JP2018100166A - Yard management apparatus, yard management method, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To be able to determine the mountain appearance of a last mountain, the order of transporting steel materials from an initial mountain to the final mountain, and a temporary mountain of steel materials temporarily placed during a transporting process.SOLUTION: A steel material information acquisition unit 101 acquires steel material information including a mountain appearance of an initial mountain and an order of payout. A final mountain derivation unit 102 derives the mountain appearance of the final mountain so that the number of final mountains and the number of initial mountain unit inversion pairs R will be low within a range that satisfies load constraints. Based on the mountain appearance of the final mountain derived by the final mountain derivation unit 102 and the mountain appearance of the initial mountain, a transfer order derivation unit 103 derives a transfer order of steel material groups and steel material groups (a steel material group to be temporarily stored) to be piled up on the temporary mountain in a conveying process from the initial mountain to the final mountain. A provisional mountain derivation unit 104 derives the mountain appearance of the temporary mountain by solving a vertex coloring problem based on the transport order of each steel material group and the temporary placement target steel material group derived by the transfer order derivation unit 103.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a yard management device, a yard management method, and a program, and in particular, in a metal manufacturing process, in a yard provided between steps, a plurality of piles in which a plurality of metal materials and containers in the logistics field are stacked. It is suitable to be used for transshipment to a plurality of piles stacked in the order of delivery to the next process.

  In the iron making process that is an example of a metal manufacturing process, for example, when transporting a steel material that is an example of a metal material from the steel making process to the next rolling process, the steel material is once placed in a temporary storage place called a yard, It is unloaded from the yard in accordance with the processing time of the next rolling process. An example of the yard layout is shown in FIG. As shown in FIG. 15, the yard is storage places 1501 to 1504 that are partitioned vertically and horizontally as a buffer area for supplying a steel material such as a slab discharged from the upstream process to the downstream process. The vertical division is often referred to as “building” and the horizontal division is referred to as “row”. That is, the cranes (1A, 1B, 2A, 2B) can move in the building and transfer steel materials between different rows in the same building. In addition, steel materials are transferred between buildings using a transfer table. When creating a transport command, by specifying the “building” and “row”, indicate where the steel material is transported (number (11) in parentheses in the locations 1501 to 1504 in FIG. 15, (See (12), (21), (22)).

  Next, a basic work flow in the yard will be described with reference to FIG. First, the steel material unloaded from the continuous casting machine 1510 in the steelmaking process, which is the previous process, is transported to the yard by the receiving table X via the pillar 1511 and partitioned by the cranes 1A, 1B, 2A, and 2B. It is conveyed to any one of ˜1504 and placed in a pile. And according to the manufacturing schedule of the rolling process which is a post process, it is mounted on the delivery table Z again by the cranes 1A, 1B, 2A and 2B, and conveyed to the rolling process. Generally, in the yard, steel materials are placed in a piled state as described above. This is to effectively utilize the limited yard area.

In the present specification, claims and drawings, “arrival mountain”, “virtual mountain”, “initial mountain”, “final mountain”, and “temporary mountain” are used in the following meaning.
Mounted mountain: A mountain that has already been formed in the yard.
Virtual mountain: A mountain when it is assumed that metal materials that have not arrived at the yard are piled up in the order of arrival in the yard earlier (not an actual mountain).
Early mountain: A generic term for existing and virtual mountains.
Final mountain: The final mountain (also called the “payout mountain”) that has been piled up for the subsequent process.
Temporary mountain: A mountain that is unavoidably temporarily placed when it is transferred from the initial mountain to the final mountain after the present time.

  In the yard, in order to reduce the fuel intensity of the heating furnace in the subsequent hot rolling process, it is required that the steel material be charged into the heating furnace while maintaining the highest possible temperature. Therefore, there is a case where a heat insulation facility is installed in the yard recently and steel materials are piled up in the yard. In order to effectively use the limited heat insulation equipment, it is necessary to stack steel materials as high as possible to the equipment limit. On the other hand, when stacking steel materials, the steel piles are stacked from the top in the order of processing in the next process so that it is easy to supply to the next process, and the final pile stack shape is not an unstable inverted pyramid. There is a restriction such as this (this is referred to as a “stacked figure restriction”). Furthermore, the work load at the time of mountain standing (creating the final mountain) is an element that cannot be overlooked. Therefore, in the yard control, it is desirable to formulate a work plan for setting up the mountain so that the final mountain is as high as possible with the smallest possible work load under the above-mentioned stacking shape restriction.

  In addition, when carrying out mountain sorting (to divide steel materials into a plurality of mountains) in order to pay out the steel materials required for the subsequent process smoothly in the yard, the steel materials scheduled to arrive are demoted (the steel materials are built in). The grade may be reduced from the originally planned use to another use due to quality troubles that occur at the time), or an unscheduled refining process may be required for the steel that is scheduled to arrive, or the size may change. By doing so, it may happen frequently that the steel material as originally scheduled does not arrive. In addition, it is almost impossible to expect the yard storage area to change indefinitely as originally planned, and it is a daily occurrence that unplanned steel materials must be placed in the unplanned storage area.

  Furthermore, the rolling order of the steel material that has been stacked on the mountain from the top in the order of delivery from the yard to the next process (hot rolling process) is changed after the steel material arrives at the yard. Since it is no longer the normal stacking in the mountain, there are frequent cases where the steel materials are forced to be reloaded according to the changed rolling order. Here, normal stacking means that at any stacking position of the mountain, one steel that is relatively above or a plurality of steel materials that are transported simultaneously is faster than a steel material that is below the steel material. A method of loading that is paid out to the next process. In addition, the order of the steel products is called the order of delivery.

However, since the transshipment work required here must be performed in parallel with the work of receiving steel from the yard and the work of paying out steel from the yard, the time zone in which the steel can be transshipped is limited. Therefore, it is required to efficiently transship steel materials.
Therefore, due to various circumstances before and after arrival at the yard, the work of reloading the piles that were no longer in normal order when they arrived at the yard so that they would be in normal order (that is, with as few transports as possible) ) The needs to do are extremely high.

  There are inventions described in Patent Documents 1 to 6 for a yard management method that requires these. The inventions described in Patent Documents 1 to 4 are inventions for a case in which a mountain sorting plan is made for steel materials that are scheduled to arrive at the yard (so-called unarrived materials), and the mountain shape of the final mountain, that is, the target steel material Consideration has been made on how to properly perform the mountain sorting. However, in the inventions described in Patent Documents 1 to 4, when the steel material that has been received is not stacked on the mountain in the correct order of delivery, although the acceptance to the yard is completed or in the process of being accepted, it becomes an appropriate final mountain. The issue of efficiently transshipment of steel has not been studied.

The invention corresponding to this problem is the invention described in Patent Documents 5 and 6.
First, in Patent Document 5, when the steel materials already in the yard are reloaded in the correct order of delivery, the optimum shape of the final mountain is taken into consideration in consideration of the necessary replacement load and stacking constraints. A method is disclosed that is formulated as a conversion problem and calculated using a tab search method. However, in the invention described in Patent Document 5, a method for obtaining the mountain shape of the final mountain is shown, but a method for obtaining the transport order from the initial mountain to the final mountain and what to do with the temporary mountain generated in the process. Is not clearly shown. In addition, since the final mountain is calculated by a heuristic method, there is no guarantee for its optimality.

  Next, the invention described in Patent Document 6 is a technique that results in a mathematical programming problem that satisfies the constraints on mountain setting and conveyance, and simultaneously optimizes mountain sorting and conveyance order. However, in the invention described in Patent Document 6, the occurrence of temporary placement, which is a factor that increases the conveyance order, can be considered only for a steel material pair having the same initial mountain. That is, the temporary placement does not occur only between pairs of steel materials having the same initial mountain, but can sufficiently occur between steel materials in different initial mountains depending on which steel material is transported first. Therefore, in the invention described in Patent Document 6, it is not possible to consider every conveyance order of steel materials, and an optimum conveyance order cannot be obtained.

  Moreover, when considering the problem of transshipment of steel to make the final pile of normal order, at least the mountain shape of the initial mountain and the steel material from the initial mountain to the final mountain are given, given the mountain shape of the initial mountain. It is necessary to determine the three elements of the order of transport and the method of grouping the steel materials temporarily placed in the transport process into the temporary mountain (the mountain shape of the temporary mountain). In that sense, the prior art is not a technique that covers all these three elements.

JP-A-6-179525 JP 2000-226123 A JP-A-11-255336 JP 2008-260630 A Japanese Patent No. 4935032 JP 2010-269929 A JP 2007-137612 A Japanese Patent Laid-Open No. 2006-81186 Japanese Patent No. 5365759

  The present invention has been made in view of the above-described problems, and includes the shape of the final mountain, the order of conveyance of steel materials from the initial mountain to the final mountain, and the temporary mountain of steel materials temporarily placed in the conveyance process. The purpose is to enable determination by a series of processes.

  The yard management device of the present invention transports the metal material of the initial mountain made of metal material piled up in the yard where the metal material is placed as a place between the processes by a transport device, and sends it to the subsequent process of the yard. A yard management device for creating a final pile made of metal materials stacked in a stacking order according to a payout order, the identification information of the initial mountain, the identification information of the metal material constituting the initial mountain, and the metal Metal material including initial mountain specifying information including a stacking order of the material in the initial mountain, metal material size information regarding the size of the metal material, and delivery order information including a delivery order of the metal material to the subsequent process Based on the acquisition means for acquiring information, the initial mountain specifying information, the metal material size information, and the payout order information, the metal material constituting the final mountain, and the metal material in the final mountain Final including product order Final mountain deriving means for determining each of the plurality of final mountains, the initial mountain specifying information, and the final mountain which is information about the final mountain derived by the final mountain deriving means. Based on the specific information, the transport order of the metal material from the initial mountain to the final mountain, and temporary storage in the temporary storage area of the yard before the transport to the final mountain is necessary Based on the transport order deriving means for determining the temporary placement target metal material that is the metal material, the transport order and the temporary placement target metal material derived by the transport order deriving means, and the metal material size information A temporary mountain deriving means for determining a mountain shape of the temporary mountain including the temporary placement target metal material constituting the temporary mountain and a stacking order of the temporary placement target metal material in the temporary mountain, The temporary mountain deriving means is the temporary placement object Minimize the number of colors to be colored at the vertices in the simple undirected graph with branches between the two vertices corresponding to the two temporary vertices corresponding to the two temporary target metal materials that cannot be stacked on the same tentative mountain. It is characterized in that the mountain shape of the temporary mountain is determined by solving the vertex coloring problem.

  In the yard management method of the present invention, as a place between processes, the metal material of an initial mountain made of a metal material piled up in a yard where the metal material is arranged is conveyed by a conveying device, and the process to the subsequent process of the yard A yard management method for creating a final pile made of metal materials stacked in a stacking order according to a payout order, the identification information of the initial mountain, the identification information of the metal material constituting the initial mountain, and the metal Metal material including initial mountain specifying information including a stacking order of the material in the initial mountain, metal material size information regarding the size of the metal material, and delivery order information including a delivery order of the metal material to the subsequent process Based on the acquisition step of acquiring information, the initial mountain specifying information, the metal material size information, and the payout order information, the metal material constituting the final mountain, and the metal material in the final mountain Final including product order A final mountain which is information about the final mountain derived from the final mountain derivation step, the initial mountain identification information, and the final mountain derived from the final mountain derivation step. Based on the specific information, the transport order of the metal material from the initial mountain to the final mountain, and temporary storage in the temporary storage area of the yard before the transport to the final mountain is necessary Based on the transport order derivation step for determining the temporary placement target metal material that is the metal material, the transport order and the temporary placement target metal material derived by the transport order derivation step, and the metal material size information A temporary mountain derivation step of determining a mountain shape of the temporary mountain including the temporary placement target metal material constituting the temporary mountain and a stacking order of the temporary placement target metal material in the temporary mountain, The temporary mountain derivation step is the temporary placement target Minimize the number of colors to be colored at the vertices in the simple undirected graph with branches between the two vertices corresponding to the two temporary vertices corresponding to the two temporary target metal materials that cannot be stacked on the same tentative mountain. It is characterized in that the mountain shape of the temporary mountain is determined by solving the vertex coloring problem.

  The program of the present invention causes a computer to function as each means of the yard management device.

  According to the present invention, it is possible to determine the shape of the final mountain, the order of conveyance of the steel materials from the initial mountain to the final mountain, and the temporary mountain of the steel material temporarily placed in the conveyance process by a series of processes.

FIG. 1 is a diagram illustrating an example of a functional configuration of a yard management apparatus. FIG. 2 is a flowchart for explaining an example of the outline of the yard management method. FIG. 3 is a diagram illustrating an example of a functional configuration of the final mountain deriving unit. FIG. 4 is a flowchart for explaining an example of the process in step S202. FIG. 5 is a diagram illustrating an example of a functional configuration of the transport order deriving unit. FIG. 6 is a flowchart for explaining an example of the process in step S203. FIG. 7 is a diagram showing an example of a form of steel material conveyance when the initial mountain has a fixing portion. FIG. 8 is a diagram illustrating an example of a simple undirected graph. FIG. 9 is a diagram for explaining an example of a first-in last-out relationship. FIG. 10 is a diagram illustrating an example of a functional configuration of the temporary mountain deriving unit. FIG. 11 is a flowchart illustrating an example of the process in step S204. FIG. 12 is a diagram illustrating an example of steel material information. FIG. 13 is a diagram illustrating a result of performing optimization calculation by the method of the present embodiment. FIG. 14 is a diagram illustrating a result of optimization calculation by the method of the present embodiment and a result of the method of the comparative example. FIG. 15 is a diagram illustrating an example of a yard layout.

  Hereinafter, an embodiment of the present invention will be described with reference to the drawings. In each of the following embodiments, in the steel manufacturing process, the steel material (slab) manufactured in the steel making process is piled up from the top in the order of conveyance to the rolling process, and the initial mountain shape and the rolling process of each steel material are transferred to the rolling process. Given the transport order, the final mountain shape, the steel materials that need to be transported and temporarily placed when transporting from the initial mountain to the final mountain, and the temporary mountain mountain shape in this order. The case of deriving will be described as an example. In the following description, steel materials that require temporary placement are referred to as temporary placement target steel materials as necessary, and the order of conveyance of each steel material to the rolling process is referred to as delivery order as necessary. In addition, steel materials that are not yet piled up in the yard are referred to as unarrived materials as necessary, and steel materials that are piled up in the yard are referred to as already-arrived materials as necessary.

<Background>
First, the process of deriving the figure of the final mountain, the order of conveyance of each steel material when transferring from the initial mountain to the final mountain, and the steel material to be temporarily placed, and the figure of the temporary mountain were explained in this order. To do.
The problem of transshipment of already-arrived materials (hereinafter referred to as “arrival material transshipment problem”) is a problem of separating unarrived materials (as described in Patent Documents 1 to 4. Hereinafter, “unarrived material segregation problem” ")" Is an essential difference and is shown below.

  In the state where the steel has not arrived at the yard, when the order in which the two steels are received into the yard is the same as the order in which the steels are paid out (that is, the order in which one of the two steels is received and the order in which the steel is discharged is greater than the other steel) If the two steel materials are to be stacked on the same final pile, it is necessary to temporarily place the steel materials previously received in the yard and change the stacking order. In other words, whether or not the temporary placement is made is determined by the relationship between the acceptance order and the payout order. On the other hand, when thinking in the state of arriving at the yard, the element corresponding to the receiving order is the stacking order of the steel materials at the initial mountain. In other words, since it can be accessed from the steel piled up on the initial mountain, this corresponds to the order of acceptance. Here, in the state where the steel materials have not arrived at the yard, the “acceptance order” is uniquely arranged for all the steel materials. On the other hand, when there are multiple initial peaks, the “conveyance order” of the arrived material is accessible to the steel material at the top of the multiple initial peaks. And the order of conveyance cannot be determined uniquely. Therefore, the “Re-arrived material transshipment problem” in which the state where the steel has already arrived at the yard is the initial state rather than the “Unarrived material separation problem” where the state in which all the steel has not arrived at the yard is the initial state. It turns out that the difficulty of the problem is high.

  The difficulty of this “arrival material transshipment problem” appears in the difficulty of counting temporary placement, which is one of the evaluations. In other words, the number of temporary placements can be determined according to the arrival order of steel materials in the “unarrived timber problem”, so if the final mountain shape is determined, it can be determined individually for each mountain (the influence of other mountains) Not) On the other hand, in the “arrival material transshipment problem”, even if a single final mountain shape is given, the temporary placement required to construct it is the steel material that constitutes the final mountain ( The appearance of the mountains in the initial mountain, the appearance of the other mountain (s) created from those initial mountains, the order of transport of steel from the initial mountains (disassembly order of the initial mountains), and the final mountain Depends on the transport order of the steel materials (the assembly order of the final pile).

  Therefore, in the “arrival material transshipment problem”, the number of temporary placements cannot be determined in units of mountains, as in the case of solving the “unarrival material mountain separation problem”. In other words, in the “arrival material transshipment problem”, when determining the final mountain shape, there is a degree of freedom in the number of the initial mountain in the transport order. The problem of solving the final mountain that minimizes the number cannot be solved. However, the optimization problem that takes into account the mountain shape of the final mountain and the order of conveyance at the same time leads to an increase in problem scale.

  Based on the above knowledge, the present inventors modified the optimal solution that solves the mountain shape of the final mountain of the “unarrived material mountain division problem” by optimal calculation so that it can cope with the problem of already arrived material, and sub-optimally Find the solution and use it as the shape of the final mountain, and determine the transport order from the initial mountain to the final mountain of each steel material. I came up with the idea of looking for a mountain. Below, the specific example of the technique of deriving the mountain figure of the last mountain, the conveyance order of each steel material from the initial mountain to the last mountain, and the mountain figure of the temporary mountain in this way will be described.

<Functional Configuration of Yard Management Device 100>
FIG. 1 is a diagram illustrating an example of a functional configuration of the yard management apparatus 100. The hardware of the yard management device 100 is realized by using, for example, an information processing device including a CPU, ROM, RAM, HDD, and various interfaces, or dedicated hardware. FIG. 2 is a flowchart for explaining an example of the outline of the yard management method executed by the yard management apparatus 100.

[Steel Information Acquisition Unit 101, Step S201]
The steel material information acquisition unit 101 acquires steel material information about a steel material to be piled up. The steel material information includes steel material group information, information for specifying the mountain shape of each steel group initial mountain, and information for specifying the maximum height of the mountain.

In the steel material group information, for each of the steel material groups (steel material group set N = {1, 2,..., N}) for which the final mountain is to be created, the identification information, the order of delivery, the number of steel materials, The maximum width, the minimum width, the maximum length, and the minimum length information are included. The steel material group refers to a group of steel materials that are not divided (becomes the minimum unit) when transported by a transport device (mainly a crane).
The identification information is identification information (steel group ID) that uniquely identifies each steel group.
The delivery order is the delivery order of each steel material group (order of conveyance to the rolling process).

The number of steel materials (w: N → Z +) is the number of steel materials constituting each steel material group. The number w (i) of steel materials included in one steel material group is, for example, 1 or more and 6 or less (∀iεN, 1 ≦ w (i) ≦ 6). As described above, the steel material group may include not only a plurality of steel materials but also only one steel material.
The maximum width / minimum width are the maximum width / minimum width of each steel material constituting each steel material group. Instead of the maximum width / minimum width, the width of each slab constituting each steel group may be included in the steel group information.
The maximum length and the minimum length are the maximum length and the minimum length of the steel materials constituting each steel material group, respectively. In addition, instead of the maximum length / minimum length, the length of each steel material constituting each steel material group may be included in the steel material group information.

The information that identifies the mountain shape of the initial mountain includes an initial mountain ID that is identification information for uniquely identifying the initial mountain, and a steel group ID that is located in each stack of the initial mountain identified by the initial mountain ID. .
As described above, the initial mountain includes the existing mountain and the virtual mountain. Assuming that the virtual mountain has piled up steel materials that have not yet been piled in the yard at the time the steel material information is created, so that the earlier the arrival order to the yard, the higher the pile in the yard. It is a mountain when assumed. In the present embodiment, it is assumed that all steel materials that have not yet arrived at the yard and are not yet piled up are piled up in one virtual pile among the steel materials to be created for the final pile. As described above, in this embodiment, steel materials that have not arrived at the yard and have not yet been piled up are piled up as virtual piles (that is, all the steel materials for which the final pile is to be created are piled up at the yard. ).

The information specifying the maximum height of the mountain is information including the upper limit h _max (∈Z +) of the number of steel materials that can be stacked as the temporary mountain and the final mountain. The upper limit h _max of the number of steel materials that can be stacked as the temporary mountain and the final mountain is 10, for example. Here, assuming that the thicknesses of the steel materials are the same, the information for specifying the maximum height of the mountain is the upper limit of the number of steel materials that can be stacked as a temporary mountain and a final mountain. When information on the thickness of each steel material is included in the steel material information, the maximum height of the temporary mountain and the final mountain may be adopted as information for specifying the maximum height of the mountain.
In addition, when all the steel materials for which the final mountain is to be created are transported one by one, the identification information (steel ID), payout order, width, and length information are replaced with the steel group information for each steel material. To be acquired.
As an acquisition form of steel material information, input operation of the user interface of the yard management apparatus 100, transmission from an external apparatus, or reading from a portable storage medium is mentioned, for example.

[Final Mountain Deriving Unit 102, Step S202]
The final mountain deriving unit 102, based on the mountain shape of the initial mountain, satisfies the stacking constraints described later, and reduces the number of initial mountain unit reversal pairs (described later) and the total number of final mountains. The mountain shape is derived by performing an optimal calculation.

  As described in the section “Background”, in the “unarrived material mountain division problem”, the temporary storage number is determined for each final mountain when the final mountain is created. In contrast, in the “arrival material transshipment problem” as in the present embodiment, the number of temporary placements cannot be uniquely determined for each final mountain when the final mountain is created. In the “unarrived divide problem”, an inverted pair set is used to evaluate the provisional number. Here, the reverse pair can be piled up on the same final pile, but when piled up on the same final pile, the order of arrival at the yard and the pile order (from the bottom) in the same final pile Refers to a pair of steel material groups that are in a reverse relationship, and a set of such reverse pairs is a reverse pair set. For example, when the first steel group that arrives at the yard relatively early and the second steel group that is relatively late are piled on the same final pile, When the payout order of the group is earlier than that of the second steel material group (that is, stacked on top), the first steel material group and the second steel material group are reversed. The order of arrival at the yard is because the first steel group is earlier than the second steel group, but the payout order is earlier for the first steel group than for the second steel group.

  When applying the “unarrived material separation problem” to the “arrived material transshipment problem”, the reverse pair set cannot be defined sufficiently (exactly because the reverse pair itself depends on the transport order, so the transport order is fixed) Unless you do this, you cannot define a reverse pair). Therefore, the present inventors set the pair of two steel material groups, whose temporary placement is unavoidable from the initial mountain shape regardless of the order of conveyance, as the initial mountain unit reverse pair R, and the reverse pair in the “unarrived material mountain separation problem”. As an initial mountain unit reversal pair R, the inventors have come up with the idea of deriving the mountain shape of the final mountain by solving the “unarrived timber splitting problem” by performing an optimal calculation.

  As described above, in this embodiment, a pair of steel material groups that are reverse pairs only from the mountain shape of the initial mountain is an initial mountain unit reverse pair R. In the initial mountain, the stacking order can be transported from the upper steel group, and therefore, the reverse pairs are extracted for each initial mountain, assuming the product order as the arrival order. Specifically, for any two steel groups in the same initial mountain, if the vertical positional relationship of the relative stacking position in the initial mountain is the same vertical relationship in the final mountain, the two steel group Becomes the initial mountain unit reverse pair R. For example, in the same initial mountain, the first steel group is relatively above and the second steel group is relatively below, and in the same final mountain, the first steel group is relative. When the second steel material group is relatively lower and the second steel material group is relatively lower, the first steel material group and the second steel material group become the initial mountain unit reverse pair. The first steel material group and the second steel material group are not limited to those adjacent to each other in the same initial mountain (for example, the third steel material group between the first steel material group and the second steel material group Even if there is a steel material group, the first steel material group and the second steel material group will be an initial mountain unit reversal pair if the above-described relationship is satisfied). Of the two steel material groups constituting such an initial mountain unit reverse pair, the steel material group relatively above in the same initial mountain is a temporary placement target.

  The “unarrived material separation problem” itself can be realized by a known technique. For example, Patent Documents 7 and 8 show examples of solving the “unarrived material mountain division problem” as the set division problem. Therefore, in the present embodiment, in the “unarrived material mountain division problem” described in Patent Documents 7 and 8, the temporary placement (mount creation load) is evaluated by the initial mountain unit reverse pair R instead of the reverse pair. The mountain deriving unit 102 derives the final mountain shape.

<< Functional configuration of final mountain derivation unit 102 >>
FIG. 3 is a diagram illustrating an example of a detailed functional configuration of the final mountain deriving unit 102. FIG. 4 is a flowchart for explaining an example of detailed processing of the final mountain deriving unit 102 (step S202).

[Achievable mountain extraction unit 301, step S401]
The feasible mountain extraction unit 301 extracts a subset satisfying the stacking constraint as a feasible mountain from the subset N of the steel material group set N.

Here, an example of the stacking constraint described above will be described.
In the present embodiment, the width constraint, the length constraint, and the height constraint are set as stacking constraints when extracting a feasible mountain.
Width condition If a maximum width of a certain steel group is narrower than a minimum width of a steel group located under the certain steel group, the certain steel group is unconditionally changed to a lower steel group. Can be placed on top. When the maximum width of a certain steel material group is wider than the minimum width of a steel material group positioned below the certain steel material group, the difference between the two widths is a reference value determined by work constraints (for example, 200 [mm]) ), The certain steel group can be placed on the lower steel group, but cannot be placed beyond that.

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

-Length condition If a maximum length of a steel group is shorter than a minimum length of a steel group located below the steel group, the steel group is unconditionally placed below the steel group. Can be placed on a group. When the maximum length of a certain steel material group is longer than the minimum length of a steel material group positioned below the certain steel material group, the difference between the lengths of both is determined by a reference value (for example, 2000 [mm ]), The certain steel material group can be placed on the steel material group located below, but cannot be placed beyond that.

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

-Height restriction The number h of stacks of final piles must be below the upper limit h _max of the number of steel materials that can be piled up as final piles.

  Here, the length constraint may be defined only by the relationship with the steel group located one level below a certain steel group, but as described in the length condition, By restricting and setting a stricter constraint than that, it is uniquely determined whether or not the steel group i, j can be loaded on the same final pile for any pair of steel groups {i, j} ⊆N. Therefore, as shown in the following formulas (1) and (2), the pair F of steel material groups can be defined as a forbidden pair set. A forbidden pair set refers to a set of two steel group groups (prohibited pairs) that cannot be stacked on the same final pile.

  Based on the steel material information, the feasible mountain extraction unit 301 prevents the forbidden mountain from including the forbidden pair set (the set F of steel material group pairs) determined by the above formulas (1) and (2). At the same time, the feasible mountain is extracted so that the mountain that violates the height constraint is not included in the feasible mountain.

[Constraint Expression / Objective Function Setting Unit 302, Steps S402 and S403]
Based on the steel material information, the constraint equation / objective function setting unit 302 derives an evaluation value for each of the feasible mountains that are elements of the set of feasible mountains (set family). The evaluation value is higher as the number of initial mountain unit reverse pairs is smaller (the value is smaller), and the higher the height of the realizable mountain (that is, the smaller the number of realizable mountains), the higher the evaluation is. It is determined to be high (value is small). In addition, a feasible mountain adoption variable is used as a decision variable. The feasible mountain adoption variable is, for example, “1” when the final mountain derivation unit 102 adopts the set of feasible mountain (realizable mountain) as the final mountain (optimal solution), and “0” when it is not adopted. It is a 0-1 variable that becomes (zero) ".

  Then, the constraint equation / objective function setting unit 302 uses the feasible mountain adoption variable (decision variable) and the evaluation value for each feasible mountain to calculate the evaluation value for the feasible mountain to be adopted as an optimal solution. An objective function for the purpose of minimizing the sum is set based on the realizable mountain information extracted as described above. In addition, the constraint equation / objective function setting unit 302 is that any steel material group must not be overlapped with a plurality of realizable mountains, and must be arranged in any realizable mountain, A constraint condition (constraint expression) expressed using a feasible mountain adoption presence / absence variable (decision variable) is set based on the information of the feasible mountain extracted as described above.

[Optimization calculation unit 303, steps S404 and S405]
The optimization calculation unit 303 realizes when the value of the objective function set by the constraint equation / objective function setting unit 302 is minimized within a range satisfying the constraint equation set by the constraint equation / objective function setting unit 302 The possible mountain adoption variable (decision variable) is derived by performing an optimal calculation. The feasible mountain adopted as the final mountain is specified by the feasible mountain adoption variable. Further, by stacking the steel material groups constituting the feasible mountain so as to satisfy the above-described stacking constraints, the stacking position (that is, the mountain shape) of each steel material group in each final mountain is specified. These specified information is the final mountain specifying information. Each final mountain is set with a final mountain identification number (final mountain ID).

  This optimization calculation is a 0-1 programming problem. For example, a known algorithm (solver) for solving an optimization problem such as a branch and bound method by a mathematical programming method such as a 0-1 integer programming method is used. It can be realized by using. Although the minimization problem is solved here, for example, the evaluation value may be set so that the value becomes larger as the evaluation becomes higher, and the problem may be maximized. Details of the above processing (a method for extracting feasible mountains, specific constraint expressions, objective function contents, and the like) are described in Patent Documents 7 and 8, and detailed description thereof is omitted here. .

[Conveyance Order Deriving Unit 103, Step S203]
In the initial mountain unit reversal pair R, it is not possible to extract all pairs of steel groups to be temporarily placed as in the case of the reverse pair in the “unarrived material separation problem”. Insufficient pair extraction. Therefore, it is assumed that the final mountain deriving unit 102 derives a solution for which the temporary placement number cannot be sufficiently evaluated. Therefore, in the present embodiment, the transport order deriving unit 103 transports each steel material group in order to transship a given initial mountain shape to the final mountain shape derived by the final mountain deriving unit 102. The order of conveyance of each steel material group is derived so that the number of times of conveyance (that is, the number of occurrences of temporary placement) is minimized. By doing in this way, it can be expected that a solution that suppresses the occurrence of temporary placement that could not be sufficiently considered by the final mountain deriving unit 102 as much as possible can be obtained. In the following, two specific examples of processing performed by the conveyance order deriving unit 103 will be described. First, a first example of processing of the conveyance order deriving unit 103 will be described.

<< Assumptions and problem settings >>
The transport order deriving unit 103 uses the final mountain deriving unit 102 from the initial mountain specified from the steel material information (information specifying the mountain shape of the initial mountain) acquired by the steel material information acquiring unit 101 under the following assumptions. The order of transport of steel materials when transferring steel materials to the final mountain where the mountain shape was derived is obtained. In the following description, information for specifying the initial mountain figure is referred to as initial mountain figure specifying information as necessary. In addition, the information specifying the mountain shape of the final mountain derived by the final mountain deriving unit 102 is referred to as final mountain image specifying information as necessary.

(1) The number of conveyances from the initial mountain (initial storage site) to the final mountain (final storage site) is a maximum of 2 times for any steel material. That is, the steel material transported to the temporary mountain (temporary storage site) must be transported to the final mountain (final storage site) at the time of the next transport, and is not transported between different temporary mountains (temporary storage site). To do.
(2) The yard of the initial mountain and the final mountain are different, and all steel materials must be transported from the initial mountain (initial yard) to the final mountain (final yard) (that is, all steel materials are transported). )

Moreover, in this example, the optimization problem aiming at minimizing the conveyance frequency of steel materials is solved under the following restrictions.
(I) The steel material of each initial mountain can be conveyed only in order from the top of the initial mountain.
(Ii) When creating the final mountain, it can only be stacked in order from the bottom.
(Iii) The number of steel materials that can be transported simultaneously depends on the number and capacity of the cranes that can be used. In this example, in order to simplify the explanation, a case where the number of usable cranes is “1”, that is, a case where the number of steel materials included in one steel material group is “1” will be described as an example. To do.
As described above, since the number of times of transport from the initial mountain (initial place) to the final mountain (final place) is a maximum of 2 times for any steel material (see the premise of (1) above), the number of times the steel material is transported Minimizing is equivalent to minimizing the number of temporary placements.

<< Determination variable >>
In this example, the variable that determines the order in which the steel materials are removed from the initial mountain is an independent variable, and whether or not each steel material needs to be temporarily placed is determined based on the mountain shape of the final mountain. The reason why the order of removing the steel material from the initial mountain is set as an independent variable is to reduce the variable by paying attention to the fact that the mountain shape of a given final mountain has information on the final conveyance order. In addition, the initial transport order variable, which is a variable indicating the order in which the steel material is removed from the initial pile, is made a relative order variable instead of an absolute order variable so that the order constraint between the two steel materials can be expressed concisely and clearly. To do. By using such an initial transport order variable, the scale of the independent variable can be reduced from _n ² to _n C ₂ as compared with the case where an absolute order variable is used as the initial transport order variable.

  For an arbitrary steel group pair (two steel material groups), an initial transport sequence variable y (s, s') that determines the order in which the steel material is removed from the initial mountain, and whether or not temporary placement has occurred for any steel material group The temporary placement occurrence variable x (s) is defined as follows.

(A) Initial transfer order variable y (s, s ′): number of variables = _n C ₂
Let G = (N, E) be a fully directed graph in which each element of the set N of steel material groups has one vertex. At this time, E = {(s, s ′) εN ² | s ≠ s ′). The 0-1 variable y (e) (ｅe∈E) defined on the directed edge set E is introduced, and the initial transport order variable y (s, s ′) is defined as in the following equation (3) To do.

Here, initial conveyance means conveyance of the steel material group in the initial mountain to the final mountain (final storage site) or temporary mountain (temporary storage site). On the other hand, final conveyance means conveying the steel materials in an initial mountain or a temporary mountain (temporary storage place) to the final mountain (final storage place). s is a variable that specifies the initial conveyance of each steel material group, and a different value is set for each steel material group (s ′ is described so as to be distinguished from s, and s ′ and will be described later (6) S ″ in the equation is also a variable that specifies the initial conveyance of each steel material). As described above, the number of steel material groups is n. A variable s that specifies the initial conveyance is set for each of these steel material groups. In this example, the case where the variable s is a steel group ID will be described as an example.
(B) Temporary placement occurrence variable x (s): Number of variables = n
The temporary placement occurrence variable x (s) indicates whether the initial transport is to the temporary mountain (temporary storage site) or the final mountain (final storage site) when the steel material group is initially transported from the initial mountain to the final mountain. It is a 0-1 variable that indicates whether it is transported to. Therefore, a temporary placement occurrence variable x (s) is defined as in the following equation (4).

The total number of decision variables in this example is ( _n C ₂ + n).
<< Functional configuration of transport order deriving unit 103 >>
FIG. 5 is a diagram illustrating an example of a detailed functional configuration of the transport order deriving unit 103. FIG. 6 is a flowchart for explaining an example of detailed processing of the transport order deriving unit 103 (step S203).

[Constraint Expression / Objective Function Setting Unit 501, Steps S601 and S602]
The constraint equation / objective function setting unit 501 sets a constraint equation that expresses the above-described constraint in a mathematical expression and an objective function that expresses the above-described objective in a mathematical equation.
[[Constraint expression]]
First, the constraint equation will be described.
(A) Definition restriction of initial conveyance order variable y (s, s ′) The order of removing any two steel material groups from the initial mountain is the total order of the set N of steel material groups (transitional (the following (6) Formula), an antisymmetric and complete (refers to the following (5) formula binomial relationship), and therefore an initial transport forward variable y (which defines the relative order of removing any two steel groups from the initial pile. s, s ′) satisfies the perfect law (comparable) represented by the following expression (5) and the transition law represented by the following expression (6). Moreover, the initial conveyance order variable y (s, s ′) satisfying the following expressions (5) and (6) corresponds to the entire order of the steel material groups.

The expression (5) indicates that one of the initial conveyance of the steel group specified by the variable s and the initial conveyance of the steel group specified by the variable s ′ are always first and the other after. Note that these two steel material groups are different steel material groups.
In the equation (6), the initial conveyance of the steel group specified by the variable s is ahead of the initial conveyance of the steel group specified by the variable s ′, and the initial conveyance of the steel group specified by the variable s ′ is , The initial conveyance of the steel group specified by the variable s ″ is earlier than the initial conveyance of the steel group specified by the variable s ″. Indicates that These three steel material groups are different steel material groups.

  Moreover, it is necessary to perform the operation | work which removes a steel material group from an initial mountain in order from the top of each initial mountain. Therefore, in the same initial mountain, when the steel material group that performs the initial conveyance specified by the variable s ′ is lower than the steel material group that performs the initial conveyance specified by the variable s, On the other hand, the following expression (7) holds. As described above, the variable s for specifying the initial conveyance is set for each steel material group.

The expression (7) indicates that in the same initial mountain, the steel material group above the steel material group below must be initially transported first.
(B) Temporary placement restrictions caused by transport to the final mountain The final transport order of the steel group follows the stacking order from the lowest level of the mountain in the mountain shape of the final mountain. Therefore, when the final transport order (the final pile stacking order) and the initial transport order are different, the steel material group that is initially transported first needs to be temporarily placed. That is, in the same final mountain, when the initial conveyance order of the upper steel material group is ahead of the initial conveyance order of the lower steel material group, the steel material group that is initially conveyed first needs to be temporarily placed. . Therefore, in the same final mountain, when the steel material group that performs the initial conveyance specified by the variable s ′ is lower than the steel material group that performs the initial conveyance specified by the variable s ′, On the other hand, the following equation (8) holds.

Equation (8) indicates that, in the same final mountain, when initially transporting a steel group above the steel group below, the steel group to be transported initially needs to be temporarily placed. Show.
The constraint equation / objective function setting unit 501 sets the constraint equations of equations (5) to (8) by setting variables s, s ′, and s ″ for equations (5) to (8). To do.

When setting the formula (7), from the initial mountain shape identification information, the steel material group that is relatively lower and the upper steel material group are specified in the same initial mountain, and the upper of the two steel material groups is identified. Let s be the variable set for s and s' for the variable set below.
(8) When setting the formula, from the final mountain figure identification information, the steel material group that is relatively lower and the upper steel material group in the same final mountain are specified, and the upper of the two steel material groups is specified. Let s be the variable set for s and s' for the variable set below.

  As for the expression (5), s and s ′ are set for each of the combinations of two arbitrary steel material groups in the set N of steel material groups. As for the expression (6), s, s ′, and s ″ are set for each of combinations of arbitrary three steel material groups in the set N of steel material groups.

[[Objective function]]
Next, the objective function will be described.
As described above, in this example, since the purpose is to minimize the number of times the steel material is conveyed, that is, to minimize the number of temporary placements, the objective function J shown in the following equation (9) is used.

  The constraint equation / objective function setting unit 501 sets the objective function J of (9) by setting the variable s to the equation (9).

[Optimization calculation unit 502, step S603]
The optimization calculation unit 502 is an initial transport forward variable y (s, s) when the value of the objective function J in the equation (9) is minimized within a range satisfying the constraint equations in the equations (5) to (8). ') And the temporary placement occurrence variable x (s) are calculated as optimum solutions. The calculation of the optimal solution can be realized by using a known algorithm (solver) for solving the optimization problem by mathematical programming such as mixed integer programming.

[Post-Processing Unit 503, Step S604]
When the initial transport order variable y (s, s ′) is derived as described above, the initial transport order (the order of removal from the initial mountain) of each steel group included in the set N of steel material groups can be determined. it can. However, the steel material group determined to be temporarily placed (the steel material group in which the variable s where the temporary placement occurrence variable x (s) is set to “1”) is set to the final transport order (temporary mountain (temporary placement place)). Since the order of transport to the mountain (final storage area) is not fixed, it is necessary to determine this. That is, it is necessary to determine where in the initial conveyance order determined as described above, the final conveyance order of the steel material group determined to cause temporary placement is to be interrupted. Therefore, in this example, the post-processing unit 503 determines the final conveyance order of each steel material group as follows.

  For the steel material group that is determined to be temporarily placed, it is necessary to carry twice the initial conveyance and the final conveyance. On the other hand, the initial conveyance and the final conveyance coincide with each other for a steel material group that is determined to have no temporary placement. Therefore, for the steel material group determined to cause temporary placement, the ID for these two transports is set as the variable s. That is, about the said steel material group, although there are two virtually different steel material groups, two variables s are set. Accordingly, the number of steel material groups to be transported here is a value obtained by adding the number of steel material groups determined to be temporarily placed to the number of actual steel material groups to be transported. In this way, by changing the information given to the algorithm described above, all steel groups to be transported can be transshipped from the initial mountain to the final mountain by initial transport, and the final transport order of each steel group is obtained. be able to. Specifically, the following modifications are performed on the algorithm described above. In the following description, a steel material group determined to cause temporary placement is referred to as a temporary placement target steel material group as necessary.

  The variable s is a variable that specifies initial conveyance, and is set for each steel material group included in the set N of steel material groups. In addition, two variables s are set for the temporary placement target steel material group. As described above, in this example, the variable s for each steel material group is the steel material group ID of the steel material group. Accordingly, an ID different from the steel material group ID is set for each temporary placement target steel material group as a virtual steel material group ID. Then, the steel material group ID of the temporary placement target steel material group and the virtual steel material group ID set for the temporary placement target steel material group are set as two variables s for the temporary placement target steel material group. When the number of temporary placement target steel material groups is t, the number of variables s is (n + t). Thus, for the temporary placement target steel material group, two variables s that specify initial conveyance are set. One of these two variables s is a variable that specifies the initial conveyance from the initial mountain, and the other is a variable that specifies the initial conveyance from the temporary mountain. As described above, the steel material group that is determined to be temporarily placed is regarded as two steel material groups, so that the steel material group is transported twice (initial transfer from the initial mountain to the temporary mountain, and the temporary mountain to the final mountain). Can be treated as initial transport.

  Next, the initial shape of the initial mountain for the temporary placement target steel material group specified by the variable s that specifies the initial conveyance from the initial mountain is earlier in the initial conveyance order determined by the initial conveyance order variable y (s, s ′). It is assumed that one virtual first mountain is stacked in order from the steel material group. The number of product stages of this first mountain is n. Further, each product stage of the first mountain is assigned a steel group ID of the corresponding steel group from the top in accordance with the initial conveyance order calculated by the optimization calculation unit 502. On the other hand, the initial mountain for the steel material group determined to be temporarily placed by the optimization calculating unit 502 is a virtual second mountain having two product stages. The second level is s which is the steel group ID of the steel group, and the first level is n + s which is a steel group ID corresponding to the final transport (transport from the temporary mountain to the final mountain) of the steel group.

Here, as the initial peak, the first peak of the number n of product stages is created by setting the initial conveyance order of all the steel material groups determined by the optimization calculation unit 502 (step S603) to the post-processing unit 503 (step This is for maintaining the order of conveyance obtained in S604). Moreover, the reason why the second peak having two product stages corresponding to the temporary placement target steel material group is created is to define the order of initial conveyance and final conveyance for the temporary placement target steel material group. The steel material group ID corresponding to the initial conveyance of the temporary placement target steel material group is assigned to both the first crest of the product stage number n and the second crest of the product stage number 2 so that the temporary placement target steel material group The post-processing unit 503 (step S604) simultaneously determines the order relationship between the initial conveyance and the initial conveyance of the steel material group that goes straight to the final mountain, and the order relationship between the initial conveyance and the final conveyance of the temporary placement target steel material group. .
Next, the mountain shape of the final mountain is obtained by replacing the steel material ID of the steel group that is the temporarily placed steel group with the virtual steel group ID given to the temporarily placed steel group for the final mountain shape specifying information. It becomes.
Further, the following constraint formula (10) is set for each temporarily placed steel group.

In the equation (10), s is a variable (steel group ID of the temporary placement target steel group) that specifies initial conveyance from the initial mountain of the temporary placement target steel group, and n + s is a temporary of the temporary placement target steel group. It is assumed that it is a variable (virtual steel group ID of a temporary placement target steel group) that specifies initial conveyance from a mountain. The expression (10) indicates that the initial conveyance order (initial conveyance from the initial mountain) of the temporary placement target steel material group precedes the final conveyance order (initial conveyance from the temporary mountain).
The post-processing unit 503 sets the variables s, s ′, s ″, n for the expressions (5) to (8) and (10), and sets the variable s for the expression (9). However, N in the formula (9) includes the virtual steel group ID. Then, the post-processing unit 503 performs the initial transport order when the value of the objective function J in the equation (9) is minimized within a range that satisfies the constraint equations in the equations (5) to (8) and (10). The variable y (s, s ′) is calculated as the optimal solution. Alternatively, in this post-processing, it is clear that the objective function of equation (9) is “0”, so the objective function of equation (9) is not set, but instead the following constraints of equation (9-2): An expression may be added.

  The post-processing unit 503 determines that each steel material group included in the set N of steel material groups reaches from the initial mountain to the final mountain based on the optimal solution of the initial transfer forward variable y (s, s ′) calculated in this way. The order of all the transports is derived. The post-processing unit 503 derives a temporary placement target steel material group from the temporary placement occurrence presence / absence variable x (s). In the following description, the order of all the transports from the initial peak to the final peak of each steel group included in the set N of steel material groups is referred to as the transport order of each steel group as necessary.

In this example, an initial transport order variable y (s, s ′), which is a binary variable that determines the relative order of initial transport of any two steel material groups, and whether or not the initial transport is transport to a temporary mountain. In the case where the steel material group above the steel material group below is initially transported in the same final mountain using the temporary placement occurrence variable x (s) which is a variable for determining The steel material group to be initially conveyed sets a constraint equation including a linear inequality that indicates that temporary placement is required. Then, the initial transfer order variable y (s, s ′) and the temporary placement when the value of the objective function J for the purpose of minimizing the occurrence of the temporary placement is minimized so as to satisfy the set constraint equation. Occurrence presence / absence variable x (s) is derived, and based on these, the transport order from the initial peak to the final peak of each steel group included in the set N of steel groups and the temporary placement target steel group are transported・ Derived as temporary storage material specific information. Therefore, the conveyance order of the steel materials when the steel materials are reloaded from the initial mountain to the final mountain can be obtained at high speed and appropriately.
Here, the problem of minimizing the objective function J has been described as an example. However, for example, the objective function may be obtained by multiplying the right side of equation (9) by (−1), and the objective function may be maximized.

  Next, a second example of processing by the conveyance order deriving unit 103 will be described. In the first example, the initial mountain and the final mountain have different storage locations, and it is assumed that all steel material groups must be transported from the initial mountain (initial storage site) to the final mountain (final storage site). Explained with an example. However, in the initial mountain, there is a case where the product order from the lowest stage is already the payout order (the payout order is descending from bottom to top). In such a case, in the initial mountain, it is not necessary to reload the portion in which the product order from the lowest level is the payout order (the payout order is descending from the bottom to the top). Therefore, in this example, a case will be described in which such a portion is allowed to have the same location for the initial mountain and the final mountain (that is, not moved from the initial mountain state). As described above, this example and the first example are mainly different in processing due to the difference in the premise (2) described in the first example. Therefore, in the description of this example, the same parts as those in the first example are denoted by the same reference numerals as those in FIGS.

In the present embodiment, the following premise (3) is adopted instead of the premise (2) described in the first example.
(3) The initial mountain and the final mountain are allowed to be in the same place, and the part of the initial mountain where the product order from the lowest level is the delivery order (the delivery order is descending from bottom to top) is transported. (That is, it is assumed that some steel material groups (one or more steel material groups continuous from the lowest level) of the initial mountain may not be transported).

  The difference between the premise of (2) described in the first example and the premise of (3) is that, under the premise of (3), the same place (mountain) that cannot occur under the premise of (2) The upper steel group is allowed to be replaced. In order to replace such steel material groups, the steel material group that existed in the upper part of the initial mountain is transported to the temporary mountain or the final mountain, and another steel material group is placed on the remaining part (lower part) of the initial mountain. Will be transported. The steel group transported on the lower part of the initial mountain is temporarily placed on the temporary mountain among the steel group on the initial mountain different from the initial mountain and the steel group on the upper part of the initial mountain. And steel group.

  Therefore, the “initial transport order” of the steel group originally in the initial pile must precede the “final transport order” of the steel group transported from other piles on the remaining part of the initial pile ( In the following description, this is referred to as a constraint condition for replacement if necessary). In order to strictly set the constraint conditions for this replacement, it is necessary to define the order relationship between the initial transport order and the final transport order between any two steel groups. The constraint condition for replacement is expressed as a sufficient condition in the variable system of the algorithm described in the first example without setting the problem. In the following explanation, in the initial mountain, the product order from the lowest level is the payout order (the payout order is descending from the bottom to the top), and the part that is not transported for transshipment is necessary as necessary. The part that carries the transport for transshipment above the fixed part in the initial mountain is called a moving part as necessary.

This algorithm can be realized by making the following changes to the constraint equations (5) to (8) in the first example.
First, a constraint equation added to the constraint equations (5) to (8) described in the first example will be described.
If all steel groups are not transported and a part of the initial pile is used as the final pile as it is, the following cases are assumed that do not cover all steel materials for transportation. Additional constraints need to be added.
FIG. 7 is a diagram showing an example of a form of steel material conveyance when the initial mountain has a fixing portion.
In the initial mountain shown in FIG. 7, it is assumed that the steel material groups I and II in the two tiers from the bottom are fixed portions, and the steel material groups III, IV, and V thereon are moving portions. In this case, the steel material groups I and II of the fixed part remain as they are in the final mountain. Of the steel material groups III, IV, and V of the moving portion of the initial mountain, the steel material groups III and V are transported to another final mountain, and the steel material group IV is transported to the temporary mountain and then again to the initial mountain (that is, The steel group VI, VII is transported from another initial mountain onto the steel group IV. Even in such a case, in order to appropriately calculate the transport order, it is necessary to provide a restriction on the initial transport order.

When a steel group is transported from another initial mountain or temporary mountain to an initial mountain having a fixed part (that is, the final mountain), the steel group III, IV, V of the moving part above the fixed part is initially transported. Only after this can the final transport of steel groups IV, VI and VII be possible. Therefore, it is necessary to set a restriction that the final conveyance of the steel material groups IV, VI, and VII must be performed after the initial conveyance of the steel material groups III, IV, and V. Therefore, the initial conveyance order of the steel group at the upper part of the fixed part such as the steel group III, IV, V is transferred from another initial mountain or temporary mountain such as the steel materials IV, VI, VII to the upper part of the fixed part. It is a necessary and sufficient condition that it is ahead of the final conveyance order of the steel group. However, in the algorithm described in the first example, the independent variable is only the initial transport order variable y (s, s ′) (there is no variable that determines the final transport order). Therefore, in this example, a constraint expression that gives sufficient conditions is added as follows.
That is, the variable that specifies the initial conveyance of the steel group of the moving part of the initial mountain l is i _U , and the initial value of the steel group conveyed to the initial mountain l from a different mountain (initial mountain or temporary mountain) from the initial mountain l The variable specifying the transport is i _T , and the following constraint expression (11) is added.

When the initial conveyance specified by the variable i _T is the conveyance to the final mountain, the expression (11) satisfies the above-mentioned necessary and sufficient conditions, but the initial conveyance specified by the variable i _T is the conveyance to the temporary mountain. In this case, the expression (11) becomes a sufficient condition and becomes excessively restricted.
In the case of a steel group that is initially transported from the initial peak l and returns to the initial peak l again (ie, i _U and i _T ), such as the steel group IV in the example of FIG. Does not make sense, but the following equation (12) is set for such a steel group.

Next, a description will be given of a portion to be changed with respect to the constraint expressions of the expressions (5) to (8) described in the first example.
As described above, since the steel material group of the fixed portion of the initial mountain is given, the steel material group in which the initial conveyance is not performed is known. Therefore, in the equation (7), when at least one of the variables s and s ′ for specifying the initial conveyance is a variable set for the steel group of the fixed portion of the initial mountain, It is assumed that the constraint equation (7) is not set for the initial conveyance order variable y (s, s ′) by the variables s and s ′. For the other initial transfer order variable y (s, s ′), the constraint expression of Expression (7) is set.

  Further, if the initial conveyance is not performed, temporary placement does not occur. Therefore, in the equation (8), when at least one of the variables s and s ′ for specifying the initial conveyance is a variable set for the steel group of the fixed portion of the initial mountain, It is assumed that the constraint equation (8) is not set for the initial transport order variable y (s, s ′) by the variables s and s ′. For the other initial transporting order variable y (s, s ′), the constraint equation (8) is set.

  When at least one of the variables s, s ′, and s ″ for specifying the initial conveyance is a variable set for the steel group of the fixed portion of the initial mountain, the variables s and s For initial transfer order variables y (s, s '), y (s', s), y (s ', s "), y (s, s") by', s ", (5) It is assumed that neither the expression nor the constraint expression of the expression (6) is set. Alternatively, by expanding the expression (7) as follows, all the constraint expressions other than the expression (7) may be set in the same manner as the steel group of the moving part (non-fixed part) for the steel part of the fixed part. .

  That is, the above formula (7) is for the steel material of the moving part (non-fixed part), but when one steel group is a fixed part and the other steel group is a non-fixed part, (13) is set, and if both steel groups are fixed parts and they are in the same initial mountain, the following constraint formula (14) is set.

  In the present embodiment, the constraint equation / objective function setting unit 501 sets the constraint equations (5) to (8), (11), and (12) as described above. Note that, as described above, the constraint equations (13) and (14) may be set. And the optimization calculation part 502 is (5) Formula-(8) Formula, (11) Formula, and (12) Formula (or (5) Formula-(8) Formula and (11) Formula-(14) Formula. ) Within the range satisfying (), the initial transfer order variable y (s, s ′) and the temporary placement occurrence variable x (s) when the value of the objective function J in equation (9) is minimized are calculated.

  As described above, in this example, when at least one group of steel materials is a steel material group of the fixed portion of the initial mountain, the equation (7) that represents a constraint when conveying the steel material group is not set. Alternatively, the constraint equations (13) and (14) are set. Moreover, the initial conveyance of the steel material group of the moving part of the initial mountain is preceded by the initial conveyance of the steel material group conveyed to the initial mountain having the moving part by using the initial conveyance order variable y (s, s ′). A constraint expression (equation (11)) is expressed. Therefore, in addition to the effects described in the first example, the steel material transfer order when the metal material is reloaded from the initial mountain to the final mountain so as not to convey the steel material group of the fixed portion of the initial mountain that does not need to be conveyed. Can be requested.

  As described above, since the expression (11) expresses the constraint condition for replacement with sufficient conditions, the solution obtained in this way is not guaranteed to be an optimal solution, and the executable solution space is narrowed. In extreme cases, there may be an optimal solution but it may be calculated as infeasible (no solution). Therefore, instead of the equation (11), the constraint equation of the following equation (15) that expresses the constraint condition for replacement as a necessary condition may be used.

  When the steel material group conveyed to the initial mountain having the moving part of the initial mountain is temporarily placed, the order of the initial conveying of the steel material group and the initial conveying of the steel group of the moving part is as follows: Regardless, if not, the initial conveyance of the steel group of the moving part of the initial mountain is preceded by the initial conveyance of the steel group conveyed to the initial mountain having the moving part, as in the equation (11). It shows that it becomes. In the equation (15), when the steel group to be transported to the initial mountain having the moving part is temporarily placed, since there is no limit, it becomes only a necessary condition, and the solution obtained because the executable solution space is expanded. There is a possibility that the solution cannot be realized (that is, the obtained solution cannot be conveyed).

For example, if you want to reliably prevent a solution that is not feasible, use the formula (11), and if it is rare that a steel group to be transported to an initial mountain with a moving part is temporarily placed What is necessary is just to select the constraint formula to employ | adopt like using (15) Formula. If a feasible solution is obtained using equation (15), it is a true optimal solution.
Also in this example, the modification described in the first example can be employed.

  In addition to the first and second examples described above, it is possible to derive the transport order of each steel group based on the mountain shape of the initial mountain and the mountain shape of the final mountain. Can be realized. For example, the technique described in Patent Document 9 can be used. That is, the initial conveyance time (the conveyance start time from the initial mountain to the temporary mountain or the final mountain) and the final conveyance time (the final mountain to the final mountain from the initial mountain or the temporary mountain) of each steel group to be conveyed including the unarrived material and the already arrived material The objective function value indicating the time that the steel group stays in the process of being transported to the last mountain is minimized within the range that satisfies the constraint formula related to the transport time of the steel group. The optimum values of the initial transfer time and the final transfer time are derived.

  And based on the optimal value of these initial conveyance time and final conveyance time, it is determined whether the steel material group of conveyance object is a temporary placement object steel material group. And the product stage relation variable which is 0-1 variable showing the allocation to the temporary mountain of the temporary placing object steel material group and the product order of the said temporary mountain is used as a decision variable, and the constraint formula regarding the product order in the temporary mountain is satisfied. In the range, the optimum value of the product-stage related variable when the value of the objective function representing the number of temporary mountains is minimized is derived.

  In the technique described in Patent Document 9, unlike the first and second examples described above, the variable indicating the order in which the steel material is removed from the initial mountain is an absolute sequence variable, so that the final mountain is created. As the number of steel material groups increases, the calculation time increases. Therefore, it is preferable to use the method described in the first and second examples described above, but when the number of steel material groups for which the final mountain is to be created is small or when the time allowed as the calculation time is long. The technique described in Patent Document 9 can be used.

[Takeyama deriving unit 104, step S204]
The temporary mountain deriving unit 104 includes a temporary placement target steel material group derived by the conveyance order deriving unit 103, and a conveyance order of each steel group derived by the conveyance order deriving unit 103 (from the initial mountain of the temporary placement target steel group) And the steel group information (maximum width and minimum width) of the temporary placement target steel group included in the steel material group information acquired by the steel material information acquisition unit 101. Based on the maximum length and the minimum length, the figure of the temporary mountain is derived.

In the present embodiment, a case where the vertex coloring problem in the graph theory is applied to the temporary mountain optimization problem will be described as an example.
The vertex coloring problem is one of the prominent problems in graph theory, and is defined on a simple undirected graph G = (V, E) (V: vertex set of graph, E: edge (branch) set of graph) ). As shown in FIG. 8, when each vertex of the simple undirected graph G is painted with a certain color and any two adjacent vertices (connected by edges) can be painted with different colors, this coloring is simply undirected. This is called the coloring of the graph G. In FIG. 8, for the sake of notation, the difference in color is expressed by the difference in the direction of diagonal lines. When the color used for coloring is c color (c is an integer of 2 or more), the simple undirected graph G is said to be c-colorable. The minimum value of c that enables simple undirected graph G to be c-colored is called the number of colors of simple undirected graph G, and is represented by χ (G). The vertex coloring problem is a problem of obtaining the number of colors χ (G) in the simple undirected graph G. In this embodiment, a simple undirected graph is created by setting a branch between two vertices corresponding to two temporary placement target steel groups that cannot be stacked on the same temporary pile, with the temporary placement target steel group corresponding to the vertex. Then, the number of colors at the vertices of the simple undirected graph is minimized.

  The condition that the two temporary placement target steel material groups cannot be stacked on the same temporary pile is a case where the first-in last-out (last-in first-out) relationship is not satisfied for the two temporary placement target steel material groups. First-in-last-out relationship for the two temporary placement target steel groups is that of the temporary placement target steel groups whose timing to be transported from the initial mountain to the temporary storage site is early among the two temporary placement target steel groups. The timing at which the temporary storage site is transported to the final mountain is later than the timing at which the other temporary placement target steel group is transported from the temporary storage site to the final mountain. FIG. 9 is a diagram illustrating an example of a first-in last-out relationship for two temporary placement target steel material groups.

In FIG. 9, for the three temporary placement target steel material groups SL1, SL2, and SL3, the temporary transfer timing from the initial mountain to the temporary storage location is indicated by an arrow, and the initial transfer timing from the temporary storage location to the final storage location is indicated by an arrow. The time zone when the placement target steel material groups SL1, SL2, and SL3 are placed in the temporary storage place is expressed.
For example, in the temporary placement target steel material groups SL1 and SL3, the temporary placement target steel material group SL1 is transported to the temporary storage place before the temporary placement target steel material group SL3, and then transported to the final pile. Therefore, the temporary placement target steel material groups SL1 and SL3 satisfy the first-in last-out relationship, and thus can be stacked on the same temporary mountain. Similarly, the temporary placement target steel material groups SL2 and SL3 can be stacked on the same temporary pile.

On the other hand, in the temporary placement target steel material groups SL1 and SL2, the temporary placement target steel material group SL1 is transported first to the temporary storage site, and the temporary placement target steel material group SL1 is transported to the final mountain. Accordingly, the temporary placement target steel material groups SL1 and SL3 do not satisfy the first-in last-out relationship, and thus cannot be stacked on the same temporary mountain.
In the following description, as shown in this example, the shorter arrow indicating the time zone placed in the temporary storage area is not included in the longer one, but there is a time zone in which the arrows cross, A relationship in which there is a time for each temporary placement target steel material group to exist alone in the temporary storage place before and after (that is, a relationship that does not satisfy the first-in, last-out relationship) is referred to as a cross relationship. When the two temporary placement target steel material groups are in a cross relationship, the two temporary placement target steel material groups cannot be stacked on the same temporary mountain.

Therefore, the temporary mountain deriving unit 104 sets one vertex for one of the temporary placement target steel material groups derived by the transport order deriving unit 103. Next, the temporary mountain deriving unit 104 stretches a branch between two vertices corresponding to the two temporary placement target steel material groups in a cross relationship. Further, the temporary mountain deriving unit 104 has the stacking constraint (width) described in the section of [final mountain deriving unit 102, step S202] among the two vertices corresponding to the two temporary placement target steel material groups with no branches. A branch is also stretched between the two vertices corresponding to the two temporary placement target steel material groups that violate the constraint and the length constraint. Here, the temporary target steel group, (2) instead of expression, as in the following equation (16), and prohibits pair set the set F _T of the pair of temporary target steel group.

  The temporary mountain deriving unit 104 solves the vertex coloring problem for the simple undirected graph G = (V, E) created as described above, thereby solving the temporary mountain optimization problem (the mountain of each temporary mountain). It is possible to derive an optimal solution for the appearance. An example of the functional configuration of the temporary mountain deriving unit 104 for formulating the above vertex coloring problem (temporal mountain optimization problem) and deriving the optimal solution of the mountain shape of each temporary mountain will be described.

<< Functional structure of temporary mountain deriving section 104 >>
FIG. 10 is a diagram illustrating an example of a detailed functional configuration of the temporary mountain deriving unit 104. FIG. 11 is a flowchart for explaining an example of detailed processing of the temporary mountain deriving unit 104 (step S204).
[Constraint Expression / Objective Function Setting Unit 1001, Steps S1101 and S1102]
In the present embodiment, the tentative mountain allocation variable x [i] [m] and the tentative mountain presence / absence variable δ [m] are used as decision variables.
The temporary mountain assignment variable x [i] [m] is “1” when the temporary placement target steel group (vertex) i is assigned to the temporary mountain (color) m, and becomes “0 (zero)” when not assigned. -1 variable. The temporary mountain presence / absence variable δ [m] is a 0-1 variable that is “1” when a temporary placement target steel group assigned to the temporary mountain (color) m exists, and is “0 (zero)” when it does not exist. It is.

[[Constraint expression]]
The constraint equation / objective function setting unit 1001 sets the following constraint equation.
(A) Mountain allocation constraint The mountain allocation constraint is a constraint indicating that all temporary placement target steel material groups (vertices) i must be allocated only once (one color) to any temporary mountain (color) m. And is expressed by the following equation (17).

In the equation (17), t is an upper limit value of the number of temporary mountains. Note that the number of temporary mountains corresponding to the upper limit value t is an optimal temporary mountain candidate, and an identification number (temporary mountain ID) is set for each temporary mountain.
(B) Same mountain assignment impossible restriction The same mountain assignment impossible restriction means that two temporary placement target steel material groups (vertices) i with branches in the simple undirected graph G described above are colored in the same color. This is a constraint indicating that it cannot be performed, and is expressed by the following equation (18).

(18) In the equation, the temporary target steel group at both ends of the branches e _c a simple undirected graph G (vertex) and i _1, i _2. In addition, F _c violates two temporary placement target steel group (vertex) pair set and stacking constraints (width constraint and length constraint) in a cross relationship, that is, pair set F _T (prohibition of temporary placement target steel group) It is a union with (pair set).

(C) Mountain height constraint The mountain height constraint is a constraint indicating that the number of steel materials that can be stacked on a temporary mountain is equal to or less than the upper limit h _max (∈Z +), and is expressed by the following equation (19). .

  In the equation (19), w [i] is the number of steel materials constituting the temporary placement target steel material group (vertex) i. Further, k is the total number of temporary placement target steel material groups. T is a set of tentative mountains (candidates) of the upper limit t.

(D) Mountain priority order constraint The mountain priority order constraint is a constraint on the order of creation of temporary mountains. In the present embodiment, the mountain priority order constraint is a constraint indicating that a temporary mountain having a small temporary mountain identification number (temporary mountain ID) is preferentially created, and is expressed by the following equation (20).

(E) Color identification constraint In the vertex coloring problem, the identification of the first color, the second color, the third color,... Is not essential. Absent. For example, when the first temporary placement target steel group group is colored red and the second temporary placement target steel group group is colored blue, the second temporary placement target steel group group is colored red, This is equivalent to the case where the first temporary placement target steel group group is colored blue. In this way, in the temporary mountain optimal solution problem, a solution in which the identification numbers (provisional mountain IDs) of a plurality of temporary mountains derived as the optimal solution are replaced is also the optimal solution. Therefore, there are a plurality of optimal solutions (the number of temporary mountains (colors)! (Factorial)), and a plurality of optimal solutions equivalent to each other can be obtained. Therefore, in order to prevent the plurality of mutually equivalent optimum solutions from being obtained, a color identification constraint is provided as a constraint for identifying the temporary mountain (color) m. In the present embodiment, the color identification constraint is a constraint indicating that the smaller the temporary mountain identification number (temporary mountain ID), the greater the number of vertices (that is, the higher the mountain). (21).

[[Objective function]]
Since the purpose is to minimize the number of temporary mountains (colors), the objective function J shown in the following equation (22) is used.

The constraint equation / objective function setting unit 1001 sets i, i ₁ , i ₂ , j, k based on each temporary placement target steel material group derived by the conveyance order deriving unit 103, and t given in advance. Is set, the constraint equations of Equations (16) to (21) are set. Also, the constraint equation / objective function setting unit 1001 sets the objective function J of the equation (22) by setting t given in advance to the equation (22).

[Optimization calculation unit 1002, steps S1103 and S1104]
The optimization calculation unit 1002 provides a temporary mountain allocation variable x [i] [when the value of the objective function J in the expression (22) becomes the minimum within the range satisfying the constraint expressions in the expressions (16) to (21). m] and the temporary mountain existence variable δ [m] are calculated as optimum solutions. The calculation of the optimal solution can be realized by using a known algorithm (solver) for solving the optimization problem by mathematical programming such as 0-1 integer programming. Temporary storage target variable provision variable x [i] [m] corresponding to temporary mountain (color) m corresponding to the temporary mountain (color) m of temporary mountain existence variable δ [m] is “1”. Steel material groups (vertex) i are piled up. By stacking the temporary placement target steel material groups constituting the temporary mountain so as to satisfy the above-described stacking constraints, the stacking position (that is, the mountain shape) of each temporary placement target steel material group in each temporary mountain is specified. The information specified in this way is temporary mountain specifying information.
Here, the problem of minimizing the objective function J has been described as an example. However, for example, the objective function may be obtained by multiplying the right side of equation (22) by (−1), and the objective function may be maximized.

[Output unit 105, step S205]
The output unit 105 includes a mountain shape of the final mountain derived by the final mountain deriving unit 102, a conveyance order of each steel group derived by the conveyance order deriving unit 103, and the tentative mountain derived by the temporary mountain deriving unit 104. Outputs information including mountain figures. The form of output includes at least one of display on a computer display, storage on a storage medium inside or outside the yard management apparatus 100, and transmission to an external apparatus. Examples of the external device include a crane or a control device that controls the operation of the crane.

<Example>
Next, examples will be described.
In the following examples, the calculation was performed in the following calculation environment.
(I) Processor: Intel (registered trademark) Xeon (registered trademark) CPU E5-2687W @ 3.1.GHz (two processors)
(Ii) Mounted memory (RAM): 128GB
(Iii) OS: Windows (registered trademark) 7 Professional 64-bit operating system (iv) Optimal calculation software: ILOG CPLEX Cplex11.0 Concert25 (registered trademark)

  In this example, the acceptance of the steel material (slab) for which the final pile is to be created into the yard is completed, and when the change such as the rolling schedule is found, the pile piled in the yard is defined as the initial pile, and the initial pile is defined as the initial pile. , It shall be transferred to the last pile that is piled up in order of withdrawal. Moreover, the steel materials shall be conveyed one by one. FIG. 12 is a diagram illustrating an example of steel material information. In FIG. 12, SLID is a steel material identification number (steel material ID). The SL width is the width of the steel material, and the SL length is the length of the steel material. The product level shown next to the initial mountain ID is the product level in the initial mountain of the initial mountain ID (the lowest level is 1). Moreover, in FIG. 12, the part shown with gray shows the steel material (fixed part) which was not made into the conveyance object.

FIG. 13 is a diagram illustrating a result of performing optimization calculation by the method of the present embodiment using the steel material information illustrated in FIG. 12 as an input. In FIG. 13, the initial transmission order is the conveyance order from the initial mountain, and the final transmission order is the conveyance order from the temporary mountain to the final mountain. The product level shown next to the final mountain ID is the product level in the final mountain of the final mountain ID (the lowest level is 1).
The fact that the initial feeding order in FIG. 13 is “0 (zero)” indicates that no conveyance is performed (the steel material whose initial sending order is “0 (zero)” is a fixed part). . Further, in the result shown in FIG. 13, since none of the steel materials was temporarily placed, all the columns of the final delivery order, the temporary mountain ID, and the product level are “/”.

  As shown in FIG. 13, in the method of the present embodiment, it can be seen that the steel materials are stacked in order from each of the initial piles (refer to the initial feeding order, the initial pile ID, and the stacking stage). It can also be seen that each steel pile is piled up in the order of conveyance from the top without violating the above-described stacking restrictions in each final pile (see final pile ID, stacking stage, paying order, SL width, SL length).

  In order to verify the effect of the optimum calculation method described in the present embodiment, a method based on a greedy method rule that is considered to be used when a person decides how to reload steel materials is used as a comparative example. In the greedy method rule used as a comparative example, the steel materials are transshipped based on the following rules.

If an initial mountain group is given, the transshipment rule (algorithm) that creates the final mountain with the smallest number of temporary placements and the number of temporary mountains as much as possible is shown below. .
A steel material to be conveyed one by one from the initial mountain or temporary mountain to the final mountain, and a final mountain or temporary mountain to which the steel material is conveyed are determined for each conveyance. Therefore, in the transshipment rule (algorithm), it is only necessary to be able to specify 1) the steel material to be transported and 2) the mountain of the transport destination in each transport. It should be noted that the end of transport in this problem is considered to be the time when the initial mountain and tentative mountain disappeared and only the final mountain was reached (if this is the final state, the transport destination from the initial mountain is only the final mountain or temporary mountain, Since the transport destination from the temporary mountain is only the final mountain, the final state is reached at most 2n (n is the number of steel materials for which the final mountain is to be created). Therefore, at each transfer timing, the algorithm is such that 1) the steel material to be transferred (From) and 2) the designation of the transfer destination peak (To).

(A) The steel material at the top of the initial mountain (the remaining mountain of the initial mountain) and the temporary mountain that is being disassembled, and the steel material with the largest payout order among the steel materials that can be loaded in the correct order in the final pile “Slab to be transported (From)”. In addition, among the final piles that are currently being built that can be piled up “steel materials to be transported,” the final pile that is being constructed is the closest to the payout order of “steel materials to be transported” in the topmost steel pile. It ’s called “To”.

(B) If there is no steel material that can be loaded in the order of delivery in the final pile under construction, the steel material with the maximum delivery order among the steel materials at the top of the initial mountain being disassembled (the remaining mountain of the initial mountain) Target steel (From) ”. In this case, the method shown in (c) below is used to indicate whether the “destination mountain (To)” of the “steel to be transported” is the lowest level (final storage site) or temporary storage site of the new final mountain. Judge with.

(C) When [the number of final piles under construction <ceil (n / h _max ) and the order of payout of “steel to be transported”> h _max ] or [“steel to be transported” In the case of “the order of payout = the maximum payout order”, a new final pile is provided, and “steel material to be conveyed” is placed at the bottom of the final pile. On the other hand, in other cases, “steel material to be transported” is placed in the temporary storage area. When placing “steel to be transported” in a temporary storage site, it is determined which temporary mountain is to be piled up by the method shown in (d) below. Note that ceil (*) is a function that rounds up the decimal point of * to an integer. Here, n is the total number of steel materials for which the final mountain is to be created.

(D) In the case shown in (c) above, if it is determined that the temporary pile will be piled up, the “steel to be transported” will be loaded in the temporary pile under construction, satisfying the above-mentioned stacking constraints and in the reverse order of withdrawal. Among the temporary mountains, the temporary mountain that is the closest in the payout order of the “steel to be transported” in the order of payout of the topmost steel material is defined as the “transport destination mountain (To)”. If there is no mountain in the temporary mountain where “steel material to be transported” can be piled up, a new temporary mountain is provided and “steel material to be transported” is placed at the lowest level. Note that the reverse order of payout refers to the reverse of the normal order of payout, and the order of products is such that the steel material that is relatively below is discharged to the next process earlier than the steel material that is above the steel material. Say.

FIG. 14 is a diagram showing the results of optimization calculation by the method of this embodiment and the results of the method of the comparative example in a table format. The trie of the calculation conditions in FIG. 14 identifies steel material information, and indicates that the method of this embodiment and the method of the comparative example are being compared for seven types of steel material information. Moreover, the peak of calculation conditions is the number of initial peaks. Moreover, SL of calculation conditions is the number of steel materials for which the final mountain is to be created, and the number in parentheses is the number of steel materials to be transported. For example, in PN140, 26 of 38 steel materials are steel materials to be conveyed, and the remaining 12 steel materials are not conveyed (fixed portions). The final mountain, temporary mountain, and temporary placement in the comparative example (greedy method) and the invention example ((individual) optimization) are the number of final mountain, the number of temporary mountain, and the number of temporary placement, respectively. In addition, PN173 of FIG. 14 uses the steel material information shown in FIG. Therefore, the invention example of PN173 in FIG. 14 corresponds to the result shown in FIG.
As shown in FIG. 14, it can be seen that the method of the present embodiment can reduce the number of final peaks, the number of temporary mountains, and the number of temporary placements compared to the method of the comparative example.

<Summary>
As described above, in this embodiment, the initial mountain shape and the payout order are given. The mountain shape of the final mountain is derived so that the number of the final mountain and the initial mountain unit reverse pair R are reduced within a range satisfying the stacking constraint. The initial mountain unit reverse pair R is two steel groups in which the relative stacking position relationship in the initial mountain is the same positional relationship in the final mountain. Next, based on the figure of the final mountain derived in this way and the mountain figure of the initial mountain, the transfer order of each steel group and the temporary mountain in the process of conveyance from the initial mountain to the final mountain Deriving the piled steel material group (temporary placement target steel material group). Next, the mountain shape of the temporary mountain is derived by solving the vertex coloring problem based on the conveyance order of each steel material group and the temporary placement target steel material group. Therefore, the number of the final mountains and the transport of each steel group are determined by performing the solution-solving chain with the last mountain top, the transport order of each steel group, and the temporary mountain tops in this order, with the solution of the immediately preceding process as input. While making the number of times and the number of temporary mountains appropriate (less), the conveyance is started in order from the steel material located at the top in the initial mountain, and the steel is located at the top in the final mountain so that it is discharged to the next process in order. The final mountain can be configured.

  In addition, as a place between two manufacturing processes, it may be a place between two manufacturing processes, as a metal material, a semi-finished product, and as a place between processes, a place between a manufacturing process and a shipping process is targeted. The final product may be used as the metal material. At this time, when a plurality of metal materials are accommodated in a container for transportation and arrangement, the container in which the metal material is accommodated may be handled as one metal material. Furthermore, the place between the processes is not limited to the place in the metal manufacturing process, but may be a distribution and transport between general processes. In the physical distribution field, the present invention is not limited to contents, and can be applied to container transportation and arrangement. Therefore, in the present invention, the metal material includes any one of a final product, a semi-finished product, and a container.

The embodiment of the present invention described above can be realized by a computer executing a program. Further, a computer-readable recording medium in which the program is recorded and a computer program product such as the program can also be applied as an embodiment of the present invention. As the recording medium, for example, a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a nonvolatile memory card, a ROM, or the like can be used.
In addition, the embodiments of the present invention described above are merely examples of implementation in carrying out the present invention, and the technical scope of the present invention should not be construed as being limited thereto. Is. That is, the present invention can be implemented in various forms without departing from the technical idea or the main features thereof.

<Relationship with Claims>
Below, an example of the relationship between a claim and embodiment is shown. In addition, as described above, the description of the claims is not limited to the description of the embodiment.
[Claim 1]
An acquisition means (process) is implement | achieved by using the steel material information acquisition part 101 (step S201), for example.
The metal material information is realized by, for example, steel material information.
The initial mountain specifying information is realized by, for example, information for specifying the mountain shape of each steel group initial mountain.
The identification information of the initial mountain is realized, for example, by using the initial mountain ID.
The stacking order of the metal material constituting the initial mountain and the initial peak of the metal material is realized, for example, by using a steel material group ID positioned at each product stage of the initial mountain identified by the initial mountain ID. The
The metal material size information is realized by using, for example, steel material group information (maximum width, minimum width, maximum length, and minimum length).
The payout order information is realized, for example, by using steel material group information (payout order).
The final mountain deriving means (process) is realized by using, for example, the final mountain deriving unit 102 (step S202).
The transport order deriving means (process) is realized by using, for example, the transport order deriving unit 103 (step S203). The temporary placement target metal material is realized, for example, by using a temporary placement target steel material group.
The temporary mountain deriving means (process) is realized by using, for example, the temporary mountain deriving unit 104 (step S204).
[Claim 2]
Stack constraints are realized by using width, length, and height constraints.
The initial mountain unit reverse pair is realized, for example, by using an initial mountain unit reverse pair R (a pair of steel material groups that become a reverse pair only from the mountain shape of the initial mountain).
[Claim 3]
The realizable mountain extracting means is realized by using the realizable mountain extracting unit 301, for example.
The first constraint equation setting unit and the first objective function setting unit are realized by using a constraint equation / objective function setting unit 302, for example.
The first optimization calculation means is realized by using the optimization calculation unit 303, for example.
[Claim 4]
The second constraint equation setting unit and the second objective function setting unit are realized by using, for example, a constraint equation / objective function setting unit 501. The temporary placement determination constraint equation set by the second constraint equation setting unit is realized by using, for example, equation (8). The second objective function set by the second objective function setting means is realized, for example, by using equation (9).
The second optimization calculation unit is realized by using the optimization calculation unit 502, for example.
[Claim 5]
The derivation means is realized by using the post-processing unit 503, for example.
The temporary storage material initial conveyance order regulation constraint formula is realized by using, for example, formula (10).
[Claim 6]
The temporary placement generation constraint expression is realized by using, for example, Expression (9-2).
[Claim 7]
The initial mountain initial conveyance order regulation constraint expression is realized by using, for example, Expression (11).
[Claims 8 and 9]
The third constraint equation setting unit and the third objective function setting unit are realized by using, for example, a constraint equation / objective function setting unit 1001.
The mountain allocation constraint equation is realized by using, for example, equation (17).
The same mountain assignment impossible constraint formula is realized by using, for example, formula (18).
The height constraint equation is realized by using, for example, the equation (19).
The third objective function set by the third objective function setting means is realized by using, for example, equation (22).
The third optimization calculation unit is realized by using, for example, the optimization calculation unit 1002.

  DESCRIPTION OF SYMBOLS 100: Yard management apparatus, 101: Steel material information acquisition part, 102: Final mountain derivation part, 103: Conveyance order derivation part, 104: Temporary mountain derivation part, 105: Output part

Claims (14)

As a place between processes, the metal material of the initial mountain made of metal material piled up in the yard where the metal material is placed is transported by a transporting device, and stacked in the stacking order according to the delivery order to the subsequent process of the yard. A yard management device for creating a final mountain made of metal material,
Initial mountain identification information including the identification information of the initial mountain, the identification information of the metal material constituting the initial mountain, and the stacking order of the metal material in the initial mountain, and the metal material size information regarding the size of the metal material And obtaining means for obtaining metal material information including the dispensing order information including the dispensing order to the subsequent process of the metal material,
Based on the initial mountain specifying information, the metal material size information, and the payout order information, the metal material constituting the final mountain and the stacking order of the metal material in the final mountain A final mountain deriving means for determining a mountain figure for each of the plurality of final mountains;
The metal material from the initial mountain to the final mountain based on the initial mountain specific information and final mountain specific information which is information about the mountain shape of the final mountain derived by the final mountain deriving means. A transport order deriving means for determining a temporary placement target metal material that is the metal material that needs to be temporarily placed as a temporary mountain in the temporary storage area of the yard before the transport to the final mountain,
Based on the transport order and the temporary placement target metal material derived by the transport order deriving means, and the metal material size information, the temporary placement target metal material constituting the temporary mountain, and the temporary placement target metal A temporary mountain deriving means for determining the mountain shape of the temporary mountain including the order of the materials in the temporary mountain,
The temporary mountain derivation means has a simple undirected structure in which the temporary placement target metal material corresponds to a vertex and a branch is stretched between two vertexes corresponding to two temporary placement target metal materials that cannot be stacked on the same temporary mountain. A yard management device characterized by determining a mountain shape of the temporary mountain by solving a vertex coloring problem that minimizes the number of colors to be colored at a vertex in a graph. The final mountain derivation means is a mathematical programming method based on a stacking constraint which is a constraint imposed when the metal material is stacked on the final mountain, and an evaluation value including the number of temporary placements and the height of the final mountain. Determine the final mountain shape by performing optimization calculation with
The number of temporary placements is the number of initial mountain unit reverse pairs,
2. The yard management device according to claim 1, wherein the initial mountain unit reverse pair is the two metal materials having the same vertical relationship in the final mountain as to the stacking position in the initial mountain. The final mountain derivation means uses a realizable mountain adoption variable to determine whether or not to adopt a realizable mountain that is stacked to satisfy the stacking constraint as an optimal solution,
Based on the metal material information, a feasible mountain extraction means for extracting the combination of the realizable mountains,
The fact that any of the metal materials must not be overlapped on a plurality of the realizable mountains and must be arranged on any of the realizable mountains, First constraint equation setting means for setting a constraint equation to be expressed based on the realizable mountain extracted by the realizable mountain extracting device;
An objective function for the purpose of optimizing the evaluation value for the realizable mountain to be adopted as the optimal solution, the first function expressed using the realizable mountain adoption variable and the evaluation value. First objective function setting means for setting the objective function based on the realizable mountain extracted by the realizable mountain extracting means,
The value when the value of the first objective function set by the first objective function setting means is minimum or maximum within a range satisfying the constraint expression set by the first constraint expression setting means. 3. The method according to claim 2, further comprising first optimization calculation means for performing the optimization calculation by mathematical programming to derive the value of the feasible mountain adoption presence / absence variable as an optimal solution. The yard management device described. The transport order deriving means is an initial transport order variable that is a binomial variable that defines a relative order of initial transport that is transport from the initial mountain for any two of the metal materials, and the metal material A temporary variable occurrence presence / absence variable, which is a variable that determines whether initial conveyance from the initial mountain is conveyance to the temporary storage area of the yard, is a decision variable,
In the same final mountain, when the metal material that is above the metal material below is initially conveyed first, the metal material that is initially conveyed first is transferred to the temporary mountain before the conveyance to the final mountain. The metal material information and the final mountain specifying information include a constraint expression including a temporary placement determination constraint expression that indicates that it is necessary to temporarily place it in a storage area using the initial transfer order variable and the temporary placement occurrence variable. Second constraint equation setting means for setting based on
A second objective function, which is an objective function for minimizing the number of the metal materials in which the temporary placement occurs and is expressed using the temporary placement occurrence variable, is included in the metal material information. Second objective function setting means for setting based on;
The initial value when the value of the second objective function set by the second objective function setting means is minimized or maximized within a range satisfying the constraint expression set by the second constraint expression setting means And a second optimization calculation means for performing the optimization calculation by mathematical programming to derive the values of the transport order variable and the temporary placement occurrence variable as an optimal solution. The yard management device according to any one of claims 1 to 3. In addition to the identification information of the metal material, the metal material in which the temporary placement occurs is determined based on the temporary placement occurrence presence / absence variable derived by the second optimization calculation unit. Given identification information different from the identification information, the final transport of the metal material from the temporary storage site to the final mountain is regarded as the initial transport of the virtual metal material given the other identification information. ,
Changing the identification information of the metal material at the stack position of the metal material where the temporary placement in the final mountain occurs to the other identification information given to the metal material;
One pile piled according to the initial conveyance order from the initial pile of the metal material, which is determined based on the initial conveyance order variable derived by the second optimization calculation means, and the temporary placement occur. A virtual mountain having two metal stages, each having a metal material arranged in the upper stage and a virtual metal material corresponding to the final conveyance of the metal material in which the temporary placement occurs, is regarded as the initial mountain. And
Setting the initial transport sequence variable as a binary variable that defines the relative order of the initial transport from the initial mountain or the temporary storage of any two of the metal materials including the virtual metal material;
The initial transport order variable that has been set is that the order of initial transport of the metal material from which the temporary placement occurs from the initial mountain is ahead of the order of initial transport of the metal material from the temporary storage site. In addition to the constraint equation set by the second constraint equation setting means, the temporary storage material initial conveyance order regulation constraint equation that is expressed using
After setting the second objective function,
Deriving the set initial transport forward variable when the value of the second objective function is minimum or maximum within a range satisfying the constraint equation, and based on the derived initial transport forward variable, 5. The yard management apparatus according to claim 4, further comprising derivation means for deriving the order of conveyance from the initial mountain to the final mountain. Instead of setting the second objective function, the derivation means uses the temporary placement occurrence variable to indicate that the number of the metal materials on which the temporary placement occurs is 0 (zero). A temporary placement occurrence constraint equation, which is an equation, is set in addition to the constraint equation;
Instead of deriving the set initial transport forward variable when the value of the second objective function is minimum or maximum within the range satisfying the constraint equation, the set value when satisfying the constraint equation is set. The yard management device according to claim 5, wherein an initial conveyance order variable is derived.   The constraint formula set by the second constraint formula setting means is that the product order from the lowest level of the initial peak is from the lowest level of any of the final peaks among the metal materials constituting the initial peak. The order of the initial transportation from the initial mountain of the metal material present above the portion that coincides with the stacking order of the initial material is transported to the initial mountain from the initial mountain or the temporary storage site different from the initial mountain. It further has an initial mountain initial transfer order regulation constraint equation that is an expression that represents the order of the initial transfer of the metal material to the initial mountain using the initial transfer sequence variable. The yard management device according to any one of claims 4 to 6. The two temporary placement target metal materials that cannot be stacked on the same temporary pile include the two temporary placement target metal materials that do not satisfy the stacking constraint that is imposed when the metal material is stacked on the final pile. The two metal objects to be temporarily placed that do not satisfy the relationship of putting out and putting out;
The first-to-last-out relationship is that, of the two temporary placement target metal materials, one of the temporary placement target metal materials whose timing to be transported from the initial pile to the temporary placement site is early, from the temporary placement site to the final pile. The timing of being transported to the second temporary placement target metal material is in a relationship that is later than the timing of transporting from the temporary storage site to the final mountain, according to any one of claims 1 to 7. The yard management device described. The temporary mountain derivation means includes a temporary mountain allocation variable that determines whether or not the temporary storage target metal material is allocated to the temporary mountain, and the temporary storage target metal material allocated to the temporary mountain for each of the temporary mountains. The tentative mountain presence / absence variable that determines whether or not there is a decision variable,
All of the temporary placement target metal materials are constraint equations that stipulate that any one of the temporary mountains must be allocated only once, and are mountain allocation constraint equations expressed using the temporary mountain allocation variable And a constraint expression for determining two temporary placement target metal materials that cannot be stacked on the same tentative mountain, and is a constraint expression expressed by using the tentative mountain allocation variable and the tentative mountain existence variable. A constraint formula and a constraint formula that determines that the height of the tentative mountain is less than or equal to an upper limit value, and is a constraint formula that is expressed using the tentative mountain allocation variable and the tentative mountain existence variable. A third constraint equation setting unit that sets a constraint equation including: the temporary placement target metal material derived by the transport order deriving unit and the transport sequence of the temporary placement target metal material;
Third objective function setting for setting a third objective function for setting an objective function expressed using the temporary mountain existence variable, which is an objective function for minimizing the number of temporary mountains. Means,
The temporary mountain allocation variable when the value of the objective function set by the third objective function setting means is minimum or maximum within a range satisfying the constraint expression set by the third constraint expression setting means And deriving the value of the temporary mountain presence / absence variable as an optimal solution further by third optimization calculation means for performing optimization calculation by mathematical programming. The yard management device described. The initial mountain includes an existing mountain and a virtual mountain,
The existing mountain is a mountain piled up in the yard,
It is assumed that the virtual mountain is a metal material that has not arrived at the yard, and the metal materials for which the final mountain is to be created are piled so that the arrival order at the yard is earlier The yard management device according to any one of claims 1 to 9, wherein the yard management device is a single mountain in a case where the yard management is performed.   The final figure of the final mountain, the order of conveyance of the metal material from the initial mountain to the final mountain, the metal material to be temporarily placed, and the mountain figure of the temporary mountain are made of a plurality of metal materials. The yard management device according to claim 1, wherein the yard management device is determined in units of groups. The yard is a place between a steel making process and a rolling process in a steel manufacturing process,
The yard management device according to claim 1, wherein the metal material is a steel material. As a place between processes, the metal material of the initial mountain made of metal material piled up in the yard where the metal material is placed is transported by a transporting device, and stacked in the stacking order according to the delivery order to the subsequent process of the yard. A yard management method for creating a final mountain made of metal material,
Initial mountain identification information including the identification information of the initial mountain, the identification information of the metal material constituting the initial mountain, and the stacking order of the metal material in the initial mountain, and the metal material size information regarding the size of the metal material And obtaining the metal material information including the dispensing order information including the dispensing order to the subsequent process of the metal material,
Based on the initial mountain specifying information, the metal material size information, and the payout order information, the metal material constituting the final mountain and the stacking order of the metal material in the final mountain A final mountain derivation step for determining a mountain figure for each of the plurality of final mountains;
The metal material from the initial mountain to the final mountain based on the initial mountain specific information and final mountain specific information that is information about the mountain shape of the final mountain derived in the final mountain deriving step. A transport order deriving step of determining a temporary placement target metal material that is the metal material that needs to be temporarily placed as a temporary mountain in the temporary storage area of the yard before the transport to the final mountain,
Based on the transport order and the temporary placement target metal material derived in the transport order deriving step, and the metal material size information, the temporary placement target metal material constituting the temporary mountain, and the temporary placement target metal A temporary mountain derivation step for determining a mountain shape of the temporary mountain including a stacking order of the material in the temporary mountain,
In the temporary mountain derivation step, the temporary placement target metal material corresponds to a vertex, and a simple undirected structure in which a branch is stretched between two vertexes corresponding to two temporary placement target metal materials that cannot be stacked on the same temporary mountain. A yard management method comprising: determining a mountain shape of the temporary mountain by solving a vertex coloring problem that minimizes the number of colors to be colored at vertices in a graph.   A program that causes a computer to function as each unit of the yard management device according to any one of claims 1 to 12.

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