the ejection order of steel material i is later than the ejection order of steel material i', and when steel materials i and i' are not included in the steel material set I _m for which movement is required, and when steel materials i and i' are placed in the same final pile j, and when steel materials i and i' are both moving steel materials (y _i = y _i' = 1), the final transportation of steel material i will be before the final transportation of steel material i' (v _i+n,i'+n = 1).

(j-3) Temporary placement occurrence condition constraint In a steel pair (i, i') (∈N ² ) consisting of two steel materials, if the initial transport of steel material i precedes the initial transport of steel material i' and the final transport of steel material i' precedes the final transport of steel material i (steel materials v _i,i' = 1 and v _i'+n,i+n = 1), steel material i will be initially transported from the initial pile S _k , followed by initial transport of steel material i', and steel material i' will be finally transported to the final pile, followed by final transport of steel material i. In this case, since the initial transport order and final transport order of the steel materials of the steel pair (i, i') are different, steel material i must be temporarily placed. Therefore, the following formula (37) holds.

(j-4) Fixed section upper part (movable section) replacement constraint In this embodiment, the initial transport order and final transport order of steel material i are determined, so that the fixed section upper part replacement constraint can be formulated as a constraint showing a necessary and sufficient condition for replacement. If the steel material in the next step above steel material i _k in max(S _k ) is steel material i _k' , the necessary and sufficient condition for replacement ("initial transport order of steel material i _k' < final transport order of any steel material i _E in steel material set E _k loaded ^on the fixed section") is expressed as the following formula (38).

Equation (38) indicates that when steel material i _k is in max(S _k ) and steel material i is included in a steel material set I _m for which movement is required, steel material i _k is a non-moving steel material at the top (x _ik =1), and when steel material i is placed in the initial pile S _k , the initial transport order of steel material i _{k '} is earlier than the final transport order of steel material i (v _{ik ',i+n} =1). However, i+n in v _{ik ',i+n} is the final transport order of steel material i that is finally transported from a pile other than the initial pile S _k to the initial pile S _k . In addition, in equation (38), k in x _ik is expressed as a subscript of i. k in _{v ik ',i+n} is expressed as a subscript of i.

The other constraint equations are the same as those described in the first embodiment. In addition, the objective function J is the same as the objective function J (equation (30)) described in the first embodiment.

[Optimization calculation unit 403, optimization calculation step S504]
In the first embodiment, the first optimization calculation and the second optimization calculation are performed using the constraint equation (equation (29-2) or (29-3)) indicating the necessary condition for replacement and the constraint equation (equation (29-1)) indicating the sufficient condition for replacement, respectively. In contrast, in the present embodiment, the constraint equation (equation (38)) indicating the necessary and sufficient condition for replacement is used. Therefore, the result of the optimization calculation (optimal solution) will never fail to satisfy the replacement condition. Therefore, the optimization calculation needs to be performed only once.

Therefore, the optimization calculation unit 403 calculates the decision variables (non-moving topmost steel material discrimination variable x j , movement/non-moving discrimination variable y i ) when the value of the objective function J in equation (30) is minimized within a range satisfying the constraint equations (9) to (13), (14-1) to (14-2), (15-1) to (15-3), (16) to (17), (18-1) or (18-2), (19), (19'), (20) to (23), (32), (32'), (31-1) to (33-9), (34), (35-1) to (35-3), (36-1) to ( _36-4 ), and (37) to ( ₃₈ ). , moving steel material final pile allocation variable z _ij , allocation pile identification variable q _j , temporary storage occurrence variable r _i , and total transport order variable v _i,i' are calculated as optimal solutions to perform optimization calculations.

[Output unit 404, output step S505]
The output unit 404 outputs information indicating the transport order from the initial pile to the final pile of each steel material included in the steel material collection N, which is specified from the result of the optimization calculation (optimal solution) by the optimization calculation unit 403. In addition to or instead of this information, the output unit 404 may output at least one of identification information of movable steel materials and non-movable steel materials, the total number of final piles, the stacking form of the final pile, and identification information of steel materials to be temporarily stored.

(summary)
As described above, in this embodiment, the yard management device 400 uses the total conveying order variable v _i,i' as a decision variable instead of the initial conveying order variable t _ii' . Therefore, the necessary and sufficient condition for replacement ("initial conveying order of steel material i _k' < final conveying order of any steel material i _E in the steel material set E _k loaded on the fixed section ^↓ ") can be formulated as the upper fixed section replacement constraint. Therefore, it is possible to more appropriately balance the minimization of the total number of final piles and the minimization of the total number of conveyances of steel materials.

In this embodiment as well, the various modified examples described in the first embodiment can be adopted.

((Third embodiment))
Next, the third embodiment will be described. In the first embodiment, the steel materials to be temporarily placed are obtained, but the shape of the temporary steel materials (shape of the temporary mountain: which temporary steel materials are located in which temporary mountain and in which stacking order) is not determined. For this reason, the shape of the temporary mountain can be derived in post-processing by a known method based on the steel materials to be temporarily placed and the transport order of the steel materials (see the section "(d) of (A) Assumption (Premise)" described in the first embodiment). In contrast, in this embodiment, a case will be described in which the shape of the temporary mountain is determined simultaneously by optimization calculation along with the transport order of the steel materials and the shape of the final mountain. Therefore, in this embodiment, there is no assumption of "(d) of (A) Assumption (Premise)" described in the first embodiment. Thus, the present embodiment and the first embodiment mainly differ in the method of determining the shape of the temporary mountain. Therefore, in the description of this embodiment, the same parts as those in the first embodiment are given the same reference numerals as those in FIG. 1 to FIG. 3, and detailed description will be omitted.

(Decision variable)
In this embodiment, in addition to the decision variables described in the first embodiment, a temporary steel material temporary mount allocation variable u _ij , an allocated temporary mount identification variable p _j , and a final transport order variable w _ii' are used as decision variables. The temporary steel material temporary mount allocation variable u _ij is defined as in the following formula (39), the allocated temporary mount identification variable p _j is defined as in the following formula (40), and the final transport order variable w _ii' is defined as in the following formula (41).

Here, the steel material to be moved that is temporarily placed will be referred to as "temporarily placed steel material" as necessary.
The temporary steel material temporary mountain allocation variable u _ij is a 0-1 variable that is 1 when the temporary steel material i is placed on the temporary mountain j, and is 0 (zero) otherwise.
The assigned temporary mountain identification variable p _j is a 0-1 variable that is set to 1 when a new mountain j (=p+1, . . . , p+m) is assigned as a temporary mountain, and is set to 0 (zero) otherwise.
The final conveying order variable w _ii' is a 0-1 variable that is 1 when the final conveying of steel material i precedes the final conveying of steel material i', and is 0 (zero) otherwise. However, the final conveying order variable w _ii' is defined as follows: when steel materials i and i' are both moving steel materials, either w _ii' or w _i'i is 1 according to formula (41), and when at least one of steel materials i and i' is a non-moving steel material, w _ii' = w _i'i = 0.

Using the temporary steel material temporary pile allocation variable u _ij , whether or not to temporarily place steel material i is determined by Σ _j∈T u _ij
(T: a set of temporary storage). Therefore, in this embodiment, the temporary storage occurrence presence/absence variable r _i is not necessary. The elements of the temporary storage set T are the identification numbers of the temporary storage, and are represented as T={1, 2, ..., t _max }.

(Functional configuration of the yard management device 100)
The yard monitoring device of this embodiment is realized by changing some of the functions of the various units of the yard management device 100 shown in Fig. 1. Therefore, the same reference numerals as those in Fig. 1 are used, and an example of the functional configuration of the yard management device of this embodiment will be described, focusing on the parts that differ from the first embodiment.

[Steel material information acquisition unit 101]
The steel material information acquiring unit 101 acquires weighting coefficient _k3 in addition to the information described in the first embodiment. Therefore, the steel material information acquired by the steel material information acquiring unit 101 includes steel material basic information, information specifying the stacking form of the initial pile of each steel material, information specifying the upper limit value h of the height of the final pile, and weighting coefficient _k3 in addition to weighting coefficients _k1 and _k2 . Note that the upper limit value of the height of the rockery is the same as the upper limit value h of the height of the final pile, so the upper limit value h of the height of the final pile is used to represent the upper limit value h of the height of the rockery.

[Constraint equation/objective function setting unit 102]
<<Constraint expression>>
In this embodiment, the constraint expressions described in the first embodiment are added and modified as follows.
(k) Constraints on the final transport order variable w _ii' Since the order in which the steel products are transported to the final pile is also a total order (transitive, antisymmetric and completely binary relation), the final transport order variable w _i,i' which determines the order of the final transport of the temporary steel products satisfies the antisymmetric law, the perfect law (comparable) and the transitive law, as shown in the following equations (42-1) to (43).

The formulas (42-1) to (42-3) correspond to the formulas (25-1) to (25-3), and the formula (43) corresponds to the formula (26).
Equations (42-1) to (43) are constraint equations added to the constraint equations explained in the first embodiment.

(j-3) Temporary placement occurrence condition constraint The condition for temporary placement of steel material i is expressed by equation (28). By using the final conveying order variable w _ii' , the condition for temporary placement of steel material i can be described more clearly. If steel material i is initially conveyed from the initial pile S _k and then steel material i' is initially conveyed, and if steel material i' is finally conveyed to the final pile and then steel material i is finally conveyed, steel material i must be temporarily placed. This is expressed by the following equation (44).

Equation (44) is a constraint equation used in place of equation (28).

(l) Constraint on whether or not temporary materials i and i' can be placed on the same temporary material mount The condition for temporary steel materials i and i' to be able to be placed on the same temporary material mount is that the initial transport order and final transport order of temporary steel materials i and i' are different (for example, if temporary steel material i is initially transported before temporary steel material i', then temporary steel material i' needs to be finally transported before temporary steel material i). In other words, if temporary steel materials i and i' are to be placed on the same temporary material mount j (u _ij = u _i'j = 1), then it is necessary that the initial transport order and final transport order of temporary steel materials i and i' are different (t _ii' = w _i'i (w _ii' = t _i'i )). This is expressed by the following equation (45).

Equation (45) is an additional constraint equation to the constraint equation described in the first embodiment.

(m) Constraint on Stacked Shape of Rock Pile The constraint on the height of rock pile j (∈T) is expressed by the following equation (46).

Equation (46) indicates that the total number of movable steel materials (temporarily placed steel materials) i placed on a temporary mountain j is equal to or less than the upper limit h of the height of the mountain j that serves as a temporary mountain.
The width constraint and length constraint of the movable steel material (temporarily placed steel material) i placed on the temporary mountain j are expressed as in the following equation (47).

Here, F' is the set of identical rock pile prohibited steel material pairs F' shown in the following formula (48).

The set F' of pairs of steel materials that are prohibited from being piled on the same temporary pile is a set of pairs of two steel materials that do not satisfy at least _one of the width and length conditions described in the first embodiment when steel material _i1 is piled on the bottom and steel material i2 on top, regardless of the order of dispensing. Note that ( _i1 , _i2 ) in formula (48) is different from { _i1 , _i2 } shown in formula (17), and ( _i1 , _i2 ) ≠ ( _i2 , _i1 ) (the two pairs of steel materials are different depending on whether steel material _i1 or _i2 is on top).

Equation (47) indicates that when steel material _i1 is stacked on the bottom and steel material _i2 on top, steel materials _i1 and _i2 that do not satisfy at least one of the width and length conditions cannot be placed on the same temporary mountain j (initial transportation of steel material _i1 before steel material _i2 (t _i1i2 =1) and placement of steel materials _i1 and _i2 on the same temporary mountain (u _i1j =u _i2j =1) are incompatible. Here, when t _i1i2 =0, that is, t _i2i1 =1, equation (47) is also established even when u _i1j =u _i2j =1, and steel materials _i1 and _i2 can be placed on the same temporary mountain j. However, unlike F, F' only prohibits the placement of steel materials _i1 and _i2 when steel material _i1 is on the bottom and steel material _i2 is on top, and does not prohibit the reverse stacking method. In addition, in formula (47), the 1 in t _i1i2 and u _i1j is expressed as a subscript of i. The 2 in t _i1i2 and u _i2j is expressed as a subscript of i.
Equations (46) to (48) are constraint equations added to the constraint equations explained in the first embodiment.

(n) Space Limitation Constraints for Temporary Steel Material Columns For Columns j, it is preferable to limit the solution space by giving priority to columns with smaller identification information, as in the following formula (49). As described above, the set of Columns T is set to {1, 2, ..., t _max }. The relationship between the temporary steel material Column allocation variable u _ij and the allocated Column identification variable p _j is expressed by the following formula (50).

Equations (49) to (50) are constraint equations that are added to the constraint equations described in the first embodiment. Note that equations (49) to (50) are used to shorten the calculation time, and a feasible solution can be derived even without equations (49) to (50).

(i-4) Fixed Section Upper Part (Moveable Section) Replacement Constraint In this embodiment, the fixed section upper part replacement constraint is also expressed by the formulas (29-1) to (29-3). However, in this embodiment, the final transport order variable w _ii' is used as a decision variable, and therefore the fixed section _upper part replacement constraint can be expressed as in the following formulas (51-1) and (51-2) by using the final transport order variable w _ii' instead of the initial transport order variable t ii'.

Formula (51-1) expresses that when steel material i _Sf is in max(S _k ) and steel material i _E is included in steel material set I _m where movement is essential, steel material i _Sf is the non-moving steel material at the top of the non-moving steel materials (x _iSf =1), and when steel material i _E is placed in the initial pile S _k (z _iEk =1), the final conveyance of steel material i _Sb at the bottom of the moving section steel material set S _k ^↑ must precede the final conveyance of steel material i _E (w _iSbiE =1). In formula (51-1), Sf of x _iSf is expressed as a subscript symbol of i. E of z _iEk is expressed as a subscript symbol of i. Sb of _{w iSbiE} is expressed as a subscript symbol of i, and E is expressed as a subscript symbol of i.

If the final transport order of steel material i _Sb is less than the final transport order (w _iSbiE ) of any steel material i _E in the set of steel materials loaded on the fixed section E _k ^↓ , then the initial transport order of steel _material i _Sb is less than the final transport order of any steel material i _E in the set of steel materials loaded on the fixed section E _k ^↓ , and therefore equation (51-1) becomes a constraint that shows a sufficient condition for replacement (fixed section upper part replacement constraint).Equation (51-2) adds the temporary placement occurrence variable r _iE for steel material i _E to the right-hand side of equation (51-1), and becomes a constraint that shows a necessary condition for replacement (fixed section upper part replacement constraint).

In addition, in formula (51-2), E in r _iE is expressed as a subscript of i. Also, in formula (51-2), a provisional occurrence variable r _iSf for steel material i _Sf may be used instead of r _iE .
The formula (51-1) is a constraint formula used in place of the formula (29-1), and the formula (51-2) is a constraint formula used in place of the formula (29-2). Note that the formulas (29-1) and (29-2) (or (29-3)) may be used instead of the formulas (51-1) and (51-2).

The constraint equation/objective function setting unit 102 sets constraint equations by setting i, j, S, S _k , T, N, and F' for, for example, equations (42-1) to (42-3), equations (43) to (50), equation (51-1), or equation (51-2). The constraint equation/objective function setting unit 102 also sets the constraint equations described in the first embodiment.

<<Objective function>>
Next, the objective function will be described.
In this embodiment, the objectives are to minimize the total number of conveyances of steel materials, the total number of final mountains, and the total number of temporary mountains. Therefore, the objective function J shown in the following equation (52) is used.

In this embodiment, as shown in equation (52), the total number of conveyances of steel materials (Σ(y _i
+r _i ), the total number of final mountains (Σq _j in equation (52)), and the total number of rock masses (Σp
_j ) is used as the objective function. As shown in equation (52), weighting coefficient _k3 is a weighting coefficient for the total number of rockery piles. In the objective function J in equation (52), the weighting coefficients _k1 , _k2 , and _k3 can be used to balance the evaluation of the total number of steel material conveyances, the evaluation of the total number of final piles, and the evaluation of the total number of rockery piles.
The constraint equation/objective function setting unit 102 sets the objective function J by setting i, j, k ₁ , k ₂ , and k ₃ for equation (52), for example.

[Optimization calculation unit 103]
The optimization calculation unit 103 performs a first optimization calculation and a second optimization calculation. The second optimization calculation is performed when the result (optimum solution) of the first optimization calculation does not satisfy the replacement condition.

In this embodiment, the optimization calculation unit 103 calculates the decision variables (non-moved topmost steel material discrimination variable x j , movement/non-movement discrimination variable y i , and moved steel material final mountain allocation variable z i ) when the value of the objective function J in equation (52) is minimized within a range satisfying the constraint equations of equations (9) to (13), (14-1) to (14-2), (15-1) to (15-3), (16) to (17), (18-1) or (18-2), (19), (19'), (20) to (23), (25-1) to (25-3), (26), (27-1) to (27-3), (42-1 ₎ to (47), (49) to ( ₅₀ ), and (51-2), when the value of the objective function J in equation (52) is minimized. _ij , assigned mountain identification variable q _j , initial transport order variable t _ii' , temporary steel material temporary mountain allocation variable u _ij , assigned temporary mountain identification variable p _j , and final transport order variable w _ii' are calculated as optimal solutions, thereby executing a first optimization calculation.

The optimization calculation unit 103 also calculates the decision variables (non-moved topmost steel material discrimination variable x j , movement/non-movement discrimination variable y i , moved steel material final mountain allocation variable z ij , allocated mountain identification variable q j ) when the value of the objective function J in equation (52) is minimized within a range satisfying the constraint equations of equations (9) to (13), (14-1) to (14-2), (15-1) to (15-3), (16) to (17), (18-1) or (18-2), (19), (19'), (20) to (23), (25-1) to ( _25-3 ), (26), (27-1) to (27-3), (42-1) to _{( 50)} , and ( _51-1) . , initial transport order variable t _ii' , temporary steel material temporary mountain allocation variable u _ij , allocated temporary mountain identification variable p _j , and final transport order variable w _ii' ) as an optimal solution, thereby executing a second optimization calculation.

[Determination unit 104]
As described in the first embodiment, the determination unit 104 determines whether or not the result (optimal solution) of the first optimization calculation by the optimization calculation unit 103 satisfies the replacement condition. If the result of this determination indicates that the result (optimal solution) of the first optimization calculation by the optimization calculation unit 103 does not satisfy the replacement condition, the optimization calculation unit 103 executes the second optimization calculation.

[Output unit 105]
As described in the first embodiment, when the judgment unit 104 judges that the result (optimal solution) of the first optimization calculation by the optimization calculation unit 103 satisfies the replacement condition, the output unit 105 outputs information indicating the transportation order of each steel material included in the steel material set N from the initial pile to the final pile, which is identified from the result (optimal solution) of the first optimization calculation.
When the judgment unit 104 judges that the result (optimal solution) of the first optimization calculation by the optimization calculation unit 103 does not satisfy the replacement condition, the output unit 105 outputs information indicating the transportation order of each steel material included in the steel material set N from the initial pile to the final pile, which is identified from the result (optimal solution) of the second optimization calculation.

In addition to or instead of this information, the output unit 105 may output at least one of the following: identification information of the movable and non-movable steel materials, the total number of final piles, the stacking shape of the final piles, identification information of the steel materials to be temporarily placed, the total number of temporary piles, and the stacking shape of the temporary piles.
The flowchart illustrating an example of a yard management method by the yard management device 100 can be realized by replacing some of the processes in the steps of FIG. 3 with the processes described in this embodiment.

(summary)
As described above, in this embodiment, the yard management device 100 _derives decision variables when the value of the objective function J, which aims to minimize the total number of transports of steel materials, the total number of final mountains, _and the total number of temporary mountains, is minimized so as to further satisfy the constraint equations (equations (42-1) to (43)) expressing the relationship between the relative orders of transport of two steel materials using decision variables (movement _presence /absence discrimination variable _{y i and} final transport order variable w _ii' ) and the constraint equations (equations (44) to (47)) expressing the constraint equations related to the steel materials i constituting the temporary mountain using decision variables (initial transport order variable t ii' , temporary steel material temporary mountain allocation variable u ij , allocated temporary mountain identification variable p j , and final transport order variable w ii' ). Therefore, in addition to the effects described in the first embodiment, in addition to the transport order of steel materials and the mountain shape of the final mountain, the mountain shape of the temporary mountain can also be determined at the same time.

Furthermore, the constraint equations for the steel materials i that make up the temporary mountain include a constraint equation (equation (45)) that indicates that two steel materials whose initial and final transport orders are different can be placed on the same temporary mountain. Therefore, the total number of temporary mountains can be appropriately determined.
In this embodiment as well, the various modified examples described in the first embodiment can be adopted.

((Fourth embodiment))
Next, a fourth embodiment will be described. In the third embodiment, in contrast to the first embodiment, a case was described in which the shape of the rockery is determined simultaneously by optimization calculation along with the order of transport of steel materials and the shape of the final mountain. In this embodiment, in contrast to the second embodiment, a case was described in which the shape of the rockery is determined simultaneously by optimization calculation along with the order of transport of steel materials and the shape of the final mountain. Thus, the main difference between this embodiment and the second embodiment is the method of determining the shape of the rockery. Therefore, in the description of this embodiment, the same parts as those in the first to third embodiments are given the same reference numerals as those in FIGS. 1 to 5, and detailed description thereof will be omitted.

(Decision variable)
In the third embodiment, the final transport order variable w _ii' is used as the decision variable. On the other hand, in the second embodiment, the total transport order variable v _s,s' is used as the decision variable. Therefore, in this embodiment, the final transport order variable w _ii is not used. In this embodiment, in addition to the decision variables described in the first embodiment, the temporary steel material temporary mountain allocation variable u _ij and the allocated temporary mountain identification variable p _j are used as decision variables.

(Functional configuration of the yard management device 400)
The yard monitoring device of this embodiment is realized by changing some of the functions of each unit of the yard management device 400 shown in Fig. 4. Therefore, the same reference numerals as those in Fig. 4 and Fig. 5 are used, and an example of the functional configuration of the yard management device of this embodiment will be described, focusing on the parts that differ from the second and third embodiments.

[Steel material information acquisition unit 401, steel material information acquisition step S501]
The steel material information acquisition unit 401 acquires a weighting coefficient _k3 in addition to the information described in the first embodiment. The steel material information acquisition unit 401 is the same as the steel material information acquisition unit 101 in the third embodiment.

[Constraint equation/objective function setting unit 402, constraint equation setting step S502, objective function setting step S503]
<<Constraint expression>>
In this embodiment, the constraint expressions described in the second embodiment are added and modified as follows.
(j-3) Provisional placement occurrence condition constraint In equation (44), t _ii' (initial transport order variable) becomes v _i,i' when all transport order variables v _s,s' are used. W _i'i (final transport order variable) becomes v _i'+n,i+n when all transport order variables v _s,s' are used. Therefore, equation (44) used in place of equation (28) in the third embodiment becomes the following equation (53) in this embodiment.

Equation (53) is a constraint equation used in place of equation (37).

(l) Same temporary mountain placement possibility constraint In formula (45), t _ii' (initial transport order variable) becomes v _i,i' when all transport order variables v _s,s' are used. W _i'i (final transport order variable) becomes v _i'+n,i+n when all transport order variables v _s,s' are used. Therefore, formula (45) used in the third embodiment becomes the following formula (54) in this embodiment.

Equation (54) is an additional constraint equation to the constraint equation described in the first embodiment.

(m) Calculated Mountain Pile Shape Constraint As the constraint equations representing this constraint, equations (46) to (48) explained in the third embodiment are used.
Equations (46) to (48) are constraint equations added to the constraint equations explained in the first embodiment.

(n) Rockery Variable Spatial Limitation Constraint As the constraint equations showing this constraint, equations (49) to (50) explained in the third embodiment are used.
Equations (49) to (50) are constraint equations added to the constraint equations explained in the first embodiment.
In this embodiment, the equation (38) described in the second embodiment is used as the constraint equation indicating the fixed portion upper replacement constraint.

The constraint equation/objective function setting unit 402 sets the constraint equations by setting i, j, S, S _k , T, n, m, N, and F' for, for example, equations (46) to (50) and equations (53) to (54). The constraint equation/objective function setting unit 102 also sets the constraint equations described in the second embodiment.

<<Objective function>>
In this embodiment, the objective function J shown in equation (52) described in the third embodiment is also used.
The constraint equation/objective function setting unit 402 sets the objective function J by setting i, j, k ₁ , k ₂ , and k ₃ for equation (52), for example.

[Optimization calculation unit 403, optimization calculation step S504]
In this embodiment, similarly to the second embodiment, the optimization calculation needs to be performed only once.
The optimization calculation unit 403 calculates the following equations: (9) to (13), (14-1) to (14-2), (15-1) to (15-3), (16) to (17), (18-1) or (18-2), (19), (19'), (20) to (23), (32), (32'), and (31-1 An optimization calculation is performed by calculating, as the optimal solution, the decision variables (non-moving topmost steel material discrimination variable x j , movement/non-movement discrimination variable y i , moved steel material final pile allocation variable z ij , assigned pile identification variable q _j , total transport order variable v i,i' , temporary steel material temporary pile allocation variable u _ij , and assigned temporary pile identification variable p _j ) when the value of the objective function J in equation (52) is minimized within the range that satisfies the _constraint equations of equations (33-9), (34), (35-1) to (35-3), (36-1 ₎ to (36-4), (38 _{), (46)} to (50), and _{(53) to (54} ).

[Output unit 404, output step S505]
The output unit 404 outputs information indicating the transport order from the initial pile to the final pile of each steel material included in the steel material collection N, which is specified from the result of the optimization calculation (optimal solution) by the optimization calculation unit 403. In addition to or instead of this information, the output unit 404 may output at least one of the identification information of the movable steel material and the non-movable steel material, the total number of final piles, the stacking form of the final piles, the identification information of the steel material to be temporarily placed, the total number of temporary piles, and the stacking form of the temporary piles.

(summary)
As described above, in this embodiment, the yard management device 400 derives decision variables when the value of the _{objective function J} , which aims to minimize the total number of transports of steel materials, the total number of final mountains _, and the total number of temporary mountains, is minimized so as to further satisfy the constraint equations (equations (46) to ( ₄₇ ), and (53) to (54)) that express the constraint equations related to the steel materials _i that make up the temporary mountains using decision variables (initial transport order variable t ii', temporary steel material temporary mountain allocation variable u ij, allocated temporary mountain identification variable p j, and final transport order variable w ii'). Therefore, in addition to the effects described in the second embodiment, the order in which the steel materials are transported and the shape of the final mountain, as well as the shape of the temporary mountains, can be determined simultaneously.

Furthermore, the constraint equations for the steel materials i that make up the temporary mountain include a constraint equation (equation (54)) that indicates that two steel materials whose initial and final transport orders are different can be placed on the same temporary mountain. Therefore, the total number of temporary mountains can be appropriately determined.
In this embodiment as well, the various modified examples described in the first embodiment can be adopted.

((Calculation example))
Next, a calculation example will be described. In this calculation example, the method described in the second embodiment is taken as an example of the invention, and the method described in Patent Document 3 is taken as a comparative example, and the example of the invention and the comparative example are compared.
Both the invention example and the comparative example are methods for simultaneously optimizing the total number of final piles and the total number of conveyances. However, in the comparative example, all of the parts (max(S _k )) of steel materials in the initial pile that are stacked in the order of dispensing (descending order of dispensing from bottom to top) from the bottom are set as non-moving steel materials (fixed parts). In contrast, in the invention example, it is determined whether all of the steel materials that are stacked in the order of dispensing (descending order of dispensing from bottom to top) from the bottom are to be moved steel materials or non-moving steel materials. Therefore, in the comparative example, all of the steel materials that can be selected as fixed parts are set as non-moving steel materials, which tends to be a more conservative decision than in the invention example. That is, in the comparative example, when there are many steel materials (non-moving steel materials) that belong to the fixed parts, the degree of freedom in re-stack of steel materials is low, and the total number of final piles tends to be large.

In formula (30), the weighting coefficient _k1 for the total number of conveyances of steel materials and the weighting coefficient _k2 for the total number of final peaks were set to 1 and 10, respectively ( _k1 = 1, _k2 = 10). Also, in the comparative example, the weighting coefficient for the total number of final peaks was set to 10 times the weighting coefficient for the total number of conveyances of steel materials. Also, the upper limit value h of the height of the final peak was set to 10 stages (h = 10).

The computation environment is as follows:
Processor: Intel(R) Xeon(R) CPU E5-2687W @ 3.1GHz (2 processors)
Installed memory (RAM): 128GB
OS: Windows (registered trademark) 7 Professional 64-bit operating system Optimal calculation software: ILOG CPLEX (registered trademark) Cplex11.0 Concert25
Twelve types of steel material information were used as the steel material information, and for each piece of steel material information, the total number of final piles, the total number of moved steel materials, the total number of temporary placed steel materials, and the total number of non-moved steel materials were derived using the methods of the invention example and the comparative example described above. The results are shown in Figure 6.

6 is a diagram showing, in a table format, the calculation results in the example and the comparative example. In FIG. 6, the number of SLs is the total number of slabs (steel materials) that make up the initial pile.
As shown in FIG. 6, the average total number of non-moving steel materials (number of non-moving steel materials) is 9.5 in the comparative example, whereas it is 5.8 in the example of the invention, which is reduced by half. Therefore, the average total number of final peaks (number of final peaks) is 5.5 in the comparative example, whereas it is 3.7 in the example of the present invention, which can be reduced by more than 30%. On the other hand, the average total number of transports of steel materials (the sum of the total number of moving steel materials and the total number of temporary storage steel materials), which is in a trade-off relationship with the total number of final peaks, is 23.7 (=0.5+23.2) in the comparative example, whereas it is 28.9 (=2.0+26.9), and the increase rate of the total number of transports of steel materials in the example of the invention compared to the comparative example is limited to just under 20%. If all steel materials are made movable steel materials, the total number of transports of steel materials is at least 32.7 (=the value in the column of the average number of SLs in FIG. 6), and the method of the example of the invention can minimize the total number of final peaks with fewer transports than when all steel materials are made movable steel materials.

((Other variations))
The above-described embodiment of the present invention can be realized by a computer executing a program. In addition, a computer-readable recording medium on which the program is recorded and a computer program product such as the program can also be applied as an embodiment of the present invention. Examples of recording media that can be used include flexible disks, hard disks, optical disks, magneto-optical disks, CD-ROMs, magnetic tapes, non-volatile memory cards, and ROMs.
Furthermore, the above-described embodiments of the present invention are merely examples of the implementation of the present invention, and the technical scope of the present invention should not be interpreted as being limited by these. In other words, the present invention can be implemented in various forms without departing from its technical concept or main features.

(Relationship with the claims)
An example of the relationship between the claims and the embodiments is shown below. Note that the claims are not limited to the embodiments as described in the modified examples.
<Claim 1, 16>
The metal material information acquisition means (step) is realized, for example, by using the steel material information acquisition units 101, 401 (steel material information acquisition steps S301, S501).
The metal material information is realized, for example, by using steel material information.
The optimization calculation means (step), for example, the constraint equation setting means (step) is realized by using, for example, the constraint equation/objective function setting unit 102, 402 (constraint equation setting steps S302, S502, objective function setting steps S303, S503) and the optimization calculation unit 103, 403 (optimization calculation steps S304, S504).
<Claim 2>
The transport order variables correspond to, for example, an initial transport order variable t _ii' , a total transport order variable v _s,s' , and a final transport order variable w _ii' .
The provisional placement occurrence presence/absence variable corresponds to, for example, the provisional placement occurrence presence/absence variable r _i .
The movement presence/absence discrimination variable corresponds to, for example, the movement presence/absence discrimination variable y _i .
The metal material final mountain allocation variable corresponds to, for example, the moving steel material final mountain allocation variable z _ij .
The objective function is realized, for example, by using equations (30) and (52). The term for evaluating the total number of times the metal materials are conveyed corresponds, for example, to the first term on the right-hand side of equations (30) and (52), and the term for evaluating the total number of final peaks corresponds, for example, to the second term on the right-hand side of equations (30) and (52).
<Claim 3>
The conveying order relationship constraint equations are realized by using, for example, equations (25-1) to (26), equations (33-1) to (34), and equations (42-1) to (43).
The initial mountain resolution order constraint equation is realized, for example, by using equation (27).
The provisional generation condition constraint equations are realized by using, for example, equations (28), (37), (44), and (53).
The transshipment constraint equation is realized, for example, by using equation (16).
The mountain height constraint equation is realized by using, for example, equation (18-2) and equation (20).
The same final peak prohibition constraint equation is realized by using, for example, equation (23).
<Claim 4>
The conveying order relationship constraint equations are realized by using, for example, equations (25-2) to (25-3), equations (33-4) to (33-9), and equations (42-2) to (42-3).
<Claim 5>
The non-moving topmost metal material discriminant variable is realized, for example, by using the non-moving topmost steel material discriminant variable x _j .
The transshipment constraint equation is realized, for example, by using equation (16).
<Claim 6>
The replacement constraint equations are realized, for example, by using equations (29-1) to (29-3), (38), and (51-1) to (51-2).
<Claim 7>
The moving metal material definition constraint equation is realized, for example, by using equation (9).
Among the metal materials in the initial pile, the metal materials stacked in the initial pile in the order of dispensing from the bottom are determined to be the mobile steel materials or the non-mobile metal materials, which corresponds to, for example, not setting a constraint equation that specifies that all steel materials belonging to max(S _k ) are non-mobile steel materials.
<Claim 8>
The initial transport order variable is realized, for example, by using the initial transport order variable t _{ii '} .
<Claim 9>
The total conveying order variable is realized, for example, by using the total conveying order variable v _s,s' .
<Claim 10>
The metal material temporary mount allocation variable is realized by using, for example, the temporary steel material temporary mount allocation variable u _ij , and the temporary mount identification variable is realized by using, for example, the assigned temporary mount identification variable p _j .
The objective function is realized by using, for example, formula (52). The term for evaluating the total number of times the metal materials are conveyed corresponds, for example, to the first term on the right side of formula (52), the term for evaluating the total number of final peaks corresponds, for example, to the second term on the right side of formula (52), and the term for evaluating the total number of temporary peaks corresponds, for example, to the third term on the right side of formula (52).
<Claim 11>
The same temporary mountain placement possibility constraint equation can be realized by using, for example, equation (45) and equation (54).
<Claim 12>
The initial transport order variable corresponds to, for example, the initial transport order variable t _ii' , and the final transport order variable corresponds to, for example, the final transport order variable w _ii' .
<Claim 13>
The total number of conveyances of the metal material is realized, for example, by integrating the first term on the right side of equation (30).

100, 400: Yard management device, 101, 4001: Steel information acquisition unit, 102, 402: Constraint equation/objective function setting unit, 103, 403: Optimization calculation unit, 104: Judgment unit, 105, 404: Output unit

Claims (16)

A yard management device for creating a final pile of metal materials piled in a stacking order according to the order of discharging to a subsequent process in the yard by conveying metal materials from an initial pile of metal materials piled in a yard that is a storage area between processes, the final pile being made up of metal materials piled in a stacking order according to the order of discharging to a subsequent process in the yard, the device comprising:
A metal material information acquisition means for acquiring metal material information about metal materials to be piled up;
an optimization calculation means for using the metal material information to solve a mathematical programming problem aimed at minimizing the total number of times the metal materials are transported and the total number of the final piles, thereby classifying the metal materials constituting the initial pile into either moved metal materials that are moved from the initial pile or non-moved metal materials that are not moved from the initial pile, and determining at least the order in which the moved metal materials are transported and whether or not temporary placement occurs when the moved metal materials are moved;
having
A yard management device characterized in that the total number of times the metal material is transported is expressed as the sum of the total number of moving metal materials, which are metal materials transported from the initial pile to the final pile in the storage yard, and the total number of temporarily stored metal materials, which are metal materials that are temporarily stored . The metal material information includes information specifying a payout order and a size of the metal material and a stacking shape of the initial pile,
The optimization calculation means includes:
The decision variables include a transport order variable indicating the relative order of transport of the two metal materials, a temporary storage occurrence variable indicating whether or not it is necessary to temporarily store the metal materials in a temporary storage area before transporting them to the final pile, a movement presence/absence discrimination variable indicating whether or not the metal materials are to be moved, and a metal material final pile allocation variable indicating which of the metal materials is to be placed in which final pile,
setting an objective function including a term for evaluating a total number of conveyances of the metal material and a term for evaluating a total number of the final peaks based on the metal material information;
deriving values of the decision variables when the value of the objective function is minimized or maximized as an optimal solution by performing optimization calculations using mathematical programming;
2. The yard management device according to claim 1. The optimization calculation means includes:
a constraint equation including a first constraint affecting the total number of conveyances of the metal material and a second constraint affecting the total number of final peaks is set based on the metal material information, and the value of the decision variable when the value of the objective function is minimized or maximized within a range that satisfies the constraint equation is derived as an optimal solution by performing optimization calculations using mathematical programming;
the first constraint includes a transport order relationship constraint equation that expresses the relationship between the relative orders of transport of the two metal materials using the decision variables, an initial pile separation order constraint equation that expresses using the decision variables that metal materials in the same initial pile must be transported starting from the metal material on top of the initial pile, and a temporary placement occurrence condition constraint equation that expresses using the decision variables that, for two metal materials transported to the same final pile, when the order of the initial transport order, which is the order of transport from the initial pile, is the same as the order of the removal order, the metal material that comes first in the initial transport order will require the temporary placement;
The second constraint includes a reloading constraint equation expressed using the decision variables, which is a constraint on the metal material that cannot be placed on the metal material that has not been moved from the initial mountain, a mountain height constraint equation expressed using the decision variables, which is a constraint on an upper limit of the mountain height of the final mountain, and a same-final-mountain prohibition constraint equation expressed using the decision variables, which is a constraint on two metal materials that are prohibited from being placed on the same final mountain.
3. The yard management device according to claim 2. The yard management device according to claim 3, characterized in that the transport order relationship constraint equation includes a constraint equation that expresses, using the decision variables, the relationship between the relative transport orders of the two metal materials when at least one of the two metal materials does not belong to a partial pile that is a portion of the initial pile that is stacked in stacking order according to the dispensing order from the bottom. The decision variables further include a non-moving topmost metal material discrimination variable indicating whether the metal material constituting the initial pile is a non-moving metal material in the topmost tier among non-moving metal materials fixed at the position of the initial pile to create the final pile;
The transshipment constraint equation is a constraint equation that expresses, using the decision variables, that if the metal material is the non-movable metal material that is at the top of the non-movable metal materials in the initial pile, the metal material that cannot be placed on the metal material cannot be placed in the original pile to which the metal material belongs;
The yard management device according to claim 3 or 4, characterized in that the original pile is a pile that is a candidate for the final pile, which consists of at least a part of a pile that was formed in the yard at the time the metal material information was created, and which does not change location from the original pile. The yard management device according to any one of claims 3 to 5, characterized in that the first constraint further includes a replacement constraint equation expressed using the decision variables, which indicates that an initial transport order, which is the order in which the moving metal material in the initial pile is transported from the initial pile, must precede a final transport order, which is the order in which the moving metal material is transported to the final pile and is transported onto a non-moving metal material that is fixed at the location of the initial pile to create the final pile. The first constraint further includes a moving metal material definition constraint equation expressed using the decision variables, which specifies that, of the metal materials in the initial pile, the metal materials that are not stacked in the initial pile in a stacking order according to the withdrawal order from the bottom are to be moved metal materials;
A yard management device as described in any one of claims 3 to 6, characterized in that, of the metal materials in the initial pile, the metal materials that are stacked in the initial pile in a stacking order according to the order of dispensing from the bottom are determined to be the mobile metal materials or the non-mobile metal materials. The yard management device according to any one of claims 3 to 7, characterized in that the transport order variables include an initial transport order variable that indicates the initial transport order as the relative order of transport of the two metal materials. The yard management device according to any one of claims 3 to 7, characterized in that the transport order variables include a total transport order variable that indicates both the initial transport order and the final transport order, which is the order of transport to the final pile, as the relative order of the two metal materials. The decision variables include a metal material ascension assignment variable indicating on which ascension the metal material is to be placed, and a ascension identification variable indicating the ascension;
The rockery is a mountain made of metal materials piled up in a temporary storage site,
the objective function includes a term for evaluating a total number of conveyances of the metal material, a term for evaluating a total number of the final mountains, and a term for evaluating a total number of the rocky mountains;
The yard management device according to any one of claims 3 to 9. The yard management device according to claim 10, characterized in that the first constraint includes a constraint expression for whether or not two metal materials can be placed on the same temporary pile, the constraint expression expressing, using the decision variable, that when the order of the initial transport order of two metal materials transported to the same final pile is different from the order of the final transport order, which is the order of transport to the final pile, the two metal materials can be placed on the same temporary pile. The yard management device according to claim 11, characterized in that the transport order variables include an initial transport order variable indicating the initial transport order and a final transport order variable indicating the initial transport order as the relative order of transport of the two metal materials. The transport is performed in units of metal material groups,
The yard management device according to any one of claims 1 to 12 , characterized in that the metal material group consists of a plurality of metal materials that are not divided when the metal materials are transported by a transport device. The yard is a storage area between a steelmaking process and a rolling process in a steel manufacturing process,
The yard management device according to any one of claims 1 to 13 , characterized in that the metal material is a steel material. A yard management method for creating a final pile of metal materials that is piled up in a yard, which is a storage area between processes, by transporting the metal materials from an initial pile using a transport device in a stacking order that corresponds to the order in which the metal materials are to be discharged to a subsequent process in the yard, comprising the steps of:
A metal material information acquisition step of acquiring metal material information about metal materials to be piled up;
an optimization calculation step of classifying the metal materials constituting the initial pile into either moved metal materials to be moved from the initial pile or non-moved metal materials not to be moved from the initial pile by solving a mathematical programming problem aimed at minimizing the total number of times the metal materials are transported and the total number of the final piles using the metal material information, and at least determining the order in which the moved metal materials are transported and whether or not temporary placement occurs when the moved metal materials are moved;
having
A yard management method characterized in that the total number of transports of the metal material is expressed as the sum of the total number of moving metal materials, which are metal materials transported from the initial pile to the final pile in the storage yard, and the total number of temporarily stored metal materials, which are metal materials that are temporarily stored . A program for causing a computer to function as each of the means of the yard management device according to any one of claims 1 to 14 .

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