JP6776873B2 - Yard management equipment, yard management methods, and programs - Google Patents

Description

The present invention relates to a yard management device, a yard management method, and a program, and particularly in a metal manufacturing process, in a yard provided between processes, a plurality of piles of a plurality of metal materials and containers in a physical distribution field or the like are stacked. , It is suitable for use for transshipment into a plurality of piles piled up in the order of payout to the next process.

In the steelmaking process, which is an example of the metal manufacturing process, when the steel material, which is an example of the metal material, is transported from the steelmaking process to the rolling process of the next process, the steel material is once placed in a temporary storage place called a yard and then placed in a temporary storage place. It is carried out from the yard according to the processing time of the rolling process, which is the next process. An example of the layout of the yard is shown in FIG. As shown in FIG. 15, the yard is a storage space 1501 to 1504 partitioned vertically and horizontally as a buffer area for supplying steel materials such as slabs discharged from the upstream process to the downstream process. The vertical division is often referred to as the "building" and the horizontal division is often referred to as the "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, the "building" and "row" are specified to indicate where to transport the steel material (numbers (11) in parentheses in the storage areas 1501 to 1504 in FIG. 15). (12), (21), (22)).

Next, the basic work flow in the yard is shown by taking FIG. 15 as an example. First, the steel material carried out from the continuous casting machine 1510 in the steelmaking process, which is the previous process, is carried to the yard by the receiving table X via the pillar 1511, and is partitioned by the cranes 1A, 1B, 2A, and 2B. It is transported to any of ~ 1504 and piled up. Then, according to the manufacturing schedule of the rolling process, which is a subsequent process, the cranes 1A, 1B, 2A, and 2B are placed on the payout table Z again and transported to the rolling process. Generally, steel materials are placed in a pile in the yard as described above. This is to make effective use of the limited yard area.

In the present specification, claims, and drawings, "already landed mountain", "virtual mountain", "initial mountain", "final mountain", and "temporary mountain" are used with the following meanings.
Already landed mountain: A mountain that has already been formed in the yard at this time.
Virtual mountain: A mountain (not a mountain that actually exists) assuming that metal materials that have not arrived at the yard at this time are piled up in the order of arrival at the yard.
Early mountain: A general term for existing mountains and virtual mountains.
Final mountain: The final mountain (also called the payout mountain) piled up for post-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 hot rolling process, which is the next process, it is required that the steel material be charged into the heating furnace while maintaining the temperature as high as possible. Therefore, in recent years, a heat insulating facility may be installed in the yard, and steel materials may be stored in a pile in the yard. In order to effectively utilize the limited heat insulation equipment, it is necessary to stack steel materials as high as possible. On the other hand, when stacking steel materials, the steel materials are stacked from the top in the processing order in the next process at the final pile so that they can be easily supplied to the next process, and the stacking shape of the final pile is not an inverted pyramid. There are restrictions such as things (this is called "stacking constraint"). Furthermore, the workload when building a mountain (creating the final mountain) is also an element that cannot be overlooked. Therefore, in yard control, it is desirable to formulate a work plan for raising the mountain so that the final mountain is as high as possible with as little workload as possible under the above-mentioned stacking restrictions.

In addition, when performing mountain sorting (dividing steel materials into multiple piles) to smoothly pay out the required steel materials in the post-process in the yard, the steel materials scheduled to arrive will be demoted (steel materials are built in). Due to quality problems that occur at the time, the grade is lowered from the originally planned use and transferred to another use), or the steel material to arrive requires unscheduled rectification treatment or the size changes. By doing so, it can often happen that the steel does not arrive as originally planned. In addition, it can hardly be expected that the state of the yard storage will change as originally planned, and it is a daily occurrence that unplanned steel materials have to be placed in unplanned storage.

Furthermore, the rolling order of the steel materials piled up in the pile from the top in the order of delivery from the yard to the next process (hot rolling process) in the next process is changed after the steel materials arrive at the yard. Since the piles are no longer stacked in the normal order, it is often the case that the steel materials are forced to be reloaded according to the changed rolling order. Here, in the forward stacking, at any stacking position of the mountain, one steel material that is relatively above or a plurality of steel materials that are simultaneously transported is faster than a steel material that is below the steel material. A stacking method that is paid out to the next process. In addition, the product order of such steel materials is called the payout normal order.

However, since the transshipment work required here must be performed in parallel with the work of receiving the steel material into the yard and the work of discharging the steel material from the yard, the time zone during which the steel material can be transshipped is limited. Therefore, it is required to efficiently transship steel materials.
Therefore, due to various circumstances before and after arriving at the yard, the work of transshipping piles that are no longer in normal order when arriving at the yard can be efficiently transshipped (that is, with as few transports as possible). ) Needs to do are extremely high.

There are inventions described in Patent Documents 1 to 6 with respect to the yard management method in which these are required. The inventions described in Patent Documents 1 to 4 are inventions for a case where a mountain sorting plan is performed for a steel material (so-called non-arrival material) scheduled to arrive at the yard, and the mountain shape of the final mountain, that is, the target steel material. There is a study on how to properly sort the mountains. However, in the inventions described in Patent Documents 1 to 4, when the acceptance into the yard is completed or is in the process of being accepted but the accepted steel materials are not piled up in the pile in the order of payout, the final pile is appropriate. No studies have been made on the issue of efficient transshipment of steel materials.

The invention corresponding to this problem is the invention described in Patent Documents 5 and 6.
First, in Patent Document 5, when transshipping the steel materials of the already arrived mountain already in the yard in the order of payout, the optimum mountain shape of the final mountain is combined in consideration of the necessary transfer load and stacking constraint. A method of formulating as a conversion problem and calculating using a tabu search method is disclosed. However, in the invention described in Patent Document 5, although the method of obtaining the mountain shape of the final mountain is shown, the method of 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 shape of the final mountain is also calculated by a heuristic method, there is no guarantee of its optimumity.

Next, the invention described in Patent Document 6 is a technique for simultaneously optimizing the mountain sorting and the transport order by reducing the result to a mathematical planning problem that satisfies the constraint condition regarding the pile standing and the transport. However, in the invention described in Patent Document 6, the occurrence of temporary placement, which causes an increase in the transport order, can be considered only for steel material pairs having the same initial peak. That is, temporary placement does not only occur between steel pairs with the same initial crest, but can also occur between steels at different initial crests, depending on which steel material is transported first. Therefore, in the invention described in Patent Document 6, all the transport orders of steel materials cannot be taken into consideration, and the optimum transport order cannot be obtained.

In addition, when considering the problem of transshipment of steel materials to make the final mountain of forward stacking, even if the mountain shape of the initial mountain is given, at least the mountain shape of the final mountain and the steel material from the initial mountain to the final mountain It is necessary to determine the three factors of the order of transportation and how to organize the steel materials temporarily placed in the transportation process into the temporary mountain (mountain appearance of the temporary mountain). In that sense, the conventional technology is not a technology that covers all of these three elements.

Japanese Unexamined Patent Publication No. 6-179525 Japanese Unexamined Patent Publication No. 2000-226123 JP-A-11-255336 Japanese Unexamined Patent Publication No. 2008-260630 Japanese Patent No. 4935032 JP-A-2010-269929 JP-A-2007-137612 Japanese Unexamined Patent Publication No. 2016-81186 Japanese Patent No. 5365759

The present invention has been made in view of the above problems, and the mountain shape of the final mountain, the order of transporting the steel material from the initial mountain to the final mountain, and the temporary pile of the steel material temporarily placed in the transport process. The purpose is to be able to determine by a series of processes.

The yard management device of the present invention transports the metal material of the initial mountain made of the metal material piled up in the yard where the metal material is placed as a storage place between the processes by a transport device, and transfers the metal material to the subsequent process of the yard. It is a yard management device for creating a final pile made of metal materials piled up in a stacking order according to a payout order, and is an identification information of the initial pile, identification information of the metal material constituting the initial pile, and the metal. Metal material including initial mountain identification information including the stacking order of the material in the initial mountain, metal material size information regarding the size of the metal material, and payout order information including the payout order of the metal material to the subsequent process. In the metal material constituting the final mountain and the final mountain of the metal material based on the acquisition means for acquiring the information, the initial mountain identification information, the metal material size information, and the payout order information. The final mountain derivation means for determining the mountain shape of the final mountain including the product order for each of the plurality of final mountains, the initial mountain identification information, and the mountain shape of the final mountain derived by the final mountain derivation means. Based on the information about the final mountain, the order in which the metal material is transported from the initial mountain to the final mountain, and the temporary mountain in the temporary storage place of the yard before the transportation to the final mountain. The transport order derivation means for determining the metal material to be temporarily placed, which is the metal material that needs to be temporarily placed, the transport order and the metal material to be temporarily placed, which are derived by the transport order derivation means, and the above. Derivation of a temporary mountain that determines the shape of the temporary mountain including the metal material to be temporarily placed and the stacking order of the metal materials to be temporarily placed in the temporary mountain based on the metal material size information. The temporary pile deriving means has means, and the temporary pile derivation means is between two vertices corresponding to two temporary metal materials that cannot be piled up on the same temporary pile because the metal material to be temporarily placed corresponds to a peak. It is characterized in that the mountain shape of the temporary mountain is determined by solving the apex coloring problem that minimizes the number of colors to be colored at the apex in a simple undirected graph with branches.

In the yard management method of the present invention, as a storage place between processes, the metal material of the initial mountain made of the metal material piled up in the yard where the metal material is arranged is transported by a transport device to the subsequent process of the yard. It is a yard management method for creating a final pile made of metal materials piled up in a stacking order according to a payout order, and is an identification information of the initial pile, identification information of the metal material constituting the initial pile, and the metal. Metal material including initial mountain identification information including the stacking order of the material in the initial mountain, metal material size information regarding the size of the metal material, and payout order information including the payout order of the metal material to the subsequent process. Based on the acquisition process for acquiring information, the initial mountain identification 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. The final mountain derivation process for determining the mountain shape of the final mountain including the product order for each of the plurality of final mountains, the initial mountain identification information, and the mountain shape of the final mountain derived by the final mountain derivation process. Based on the information about the final mountain, the order in which the metal material is transported from the initial mountain to the final mountain, and the temporary mountain in the temporary storage place of the yard before the transportation to the final mountain. The transport order derivation step of determining the metal material to be temporarily placed, which is the metal material that needs to be temporarily placed, the transport order derived by the transport order derivation step, the temporary placement target metal material, and the above. Derivation of a temporary mountain that determines the shape of the temporary mountain including the metal material to be temporarily placed and the stacking order of the metal materials to be temporarily placed in the temporary mountain based on the metal material size information. In the temporary mountain derivation process, the temporary placement target metal material corresponds to the apex, and between two apex corresponding to two temporary placement target metal materials that cannot be piled up on the same temporary mountain. It is characterized in that the mountain shape of the temporary mountain is determined by solving the apex coloring problem that minimizes the number of colors to be colored at the apex in a simple undirected graph with branches.

The program of the present invention is characterized in that a computer functions as each means of the yard management device.

According to the present invention, the shape of the final mountain, the order of transporting the steel material from the initial mountain to the final mountain, and the temporary pile of the steel material temporarily placed in the transport process can be determined by a series of processes.

FIG. 1 is a diagram showing an example of a functional configuration of a yard management device. FIG. 2 is a flowchart illustrating an example of an outline of the yard management method. FIG. 3 is a diagram showing an example of the functional configuration of the final mountain derivation unit. FIG. 4 is a flowchart illustrating an example of the process of step S202. FIG. 5 is a diagram showing an example of the functional configuration of the transport order derivation unit. FIG. 6 is a flowchart illustrating an example of the process of step S203. FIG. 7 is a diagram showing an example of a form of transporting a steel material when there is a fixed portion in the initial peak. FIG. 8 is a diagram showing an example of a simple undirected graph. FIG. 9 is a diagram illustrating an example of a first-in / second-out relationship. FIG. 10 is a diagram showing an example of the functional configuration of the temporary mountain derivation unit. FIG. 11 is a flowchart illustrating an example of the process of step S204. FIG. 12 is a diagram showing an example of steel material information. FIG. 13 is a diagram showing the result of performing the optimization calculation by the method of the present embodiment. FIG. 14 is a diagram showing the result of the optimization calculation by the method of the present embodiment and the result of the method of the comparative example. FIG. 15 is a diagram showing 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 initial mountain shape and the rolling process of each steel material are arranged so that the steel materials (slabs) manufactured in the steel making process are piled up from the top in the order of transportation to the rolling process. Given the order of transportation, the mountain shape of the final mountain, the transportation order of each steel material when transporting from the initial mountain to the final mountain, the steel materials that need to be temporarily placed, and the mountain shape of the temporary mountain are in this order. The case of deriving will be described as an example. In the following description, the steel materials that need to be temporarily placed are referred to as the steel materials to be temporarily placed, and the order of transporting each steel material to the rolling process is referred to as the payout order, if necessary. Further, steel materials that have not yet been piled up in the yard are referred to as unarrival materials as necessary, and steel materials that are piled up in the yard are referred to as already-arrival materials as necessary.

<Background>
First, I will explain the process of deriving the mountain shape of the final mountain, the transport order of each steel material when transporting from the initial mountain to the final mountain, the steel material to be temporarily placed, and the mountain shape of the temporary mountain in this order. To do.
The problem of transshipping already arrived materials (hereinafter referred to as "the problem of transshipping already arrived materials") is the problem of dividing undelivered materials into mountains (problems as described in Patent Documents 1 to 4. Hereinafter, the problem of dividing undelivered materials into mountains). There is an essential difference from (referred to as), which is shown below.

When the steel has not arrived in the yard, the order of receipt and delivery of the two steels to the yard is the same (that is, the order of receipt and delivery of one steel of the two steels is higher than that of the other steel. If you want to stack these two steels on the same final pile, you need to temporarily place the steels received in the yard first and change the stacking order. In other words, the relationship between the order of acceptance and the order of withdrawal determines whether or not it will be temporarily placed. On the other hand, when considering the state of arrival at the yard, the element corresponding to the order of acceptance is the order of stacking steel materials in the initial pile. In other words, since it can be accessed from the steel materials piled up on the initial mountain, this corresponds to the order of acceptance. Here, when the steel materials have not arrived in the yard, the "acceptance order" is uniquely ordered for all the steel materials. On the other hand, the "transportation order" of the already arrived material is that when there are multiple initial peaks, the steel material at the top of the multiple initial peaks can be accessed, so there is a degree of freedom that is several minutes of the initial peaks. Therefore, the transport order cannot be uniquely determined. Therefore, rather than the "non-arrival material pile division problem" in which all steel materials have not arrived at the yard as the initial state, the "already-arrival material transshipment problem" in which the steel material has already arrived in the yard is the initial state. It turns out that the difficulty of the problem is high.

The difficulty of this "problem of transshipment of already arrived materials" appears in the difficulty of counting temporary storage, which is one of the evaluations. In other words, the number of temporary storages can be determined by the order of arrival of steel materials in the yard in the "Unarrival material mountain division problem", so if the mountain shape of the final mountain is determined, it can be determined individually for each mountain (influence of other mountains). Not). On the other hand, in the "re-arrival material transshipment problem", even if a single final mountain was given, the temporary storage required to compose it was that the steel materials that make up the final mountain existed ( To the final mountain, the mountain appearance of the initial mountain (plural), the mountain appearance of the other (plural) final mountains made from those initial mountains, the transportation order of steel materials from the initial mountain (decomposition order of the initial mountain), and the final mountain. It also depends on the order of transportation of steel materials (the order of assembly of the final pile).

Therefore, in the "recipient material transshipment problem", the number of temporary storages that occur cannot be determined in mountain units as in the case of solving the "non-arrival material pile division problem". In other words, in the "relaying material transshipment problem", when deciding the shape of the final mountain, there is as much freedom as the number of mountains in the initial mountain in the order of transportation, so unless you think at the same time as the order of transportation, it will be temporarily placed. It is not possible to solve the problem of solving the mountain shape of the final mountain that minimizes the number. However, the optimization problem that considers the shape of the final mountain and the order of transportation at the same time causes an increase in the scale of the problem.

Based on the above findings, the present inventors have modified the optimal solution method for solving the mountain shape of the final mountain of the "undelivered timber division problem" by optimal calculation so that it can deal with the problem of already arrived timber, and are suboptimal. Find a solution, use it as the mountain shape of the final mountain, find the transportation order from the initial mountain to the final mountain of each steel material, and based on the mountain shape and transportation order of the final mountain obtained in this way, the temporary mountain I came up with the idea of seeking a mountain view. In this way, a specific example of the method of deriving the mountain shape of the final mountain, the transport order of each steel material from the initial mountain to the final mountain, and the mountain shape of the temporary mountain will be described.

<Functional configuration of yard management device 100>
FIG. 1 is a diagram showing an example of a functional configuration of the yard management device 100. 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 illustrating an outline of an outline of a yard management method executed by the yard management device 100.

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

The steel group information includes identification information, payout order, number of steel materials, and each of the steel material groups (set N = {1, 2, ..., N}) for which the final pile is to be created. Contains information on maximum width, minimum width, maximum length, and minimum length. The steel material group refers to a group of steel materials that are not divided (the smallest 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 payout order is the payout order (transportation order to the rolling process) of each steel material group.

The number of steel materials (w: N → Z +) is the number of steel materials constituting each steel material group. The number w (i) of the steel materials included in one steel material group is, for example, 1 or more and 6 or less (∀i ∈ N, 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 and the minimum width are the maximum width and the minimum width of the steel materials constituting each steel material group, respectively. Instead of the maximum width and the minimum width, the width of each slab constituting each steel material group may be included in the steel material 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. Instead of the maximum length and the minimum length, the lengths of the steel materials constituting each steel material group may be included in the steel material group information.

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

The information that identifies the maximum height of the mountain is information that includes the upper bound h _max (∈ Z +) of the number of steel materials that can be piled up as a temporary mountain and the final mountain. The upper bound h _max of the number of steel materials that can be piled up as a temporary mountain and a final mountain is, for example, 10. Here, assuming that the thickness of each steel material is the same, the information for specifying the maximum height of the mountain is defined as the upper bound of the number of steel materials that can be piled up as a temporary mountain and a final mountain. When the information on the thickness of each steel material is included in the steel material information, the maximum heights of the temporary mountain and the final mountain may be adopted as the information for specifying the maximum height of the mountain.
When all the steel materials for which the final pile is to be created are transported one by one, the identification information (steel material ID), payout order, width, and length information for each steel material is used instead of the steel material group information. To be acquired.
Examples of the acquisition form of the steel material information include an input operation of the user interface of the yard management device 100, transmission from an external device, and reading from a portable storage medium.

[Final mountain derivation unit 102, step S202]
The final mountain derivation unit 102 is based on the mountain shape of the initial mountain, and under the condition that the stacking constraint described later is satisfied, the number of the initial mountain unit reversal pairs and the total number of the final mountain described later are reduced. The mountain shape is derived by performing the optimum calculation.

As explained in the section <Background>, in the "non-arrival timber division problem", the number of temporary placements is determined for each final mountain when the final mountain is created. On the other hand, in the "problem of transshipment of already arrived materials" as in the present embodiment, the number of temporary storages cannot be uniquely determined for each final mountain when the final mountain is created. In the "non-arrival mountain division problem", a reversal pair set is used to evaluate the number of temporary placements. Here, the reversal pair can be piled up on the same final mountain, but when stacking on the same final mountain, the order of arrival at the yard and the stacking order on the same final mountain (from the bottom) Refers to a pair of steel materials groups that have a reverse relationship with each other, and such a set of reverse pairs is a reverse pair set. For example, when the first steel group having a relatively early arrival order at the yard and the second steel group having a relatively slow arrival order are piled up on the same final pile, the first steel material is piled up in the final pile. When the group is paid out earlier (that is, stacked on top) than the second steel group, the first steel group and the second steel group are reversed pairs. This is because the order of arrival at the yard is earlier in the first steel group than in the second steel group, but the order of payout is earlier in the first steel group than in the second steel group.

When applying the "undelivered material pile division problem" to the "already arrived material transshipment problem", the reversal pair assembly cannot be defined sufficiently (to be exact, the reversal pair itself depends on the transport order, so the transport order is fixed. Unless you can define a reversal pair). Therefore, the present inventors set the pair of two steel material groups whose temporary placement is unavoidable from the mountain shape of the initial mountain regardless of the order of transportation as the initial mountain unit reversal pair R, and the reversal pair in the "non-arrival material mountain division problem". As the initial mountain unit reversal vs. R, we came up with the idea of deriving the mountain shape of the final mountain by solving the "non-arrival timber division problem" by performing optimal calculation.

As described above, in the present embodiment, the pair of the steel material group that becomes the reversal pair only from the mountain shape of the initial mountain is defined as the initial mountain unit reversal pair R. In the initial pile, since the stacking order can be transported from the upper steel group, the reversal pair is extracted for each initial pile, assuming that the stacking order is the arrival order. Specifically, for any two steel group in the same initial pile, if the vertical positional relationship of the relative stacking positions in the initial pile is the same in the final pile, the two steel groups Is the initial mountain unit reversal vs. R. For example, in the same initial mountain, there is a first steel group relatively above and a second steel group relatively below, and in the same final mountain, the first steel group is relative. The first steel group and the second steel group are in the initial mountain unit reversal pair when the second steel group is relatively higher and the second steel group is relatively lower. The first steel group and the second steel group are not limited to those located adjacent to each other in the same initial mountain (for example, a third steel group between the first steel group and the second steel group). Even if there is a steel material group of, the first steel material group and the second steel material group become an initial mountain unit reversal pair if the above-mentioned relationship is satisfied). Of the two steel material groups constituting such an initial pile unit reversal pair, the steel material group that is relatively higher in the same initial pile is subject to temporary placement.

The "non-arrival timber division problem" itself can be realized by a known technique. For example, Patent Documents 7 and 8 show an example of solving the "non-arrival timber division problem" as a partitioning problem. Therefore, in the present embodiment, in the "non-arrival material mountain division problem" described in Patent Documents 7 and 8, the temporary placement (mountain creation load) is finally evaluated by the initial mountain unit reversal pair R instead of the reversal pair. The mountain derivation unit 102 derives the mountain shape of the final mountain.

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

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

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

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 the certain steel material group is the said. This is a case where the width is wider than the minimum width of the steel material group located below the steel material group and the difference between the widths is less than the reference value (for example, 200 [mm]).

-Length condition If the maximum length of a certain steel group is shorter than the minimum length of the steel group located below the certain steel group, the certain steel group is unconditionally placed under the steel group. Can be placed on top of a group. When the maximum length of a certain steel group is longer than the minimum length of the steel group located below the certain steel group, the difference between the two lengths is a reference value determined by work constraints (for example, 2000 [mm]). ]) If it is less than, the certain steel group can be placed on the steel group located below, but if it exceeds it, it cannot be placed.

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 the certain steel material group is the said. 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 two lengths is less than the reference value (for example, 2000 [mm]).

-Height constraint The number of stacks h of the final pile must be less than or equal to the upper bound h _max of the number of steel materials that can be piled up as the final pile.

Here, the length constraint may be specified only by the relationship with the steel group located one below a certain steel group, but as described in the length condition, it is applied to all the steels located below. By regulating and making the restrictions stricter than that, it is uniquely determined whether or not the steel group i, j can be loaded on the same final pile for the pair {i, j} ⊆N of any steel group. Therefore, as in the following equations (1) and (2), the pair set F of the steel material group can be defined as a prohibited pair set. A prohibited pair set refers to a set of two steel group pairs (prohibited pairs) that cannot be piled up on the same final pile.

The feasible mountain extraction unit 301 prevents the forbidden pair set (set F of pairs of steel material groups) determined by the above equations (1) and (2) from being included in the feasible mountain based on the steel material information. At the same time, the feasible mountains are extracted so that the mountains that violate the height constraint are not included in the feasible mountains.

[Constraint expression / objective function setting unit 302, steps S402, S403]
The constraint equation / objective function setting unit 302 derives an evaluation value for each of the feasible peaks, which is each element of the set of feasible peaks (set family), based on the steel material information. As for this evaluation value, the smaller the number of initial mountain unit reversal pairs, the higher the evaluation (the value becomes smaller), and the higher the height of the feasible mountain (that is, the smaller the number of feasible mountains), the higher the evaluation. It is set to be high (small value). In addition, the feasible mountain adoption / non-adoption variable is used as the coefficient of determination. The feasible mountain adoption / non-adoption variable is, for example, "1" when the final mountain derivation unit 102 adopts the element (realizable mountain) of the set of feasible mountains as the final mountain (optimal solution), and "0" when it is not adopted. (Zero) ”is a 0-1 variable.

Then, the constraint equation / objective function setting unit 302 uses the feasible mountain adoption / non-adoption variable (determination variable) and the evaluation value for each feasible mountain to obtain the evaluation value for the feasible mountain to be adopted as the optimum solution. An objective function that aims to minimize the sum is set based on the information on the feasible peaks extracted as described above. Further, the constraint expression / objective function setting unit 302 shall not be arranged in a plurality of feasible ridges in any of the steel material groups, and shall be arranged in any of the feasible ridges. Constraints (constraints) expressed using the feasible mountain adoption / non-adoption variable (determination variable) are set based on the information of the feasible mountain extracted as described above.

[Optimization calculation unit 303, steps S404, S405]
The optimization calculation unit 303 realizes when the value of the objective function set by the constraint expression / objective function setting unit 302 becomes the minimum within the range that satisfies the constraint expression set by the constraint expression / objective function setting unit 302. The possible mountain adoption / non-adoption variable (determination variable) is derived by performing the optimum calculation. This feasible mountain adoption variable specifies the feasible mountain to be adopted as the final mountain. Further, by stacking the steel material groups constituting the feasible mountain so as to satisfy the above-mentioned stacking constraint, the stacking position (that is, the mountain shape) of each steel material group in each final mountain is specified. These identified information will be the final mountain identification information. An identification number (final mountain ID) of the final mountain is set for each final mountain.

This optimization calculation is a 0-1 programming problem. For example, a known algorithm (solver) for solving an optimization problem by a mathematical programming method such as a 0-1 integer programming method such as a branch-and-bound method is used. It can be realized by using it. Further, although the minimization problem is solved here, for example, it may be a maximization problem by setting the evaluation value so that the higher the evaluation, the larger the value. Details of the above processing (method of extracting feasible peaks, specific constraint equations, contents of objective functions, etc.) are described in Patent Documents 7 and 8, and detailed description thereof will be omitted here. ..

[Transporting order derivation unit 103, step S203]
In the initial mountain unit reversal pair R, it is not possible to extract all the pairs of the steel material group to be temporarily placed, unlike the reversal pair in the "Undelivered material pile division problem", and the steel material group to be temporarily placed Insufficient pair extraction. Therefore, it is assumed that the final peak derivation unit 102 derives a solution for which the number of temporary placements has not been sufficiently evaluated. Therefore, in the present embodiment, when transporting each steel material group in order to transship the mountain shape of a given initial mountain into the mountain shape of the final mountain derived by the final mountain lead-out unit 102 in the transport order out-licensing unit 103. The transport order of each steel material group is derived so that the number of transports (that is, the number of temporary placements) is minimized. By doing so, it can be expected that a solution that suppresses the occurrence of temporary placement, which could not be sufficiently considered by the final mountain derivation unit 102, can be obtained. Two specific examples of the processing of the transport order derivation unit 103 will be described below. First, a first example of processing of the transport order derivation unit 103 will be described.

<< Assumptions and problem settings >>
Under the following premise, the transport order derivation unit 103 uses the final mountain derivation unit 102 from the initial mountain specified from the steel material information (information that identifies the mountain shape of the initial mountain) acquired by the steel material information acquisition unit 101. Find the order of transport of steel when transshipping steel to the final mountain from which the mountain shape was derived. In the following description, the information for identifying the initial mountain shape is referred to as the initial mountain shape identification information as necessary. Further, the information for identifying the mountain shape of the final mountain derived by the final mountain derivation unit 102 is referred to as the final mountain shape identification information as necessary.

(1) The maximum number of transports from the initial mountain (initial storage area) to the final mountain (final storage area) is 2 for any steel material. That is, the steel material transported to the temporary mountain (temporary storage site) shall be transported to the final mountain (final storage site) at the next transportation, and shall not be transported between different temporary mountains (temporary storage site). To do.
(2) The initial and final hills are stored differently, and it is assumed that all steel materials must be transported from the initial ridge (initial yard) to the final ridge (final yard) (that is, all steel materials are transported). Be eligible).

Further, in this example, the optimization problem for the purpose of minimizing the number of times the steel material is conveyed is solved under the following constraints.
(I) The steel material of each initial pile can be transported only in order from the top of the initial pile.
(Ii) When creating the final mountain, it can only be stacked from the bottom to the top.
(Iii) The number of steels that can be transported simultaneously depends on the number and capacity of available cranes. In this example, for the sake of simplicity, the case where the number of usable cranes is "1", that is, the case where the number of steel materials included in one steel material group is "1" is taken as an example. To do.
As described above, the maximum number of transports from the initial ridge (initial yard) to the final ridge (final yard) is 2 for any steel material (see the premise of (1) above), so the number of transports of the steel material. To minimize is equivalent to minimizing the number of temporary placements.

<< determination variable >>
In this example, the variable that determines the order of removing the steel materials from the initial pile is set as the independent variable, and it is determined whether or not each steel material needs to be temporarily placed based on the peak shape of the final pile. The reason why the order of removing the steel material from the initial pile is set as the independent variable is to reduce the variable by paying attention to the fact that the mountain shape of the given final pile has the information of the final transport order. In addition, the initial transport order variable, which is a variable indicating the order in which steel materials are removed from the initial pile, is set to a relative ordinal variable instead of an absolute ordinal variable so that the order constraint between the two steel materials can be expressed concisely and clearly. To do. Then, 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 the absolute order variable is used as the initial transport order variable.

For any steel group pair (two steel groups), the initial transport order variable y (s, s') that defines the order in which the steel is removed from the initial pile, and the presence or absence of temporary placement for any steel group are indicated. Temporary placement occurrence / absence variables x (s) are defined as follows.

(A) Initial transport 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 the steel group has one vertex. At this time, E = {(s, s') ∈ N ² | s ≠ s'). Introduce the 0-1 variable y (e) (∀e ∈ E) defined on the directed set E, and define the initial transport forward variable y (s, s') as shown in equation (3) below. To do.

Here, the initial transportation means that the steel group in the initial mountain is transported to the final mountain (final storage place) or the temporary mountain (temporary storage place). On the other hand, the final transport means to transport the steel material in the initial mountain or the temporary mountain (temporary storage place) to the final mountain (final storage place). s is a variable that specifies the initial transport of each steel material group, and a different value is set for each steel material group (s'is written so as to be distinguishable from s, and s'and later (6). The s'' in the equation is also a variable that specifies the initial transport of each steel material). As mentioned above, the number of steel group is n. A variable s that specifies the initial transport is set for each of these steel groups. In this example, the case where the variable s is the steel material group ID will be described as an example.
(B) Temporary placement variable x (s): number of variables = n
The variable x (s) for the presence / absence of temporary storage indicates that when the steel group is initially transported from the initial mountain to the final mountain, the initial transportation is to the temporary mountain (temporary storage site) or the final mountain (final storage site). It is a 0-1 variable indicating whether or not it is transported to. Therefore, the temporary placement occurrence / absence 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 derivation unit 103 >>
FIG. 5 is a diagram showing an example of a detailed functional configuration of the transport order derivation unit 103. FIG. 6 is a flowchart illustrating an example of detailed processing of the transport order derivation unit 103 (step S203).

[Constraint expression / objective function setting unit 501, steps S601, S602]
The constraint expression / objective function setting unit 501 sets a constraint expression in which the above-mentioned constraint is expressed by a mathematical expression and an objective function in which the above-mentioned purpose is expressed by a mathematical expression.
[[Constraint expression]]
First, the constraint expression will be described.
(A) Definition constraint of the initial transport order variable y (s, s') The order of removing any two steel material groups from the initial peak is the total order of the set N of the steel material groups (transitive ((6) below). Equation), antisymmetric and total (referring to the binary relation of equation (5) below)), so the initial transitive order variable y (which defines the relative order of removing any two steel group from the initial peak) s, s') satisfies the total order (comparable) expressed by the following equation (5) and the transitive law expressed by the following equation (6). Further, the initial transport order variable y (s, s') satisfying the following equations (5) and (6) corresponds to the total order of the steel material group.

Equation (5) indicates that the initial transport of the steel group specified by the variable s and the initial transport of the steel group specified by the variable s'are always one first and the other later. These two steel material groups are different steel material groups.
In equation (6), the initial transfer of the steel material group specified by the variable s is earlier than the initial transfer of the steel material group specified by the variable s', and the initial transfer of the steel material group specified by the variable s'is , If the initial transfer of the steel group specified by the variable s'' is earlier than the initial transfer of the steel group specified by the variable s, the initial transfer of the steel group specified by the variable s'' is earlier than the initial transfer of the steel group specified by the variable s''. Indicates that. These three steel material groups are different steel material groups.

In addition, the work of removing the steel group from the initial pile must be performed in order from the top of each initial pile. Therefore, in the same initial peak, if the steel group in which the initial transfer is performed specified by the variable s is lower than the steel group in which the initial transfer is performed specified by the variable s', the steel group is assigned to the steel group. On the other hand, the following equation (7) holds. As described above, the variable s that specifies the initial transport is set for each of the steel material groups.

Equation (7) indicates that in the same initial pile, the steel group above the steel group below must be initially transported first.
(B) Temporary placement restrictions caused by transportation to the final mountain The final transportation order of the steel material group follows the stacking order of each mountain from the bottom of the mountain in the shape of the final mountain. Therefore, if the final transport order (loading order of the final pile) and the initial transport order are different, the steel group to be initially transported first needs to be temporarily placed. That is, in the same final pile, if the initial transport order of the upper steel group is earlier than the initial transport order of the lower steel group, the steel group initially transported first needs to be temporarily placed. .. Therefore, in the same final mountain, if the steel group in which the initial transfer is performed specified by the variable s is lower than the steel group in which the initial transfer is performed specified by the variable s', the steel group is assigned to the steel group. On the other hand, the following equation (8) holds.

Equation (8) states that when the steel group above the lower steel group is initially transported first in the same final mountain, the steel group initially transported first needs to be temporarily placed. Shown.
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 equation (7), the steel group that is relatively lower and the steel group that is above are specified from the initial mountain shape identification information in the same initial mountain, and the upper of the two steel groups. Let s be the variable set for and s'the variable set for the bottom.
When setting equation (8), the steel group that is relatively lower and the steel group that is above are specified from the final mountain shape identification information in the same final mountain, and the upper of the two steel groups. Let s be the variable set for and s'the variable set for the bottom.

For equation (5), s and s'are set for each of the combinations of any two steel material groups in the set N of steel material groups. For equation (6), s, s', and s'' are set for each of the combinations of any 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 transported, that is, to minimize the number of times of temporary placement, the objective function J shown in the following equation (9) is used.

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

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

[Post-processing unit 503, step S604]
When the initial transport order variable y (s, s') is derived as described above, the initial transport order (order of removal from the initial peak) of each steel material group included in the set N of the steel material groups can be determined. it can. However, the final transport order (from the temporary mountain (temporary storage site)) of the steel material group determined to cause temporary storage (the steel material group in which the variable s in which the temporary storage occurrence variable x (s) is "1" is set) Since the order of transportation to the mountain (final storage) is not determined, it is necessary to determine this. That is, it is necessary to determine where in the initial transport order determined as described above the final transport order of the steel material group determined to cause temporary placement to be interrupted. Therefore, in this example, the post-processing unit 503 determines the final transfer order of each steel material group as follows.

For the steel material group determined to be temporarily placed, it is necessary to carry it twice, the initial transfer and the final transfer. On the other hand, for the steel group determined that temporary placement does not occur, the initial transfer and the final transfer match. Therefore, for the steel material group determined to cause temporary placement, the IDs for these two transports are set as the variable s. That is, for the steel material group, two variables s are set so that there are two virtually different steel material groups. Therefore, the number of steel material groups to be transported here is a value obtained by adding the number of steel material groups determined to cause temporary placement to the actual number of steel material groups to be transported. By changing the information given to the algorithm described above in this way, all the steel material groups to be transported can be transshipped from the initial peak to the final peak by the initial transport, and the final transport order of each steel material group can be obtained. be able to. Specifically, the following modifications are made to the above-mentioned algorithm. In the following description, the steel material group determined to cause temporary placement is referred to as a temporary storage target steel material group as necessary.

The variable s is a variable that specifies the initial transport, and is set for each steel material group included in the set N of the steel material groups. Further, two variables s are set for the steel material group to be temporarily placed. 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. Therefore, an ID different from the steel material group ID is set as the virtual steel material group ID for each steel material group to be temporarily placed. Then, the steel group ID of the temporary placement target steel group and the virtual steel group ID set for the temporary placement target steel group are set as two variables s for the temporary placement target steel group. Assuming that the number of steel material groups to be temporarily placed is t, the number of variables s is (n + t). In this way, two variables s that specify the initial transport are set for the steel material group to be temporarily placed. One of these two variables s is a variable that specifies the initial transport from the initial mountain, and the other is a variable that specifies the initial transport from the temporary mountain. As described above, by regarding the steel group determined to cause temporary placement as two steel groups, the steel group is transported twice (initial transport from the initial mountain to the temporary mountain and from the temporary mountain to the final mountain). (Final transport to) can be treated as initial transport.

Next, the mountain shape of the initial mountain for the steel material group to be temporarily placed specified by the variable s that specifies the initial transfer from the initial mountain has an early initial transfer order determined by the initial transfer order variable y (s, s'). Let it be one virtual first pile piled up from the top in order from the steel group. The number of stacks of this first mountain is n. Further, the steel group ID of the corresponding steel group is assigned to each stack of the first pile according to the initial transport order calculated by the optimization calculation unit 502. On the other hand, the initial pile for the steel material group determined to be temporarily placed by the optimization calculation unit 502 is a virtual second pile having two stacking stages. The second stage is s which is the steel material group ID of the steel material group, and the first stage is n + s which is the steel material group ID corresponding to the final transportation (transportation from the temporary mountain to the final mountain) of the steel material group.

Here, as the initial pile, the first pile having the number of stacks n is created by setting the initial transport 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 to maintain the transport order obtained by S604). Further, the reason why the second pile having two stacking stages corresponding to the steel material group to be temporarily placed is formed is to specify the order of initial transportation and final transportation for the steel material group to be temporarily placed. The steel group ID corresponding to the initial transport of the steel group to be temporarily placed is assigned to both the first pile having the number of stacks n and the second pile having the number of stacks 2 in duplicate, so that the steel group to be temporarily placed is assigned. The post-processing unit 503 (step S604) simultaneously determines the order relationship between the initial transfer and the initial transfer of the steel material group perpendicular to the final pile and the order relationship between the initial transfer and the final transfer of the steel material group to be temporarily placed. ..
Next, the mountain shape of the final mountain is obtained by replacing the steel material ID of the steel material group that is the temporary storage target steel material group with the virtual steel material group ID given to the temporary storage target steel material group for the final mountain shape identification information. Will be.
Further, the following constraint equation (10) is set for each temporary storage target steel group.

In equation (10), s is a variable (steel group ID of the steel group to be temporarily placed) that specifies the initial transport from the initial peak of the steel group to be temporarily placed, and n + s is the temporary transport of the steel group to be temporarily placed. It is assumed that it is a variable (virtual steel group ID of the steel group to be temporarily placed) that specifies the initial transport from the mountain. Equation (10) indicates that the initial transport order (initial transport from the initial pile) of the steel material group to be temporarily placed is earlier than the final transport order (initial transport from the temporary pile).
The post-processing unit 503 sets the variables s, s', s'', and n for the equations (5) to (8) and (10), and sets the variable s for the equation (9). However, N in Eq. (9) also includes the virtual steel group ID. Then, the post-processing unit 503 performs the initial transfer order when the value of the objective function J of the equation (9) becomes the minimum within the range satisfying the constraint equations of the equations (5) to (8) and (10). The variable y (s, s') is calculated as the optimum solution. Alternatively, in this post-processing, it is clear that the objective function of Eq. (9) is "0", so the objective function of Eq. (9) is not set, and instead, the constraint of Eq. (9-2) below is used. You may add an expression.

Based on the optimum solution of the initial transport forward variable y (s, s') calculated in this way, the post-processing unit 503 sets each steel material group included in the set N of the steel material groups from the initial peak to the final peak. Derived the order of all transports. Further, the post-processing unit 503 derives the temporary placement target steel material group by the temporary placement occurrence / absence variable x (s). In the following description, the order of all the transportation of each steel group included in the set N of the steel group from the initial peak to the final peak is referred to as the transportation order of each steel group, if necessary.

In this example, the initial transport order variable y (s, s'), which is a binomial variable that determines the relative order of the initial transport of any two steel material groups, and whether the initial transport is transport to a temporary mountain. When the steel group above the lower steel group is initially transported first in the same final mountain using the temporary placement occurrence / absence variable x (s), which is a variable that determines the value. The steel group to be initially transported sets a constraint expression including a linear inequality indicating that temporary placement is required. Then, the initial transport forward variable y (s, s') and the temporary placement when the value of the objective function J, which aims to minimize the occurrence of temporary placement, is minimized so as to satisfy the set constraint expression. The occurrence / non-occurrence variable x (s) is derived, and based on these, the transport order from the initial peak to the final peak of each steel material group included in the set N of the steel material groups and the transport order of the steel material groups to be temporarily placed are transferred. -Derived as temporary material specific information. Therefore, the transport order of the steel materials when transshipping the steel materials from the initial pile to the final pile 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 right side of Eq. (9) multiplied by (-1) may be used as the objective function, and the problem may be to maximize the objective function.

Next, a second example of the processing of the transport order derivation unit 103 will be described. In the first example, it is assumed that the initial mountain and the final mountain are stored in different places, and that all steel groups must be transported from the initial mountain (initial storage) to the final mountain (final storage). The explanation was given as an example. However, in the initial mountain, the product order from the bottom may already be the payout order (the payout order is descending from the bottom to the top). In such a case, it is not necessary to transship the portion of the initial mountain where the stacking order from the bottom is the payout order (the payout order is descending from the bottom to the top). Therefore, in this example, the case where the initial mountain and the final mountain are allowed to be placed in the same place (that is, they are not moved from the initial mountain state) will be described for such a part. As described above, the processing due to the difference in the premise of (2) described in the first example is mainly different between this example and the first example. Therefore, in the description of this example, detailed description of the same parts as those in the first example will be omitted by adding the same reference numerals as those given in FIGS. 5 to 6.

In this embodiment, the following premise (3) is adopted instead of the premise (2) described in the first example.
(3) It is also allowed that the initial mountain and the final mountain are placed in the same place, and the part where the stacking order from the bottom is the payout order (the payout order is descending from the bottom to the top) in the initial mountain is transported. Not to be carried (that is, some steel groups in the initial pile (one or more steel groups continuous from the bottom) may not be transported).

The difference between the premise of (2) explained in the first example and the premise of (3) above is that under the premise of (3), it cannot occur under the premise of (2) in the same place (mountain). The point is that the replacement of the upper steel group is allowed. In order to replace the steel group in this way, the steel group existing at the upper part of the initial mountain is transported to the temporary mountain or the final mountain, and another steel group is placed on the remaining part (lower part) of the initial mountain. It 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 in the initial mountain different from the initial mountain and the steel group in the upper part of the initial mountain. Includes steel groups.

Therefore, the "initial transport order" of the steel group originally in the initial ridge must precede the "final transport order" of the steel group transported from other ridges on top of the remaining portion of the initial ridge ( In the following description, this is referred to as a constraint for replacement as needed). In order to strictly set the constraint conditions for this replacement, it is necessary to specify the order relationship between the initial transfer order and the final transfer order between any two steel material groups, but in this example, it is a large scale to that extent. The constraint condition for replacement is expressed as a sufficient condition in the variable system of the algorithm explained in the first example without setting a problem. In the following explanation, the loading order from the bottom of the initial mountain 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 required. It is called a fixed part, and the part of the initial mountain above the fixed part that is transported for transshipment is called a moving part as necessary.

This algorithm can be realized by making the following changes to the constraint equations of equations (5) to (8) in the first example.
First, the constraint equations to be added to the constraint equations of the equations (5) to (8) described in the first example will be described.
If not all steel groups are targeted for transportation and a part of the initial mountain is used as the final mountain as it is, the following cases that are not applicable to all steel materials are assumed. Constraints need to be added.
FIG. 7 is a diagram showing an example of a form of transporting a steel material when there is a fixed portion in the initial peak.
In the initial mountain shown in FIG. 7, it is assumed that the steel material groups I and II in the lowermost stage and the second stage are the fixed parts, and the steel material groups III, IV and V above them are the moving parts. In this case, in the final ridge, the steel group I and II of the fixed portion remain as they are. Of the steel group III, IV, and V of the moving part of the initial mountain, the steel group III and V are transported to another final mountain, the steel group IV is transported to the temporary mountain, and then the initial mountain (that is, the initial mountain) is again. The steel group VI and VII are transported from another initial pile on the steel group IV. Even in such a case, it is necessary to set restrictions on the initial transport order in order to calculate the transport order appropriately.

When the steel group is transported from another initial mountain or temporary mountain to the initial mountain having the fixed portion (that is, the final mountain), the steel groups III, IV, and V of the moving portion above the fixed portion are initially transported. Only after that, the final transport of steel groups IV, VI and VII is possible. Therefore, it is necessary to set a constraint that the final transfer of steel groups IV, VI and VII must be after the initial transfer of steel groups III, IV and V. Therefore, the initial transport order of the steel group above the fixed portion, such as steel groups III, IV, V, is transported from another initial or temporary crest, such as steel IV, VI, VII, to the top of the fixed portion. It is a necessary and sufficient condition to be ahead of the final transport 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 transport of the steel material group in the moving part of the initial mountain l is i _U , and the initial stage of the steel material group transported from a mountain (initial mountain or temporary mountain) different from the initial mountain l to the initial mountain l. Let i _T be the variable that specifies the transport, and add the constraint equation of equation (11) below.

When the initial transport specified by the variable i _T is the transport to the final mountain, Eq. (11) is the necessary and sufficient condition described above, but the initial transport specified by the variable i _T is the transport to the temporary mountain. In the case of, the equation (11) becomes a sufficient condition and becomes an excessive regulation.
Further, in the case of a steel material group (that is, i _U and i _T ) that is initially transported from the initial mountain l and returns to the initial mountain l again, such as the steel material group IV in the example of FIG. 7, the equation (11) is used. Does not make sense, but for such a steel group, the following equation (12) is set.

Next, the part to be changed with respect to the constraint equations of the equations (5) to (8) described in the first example will be described.
As mentioned above, since the steel group of the fixed portion of the initial peak is given, the steel group in which the initial transfer is not performed is known. Therefore, in the equation (7), when at least one of the variables s and s'that specify the initial transport is a variable set for the steel group of the fixed portion of the initial peak, those variables The constraint equation of Eq. (7) shall not be set for the initial transport order variable y (s, s') by the variables s, s'. For the other initial transport order variables y (s, s'), the constraint equation of Eq. (7) is set.

In addition, temporary storage will not occur unless the initial transportation is carried out. Therefore, in the equation (8), when at least one of the variables s and s'that specify the initial transport is a variable set for the steel group of the fixed portion of the initial peak, those variables It is assumed that the constraint equation of Eq. (8) is not set for the initial transport order variable y (s, s') by the variables s, s'. For the other initial transport order variables y (s, s'), the constraint equation of Eq. (8) is set.

If at least one of the variables s, s', and s'' that specifies the initial transport is a variable set for the steel group of the fixed portion of the initial peak, those variables s, s. Regarding the initial transport order variables y (s, s'), y (s', s), y (s', s''), y (s, s'') by', s'', (5) It is assumed that the constraint equation of Eq. and Eq. (6) is not set. Alternatively, by extending equation (7) as follows, all constraint equations other than equation (7) may be set for the steel material of the fixed portion in the same manner as the steel material group of the moving portion (non-fixed portion). ..

That is, the above equation (7) was for the steel material of the moving part (non-fixed part), but when one steel material group is the fixed part and the other steel material group is the non-fixed part, the following When the constraint equation of the equation (13) is set and both steel group are fixed portions and they are in the same initial peak, the constraint equation of the following equation (14) is set.

In the present embodiment, the constraint equation / objective function setting unit 501 sets the constraint equations of equations (5) to (8), (11), and (12) as described above. As described above, the constraint equations of the equations (13) and (14) may be set. Then, the optimization calculation unit 502 includes equations (5) to (8), (11) and (12) (or equations (5) to (8) and (11) to (14). ) Is satisfied, and the initial transport order variable y (s, s') and the temporary placement occurrence / absence variable x (s) when the value of the objective function J in Eq. (9) is minimized are calculated.

As described above, in this example, when at least one of the steel material groups is the steel material group of the fixed portion of the initial peak, the constraint equation (7) representing the constraint when transporting the steel material group is not set. Alternatively, the constraint equations of equations (13) and (14) are set. Further, using the initial transport order variable y (s, s'), the initial transport of the steel material group in the moving portion of the initial mountain is prior to the initial transport of the steel material group transported to the initial peak having the moving portion. Add the constraint equation (Equation (11)) that expresses that. Therefore, in addition to the effect described in the first example, the order of transporting the steel material when transshipping the metal material from the initial pile to the final pile so as not to transport the steel material group of the fixed portion of the initial pile that does not need to be transported. Can be sought.

As described above, the equation (11) expresses the constraint condition for replacement with sufficient conditions, so that the solution obtained in this way is not guaranteed to be the optimum solution and narrows the feasible solution space. In extreme cases, it may be calculated as unrealizable (no solution) even though there is an optimal solution. Therefore, instead of the equation (11), the constraint equation of the following equation (15) expressing the constraint condition for replacement as a necessary condition may be used.

In equation (15), when a steel material group to be transported to an initial pile having a moving portion of the initial peak is temporarily placed, the order of the initial transport of the steel material group and the initial transport of the steel material group of the moving portion is Regardless, if this is not the case, as in Eq. (11), the initial transport of the steel group of the moving portion of the initial pile precedes the initial transport of the steel group transported to the initial pile having the moving portion. Indicates that In equation (15), when the steel material group to be transported to the initial mountain having the moving part is temporarily placed, it is only a necessary condition because there is no restriction, and the solution obtained is obtained because the feasible solution space is expanded. It may result in an unrealizable solution (ie, the resulting solution cannot be transported).

For example, when it is desired to surely prevent the unrealizable solution from being obtained, the equation (11) is used, and when it is rare that the steel material group to be transported to the initial mountain having the moving part is temporarily placed. The constraint equation to be adopted may be selected by using the equation (15). If an executable solution is obtained when Eq. (15) is used, it is a true optimal solution.
Further, also in this example, the modified example described in the first example can be adopted.

In addition to the first and second examples described above, a known technique can be used to derive the transport order of each steel material group based on the mountain shape of the initial mountain and the mountain shape of the final mountain. It can be realized. For example, the technique described in Patent Document 9 can be used. That is, the initial transportation time (transportation start time from the initial mountain to the temporary mountain or the final mountain) and the final transportation time (final from the initial mountain or temporary mountain) of each steel material group to be transported including the undelivered material and the already arrived material. The value of the objective function that represents the time that the steel material group stays in the process of being transported to the final mountain is minimized within the range that satisfies the constraint equation related to the transportation time of the steel material group) with the transfer start time to the mountain as the determinant. The optimum values for the initial transport time and the final transport time are derived.

Then, based on the optimum values of the initial transport time and the final transport time, it is determined whether or not the steel material group to be transported is the steel material group to be temporarily placed. Then, the stacking step relation variable, which is a 0-1 variable representing the allocation of the steel material group to be temporarily placed to the temporary mountain and the product order of the temporary mountain, is used as a determination variable, and the constraint equation regarding the product order in the temporary mountain is satisfied. In the range, the optimum value of the product relation variable when the value of the objective function representing the number of temporary peaks 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 of removing the steel material from the initial pile is set as the absolute ordinal variable, so that the final pile is created. The larger the number of steel groups, the longer the calculation time. 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 to be created for the final peak is small or when the time allowed as the calculation time is long. , The technique described in Patent Document 9 can be used.

[Temporary mountain derivation unit 104, step S204]
The temporary ridge lead-out unit 104 is a temporary storage place from the initial ridge of the steel material group to be temporarily placed and the transport order of each steel material group derived by the transfer order lead-out unit 103. (Transport order to and from temporary storage site to final mountain) and steel group information (maximum width, minimum width, and maximum width) of the steel material group to be temporarily stored 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 shape of the temporary mountain is derived.

In this 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: set of vertices of graph, E: set of edges (branches) of graph). ). As shown in FIG. 8, when each vertex of the simple undirected graph G is painted with a certain color, and all two adjacent vertices (connected by edges) are painted with different colors, this coloring is simply undirected. It is called the coloring of graph G. In FIG. 8, for convenience of notation, the difference in color is represented by the difference in the direction of the 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 the simple undirected graph G to be c-colored is called the number of colors of the simple undirected graph G and is represented by χ (G). The vertex coloring problem is a problem of finding the number of colors χ (G) in the simple undirected graph G. In this embodiment, a simple undirected graph is created by associating a steel material group to be temporarily placed with vertices and extending a branch between two vertices corresponding to two steel material groups to be temporarily placed that cannot be piled up on the same temporary pile. Then, the number of vertices of the simple undirected graph is minimized.

The condition that two steel material groups to be temporarily placed cannot be piled up on the same temporary pile is when the relationship of first-in and second-out (post-in first-out) is not satisfied for the two steel materials groups to be temporarily placed. The relationship between the first-in and second-out of the two temporary storage target steel groups is that of the two temporary storage target steel groups, the one of the temporary storage target steel groups that is transported from the initial mountain to the temporary storage site earlier. The timing of transportation from the temporary storage site to the final mountain is later than the timing of transportation from the temporary storage site to the final mountain of the other steel group subject to temporary storage. FIG. 9 is a diagram illustrating an example of a first-in / last-out relationship between two steel material groups to be temporarily placed.

In FIG. 9, the three temporary storage target steel groups SL1, SL2, and SL3 are tentatively indicated by arrows starting from the timing of transportation from the initial pile to the temporary storage site and ending at the timing of transportation from the temporary storage site to the final pile. Represents the time zone in which the steel group SL1, SL2, and SL3 to be placed are placed in the temporary storage place.
For example, in the temporary storage target steel group SL1 and SL3, the temporary storage target steel group SL1 is transported to the temporary storage site before the temporary storage target steel group SL3, and then to the final pile. Therefore, since the steel materials groups SL1 and SL3 to be temporarily placed satisfy the relationship of first-in and first-out, they can be piled up on the same temporary pile. Similarly, the steel group SL2 and SL3 to be temporarily placed can be piled up on the same temporary pile.

On the other hand, in the temporary storage target steel group SL1 and SL2, the temporary storage target steel group SL1 is transported to the temporary storage site first, and the temporary storage target steel group SL1 is also transported to the final mountain. Therefore, the steel materials groups SL1 and SL3 to be temporarily placed do not satisfy the relationship of first-in and first-out, and therefore cannot be piled up on the same temporary pile.
In the following explanation, as in this example, the shorter arrow indicating the time zone placed in the temporary storage place is not included in the longer one, but the crossing time zone while there is a time zone where the arrows intersect. A relationship in which each steel group to be temporarily placed has time to exist independently 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 as necessary. When two steel materials groups to be temporarily placed are in a cross relationship, the two steel materials groups to be temporarily placed cannot be piled up on the same temporary pile.

Therefore, the temporary mountain lead-out unit 104 sets one vertex for one of the temporary placement target steel material groups derived by the transport order lead-out unit 103. Next, the temporary mountain lead-out unit 104 extends a branch between the two vertices corresponding to the two temporary placement target steel material groups having a cross relationship. Further, the temporary mountain lead-out unit 104 has a stacking constraint (width) described in the section [Final mountain lead-out unit 102, step S202] among the two vertices corresponding to the two temporary placement target steel material groups without branches. Branches are also laid between the two vertices corresponding to the two temporary placement target steel groups that violate the constraints (constraints and length constraints). 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 derivation unit 104 solves the temporary mountain optimization problem (mountains of each temporary mountain) by solving the vertex coloring problem for the simple undirected graph G = (V, E) created as described above. The optimal solution of the figure) can be derived. An example of the functional configuration of the temporary mountain derivation unit 104 for formulating the above vertex coloring problem (temporary mountain optimization problem) and deriving the optimum solution of the mountain shape of each temporary mountain will be described.

<< Functional configuration of temporary mountain derivation unit 104 >>
FIG. 10 is a diagram showing an example of a detailed functional configuration of the temporary mountain derivation unit 104. FIG. 11 is a flowchart illustrating an example of detailed processing of the temporary mountain derivation unit 104 (step S204).
[Constraint expression / objective function setting unit 1001, steps S1101, S1102]
In the present embodiment, the temporary mountain allocation variable x [i] [m] and the temporary mountain presence / absence variable δ [m] are used as determining variables.
The temporary mountain allocation variable x [i] [m] is "1" when the steel material group (vertex) i to be temporarily placed is assigned to the temporary mountain (color) m, and "0 (zero)" when it is not assigned. -1 variable. The temporary mountain presence / absence variable δ [m] is a 0-1 variable that is “1” when the temporary storage target steel group assigned to the temporary mountain (color) m exists, and “0 (zero)” when it does not exist. Is.

[[Constraint expression]]
The constraint expression / objective function setting unit 1001 sets the following constraint expression.
(A) Mountain allocation constraint The mountain allocation constraint indicates that all steel group (vertices) i subject to temporary placement must be assigned only once (one color) to any temporary mountain (color) m. It is expressed by the following equation (17).

In equation (17), t is the upper limit of the number of temporary mountains. It is assumed that the temporary mountains having the upper limit value t are candidates for the optimum temporary mountains, and an identification number (temporary mountain ID) is set for each temporary mountain.
(B) Constraints that cannot be assigned to the same mountain The constraint that cannot be assigned to the same mountain is that the two temporary placement target steel group (vertices) i with branches in the simple undirected graph G described above can be colored in the same color. It 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. Further, F _c, the two temporary target steel Group (vertex) to set and loading constraints (width constraint and length constraints) that is violated, versus the set F _T (prohibition of temporary target steel group in the cross-relationship 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 piled up on a temporary mountain is less than or equal to the upper bound 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 steel material group (vertex) i to be temporarily placed. Further, k is the total number of steel material groups to be temporarily placed. Further, T is a set of (candidates for) temporary mountains having an upper limit value t.

(D) Mountain priority constraint The mountain priority constraint is a constraint regarding the order in which temporary mountains are created. In the present embodiment, the mountain priority 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, so even if those colors are exchanged, the solution is changed. Absent. For example, when the first temporary storage target steel group group is colored red and the second temporary storage target steel group group is colored blue, and when the second temporary placement target steel group group is colored red, the second temporary storage target steel group group is colored red. This is equivalent to the case where the first steel group to be temporarily placed is colored in blue. As described above, in the temporary mountain optimum solution problem, the solution in which the identification numbers (temporary mountain IDs) of the plurality of temporary mountains derived as the optimum solution are exchanged is also the optimum solution. Therefore, there are a plurality of optimum solutions (the number of temporary mountains (colors)! (Factial)), and a plurality of optimal solutions equivalent to each other can be obtained. Therefore, in order to suppress the acquisition of a plurality of optimal solutions equivalent to each other, 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 identification number (temporary mountain ID) of the temporary mountain, the larger the number of vertices (that is, the higher the mountain). It is expressed by the equation (21) of.

[[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, and k based on each temporary storage target steel group derived by the transport order derivation unit 103, and t is given in advance. By setting, the constraint equations of equations (16) to (21) are set. Further, the constraint expression / objective function setting unit 1001 sets the objective function J of the equation (22) by setting the t given in advance with respect to the equation (22).

[Optimization calculation unit 1002, steps S1103, S1104]
The optimization calculation unit 1002 determines the temporary mountain allocation variable x [i] [when the value of the objective function J of the equation (22) becomes the minimum within the range satisfying the constraint equations of the equations (16) to (21). Calculate with m] and the temporary mountain presence / absence variable δ [m] as the optimum solution. The calculation of the optimum solution can be realized by using a known algorithm (solver) for solving the optimization problem by a mathematical programming method such as the 0-1 integer programming method. Temporary mountain (color) m whose temporary mountain presence / absence variable δ [m] is "1" and temporary mountain allocation variable x [i] [m] corresponding to the temporary mountain (color) m are temporary storage targets of "1". Steel group (top) i will be piled up. By stacking the temporary storage target steel group constituting the temporary pile so as to satisfy the above-mentioned stacking constraint, the stacking position (that is, the mountain shape) of each temporary storage target steel group in each temporary pile is specified. The information specified in this way becomes the temporary mountain specific information.
Here, the problem of minimizing the objective function J has been described as an example. However, for example, the right side of Eq. (22) multiplied by (-1) may be used as the objective function, and the problem may be to maximize the objective function.

[Output unit 105, step S205]
The output unit 105 describes the mountain shape of the final mountain led out by the final mountain lead-out unit 102, the transport order of each steel material group derived by the transport order lead-out unit 103, and the temporary mountain drawn by the temporary mountain lead-out unit 104. Outputs information including the mountain shape. The form of the output includes at least one of display on a computer display, storage in an internal or external storage medium of the yard management device 100, and transmission to an external device. Examples of the external device include a crane or a control device that controls the operation of the crane.

<Example>
Next, an embodiment 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 (2 processors)
(Ii) Mounted memory (RAM): 128GB
(Iii) OS: Windows (registered trademark) 7 Professional 64-bit operating system (iv) Optimal calculation software: ILOG CPLEX Cplex11.0 Concert25 (registered trademark)

In this embodiment, the pile piled up in the yard at the time when the acceptance of the steel material (slab) to be created for the final pile into the yard is completed and the change such as the rolling schedule is found is set as the initial pile, and the initial pile is set as the initial pile. , Shall be transshipped to the final pile, which is piled up in the order of payout from the top. Further, the steel materials shall be transported one by one. FIG. 12 is a diagram showing 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 stack shown next to the initial mountain ID is the stack in the initial mountain of the initial mountain ID (the lowest level is 1). Further, in FIG. 12, the portion shown in gray indicates a steel material (fixed portion) that was not targeted for transportation.

FIG. 13 is a diagram showing the result of performing the optimization calculation by the method of the present embodiment with the steel material information shown in FIG. 12 as an input. In FIG. 13, the first delivery order is the transport order from the initial mountain, and the final delivery order is the transport order from the temporary mountain to the final mountain. The stack shown next to the final mountain ID is the stack in the final mountain of the final mountain ID (the lowest level is 1).
The fact that the initial feed order in FIG. 13 is "0 (zero)" indicates that the transport is not performed (the steel material whose initial feed order is "0 (zero)" indicates that it is a fixed portion). .. Further, in the result shown in FIG. 13, since none of the steel materials was temporarily placed, the columns of the final delivery order, the temporary mountain ID, and the stacking stage are all set to "/".

As shown in FIG. 13, in the method of the present embodiment, it can be seen that the steel materials piled up in each initial pile are transported in order (see the initial feed order, the initial pile ID, and the stacking stage). Further, it can be seen that in each final pile, each steel material is piled up in the order of transportation from the top without violating the above-mentioned stacking restrictions (see final pile ID, stacking stage, payout order, SL width, SL length).

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

If an initial mountain group is given, the transshipment rule (algorithm) for creating the final mountain as few as possible by reducing the number of temporary placements and the number of temporary mountains as much as possible is shown below. ..
The steel material to be transported one by one from the initial mountain or temporary mountain to the final mountain and the final mountain or temporary mountain to be transported to the steel material are determined for each transportation. Therefore, in the transshipment rule (algorithm), it is sufficient that 1) the steel material to be transported and 2) the peak of the transfer destination can be specified in each transfer. It should be noted that the end of transportation in this problem is considered to be the time when the initial mountain and the temporary mountain disappear and only the final mountain is left (assuming this is the final state, the transportation destination from the initial mountain is only the final mountain or the temporary mountain. Since the destination from the temporary mountain is only the final mountain, it will be in the final state after transporting at most 2n (n is the number of steel materials to be created in the final mountain). Therefore, it is an algorithm that 1) specifies the steel material (From) to be transported and 2) specifies the peak (To) of the transport destination at each transport timing.

(A) Of the steel materials at the top of the initial mountain (remaining mountain of the initial mountain) and temporary mountain that are being disassembled and that can be loaded in the final mountain under construction in the order of payout, the steel material with the largest payout order is " The slab to be transported (From) ”. In addition, among the final piles under construction that can be piled up with "steel materials to be transported", the final pile under construction whose topmost steel material payout order is closest to the payout order of "steel material to be transported" is "transported". The mountain ahead (To) ”.

(B) If there is no steel material that can be loaded in the order of payout in the final pile under construction, the steel material with the largest payout order among the steel materials at the top of the initial pile (remaining pile of the initial pile) being disassembled is "transported". Target steel material (From) ”. In this case, the method shown in (c) below indicates whether the "transportation destination mountain (To)" of the "steel material to be transported" is the lowest stage (final storage area) or the temporary storage area of the new final mountain. Judge with.

(C) [When the number of final peaks under construction <ceil (n / h _max ) and the payout order of "steel materials to be transported"> h _max ], or ["steel materials to be transported" If the payout order = maximum payout order], a new final pile is set up, and the "steel material to be transported" 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 the "steel material to be transported" in the temporary storage area, the method shown in (d) below is used to determine which temporary pile to pile up. Note that ceil (*) is a function that rounds up the decimal point of * to an integer. Further, n here is the total number of steel materials to be created in the final mountain.

(D) In the case shown in (c) above, if it is determined that the piles will be piled up on the temporary pile, the "steel materials to be transported" can be piled up in the temporary pile under construction while satisfying the above-mentioned stacking restrictions and in the reverse order of payout. Of the temporary ridges, the temporary ridge that is closest to the payout order of the "steel to be transported" in the reverse order of discharge of the steel materials at the top is the "mountain (To) of the transport destination". If there is no pile in the temporary pile that can be piled up with "steel material to be transported", a new temporary pile is set up and the "steel material to be transported" is placed at the bottom. The reverse order of payout means the reverse of the normal order of payout, and the stacking order is such that the steel material that is relatively lower is paid out to the next process earlier than the steel material that is above the steel material. Say.

FIG. 14 is a diagram showing the result of the optimization calculation by the method of the present embodiment and the result of the method of the comparative example in a table format. The trial of the calculation conditions in FIG. 14 identifies the steel material information, and shows that the method of the present embodiment and the method of the comparative example are compared with respect to the seven types of steel material information. The peak of the calculation condition is the number of initial peaks. Further, SL of the calculation condition is the number of steel materials to be created in the final pile, and the number in parentheses is the number of steel materials to be transported. For example, in the PN140, 26 of the 38 steel materials are the steel materials to be transported, and the remaining 12 steel materials are not transported (the fixed portion). The final mountain, temporary mountain, and temporary placement of the comparative example (greed method) and the invention example ((individual) optimization) are the number of final mountains, the number of temporary mountains, and the number of temporary placements, respectively. Note that PN173 in 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 peaks, and the number of temporary piles as compared with the method of the comparative example.

<Summary>
As described above, in the present embodiment, the mountain shape of the initial mountain 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 number of initial mountain unit reversals vs. R are reduced within the range that satisfies the stacking constraint. The initial pile unit reversal vs. R is a group of two steel materials in which the relative stacking position relationship in the initial pile has the same positional relationship in the final pile. Next, based on the shape of the final mountain and the shape of the initial mountain derived in this way, the order of transportation of each steel group and the process of transportation from the initial mountain to the final mountain are changed to temporary mountains. Derivation of piled steel materials group (temporary storage target steel materials group). Next, the mountain shape of the temporary mountain is derived by solving the apex coloring problem based on the transport order of each steel material group and the steel material group to be temporarily placed. Therefore, by performing a solution chain with the mountain shape of the final mountain, the transport order of each steel material group, and the mountain shape of the temporary mountain in this order, using the solution of the immediately preceding process as an input, the number of final mountains and the transport of each steel material group. While making the number of times and the number of temporary ridges appropriate (decreasing), the transportation is started in order from the steel material located above in the initial mountain, and is discharged to the next process in order from the steel material located above in the final mountain. The final mountain can be constructed.

As a storage space between processes, a storage space between two manufacturing processes may be targeted, a semi-finished product may be targeted as a metal material, and a storage space between manufacturing processes and a shipping process may be targeted as a storage space between processes. , As a metal material, the final product may be targeted. At this time, when a plurality of metal materials are housed in a container for transportation and arrangement, the container containing the metal materials may be treated as one metal material. Further, the storage space between processes is not limited to the storage space in the metal manufacturing process, and may be targeted for general distribution and transportation between processes. In the field of logistics, it can be applied not only to the contents but also to the transportation and arrangement of containers. Therefore, in the present invention, the metal material includes any one of a final product, a semi-finished product, and a container.

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

<Relationship with claims>
An example of the relationship between the claims and the embodiments is shown below. As described above, the description of the claims is not limited to the description of the embodiment.
[Claim 1]
The acquisition means (process) is realized by using, for example, the steel material information acquisition unit 101 (step S201).
The metal material information is realized by, for example, steel material information.
The initial mountain identification information is realized by, for example, information that identifies the mountain shape of the initial mountain of each steel material group.
The identification information of the initial mountain is realized by using, for example, the initial mountain ID.
The stacking order of the metal material constituting the initial mountain and the metal material in the initial mountain is realized by using, for example, a steel material group ID located in each stack of the initial mountain identified by the initial mountain ID. To.
The metal material size information is realized by using, for example, steel material group information (maximum width, minimum width, maximum length, minimum length).
The payout order information is realized by using, for example, steel material group information (payout order).
The final mountain derivation means (process) is realized, for example, by using the final mountain derivation unit 102 (step S202).
The transport order derivation means (process) is realized by using, for example, the transport order derivation unit 103 (step S203). The metal material to be temporarily placed is realized, for example, by using a steel material group to be temporarily placed.
The temporary mountain derivation means (process) is realized by using, for example, the temporary mountain derivation unit 104 (step S204).
[Claim 2]
Stacking constraints are achieved by using width, length, and height constraints.
The initial mountain unit reversal pair is realized by using, for example, the initial mountain unit reversal pair R (a pair of steel material groups that becomes a reversal pair only from the mountain shape of the initial mountain).
[Claim 3]
The feasible mountain extraction means is realized, for example, by using the feasible mountain extraction unit 301.
The first constraint expression setting means and the first objective function setting means are realized by using, for example, the constraint expression / objective function setting unit 302.
The first optimization calculation means is realized, for example, by using the optimization calculation unit 303.
[Claim 4]
The second constraint expression setting means and the second objective function setting means are realized, for example, by using the constraint expression / objective function setting unit 501. The temporary placement determination constraint formula set by the second constraint formula setting means is realized, for example, by using the formula (8). The second objective function set by the second objective function setting means is realized, for example, by using the equation (9).
The second optimization calculation means is realized, for example, by using the optimization calculation unit 502.
[Claim 5]
The derivation means is realized, for example, by using the post-processing unit 503.
The temporary transfer material initial transport order regulation constraint equation is realized by using, for example, equation (10).
[Claim 6]
The temporary placement constraint equation is realized, for example, by using equation (9-2).
[Claim 7]
The initial mountain initial transport order regulation constraint equation is realized by using, for example, equation (11).
[Claims 8 and 9]
The third constraint expression setting means and the third objective function setting means are realized, for example, by using the constraint expression / objective function setting unit 1001.
The mountain allocation constraint equation is realized, for example, by using equation (17).
The same mountain allocation non-assignable constraint equation is realized, for example, by using equation (18).
The height constraint equation is realized, for example, by using the equation (19).
The third objective function set by the third objective function setting means is realized, for example, by using the equation (22).
The third optimization calculation means is realized, for example, by using the optimization calculation unit 1002.

100: Yard management device, 101: Steel material information acquisition unit, 102: Final mountain derivation unit, 103: Transport order derivation unit, 104: Temporary mountain derivation unit, 105: Output unit

Claims (14)

As a storage place between processes, the metal material of the initial pile made of metal material piled up in the yard where the metal material is placed is transported by a transport device and piled up in the stacking order according to the payout order to the subsequent process of the yard. It is a yard management device for creating the final mountain made of metal material to be made.
Initial mountain identification information including the identification information of the initial mountain, the identification information of the metal material constituting the initial mountain, 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 the acquisition means for acquiring the metal material information including the payout order information including the payout order of the metal material to the subsequent process.
Based on the initial mountain identification information, the metal material size information, and the payout order information, the final mountain including the metal material constituting the final mountain and the product order of the metal material in the final mountain. A final mountain derivation means for determining the mountain shape for each of the plurality of final mountains,
The metal material from the initial mountain to the final mountain based on the initial mountain identification information and the final mountain identification information which is information about the mountain shape of the final mountain derived by the final mountain derivation means. And the transport order derivation means for determining the transport order and the metal material to be temporarily placed, which is the metal material that needs to be temporarily placed as a temporary pile in the temporary storage place of the yard before being transported to the final mountain.
Based on the transport order, the temporary placement target metal material, and the metal material size information derived by the transport order derivation means, the temporary placement target metal material constituting the temporary mountain and the temporary placement target metal. It has a temporary mountain derivation means for determining the mountain shape of the temporary mountain, including the stacking order of the materials in the temporary mountain.
The temporary mountain derivation means is a simple undirected method in which the metal material to be temporarily placed corresponds to a vertex and a branch is extended between two vertices corresponding to two metal materials to be temporarily placed which cannot be piled up on the same temporary mountain. A yard management device characterized in that the shape of a temporary mountain is determined by solving a vertex coloring problem that minimizes the number of colors to be colored at the vertices in a graph. The final mountain derivation means is a mathematical planning method based on a stacking constraint, which is a constraint imposed when the metal material is piled up on the final mountain, and an evaluation value including the number of temporary placements and the height of the final mountain. By performing the optimization calculation by, the mountain shape of the final mountain is determined.
The number of temporary placements is the number of initial mountain unit reversal pairs.
The yard management device according to claim 1, wherein the initial mountain unit reversal pair is two metal materials having the same vertical relationship in the stacking position in the initial mountain. The final mountain derivation means uses a feasible mountain adoption / non-adoption variable that determines whether or not to adopt a feasible mountain that is stacked so as to satisfy the stacking constraint as the optimum solution as a determining variable.
A feasible mountain extraction means for extracting a combination of feasible mountains based on the metal material information,
The fact that any of the metal materials must not be arranged in an overlapping manner on a plurality of the feasible ridges and must be arranged on any of the feasible ridges. The first constraint expression setting means for setting the constraint expression represented by the method based on the feasible mountain extracted by the feasible mountain extraction means, and
A first objective function that aims to maximize the evaluation value of the feasible mountain adopted as the optimum solution, and is expressed by using the feasible mountain adoption / non-adoption variable and the evaluation value. The first objective function setting means for setting the objective function of is based on the feasible mountain extracted by the feasible mountain extraction means, and
The said when the value of the first objective function set by the first objective function setting means becomes the minimum or the maximum within the range satisfying the constraint equation set by the first constraint expression setting means. Claim 2 is characterized in that it further has a first optimization calculation means for deriving the value of the feasible mountain adoption / non-adoption variable as an optimum solution by performing an optimization calculation by a mathematical programming method. The described yard management device. The transport order derivation means includes an initial transport order variable, which is a binomial variable that determines the relative order of initial transport, which is transport from the initial peak, for any two of the metal materials, and the said metal material. The determinant is the temporary storage occurrence / non-existence variable, which is a variable that determines whether the initial transportation from the initial mountain is the transportation to the temporary storage site of the yard.
In the same final mountain, when the metal material above the lower metal material is initially transported first, the metal material initially transported to the destination is temporarily transported before being transported to the final mountain. The metal material information and the final mountain specific information include constraint equations including a temporary placement determination constraint formula that expresses that it is necessary to temporarily place in the storage place by using the initial transport order variable and the temporary placement occurrence / absence variable. The second constraint expression setting means to be set based on
The second objective function, which is an objective function for the purpose of minimizing the number of the metal materials in which the temporary placement occurs, and is expressed by using the temporary placement occurrence / absence variable, is used in the metal material information. A second objective function setting means to be set based on
The initial stage when the value of the second objective function set by the second objective function setting means becomes the minimum or the maximum within the range satisfying the constraint equation set by the second constraint expression setting means. It is characterized by further having a second optimization calculation means for deriving the values of the transport order variable and the temporary placement occurrence / absence variable as the optimum solution by performing the optimization calculation by the mathematical programming method. The yard management device according to any one of claims 1 to 3. For the metal material in which the temporary placement occurs, which is determined based on the variable for the presence / absence of the temporary placement generated by the second optimization calculation means, in addition to the identification information of the metal material, the metal material By giving identification information different from the identification information, the final transportation of the metal material from the temporary storage place to the final mountain is regarded as the initial transportation of the virtual metal material given the other identification information. ,
Changing the identification information of the metal material at the stacking position of the metal material in which the temporary placement occurs in the final mountain to the other identification information given to the metal material,
A virtual first pile, which is determined based on the initial transport order variable derived by the second optimization calculation means, and is piled up according to the initial transport order of the metal material from the initial pile. The metal material in which the temporary placement occurs is arranged in the upper stage, and the virtual metal material corresponding to the final transport of the metal material in which the temporary placement occurs is arranged in the lower stage . Considering the mountain as the initial mountain,
Setting the initial transport order variable as a binomial variable that determines the relative order of initial transport of any two of the metal materials, including the virtual metal material, from the initial peak or temporary storage site.
The set initial transport order variable is set so that the order of initial transport of the metal material from which the temporary storage occurs is earlier than the order of initial transport of the metal material from the temporary storage site. In addition to the constraint formula set by the second constraint formula setting means, the temporary material initial transport order regulation constraint formula, which is the formula expressed using the above, is further set.
After setting the second objective function,
The set initial transport order variable when the value of the second objective function becomes the minimum or maximum within the range satisfying the constraint equation is derived, and the metal material is based on the derived initial transport order variable. The yard management device according to claim 4, further comprising a derivation means for deriving the order of transportation from the initial mountain to the final mountain. Instead of setting the second objective function, the derivation means indicates that the number of the metal materials in which the temporary placement occurs is 0 (zero) by using the temporary placement occurrence / absence variable. A temporary placement constraint expression, which is an expression, is set in addition to the constraint expression.
Instead of deriving the set initial transport order variable when the value of the second objective function becomes the minimum or maximum within the range satisfying the constraint equation, the setting when the constraint equation is satisfied The yard management device according to claim 5, wherein an initial transport order variable is derived. In the constraint formula set by the second constraint formula setting means, among the metal materials constituting the initial peak, the product order from the bottom of the initial peak is from the bottom of any of the final peaks. The order of initial transportation of the metal material from the initial mountain, which is above the portion corresponding to the product order of the above, is transferred to the initial mountain from the initial mountain different from the initial mountain or the temporary storage place. It is characterized by further having an initial mountain initial transport order regulation constraint formula, which is an equation expressed using the initial transport order variable, that the metal material is ahead of the initial transport order to the initial peak. The yard management device according to any one of claims 4 to 6. The two metal materials to be temporarily placed that cannot be piled up on the same temporary pile are the two metal materials to be temporarily placed that do not satisfy the stacking restriction that is imposed when the metal materials are piled up on the final pile. The two metal materials to be temporarily placed that do not satisfy the relationship of putting in and out,
The relationship between the first-in and the first-out is that, of the two temporary storage target metal materials, one of the temporary storage target metal materials whose timing is earlier to be transported from the initial mountain to the temporary storage site is from the temporary storage site to the final mountain. According to any one of claims 1 to 7, the timing of transportation to the metal material to be temporarily stored is later than the timing of transportation of the other metal material to be temporarily stored from the temporary storage site to the final mountain. The described yard management device. The temporary mountain derivation means includes a temporary mountain allocation variable that determines which temporary mountain the metal material to be temporarily placed is assigned to, and the metal material to be temporarily placed that is assigned to the temporary mountain for each of the temporary mountains. A tentative mountain presence / absence variable that determines whether or not it exists is used as a determinant.
All the metal materials to be temporarily placed are constraint equations that stipulate that they must be assigned to any of the temporary ridges only once, and are represented by using the temporary ridge allocation variables. The same mountain allocation is not possible, which is a constraint expression that defines two temporary placement target metal materials that cannot be piled up on the same temporary mountain, and is a constraint expression expressed using the temporary mountain allocation variable and the temporary mountain presence / absence variable. A mountain height constraint formula that is a constraint formula that determines that the height of the temporary mountain is equal to or less than the upper limit value and is a constraint formula expressed by using the temporary mountain allocation variable and the temporary mountain presence / absence variable. A third constraint expression setting means for setting the constraint expression including the above, based on the transfer order of the temporary placement target metal material and the temporary placement target metal material derived by the transfer order derivation means, and
A third objective function setting that sets a third objective function that sets an objective function that is an objective function that aims to minimize the number of temporary peaks and is represented by using the temporary mountain presence / absence variable. Means and
The temporary mountain allocation variable when the value of the objective function set by the third objective function setting means becomes the minimum or maximum within the range satisfying the constraint equation set by the third constraint expression setting means. The eighth aspect of the present invention is characterized in that it further has a third optimization calculation means for deriving the value of the temporary mountain presence / absence variable as an optimum solution by performing an optimization calculation by a mathematical programming method. The described yard management device. The initial mountain includes an existing mountain and a virtual mountain.
The already-arrival 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 to be created for the final mountain are piled up so that the earlier the arrival order at the yard is, the higher the metal material is. The yard management device according to any one of claims 1 to 9, wherein the yard management device is one mountain in the case of the above. The mountain shape of the final mountain, the transport order of the metal material from the initial mountain to the final mountain, the metal material to be temporarily placed, and the mountain shape of the temporary mountain are the metal materials composed of a plurality of metal materials. The yard management device according to any one of claims 1 to 10, wherein the yard management device is determined in units of groups. The yard is a storage place between the steelmaking process and the rolling process in the steelmaking process.
The yard management device according to any one of claims 1 to 11, wherein the metal material is a steel material. As a storage place between processes, the metal material of the initial pile made of metal material piled up in the yard where the metal material is placed is transported by a transport device and piled up in the stacking order according to the payout order to the subsequent process of the yard. It is a yard management method for creating a final mountain made of metal material to be used.
Initial mountain identification information including the identification information of the initial mountain, the identification information of the metal material constituting the initial mountain, 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 the acquisition step of acquiring the metal material information including the payout order information including the payout order of the metal material to the subsequent process, and
Based on the initial mountain identification information, the metal material size information, and the payout order information, the final mountain including the metal material constituting the final mountain and the product order of the metal material in the final mountain. The final mountain derivation process that determines the mountain shape for each of the multiple final mountains,
The metal material from the initial mountain to the final mountain based on the initial mountain identification information and the final mountain identification information which is information about the mountain shape of the final mountain derived by the final mountain derivation step. And the transport order derivation step of determining the transport order of the metal material to be temporarily placed, which is the metal material that needs to be temporarily placed as a temporary pile in the temporary storage place of the yard before the transport to the final mountain.
Based on the transport order, the temporary placement target metal material, and the metal material size information derived by the transport order derivation step, the temporary placement target metal material constituting the temporary mountain and the temporary placement target metal. It has a temporary mountain derivation process that determines the shape of the temporary mountain, including the stacking order of the materials in the temporary mountain.
In the temporary mountain derivation step, the temporary placement target metal material corresponds to the apex, and a branch is stretched between two vertices corresponding to two temporary placement target metal materials that cannot be piled up on the same temporary mountain. A yard management method characterized in that the shape of a temporary mountain is determined by solving a vertex coloring problem that minimizes the number of colors to be colored at the vertices in a graph. A program characterized in that a computer functions as each means of the yard management device according to any one of claims 1 to 12.

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