JP7035836B2 - 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 in a metal manufacturing process, a pile of metal materials is sorted in a yard provided for smoothly supplying metal materials such as slabs and coils to the next process. It is suitable to be used for this purpose.

In the steelmaking process, which is an example of the metal manufacturing process, when the steelmaking 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. 5, the yard is a storage space 501 to 504 partitioned vertically and horizontally as a buffer area for supplying a steel material such as a slab discharged from the upstream process to the downstream process. The vertical divisions are often referred to as "buildings" and the horizontal divisions are often referred to as "columns". 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 will be 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 501 to 504 in FIG. 5). (12), (21), (22)).

Next, the basic work flow in the yard is shown by taking FIG. 5 as an example. First, the steel material carried out from the continuous casting machine 510 in the steelmaking process, which is the previous process, is carried to the yard by the receiving table X via the piler 511, and is partitioned by the cranes 1A, 1B, 2A, and 2B. It is transported to any of 504 and placed in piles. Then, it is placed on the payout table Z again by the cranes 1A, 1B, 2A, and 2B according to the manufacturing schedule of the rolling process, which is a subsequent process, and is conveyed to the rolling process. Generally, steel materials are placed in a pile as described above in a yard. This is to make effective use of the limited yard area.
In the following, "Motoyama", "Virtual Mountain", "Initial Mountain", "Final Mountain", "Fixed Mountain", and "New Mountain" will be used with the following meanings.
Motoyama: At this point, it is a mountain that consists of at least a part of the mountain that has already been formed in the yard and whose location does not change from that mountain.
Virtual mountain: A mountain (not a mountain that actually exists) assuming that steel 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 the current mountain (the mountain that has already been formed in the yard) and the virtual mountain.
Final mountain: The final mountain (also called the payout mountain) that is piled up to be paid out for the post-process.
Fixed pile: The final pile including non-moving steel (non-moving steel). The non-moving steel material also includes a steel material that does not move as a result (a steel material that is temporarily placed from the original pile and then returned to the original pile).
Niiyama: A mountain that is composed of steel materials transferred from the initial mountain and has no non-moving steel materials (composed of only moving steel materials).
Motoyama and Shinzan are candidates for the final mountain, and among the candidates, the final mountain that remains as a fixed mountain or a new mountain is the final mountain.

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. For this reason, heat insulation equipment may be installed in the yard these days, and steel materials may be stored in piles. 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 in 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 unstable inverted pyramid shape. There are restrictions such as things (this is called "stacking constraint"). Furthermore, the workload when setting up 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 final mountain 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 steel materials required for 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 be arrived requires unplanned scouring, or the size changes. By doing so, it can often happen that the steel material does not arrive as originally planned. In addition, it can hardly be expected that the state of the yard will change as originally planned, and it is a daily occurrence that unplanned steel materials have to be placed in unplanned yard.

Furthermore, the rolling order of the steel materials piled up in the pile in the order of delivery from the yard to the hot rolling process, which is the post-process, in the hot rolling process, which is the post-process, will be changed after the steel materials arrive at the yard. As a result, the piles are no longer stacked in the payout order, and it is often the case that the steel materials are forced to be reloaded according to the changed rolling order. Here, the fact that steel materials are piled up in a pile in the order of discharge means that one or a plurality of steel materials that are relatively above and simultaneously transported are below the steel material at any of the pile positions of the pile. It means that it is paid out to the post-process earlier than a certain steel material.

However, 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. Storage space is limited. Therefore, it is required to efficiently and space-saving transshipment work of steel materials.
Therefore, due to various circumstances before and after arriving at the yard, the work of transshipping mountains whose stacking appearance at the time of arrival at the yard is no longer in the payout order can be efficiently (that is, with as few transports as possible) and as few finals as possible. The need to have a mountain number is extremely high.

There are inventions described in Patent Documents 1 to 3 as a conventional technique for transshipping a steel material from an initial pile to a final pile as described above.
First, in Patent Document 1, when transshipping the steel materials of the original mountain already in the yard in the order of payout, the optimum stacking shape of the final pile is optimized in consideration of the necessary transfer load and stacking shape restrictions. A method of formulating as a problem and calculating using a tabu search method is disclosed. However, in the invention described in Patent Document 1, although the method for obtaining the stacking shape of the final mountain is shown, the point of how to obtain the transportation order from the initial mountain to the final mountain is clearly shown. Not.

Next, in Patent Document 2, in the situation where steel materials that have arrived at the yard and materials that have not arrived are mixed, the initial mountain state and the final mountain state at that time are given. For the problem of transshipment and transfer of steel materials from the state of It has been disclosed.
Finally, Patent Document 3 discloses a method of simultaneously optimizing the mountain sorting and the transport order by reducing the result to a mathematical planning problem that satisfies the constraint conditions relating to the pile standing and the transport.

Japanese Patent No. 4935032 Japanese Patent No. 5365759 Japanese Patent No. 5434267

However, in the techniques described in Patent Documents 1 to 3, when transshipment of a mountain, a problem is set on the premise that all the steel materials are moved or the steel materials that do not move (fix) are given in advance.

When transshipping mountains that are already piled up in the yard, in actual operation, unless there is a request to change the mountain yard itself, it is possible to move the mountains together instead of transshipping them. In order to reduce the number of transshipments, a method of avoiding unnecessary movement of steel materials is adopted. That is, in the case of such transshipment, it is required to transship the steel material that does not need to be moved in the initial pile with the minimum number of transports as it is. To achieve this, it is not always the best way to prevent all steel materials that can be non-moving (fixed) from moving. This is because there may be a case where the number of final peaks increases because the steel material that can be non-moving (fixed) is not moved. Therefore, if the pros and cons of moving the steel material for minimizing the number of peaks of the final peak are not taken into consideration as in the techniques described in Patent Documents 1 to 3, the number of peaks of the final peak may increase. In addition, in order to guarantee that the number of final peaks determined by considering the pros and cons of moving steel materials to minimize the number of final peaks is a feasible number, the product of final peaks. It is also necessary to consider the appearance.

The present invention has been made in view of the above problems, and when creating a transfer plan for metal materials for transshipping metal materials from the initial mountain to the final mountain, the total number of final mountains is minimized. The purpose is to balance with the minimization of the number of metal materials moving from the initial mountain.

The yard management device of the present invention transports the metal material of the initial pile made of metal material piled up in the yard, which is a storage place between processes, by a transport device, and stacks the metal material according to the delivery order to the subsequent process of the yard. When creating a final pile made of metal materials that are piled up in order, a moving metal material that is a metal material transported from the initial pile to the final pile at the yard and the final pile in the same place as the initial pile. A yard management device for at least determining a non-moving metal material fixed at the location of the initial mountain and a metal material constituting the final mountain for creating the initial mountain, and the metal constituting the initial mountain. The non-moving uppermost metal material discriminating variable indicating whether or not the material is the uppermost metal material among the non-moving metal materials in the initial mountain, and the moving metal material are arranged in the final mountain. The determination variable is a moving metal final mountain allocation variable indicating whether or not the final mountain is used, and an allocation mountain identification variable indicating whether or not the candidate mountains of the final mountain, Motoyama and Shinzan, are the final mountains. A metal material information acquisition means for acquiring metal material information including the identification information of the initial mountain, the identification information of the metal material at each stacking position of the initial mountain, and the payout order of the metal material, and the Motoyama. The first constraint equation expressing the condition of the moving metal material that can be arranged in the above using the determination variable and the condition of the moving metal material that can be arranged in the new mountain are expressed by using the determination variable. The constraint formula setting means for setting the constraint formula including the second constraint formula represented by the above, based on the metal material information, the term for evaluating the total number of the moving metal materials, and the total number of the final peaks are evaluated. An objective function setting means for setting an objective function including a term based on the metal material information, and a value of the determination variable when the value of the objective function becomes the minimum or maximum within a range satisfying the constraint equation. It has an optimization calculation means that executes the derivation as an optimum solution by performing an optimization calculation by a mathematical programming method, and the Motoyama is a mountain that is a candidate for the final mountain, and the metal. It is a mountain that consists of at least a part of the mountain formed in the yard at the time when the material information is created, and the location does not change from the mountain, and the new mountain is a candidate mountain for the final mountain. It is characterized by being a mountain made of only the moving metal material.

In the yard management method of the present invention, the metal material of the initial pile made of metal material piled up in the yard, which is a storage place between processes, is conveyed by a transport device, and the yard is stacked according to the order of delivery to the subsequent process. When creating a final pile made of metal materials that are piled up in order, a moving metal material that is a metal material transported from the initial pile to the final pile at the yard and the final pile in the same place as the initial pile. It is a yard management method for determining at least a non-moving metal material fixed at the place of the initial mountain and a metal material constituting the final mountain in order to create the initial mountain, and the metal constituting the initial mountain. The non-moving uppermost metal material discriminating variable indicating whether or not the material is the uppermost metal material among the non-moving metal materials in the initial mountain, and the moving metal material are arranged in the final mountain. The determination variable is a moving metal final mountain allocation variable indicating whether or not the final mountain is used, and an allocation mountain identification variable indicating whether or not the candidate mountains of the final mountain, Motoyama and Shinzan, are the final mountains. The metal material information acquisition step for acquiring the metal material information including the identification information of the initial mountain, the identification information of the metal material at each stacking position of the initial mountain, and the payout order of the metal material, and the Motoyama. The first constraint equation expressing the condition of the moving metal material that can be arranged in the above using the determination variable and the condition of the moving metal material that can be arranged in the new mountain are expressed by using the determination variable. The constraint formula setting step for setting the constraint formula including the second constraint formula represented by the above, based on the metal material information, the term for evaluating the total number of the moving metal materials, and the total number of the final peaks are evaluated. The objective function setting step for setting the objective function including the term based on the metal material information, and the value of the determination variable when the value of the objective function becomes the minimum or the maximum within the range satisfying the constraint equation. It has an optimization calculation step that executes the derivation as an optimum solution by performing an optimization calculation by a mathematical programming method, and the Motoyama is formed in the yard when the metal material information is created. It is a mountain that consists of at least a part of the mountain and whose location does not change from that mountain, and that the new mountain is a candidate mountain for the final mountain and is a mountain consisting only of the moving metal material. It is a feature.

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, when creating a transfer plan for metal materials for transshipping metal materials from the initial mountain to the final mountain, the total number of final mountains is minimized and the number of metal materials moved from the initial mountain is minimized. It can be balanced with the conversion.

It is a figure which shows an example of the functional structure of a yard management device. It is a flowchart explaining an example of a yard management method. It is a figure which shows the calculation result in the invention example and the comparative example 1. FIG. It is a figure which shows the calculation result in the invention example and the comparative example 2. It is a figure which shows an example of the layout of a yard.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings. In the present embodiment, in the steel manufacturing process, given the stacking shape of the initial pile, it is determined from the steel materials constituting the initial pile, the steel material that should be moved (transported) and the steel material that should not be moved (transported). Doing and determining the total number and stacking of the final mountains at the same time. Then, assuming that only the steel material to be moved is moved, the transport order of each steel material when transporting from the initial pile to the final pile is derived by a known method. It is assumed that the steel materials (slabs) manufactured in the steelmaking process are not stacked in the order of transportation to the rolling process in at least a part of the initial pile. Further, in the following description, the order of transporting each steel material to the rolling process is referred to as the payout order as necessary. Further, the steel material determined to be moving according to the present invention is referred to as a moving steel material as necessary, and the steel material determined not to be moved is referred to as a non-moving steel material as necessary. Further, in the following description, "moving steel material" and "non-moving steel material" may be referred to as "moving steel material" and "non-moving steel material", respectively.

First, the points to be focused on when realizing the present embodiment will be described.
In this embodiment, the problem of minimizing the total number of final piles and the total number of moving steel materials at the same time is considered. Here, all steel materials can be identified as either mobile steel materials or non-moving steel materials. Further, the steel material that can be a non-moving steel material can be determined from the initial pile shape. The steel material that can be a non-moving steel material is the part where the product order from the bottom of the initial pile is the payout order (the payout order is descending from the bottom to the top). In addition, if a certain steel material is a non-moving steel material in each initial mountain, the steel material group under it must also be a non-moving steel material. This is because in order to move the group of steel materials below the non-moving steel material, the non-moving steel material must be moved. Therefore, among the non-moving steel materials in each initial pile, all the steel materials above the non-moving steel material at the uppermost stage are mobile steel materials.

In order to minimize the total number of final ridges and the total number of moving steels at the same time, it is necessary to determine the moving steels in consideration of the feasibility of the final ridges. Therefore, not only the moving steel material but also the stacking shape of the final pile after transshipment (constituent steel material constituting each final pile) is specified from the decision variable. The stacking constraint on the final pile can be realized by the constraint that prohibits the placement of two specific steel materials on the same final pile. In addition, there is no guarantee that the minimum value of the total number of final mountains will be determined by ceil (n / h). Therefore, the total number of final peaks is also evaluated by the objective function. Here, n is the total number of steel materials, h is the upper limit of the height of the final peak, and ceil (n / h) represents the ceiling function (the smallest integer value of n / h or more).

Based on these requests, in the present embodiment, the variable z _ij for the final pile of the moving steel material (1 when the steel material i is moved and placed at the original mountain or the new mountain j, and 0- (zero) otherwise. 1 variable) is introduced as a decision variable. Further, the assigned mountain identification variable q _j (a 0-1 variable that becomes 1 when the mountain j which is a candidate for the final mountain is the final mountain, and 0 (zero) when the mountain j is not the final mountain) is introduced as a determinant. Further, the non-moving uppermost steel material discriminant variable x _i (1 when the steel material i constituting a certain initial pile is the non-moving steel material at the uppermost stage among the non-moving steel materials, and 0 (zero) when it is not. The 0-1 variable) and the movement presence / absence discrimination variable y _i (a 0-1 variable that becomes 1 when the steel material i is a moving steel material and 0 (zero) when the steel material i is not) are introduced as determination variables.

In this embodiment, these determinants are used to create an objective function aimed at minimizing the total number of final ridges and the total number of moving steel materials, and constraint equations for the determinants, moving steel materials, and final ridges. Construct and derive a decision variable that minimizes or maximizes the value of the objective function within the range that satisfies the constraint expression. An example of this detail will be described below.

(Assumption of problem)
In the present embodiment, the stacking shape and the payout order (rolling order) of the initial piles of each steel material are given.
Here, the set of steel materials is expressed as N = {1, 2, ..., N}.

The initial mountains include Motoyama and virtual mountains. The original mountain as the initial mountain is the mountain itself that is formed in the yard at the time when the steel material information is created (that is, when the final mountain is created) among the steel materials to be created for the final mountain. After that, even if some of the steel materials that make up the initial mountain are piled up on another mountain, if some of the steel materials that make up the initial mountain remain on the initial mountain, that mountain is also the original mountain. And. In this way, Motoyama consists of at least a part of the mountain that is formed in the yard at the time when the steel material information is created (that is, when the final mountain is created), and it is a mountain whose location does not change from that mountain. be. In the virtual mountain, among the steel materials to be created for the final mountain, the steel materials that have not yet been piled up in the yard at the time when the steel material information is created (that is, when the final mountain is created) are scheduled to arrive at the yard in the order of arrival. It is a mountain when it is assumed that the earlier ones are piled up. 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. As for the steel materials (non-arrival materials) that make up the virtual pile, it is assumed that there are no non-moving steel materials, and all of them are mobile steel materials. Therefore, the steel material constituting the virtual crest is treated as a moving steel material when determining either the moving steel material or the non-moving steel material.

It is assumed that the stacking shape of the initial mountain is known, but the stacking shape of the final mountain is unknown. It is assumed that the final mountain is a mountain piled up in the order of payout from the top, and the total number of final mountains is unknown.
In addition, 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 to be transported twice will be temporarily placed, but the steel material transported to the temporary mountain (temporary storage site) will always be transported to the final mountain (final storage site) at the next transportation, and will be different. It shall not be transported between mountains (temporary storage).
In addition, the place where the initial mountain with the non-moving steel material is located becomes the place where the final mountain containing the non-moving steel material is placed. The final mountain (new mountain) composed only of moving steel materials will be placed in a different storage area from the initial mountain storage area containing the moving steel materials.

Further, in the present embodiment, the following width constraint, length constraint, and height constraint are used as stacking constraints.
-Width constraint If the width of a steel material is narrower than the width of any steel material located under the steel material, the steel material can be placed unconditionally on the steel material located under the steel material. When the width of a certain steel material is wider than the width of any steel material located under the certain steel material, the width of both (the certain steel material and the steel material located under the certain steel material) If the difference is less than the reference value (for example, 200 [mm]) determined by the work constraint, the certain steel material can be placed on the steel material located below the steel material, but if it exceeds it, it cannot be placed.

That is, the width constraint is satisfied when the width of a certain steel material is narrower than the width of the steel material located under the certain steel material and when the width of the certain steel material is located below the certain steel material. When it is wider than the width of the steel material and the difference between the width of the certain steel material and the width of all the steel materials located under the certain steel material is less than the reference value (for example, 200 [mm]). Is.

-Length constraint If the length of a certain steel material is shorter than the length of any steel material located under the certain steel material, the certain steel material is unconditionally placed on the steel material located below the certain steel material. Can be placed. When the length of a certain steel material is longer than the length of any steel material located under the certain steel material, the lengths of both (the certain steel material and the steel material located under the certain steel material). If the difference is less than the reference value (for example, 2000 [mm]) determined by the work constraint, the certain steel material can be placed on the steel material located below the steel material, but if it exceeds that, it cannot be placed.

That is, the length constraint is satisfied when the length of a certain steel material is shorter than the length of the steel material located under the certain steel material, and when the length of the certain steel material is under the certain steel material. It is longer than the length of the steel material located in, and the difference between the width of the certain steel material and the width of all the steel materials located under the certain steel material is less than the reference value (for example, 2000 [mm]). If.

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

In addition, the yard for the initial mountain (Motoyama) with non-moving steel will be the yard for the final mountain. The final mountain consisting only of moving steel is Shinzan. As mentioned above, the yard of the new mountain is different from the yard of the early mountain.

(Coefficient of determination)
<Coefficient of determination used when determining non-moving steel materials and moving steel materials and determining the total number and stacking shape of the final pile>
In the present embodiment, the non-moving uppermost stage steel material discriminating variable x _i and the moving presence / absence discriminating variable y _i are set as determining variables for any steel material i. The non-moving uppermost steel material discriminating variable x _i is defined as the following equation (1), and the moving presence / absence discrimination variable y _i is defined as the following equation (2). It is assumed that the variable i is numbered in the order in which the steel materials are paid out (the value of the variable i is smaller as the payout order is earlier).

The non-moving uppermost steel material discriminant variable x _i is 1 when the steel material i constituting a certain initial peak is the non-moving steel material at the uppermost stage among the non-moving steel materials, and 0 (zero) when it is not. It is a 0-1 variable. As described above, if there is no non-moving steel material in the initial pile, the non-moving uppermost steel material discriminant variable x _i for all the steel materials i constituting the initial pile becomes 0 (zero). On the other hand, if there is one or more non-moving steel materials in the initial pile, only the non-moving uppermost stage steel material discriminant variable x _i for the non-moving steel material i at the uppermost stage of the non-moving steel materials becomes 1. In this case, the non-moving uppermost steel material discriminating variable x _i with respect to the other steel materials i constituting the initial pile becomes 0 (zero) (even if the steel material i is a non-moving steel material). That is, the maximum number of steel materials in which the non-moving uppermost stage steel material discriminant variable x _i is 1 for one initial pile is 1.
The movement presence / absence discriminant variable y _i is a 0-1 variable that becomes 1 when the steel material i is a moving steel material and becomes 0 (zero) when the steel material i is not.

Further, in the present embodiment, the final mountain allocation variable z _ij of the moving steel material and the allocation mountain identification variable q _j are used as decision variables. The final mountain allocation variable z _ij of the moving steel material is defined as the following equation (3), and the allocation mountain identification variable q _j is defined as the following equation (4). Note that j is identification information (ID) that uniquely identifies each mountain. For example, the identification number of the steel material storage place in the yard can be adopted as j.

The final mountain allocation variable z _ij of the moving steel material is the steel material i, which is the moving steel material, as the original mountain j (= 1, ..., p (p> 1)) or the new mountain j (= p + 1, ..., p + m (m =). n) It is a 0-1 variable that becomes 1 when it is placed in)) and 0 (zero) when it is not placed. When the steel material i is a non-moving steel material (that is, when the moving presence / absence discrimination variable y _i is a steel material i having 0 (zero)), the moving steel material final pile allocation variable z _ij is 0 for any final pile j. (Zero).
The assigned mountain identification variable q _j (j = 1, ..., p, p + 1, ..., p + m) is the final mountain, Motoyama j (= 1, ..., p) or Shinyama j (= p + 1,). ..., It is a 0-1 variable that becomes 1 when p + m) is assigned, and becomes 0 (zero) when it is not assigned. As described above, Motoyama j and Shinyama j are candidates for the final mountain.

<Determining variable used when determining the transport order>
In the present embodiment, after the non-moving steel material and the moving steel material are determined and the stacking shape of the final pile is determined, only the moving steel material is moved (transported), and the transshipment from the initial pile to the final pile is performed. The transport order of each steel material i is determined. A method for determining each steel material i at the time of transshipment from the initial pile to the final pile can be realized by a known technique. For example, the method described in Patent Document 2 can be used. In Patent Document 2, the initial transport time k_it [i] of the steel material i to be transported and the final transport time k_ft [i] of the steel material i to be transported are set as determining variables. Since the details of these decision variables are described in Patent Document 2, the detailed description thereof will be omitted here, and only the outline will be described.

For undelivered materials, the time at which transportation to the yard is first started after arriving at the receiving port such as a receiving table is the initial transportation time k_it [i] of the steel material i to be transported. For the already arrived material, the time when the first transfer is started from the storage place where the material is placed at the current time is the initial transfer time k_it [i] of the steel material i to be transferred. Further, the time at which the transfer target steel material i is started to be transferred to the final pile is the final transfer time k_ft [i] of the transfer target steel material i.

(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 having a CPU, ROM, RAM, HDD, and various interfaces, or dedicated hardware. FIG. 2 is a flowchart illustrating an example of a yard management method executed by the yard management device 100.
[Steel material information acquisition unit 101, steel material information acquisition 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 basic steel material information, information for specifying the stacking shape of the initial pile of each steel material, information for specifying the upper limit value h of the height of the final pile, and weight coefficients k ₁ and k ₂ .

The basic steel material information includes identification information, payout order, number of steel materials, and width for each of the steel materials (set of steel materials N = {1, 2, ..., N}) for which the final pile is to be created. , Contains length information. Here, for the sake of simplicity, it is assumed that all the steel materials have the same thickness.
The identification information is identification information (steel material ID) that uniquely identifies each steel material.
The payout order is the payout order of each steel material (transportation order to the rolling process). In this embodiment, since the identification information is in the payout order, the payout order does not have to be included in the steel material basic information.

The information for specifying the stacking shape of the initial mountain includes an initial mountain ID which is identification information uniquely identifying the initial mountain, and a steel material ID located in each stack of the initial mountain identified by the initial mountain ID.

Examples of the form of acquiring 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.

[Constraint expression / objective function setting unit 102, constraint expression setting step S202, objective function setting step S203]
The constraint expression / objective function setting unit 102 sets a constraint expression in which the above-mentioned constraint is expressed by a mathematical formula 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) Restrictions on moving steel The set of the subset Sk ( _⊂N ) of the steel obtained by dividing the set N of the steel is expressed as S = {S ₁ , S ₂ , ..., S _r }. Each of the subsets _Sk of this steel material is the initial peak. Further, as described above, it is assumed that the variable i for identifying the steel material is numbered in the payout order of the steel material (the value of the variable i is smaller as the payout order is earlier). Therefore, the following equations (5) and (6) are established.

In each initial mountain _Sk , the partial mountain obtained by extracting all the parts of the steel material whose product order is the payout order from the bottom (the payout order is descending from the bottom to the top) from the initial mountain _Sk . Let it be max (S _k ). A partial mountain here is a mountain composed of a certain steel material of a given mountain and all the steel materials below it, stacked in the same order as the given mountain. At this time, the steel material that is not in max (S _k ) is always a moving steel material. This is expressed by the following equations (7) and (8).

Equation (7) indicates that the steel material i in the portion _{where max (S k )} is removed from the initial mountain Sk is moved (becomes a moving steel material). Equation (8) indicates that the steel material i in the portion _{obtained by removing max (S k )} from the initial mountain Sk is not the steel material at the uppermost stage among the non-moving steel materials in the initial mountain _Sk . .. According to the equations (7) and (8), the steel material _i whose product order is not in the payout order (the payout order is descending from the bottom to the top) from the bottom in each initial mountain Sk can move. expressed.

(B) Restrictions on the non-moving uppermost steel material discriminating variable x _i In each initial mountain Sk, the maximum value of the number of steel materials _i for which the non-moving uppermost steel material discriminating variable x _i is 1 (x _i = 1) is 1. be. Therefore, the following equation (9) holds.

Further, the total number of initial mountains (moto mountains) with non-moving steel material i cannot exceed the total number p of final mountains. Therefore, the following equation (10) holds. However, this formula is a constraint that is meaningful only when the total number p of the final mountains is given as a constraint, and cannot be set when the total number p of the final mountains is evaluated as an objective function.

(C) Constraints on the variable y _i for determining whether or not to move In each initial mountain Sk, all the steel materials above the moving steel material _i move. Therefore, if the payout order (= i (identification number of steel material)) when viewed from the bottom to the top of each initial mountain Sk is _{k 1} , k ₂ , ..., The following (11) The formula holds.

(D) Restriction defining the relationship between the non-moving uppermost steel material discriminating variable x _i and the moving presence / absence discriminating variable y _i All steel materials i are uniquely identified as either a moving steel material or a non-moving steel material. In the initial mountain Sk, the number of stacked stages when counting from the bottom of the steel material _i (the number of stacked stages including the steel material and below it, and the number of stacked stages at the bottom is 1) is b. _{If i} , the total number of non-moving steel materials can be expressed as Σ i _{∈ N} b _i · x _i using the non-moving top-stage steel material discriminant variable x _i . Further, the total number of moving steel materials can be expressed as Σ _{i ∈ N} y i by using the moving presence / absence discriminant variable y _i . Therefore, the following equation (12) is established, which indicates that the sum of the total number of non-moving steel materials and the total number of moving steel materials is the total number n of steel materials constituting the initial mountain (former mountain and virtual mountain).

If the variable y _i for determining whether or not to move with respect to the steel material i is 1 (y _i = 1), the non-moving uppermost steel material discriminating variable x _i for all of the steel material i and the steel materials _i above it in the initial mountain Sk. Is 0 (zero, x _i = 0). On the contrary, if the movement presence / absence discriminant variable y _i with respect to the steel material i is 0 (zero, y _i = 1), one of the steel material i and the steel material _i above it in the initial mountain Sk is one steel material i. Only the non-moving uppermost steel material discriminant variable x _i with respect to is 1 (x _i = 1). Therefore, for the steel material _i ∈ Sk, if the set of the steel material i and the steel material _i above it is defined as Sk ^↑ ( _i ) in the initial mountain Sk (see equation (14) below). ), The following equation (13) holds.

In the equation (13), for any steel material _i of the initial mountain Sk, if the steel material i is a moving steel material, there is no non-moving steel material above it, and if the steel material i is not a moving steel material, the steel material is concerned. It means that i or one of the steel materials above the steel material i becomes the non-moving steel material located at the uppermost stage among the non-moving steel materials (that is, there is only one non-moving steel material having x _i = 1).

(E) Constraints that define the relationship between the moving steel final mountain allocation variable z _ij and the moving presence / absence discrimination variable y _i Any steel material i is the original mountain j (= 1, ..., p (p> 1)) or It must be placed at Niiyama j (= p + 1, ..., p + m (m = n)). Further, as described above, the moving steel final mountain allocation variable z _ij for the non-moving steel material i (that is, the steel material i for which the movement presence / absence discrimination variable y _i is 0 (zero)) is 0 for any mountain j. It is defined as (zero, z _ij = 0). Therefore, the following equations (15), (15'), and (15 ″) are established.

In the equation (15), if the steel material i is a moving steel material, the steel material i is a steel material that moves to any one of the original mountain j and the new mountain j, and if the steel material i is a non-moving steel material, the steel material i is a non-moving steel material. It means that the steel material i does not move to either the original mountain j or the new mountain j. Equation (15') indicates that the steel material i in the portion _{where max (S k )} is removed from the initial mountain Sk is a steel material that moves to any one of the original mountain j and the new mountain j. In equation (15''), even if the steel material i in the max (S _k ) portion of the initial mountain _Sk moves to any one of the original mountain j and the new mountain j, the original mountain j and the new mountain j It means that it does not have to move to any of the above (that is, it may be a moving steel material or a non-moving steel material).

(F) Constraints when transshipping to the original pile (constraints that define the moving steel final pile allocation variable z _ij , the non-moving top-stage steel discriminant variable x _i , the moving steel final pile allocation variable z _ij , and the allocation peak discrimination variable q Constraints that define the relationship with _j )
For the steel material i_k (∈ max (S _k )) that constitutes the original mountain (initial mountain) k (= 1, ..., P), the set of the set of steel materials i that can be placed on the steel material i_k is U (i_k). ). When the steel material i_k is a non-moving steel material at the uppermost stage of the non-moving steel materials in the original mountain k (that is, when the non-moving uppermost stage steel material discriminant variable x _i is 1 (x _i = 1)), the steel material i_k The steel material i that cannot be placed cannot be placed on the original mountain k to which the steel material i_k belongs. This is expressed by the following equation (16). According to the equation (16), it is possible to prevent the unrealizable final mountain from being obtained.

Here, in the present embodiment, the set U (i_k) of the steel materials i that can be placed on the steel material i_k is specified by the same pile prohibited steel material pair set F. The same pile prohibited steel pair set F is a set of pairs {i, j} ⊆N of any two steel materials as shown in the following equation (17), and is at least one of the above-mentioned width condition and length condition. It is a set of pairs of two steel materials that do not satisfy one of them. Further, the set U (i_k) of the steel materials i that can be placed on the steel material i_k is determined in consideration of not only the steel material i_k but also the relationship with all the steel materials under the steel material i_k. That is, when each pair of the steel material i_k and all the steel materials under it and the steel material that is a candidate to be placed on the steel material i_k is not included in the same pile prohibited steel material pair assembly F, the steel material i_k The steel material that is a candidate for mounting is included in the set U (i_k) of the steel material i that can be mounted on the steel material i_k.

Further, the number of steel materials that can be placed on the steel material i_k in the final mountain is limited by the height constraint described above. The number of stacked stages in the steel material i_k belonging to the original mountain k (the number of stacked stages including the steel material, the number of steel materials below it, and the number of stacked stages in the lowest stage is 1) is b _i . If _{_k} , the following equation (18) holds.

In the equation (18), the total number of steel materials i moving to the original mountain k is the number of steel materials that can be placed on the uppermost non-moving steel material among the non-moving steel materials belonging to the original mountain k (initial mountain). Indicates that it must be less than or equal to the upper limit of. The right side of the equation (18) represents an empty space (number of steel materials) formed on the steel material i_k at Motoyama k. According to the equation (18), it is possible to prevent the unrealizable final mountain from being obtained.

Further, the steel material i_k belonging to the initial mountain k (= 1, ..., P) is the non-moving steel material at the uppermost stage among the non-moving steel materials (the non-moving uppermost stage steel material discriminant variable x _i is 1 (x _i) . = 1)) Since the initial mountain (Motoyama) k is the final mountain, the following equation (19) holds.

(G) Mountain height constraint on the final mountain (new mountain) other than the original mountain The constraint on the height of the final mountain other than the original mountain, the new mountain j (= p + 1, ..., p + m), is based on the following equation (20). expressed.

Equation (20) indicates that the total number of moving steel materials moving from the initial mountain to the mountain j is equal to or less than the upper limit h of the height of the mountain j which is the final mountain. According to the equation (20), it is possible to prevent the unrealizable final mountain from being obtained.
Further, for Niiyama j, it is preferable to limit the solution space by preferentially constructing the one with small identification information as in the following equation (20').

The equation (20') does not apply to Motoyama (∀j ∈ {1, ..., p}).
(H) Same final mountain prohibition constraint (width, length constraint)
When the moving steel material is placed on the final pile, the final pile satisfies the stacking constraint (width constraint, height constraint), so the pair of two steel materials i1 and i2 belonging to the same pile prohibited steel material pair set F is the same final. The constraint prohibiting the placement on the mountain j is defined as the following equation (21).

The constraint of the formula (21) is a stacking constraint between the moving steel materials, and the stacking constraint between the non-moving steel material and the moving steel material is defined by the above-mentioned equation (17). According to the equation (21), it is possible to prevent the unrealizable final mountain from being obtained.

The constraint expression / objective function setting unit 102 may be changed to, for example, equations (7) to (13), (15), (15'), (15''), and (16) to (21). On the other hand, by setting _i , _j , S, Sk, p, n, F, h, bi, and m, the equations (7) to (13), (15), and (15') are set. The constraint equations of equations (15'') and (16) to (21) are set.

<< Objective function >>
Next, the objective function will be described.
As described above, in the present embodiment, the purpose is to minimize the total number of moving steel materials (or to maximize the total number of non-moving steel materials) and to minimize the total number of final peaks. The objective function J is used.

In this embodiment, as shown in Eq. (22), the purpose is a weighted linear sum of the total number of moving steel materials (Σy _i in Eq. (22)) and the total number of final peaks (Σq _j in Eq. (22)). Let it be a function. The weighted linear sum is the sum of the weighting coefficient k ₁ for the total number of moving steel materials and the weighting coefficient k ₂ for the total number of final peaks multiplied by the total number of moving steel materials and the total number of final peaks, respectively. .. The weighting coefficient k ₁ for the total number of moving steel materials is a coefficient representing the balance between the evaluation for the total number of moving steel materials and the evaluation for the total number of final peaks. The weighting coefficient k ₂ for the total number of final mountains is a coefficient representing the balance between the evaluation for the total number of final mountains and the evaluation for the total number of final mountains. When a weight coefficient k ₁ for the total number of moving steel materials is set to a value larger than the weighting factor k ₂ for the total number of final piles, for example, the total number of moving steel materials is reduced by 1 rather than the total number of final piles is reduced by 1. However, the amount of decrease in the value of the objective function J becomes large. Therefore, the objective function J in this case is an objective function that emphasizes the evaluation of the total number of moving steel materials rather than the evaluation of the total number of final peaks. Conversely, if a weighting factor k ₂ for the total number of final piles is set to a value larger than the weighting factor k ₁ for the total number of moving steel materials, for example, the total number of final piles is one rather than reducing the total number of moving steel materials by one. As the value is reduced, the amount of decrease in the value of the objective function J becomes larger. Therefore, the objective function J in this case is an objective function that emphasizes the evaluation of the total number of final peaks rather than the evaluation of the total number of moving steel materials. In this way, in the objective function J of Eq. (22), the evaluation of the total number of moving steel materials and the evaluation of the total number of final peaks can be balanced by the weighting coefficients k ₁ and k ₂ . That is, Eq. (22) is the minimum value of the total number of moving steel materials and the minimum value of the total number of final peaks after balancing such evaluations (under the condition of such evaluation balance). It is an objective function to find. In this way, by using Eq. (22), which has the total number of moving steel materials and the total number of final peaks as determining variables, as the objective function J, the total number of moving steel materials can be minimized and the total number of final peaks can be minimized. You will be able to balance.

The constraint expression / objective function setting unit 102 sets the objective function J of the equation (22), for example, by setting i, j, k ₁ , and k ₂ for the equation (22).

[Optimization calculation unit 103, optimization calculation step S204]
The optimization calculation unit 103 satisfies the constraint equations of equations (7) to (13), (15), (15'), (15''), and (16) to (21). Determining variables when the value of the objective function J in Eq. (22) is minimized in the range (non-moving top-stage steel material discriminant variable x _j , moving presence / absence discriminant variable y _i , moving steel material final pile allocation variable z _ij , and allocation Calculate the mountain discriminant variable q _j ) as the optimum solution. Further, the calculation of the optimum solution can be realized by using a known algorithm (including the use of a solver or the like) for solving the optimization problem by a mathematical programming method such as a mixed integer programming method.

[Post-processing unit 104, post-processing step S205]
When the optimum solutions of the non-moving uppermost steel material discriminant variable x _j , the moving presence / absence discriminant variable y _i , the moving steel material final pile allocation variable z _ij , and the allocation pile discriminant variable q _j are derived as described above, the set of steel materials is obtained. It is possible to determine whether or not to move each steel material contained in N (that is, whether it is a moving steel material or a non-moving steel material), the total number of final piles, and the stacking shape of the final piles. As explained in the section (Premise of the problem), the stacking shape of the final pile is determined by arranging the steel materials in the order of payout from the top. The final mountain will be either a fixed mountain or a new mountain. The fixed mountain is a mountain that includes non-moving steel materials in the former mountain, and the new mountain is a mountain that consists only of moving steel materials. In this way, the non-moving steel material and the steel material constituting each final pile are determined.

Then, as for the non-moving steel material, it is assumed that only the moving steel material is moved (transported) without moving (transporting), and the transporting order of each steel material when transshipping the steel material from the initial pile to the final pile is determined as a post-treatment. May be good. In this case, the post-processing unit 104 is activated. The post-treatment unit 104 determines the transport order of each steel material when transshipping the steel material from the initial pile to the final pile. This determination can be achieved with known techniques. As described above, in the present embodiment, the method described in Patent Document 2 is used to determine the transport order of steel materials when transshipping steel materials from the initial pile to the final pile. As shown in Patent Document 2, the post-processing unit 104 has a decision variable that minimizes the value of the transfer time objective function within a range that satisfies the transfer constraint equation (initial transfer time k_it [i] and final transfer of the steel material i to be transferred). By deriving the time k_ft [i]), the transport order of each steel material is determined. However, as a transport constraint formula, a constraint formula indicating that the non-moving steel material is not moved (transported) is added to the constraint formula described in Patent Document 2. In Patent Document 2, the initial mountain in the present specification is referred to as Motoyama, and the final mountain is referred to as Motoyama. Since the specific contents of the transport constraint equation and the transport time objective function are described in Patent Document 2, detailed description thereof will be omitted here. Further, as described in Patent Document 2, how the post-treatment unit 104 determines that the steel material is temporarily placed when determining the transport order of the steel material when transshipping the steel material from the initial pile to the final pile. It may also be decided whether to pile up on a 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). Such determination of the stacking shape of the temporary mountain can also be realized by a known technique. If there is room in the storage space, for example, the steel material judged to be temporary storage can be placed flat in an empty storage space (only one sheet needs to be placed), and it is not essential to create a temporary mountain. do not have.

[Output unit 105, output step S206]
The output unit 105 outputs information indicating the transport order from the initial pile to the final pile of each steel material contained in the steel material assembly N, which is derived from the post-processing unit 104. In addition to or in place of this information, the output unit 105 may output identification information of the moving steel material and the non-moving steel material, the total number of the final piles, and the stacking shape of the final piles. 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 for controlling the operation of the crane.

(summary)
As described above, in the present embodiment, the yard management device 100 determines the constraints indicating the conditions of the moving steel material that can be placed on the original mountain as the determination variables (non-moving top-stage steel material discriminant variable x _i and the moving steel material final pile allocation variable). The constraint formula expressed using z _ij ) and the constraint indicating the conditions of the moving steel material that can be placed in the new mountain are expressed using the decision variables (moving steel material final mountain allocation variable z _ij and allocation mountain identification variable q _j ). To satisfy the equation, we derive the determinants when the value of the objective function J, which aims to minimize the total number of moving steel materials and the total number of final peaks, is minimized, and derive non-moving steel materials and moving steel materials. And the total number of final mountains and the stacking of final mountains. Therefore, when creating a transfer plan for steel materials for transshipping steel materials from the initial mountain to the final mountain, when creating a transfer plan for metal materials for transshipping metal materials from the initial mountain to the final mountain, the final mountain. It is possible to balance the minimization of the total number of metal materials and the minimization of the total number of metal materials moving from the initial mountain.

<Calculation example>
Next, a calculation example will be described. In this embodiment, the total number of final piles and the total number of moving steel materials are minimized by appropriately selecting non-moving steel materials. Therefore, in the technique described in Patent Document 3, the portion (max ( _Sk )) in which the product order from the bottom of the initial mountain is the payout order (the payout order is descending from the bottom to the top) is not moved. We compare the method of deriving the stacking shape of the final pile without moving as a steel material with the method of this embodiment, and show that the method of this embodiment can reduce the total number of final piles. In the method of the present embodiment, the transport order of each steel material is determined by the method described in Patent Document 2 by post-processing.
Further, in the technique described in Patent Document 3, the method of deriving the stacking shape of the final piles using all of them as moving steel materials is compared with the method of the present embodiment, and it is shown that the total number of final peaks does not change between the two methods. ..

Here, the outline of the optimization calculation described in Patent Document 3 will be described. Since the details of the optimization calculation are described in Patent Document 3, the detailed description thereof will be omitted here.
In Patent Document 3, the mountain sorting / transporting order variable x [i] [m] [s], the temporary placement determination variable y [p] [s ₁ ] [s ₂ ], and the optimum mountain existence determination variable δ [m] And are the decision variables. As constraint equations, one steel material i is not assigned to a plurality of transport orders and a plurality of final piles (unique constraint of a transport lot), and a plurality of steel materials i or a final material i or a final material in one transport order s. The constraint that the mountain m is not assigned (unique constraint of transport order) and the stacking constraint (length constraint, width constraint, height constraint) are used. As the objective function J', as shown in the following equation (23), a weighted linear sum of the objective function J ₁ for evaluating the total number of final peaks and the objective function J ₂ for evaluating the total number of transports is used. ..

In the equation (23), the weight coefficients Weight1 and Weight2 are set in advance depending on how much each evaluation item is emphasized, and are between each evaluation item (the number of mountains of the final mountain, the total number of times of transportation). Represents the balance of evaluation. For example, when the number of final peaks is an important evaluation item rather than the total number of times the steel material is transported, the size of the weighting factor Weight1 is made larger than the size of the weighting factor Weight2.

In Patent Document 3, the determination variable (mountain sorting / transport order variable x [i] [m] [s], temporary placement determination variable y [, which minimizes the value of the objective function J'within the range satisfying the above-mentioned constraint equation. Find p] [s ₁ ] [s ₂ ] and the optimum mountain existence determination variable δ [m]). From these decision variables, the transport order of each steel material i and the stacking shape of the final pile can be obtained. Here, among the variables in which the optimum solution y _opt [p] [s ₁ ] [s ₂ ] of the temporary placement determination variable is 1, if there is a variable in which s ₁ > s ₂ , there is a pair of steel materials p. , The steel material above is subject to temporary placement. In this way, the steel material i to be temporarily placed can be obtained.

Patent Document 3 is premised on moving all steel materials. Therefore, when the method described in Patent Document 3 is applied assuming that the non-moving steel material is not moved (transported) but only the moving steel material is moved (transported) as in the present embodiment, it is necessary to do as follows. There is.
First, the mountain sorting / transport order variable x [i] [m] [s] for the final mountain m of the steel material i, which cannot be the same final mountain as the non-moving steel material, is fixed to 0 (zero). As described above, the mountain sorting / transport order variable x [i] [m] [s] is 1 when the steel material i is transported to the final pile m in the transport order s, and is 0 (zero) otherwise. It is a 0-1 variable.

For example, if an initial pile containing two steel materials i ₁ and i ₂ as non-moving steel materials is allocated to the final pile m ₁ , the following constraint (24) is added as a stacking constraint for the final pile m ₁ . There is a need to. Note that F (i ₁ ) represents a set of steel materials that cannot be the same final pile as the steel material i ₁ .

Further, the mountain height constraint of (Equation 4-1) and (Equation 4-2) of Patent Document 3 is rewritten as the following equations (25) and (26) in consideration of the non-moving steel material.

Here, H _f is the sum of the thicknesses of all non-moving steel materials. P _f is the total number of non-moving steel materials. H and P represent the upper limit of the height of the final mountain described by the thickness and the number of sheets, respectively. The thickness [i] is the thickness of the steel material i.

(Calculation condition)
In the example of the invention, the initial pile shape is given based on the operation data, and the non-moving steel material and the moving steel material are determined and the total number and the pile shape of the final piles are determined by the algorithm described in this embodiment. Then, on the premise of this, the post-treatment based on Patent Document 2 is executed to determine the transport order of each steel material. On the other hand, in Comparative Example 1, the portion (max (S _k )) in which the product order from the bottom of the initial mountain is the payout order (the payout order is descending from the bottom to the top) is used as the non-moving steel material. On the premise of the above, the stacking shape of the final pile and the transport order of the steel material are determined at the same time by the method described in Patent Document 3. Further, in Comparative Example 2, all the steel materials are used as moving steel materials, and on the premise of this, the stacking shape of the final pile and the transport order of the steel materials are simultaneously determined by the method described in Patent Document 3.

Here, the upper limit value h of the height of the final mountain is set to 10 steps (h = 10). Further, in the equation (22), the weighting coefficient k ₁ for the total number of moving steel materials and the weighting coefficient k ₂ for the total number of final peaks were set to 1 and 10 (k ₁ = 1, k ₂ = 10), respectively. Further, the weight coefficients Weight1 and Weight2 in the equation (23) were set to 10 and 1 (Weight1 = 10, Weight2 = 1), respectively.

The calculation environment is as follows.
Processor: Intel (registered trademark) Xeon (registered trademark) CPU E5-2687W @ 3.1GHz (2 processors)
Mounted memory (RAM): 128GB
OS: Windows (registered trademark) 7 Professional 64-bit operating system Optimal calculation software: ILOG CPLEX (registered trademark) Cplex11.0 Concert25
Twelve types of steel material information were used as the steel material information, and the total number of moving steel materials and the total number of final peaks were derived for each steel material information by the methods of the invention example, comparative example 1 and comparative example 2 described above. The results are shown in FIGS. 3 and 4.

FIG. 3 is a diagram showing the calculation results in the invention example and the comparative example 1 in a tabular format. As described above, in Comparative Example 1, the portion (max (S _k )) in which the product order from the bottom of the initial mountain is the payout order (the payout order is descending from the bottom to the top) is used as the non-moving steel material. On the premise of this, the stacking shape of the final pile and the transport order of the steel material are determined at the same time by the method described in Patent Document 3. In addition, in FIGS. 3 and 4, the SL number is the total number of slabs (steel materials) constituting the initial mountain. The fixed number of mountains is the number of original mountains that became the final mountain.
As shown in FIG. 3, in the invention example, the total number of moving steel materials is increased by about 3 (about 12%) on average, and the total number of final peaks is increased from 5.5 to 3.7 as compared with Comparative Example 1. It can be seen that it can be reduced by about 33%.

FIG. 4 is a diagram showing the results of the invention example and the comparative example 2 in a tabular format. As described above, in Comparative Example 2, all the steel materials are used as moving steel materials, and on the premise of this, the stacking shape of the final pile and the transport order of the steel materials are simultaneously determined by the method described in Patent Document 3.
As shown in FIG. 4, in the example of the invention, while securing an average of 6.4 sheets (= 32.7-26.3) of non-moving steel materials, the total number of final piles is assumed to move all the steel materials. It can be seen that the number can be the same as that of Comparative Example 2 (= 3.7).

When transshipping (replacement) the steel materials of the initial piles that are not in the order of payout from the top in the yard, the steel materials are moved for each pile and a new storage place. If there is a part in the bottom of the initial mountain where the payout order is in descending order from the bottom to the top, make the best use of it and replace only the upper part of the initial mountain. In some cases, the total number of transports may be reduced. In the present embodiment, for the latter case, a solution algorithm (this algorithm) for a problem that minimizes the total number of moving steel materials while keeping the total number of final peaks to a minimum has been developed. Then, in the calculation example, it was shown that the verification test based on the actual data can realize the minimum number of ridges obtained under the condition without the non-moving steel material while securing the maximum total number of the non-moving steel materials.
As described above, given the stacking shape of the initial pile, when transshipping the steel material of the initial pile to the final pile piled up in the order of payout, while minimizing the total number of the final pile, the non-moving steel material A transshipment transfer plan can be created to maximize the total number (minimize the total number of mobile steel materials).

(Modification example)
In this embodiment, the minimization problem that minimizes the value of the objective function J in Eq. (22) has been described as an example. However, for example, by multiplying each term on the right side of the equation (22) by (-1), it may be a maximization problem.

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

Further, it is preferable to use the movement presence / absence discriminant variable y _i as in the present embodiment because the algorithm (constraint expression and objective function) can be described intuitively and easily. However, as shown in the equation (15), the movement presence / absence discriminant variable y _i can be expressed by using the movement steel material final mountain allocation variable z _ij . Therefore, it is not always necessary to use the movement presence / absence discrimination variable y _i .

Further, 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.

<Other variants>
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)
The following is an example of the relationship between the claims and the embodiments. It should be noted that the description of the claims is not limited to the description of the embodiment, as shown in the modified examples and the like.
<Claims 1 and 8>
The non-moving top-stage metal material discriminating variable corresponds to, for example, the non-moving top-stage steel material discriminating variable x _i .
The moving metal final pile allocation variable corresponds to, for example, the moving steel final pile allocation variable z _ij .
The allocation mountain identification variable corresponds to, for example, the allocation mountain identification variable q _j .
The metal material information acquisition means (step) is realized by using, for example, the steel material information acquisition unit 101 (steel material information acquisition step S201).
The metal material information is realized, for example, by using the steel material information. The identification information of the initial pile and the identification information of the metal material at each stacking position of the initial pile are, for example, information for specifying the stacking shape of the initial pile of each steel material (initial pile ID and the initial pile ID). It is realized by using the steel material ID) located in each stack of the initial pile.
The constraint expression setting means (step) is realized by using, for example, the constraint expression / objective function setting unit 102 (constraint expression setting step S202).
The first constraint equation is realized, for example, by using at least one of equations (16) and (18).
The second constraint equation is realized, for example, by using at least one of the equations (20) and (21).
The objective function setting means (step) is realized, for example, by using the constraint expression / objective function setting unit 102 (constraint expression / objective function setting step S203).
An objective function including a term for evaluating the total number of moving metal materials and a term for evaluating the total number of final peaks is realized by using, for example, Eq. (22). The term for evaluating the total number of moving metal materials corresponds to, for example, the first term on the right side of the equation (22), and the term for evaluating the total number of the final peaks corresponds to, for example, the second term on the right side of the equation (22). handle.
The optimization calculation means (step) is realized by using, for example, the optimization calculation unit 103 (optimization calculation step S204).
<Claim 2>
The movement presence / absence discrimination variable is realized by using, for example, the movement presence / absence discrimination variable y _i .
The third constraint equation is realized, for example, by using the equation (15).
<Claim 3>
The fourth constraint equation is realized, for example, by using the equation (12). The sum of the total number of the moving metal materials and the total number of the non-moving metal materials corresponds to, for example, the left side of the equation (12). The total number of the metal materials constituting the initial mountain corresponds to, for example, the right side of the equation (12).
<Claim 4>
The fifth constraint equation is realized, for example, by using the equation (13).
When the metal material is the moving metal material, the metal material above the metal material in the initial mountain does not become the non-moving metal material, for example, in the equation (13), it is determined whether or not the metal material has moved. Corresponds to the case where the value of the variable y _i is 1.
When the metal material is the non-moving metal material, only one of the metal material or the metal material above the metal material in the initial mountain is at the top of the non-moving metal material. Being a certain metal material corresponds to, for example, the case where the value of the movement presence / absence discriminant variable y _i is 0 (zero) in the equation (13).
<Claim 5>
The stacking constraint corresponds to, for example, a width constraint and a length constraint.
The set of the metal materials that can be placed on the metal material corresponds to, for example, the set U (i_k) of the steel materials i that can be placed on the steel material i_k.
The Motoyama arrangement constraint equation corresponds to, for example, equation (16).
When the metal material is the non-moving metal material at the uppermost stage of the non-moving metal materials in the initial mountain, for example, in the equation (16), the moving uppermost stage steel material discriminating variable x _i _ _k is 1. Corresponds to the case of (x _i _ _k = 1). The fact that the metal material that cannot be placed on the metal material cannot be placed on the original mountain to which the metal material belongs is that, for example, in the equation (16), the moving uppermost stage steel material discriminating variable x _i _ _k is 1 ( In the case of x _i _ _k = 1), it corresponds to the fact that the final pile allocation variable z _ij of the moving steel material becomes 0 (zero).
The Motoyama height constraint equation corresponds to, for example, equation (18).
The number of the metal materials determined based on the preset upper limit of the height of the final mountain, which is arranged on the non-moving metal material at the uppermost stage of the non-moving metal materials in the initial mountain. The number of the metal materials that can be used corresponds to, for example, the right side of the equation (18). The total number of the moving metal materials moving to the original mountain to which the non-moving metal material belongs corresponds to, for example, the left side of the equation (18).
<Claim 6>
The stacking constraint corresponds to, for example, a width constraint and a length constraint.
The Niiyama height constraint equation corresponds to, for example, equation (20).
The total number of the moving metal materials constituting the new mountain corresponds to, for example, the left side of the equation (20). The number of the metal materials determined based on the preset upper limit of the height of the final mountain corresponds to, for example, the right side of the equation (20).
The moving metal material stacking constraint equation corresponds to, for example, equation (21).
The fact that the two moving metal materials that do not satisfy the stacking constraint cannot be placed on the same final mountain means that both the first and second terms on the left side of Eq. (21) cannot take 1. handle.

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

Claims (10)

The metal material of the initial pile consisting of the metal material piled up in the yard, which is the storage place between the processes, is transported by the transport equipment, and the metal material piled up in the stacking order according to the delivery order to the subsequent process of the yard. When creating the final mountain, the moving metal material, which is the metal material transported from the initial mountain to the final mountain in the storage place, and the initial mountain in order to create the final mountain in the same place as the initial mountain. It is a yard management device for determining at least the non-moving metal material fixed to the place of the above and the metal material constituting the final mountain.
The non-moving uppermost metal material discriminating variable indicating whether or not the metal material constituting the initial mountain is the metal material at the uppermost stage among the non-moving metal materials in the initial mountain, and the moving metal. The moving metal final mountain allocation variable indicating whether or not the material is placed in the final mountain, and the allocation mountain identification indicating whether or not the Motoyama and Shinyama, which are candidate mountains of the final mountain, are designated as the final mountain. A variable and a determinant
Metallic material information acquisition means for acquiring metal material information including the identification information of the initial mountain, the identification information of the metal material at each stacking position of the initial mountain, and the payout order of the metal material.
The first constraint equation expressing the conditions of the moving metal material that can be placed on the original mountain using the coefficient of determination and the conditions of the moving metal material that can be placed on the new mountain are determined. A constraint expression setting means for setting a constraint expression including a second constraint expression expressed using a variable based on the metal material information, and a constraint expression setting means.
An objective function setting means for setting an objective function including a term for evaluating the total number of moving metal materials and a term for evaluating the total number of final peaks based on the metallic material information.
Optimization executed by performing optimization calculation by a mathematical programming method to derive the value of the decision variable when the value of the objective function becomes the minimum or the maximum within the range satisfying the constraint equation as the optimum solution. Calculation means and
Have,
The Motoyama is a mountain that is a candidate for the final mountain, and consists of at least a part of the mountains formed in the yard at the time when the metal material information is created, and the location does not change from the mountain. And
The new mountain is a mountain that is a candidate for the final mountain, and is a mountain made of only the moving metal material. The determination variable further includes a movement presence / absence discriminant variable indicating whether or not the metal material is a moving metal material.
The constraint formula further includes a third constraint formula using the coefficient of determination to indicate that any metal material must be placed on any one of the original mountain and the new mountain. The yard management device according to claim 1. The constraint formula uses the coefficient of determination to indicate that the sum of the total number of the moving metal materials and the total number of the non-moving metal materials is equal to the total number of the metal materials constituting the initial mountain. The yard management device according to claim 2, further comprising a fourth constraint equation. In the constraint equation, when the metal material is the moving metal material, the metal material above the metal material in the initial mountain does not become the non-moving metal material, and the metal material is the non-moving metal material. In the case of a metal material, only one of the metal material or the metal material above the metal material in the initial mountain becomes the metal material at the uppermost stage among the non-moving metal materials. The yard management device according to claim 2 or 3, further comprising a fifth constraint equation expressed using the determination variable. The constraint type setting means is a constraint preset using the size of the metal material, and is based on a stacking constraint indicating a condition of the metal material that cannot be arranged in the same final mountain. Identify the set of the metal materials that can be placed on the metal material,
In the first constraint equation, when the metal material is the non-moving metal material at the uppermost stage of the non-moving metal materials in the initial mountain, the metal material is attached to the original mountain to which the metal material belongs. The fact that the metal material that cannot be placed on the metal material cannot be placed is preset with the original mountain placement constraint formula that expresses that the non-moving uppermost metal material discrimination variable and the moving metal material final mountain allocation variable are used. The number of the metal materials determined based on the upper limit of the height of the final mountain, and can be arranged on the non-moving metal material at the uppermost stage of the non-moving metal materials in the initial mountain. The number of the non-moving metal materials must be equal to or greater than the total number of the moving metal materials moving to the original mountain to which the non-moving metal material belongs. The yard management device according to any one of claims 1 to 4, wherein the yard management device is represented by using a mountain allocation variable and includes a source mountain height constraint expression. The constraint type setting means is the same based on the constraint set in advance using the size of the metal material and the stacking constraint indicating the condition of the metal material that cannot be arranged in the same final mountain. Identify the metal material that cannot be placed on the final mountain of
The second constraint equation states that the total number of the moving metal materials constituting the new mountain is equal to or less than the number of the metal materials determined based on the preset upper limit of the height of the final mountain. The new mountain height constraint equation expressed using the moving metal final mountain allocation variable and the allocation mountain identification variable, and the two moving metal materials that do not satisfy the stacking constraint cannot be placed on the same final mountain. The yard management device according to any one of claims 1 to 5, wherein the yard management device includes a moving metal material stacking shape constraint formula expressed by using the moving metal material final mountain allocation variable. The movement is performed in units of metal group,
The yard according to any one of claims 1 to 6, wherein the metal material group is composed of a plurality of the metal materials that are not divided when the metal material is transported by a transport device. Management device. The yard is a storage place between the steelmaking process and the rolling process in the steelmaking process.
The yard management device according to any one of claims 1 to 7, wherein the metal material is a steel material. The metal material of the initial pile consisting of the metal material piled up in the yard, which is the storage place between the processes, is transported by the transport equipment, and the metal material piled up in the stacking order according to the delivery order to the subsequent process of the yard. When creating the final mountain, the moving metal material, which is the metal material transported from the initial mountain to the final mountain in the storage place, and the initial mountain in order to create the final mountain in the same place as the initial mountain. It is a yard management method for at least determining the non-moving metal material fixed to the place of the above and the metal material constituting the final mountain.
The non-moving uppermost metal material discriminating variable indicating whether or not the metal material constituting the initial mountain is the metal material at the uppermost stage among the non-moving metal materials in the initial mountain, and the moving metal. The moving metal final mountain allocation variable indicating whether or not the material is placed in the final mountain, and the allocation mountain identification indicating whether or not the Motoyama and Shinyama, which are candidate mountains of the final mountain, are designated as the final mountain. A variable and a determinant
A metal material information acquisition step for acquiring metal material information including the identification information of the initial mountain, the identification information of the metal material at each stacking position of the initial mountain, and the payout order of the metal material.
The first constraint equation expressing the conditions of the moving metal material that can be placed on the original mountain using the coefficient of determination and the conditions of the moving metal material that can be placed on the new mountain are determined. A constraint expression setting step for setting a constraint expression including a second constraint expression expressed using a variable based on the metal material information, and a constraint expression setting step.
An objective function setting step for setting an objective function including a term for evaluating the total number of moving metal materials and a term for evaluating the total number of final peaks based on the metallic material information.
Optimization executed by performing optimization calculation by a mathematical programming method to derive the value of the decision variable when the value of the objective function becomes the minimum or the maximum within the range satisfying the constraint equation as the optimum solution. Calculation steps and
Have,
The Motoyama is a mountain that is a candidate for the final mountain, and consists of at least a part of the mountains formed in the yard at the time when the metal material information is created, and the location does not change from the mountain. And
The yard management method, wherein the new mountain is a mountain that is a candidate for the final mountain and is a mountain made of only the moving metal material. A program characterized in that a computer functions as each means of the yard management device according to any one of claims 1 to 8.

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