JP2019218151A - Yard management device, yard management method and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To minimize the total number of final mountains and to minimize the number of metal materials to be moved from the initial mountain when creating a transport plan for metal materials for transshipping metal materials from the initial mountain to the final mountain. Be balanced. SOLUTION: A yard management device 100 expresses a constraint indicating a condition of a moving steel material that can be placed in a source pile by using a determination variable (non-moving uppermost stage steel material discriminant variable xi and moving steel material final pile allocation variable zij). Move so as to satisfy the constraint equation and the constraint equation that expresses the constraint indicating the condition of the moving steel material that can be placed in the new mountain using the decision variables (moving steel material final mountain allocation variable zij and allocation mountain identification variable qj). Derivation of the determinants when the value of the objective function J, which aims to minimize the total number of steel materials and the total number of final ridges, is minimized, the determination of non-moving steel materials and moving steel materials, and the total number of final ridges. , Determine the final mountain pile. [Selection diagram] Fig. 1

Description

  The present invention relates to a yard management device, a yard management method, and a program, and in a metal manufacturing process, sorts metal materials in a yard provided to smoothly supply metal materials such as slabs and coils to the next process. It is suitable for use.

  In the iron making process, which is an example of the metal manufacturing process, for example, from the steel making process to the rolling process of the next process, when transporting the steel material, which is an example of the metal material, after the steel material is once placed in a temporary storage location called a yard, It is carried out of the yard in accordance with the processing time of the rolling process that is the next process. FIG. 5 shows an example of the layout of the yard. As shown in FIG. 5, the yards are storage spaces 501 to 504 that are partitioned vertically and horizontally as a buffer area for supplying a steel material such as a slab paid out from an upstream process to a downstream process. The vertical division is often referred to as “building”, and the horizontal division is referred to as “row”. That is, the cranes (1A, 1B, 2A, 2B) are movable in the building and transfer the steel material between different rows in the same building. In addition, the transfer of the steel material between buildings is carried out by the transfer table. When creating the transfer command, the "building" and "row" are designated to indicate where the steel material is to be transferred (the numbers (11) in parentheses attached to the depots 501 to 504 in FIG. 5, (See (12), (21) and (22)).

Next, a basic work flow in the yard will be described with reference to FIG. First, the steel material carried out from the continuous casting machine 510 in the steelmaking process, which is the preceding process, is transported to the yard at the receiving table X via the pillar 511, and is partitioned by the cranes 1A, 1B, 2A, and 2B. To 504, and are piled up. Then, the crane 1A, 1B, 2A, 2B again mounts on the payout table Z according to the production schedule of the subsequent rolling process, and is transported to the rolling process. Generally, in the yard, steel materials are placed in a piled state as described above. This is to effectively utilize the limited yard area.
Hereinafter, “moto mountain”, “virtual mountain”, “initial mountain”, “final mountain”, “fixed mountain”, and “new mountain” are used in the following sense.
Motoyama: A mountain that consists of at least a part of the mountain already formed in the yard at the moment, and does not change its location from the mountain.
Virtual mountain: A mountain assuming that steel materials that have not yet arrived at the yard are piled up earlier in the order of arrival at the yard (not actually existing mountains).
Initial Mountain: A generic term for Motoyama (the mountain already formed in the yard) and virtual mountain at the present time.
Final pile: The final pile piled up to be paid out to the post-process (also called the payout pile).
Fixed pile: The last pile containing steel that does not move (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 back from the former mountain and returned to the former mountain again).
Shinyama: A mountain composed of steel materials transferred from an initial mountain and having no non-moving steel materials (composed of only moving steel materials).
Wonsan and Newshan are candidate mountains for the final mountain, and among the candidates, the mountain that finally remains as a fixed mountain or a new mountain is the final mountain.

  In the yard, in order to reduce the unit fuel consumption of the heating furnace in the subsequent hot rolling step, it is required that the steel material be charged into the heating furnace while maintaining the temperature as high as possible. For this reason, there is a case where a heat insulating facility is installed in a yard these days, and steel materials are stored in a piled state therein. In order to make effective use of limited heat insulation equipment, it is necessary to pile up steel materials as high as possible to the equipment limit. On the other hand, when stacking steel materials, in the final pile, the steel materials are stacked from the top in the processing order in the next step, and the pile shape of the final pile is not an unstable inverted pyramid shape so that it can be easily supplied to the next process. And so on (this is called “stacking constraint”). Further, the work load in performing the hilling (making the final hill) is also an element that cannot be overlooked. Therefore, in the yard control, it is desired to formulate a work plan for performing the hill setting so as to have the highest possible final hill with the minimum possible workload under the above-described restrictions on the stacked figure.

  Also, when performing pile sorting (separating steel into multiple piles) in the yard to pay out the required steel smoothly in the post-process, the steel arriving will be demoted (the steel build-in). Lowering the grade from the originally planned use to another one for reasons such as quality problems that occur at the time), or needing unplanned refining treatment to the steel material to be arrived or changing its size As a result, it is often possible that the steel material does not arrive as originally planned. In addition, it is hardly expected that the state of the yard storage area will change plainly as originally planned, and it is a daily occurrence that unscheduled steel materials must be placed in unplanned storage areas.

  Furthermore, the rolling order in the hot rolling process, which is the post-process, of the steel material stacked on the pile in the order of dispensing from the yard to the hot rolling process, which is the post-process, is changed after the steel material reaches the yard. As a result, the piles may not be stacked in the order of dispensing, and the steel materials may have to be transshipped according to the changed rolling order. Here, that the steel materials are piled up on the pile in the order of payout means that, at any pile position of the pile, one or more steel materials that are conveyed at a relatively higher position are lower than the steel material at the same time. It is paid out to a later 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 to the yard and the work of paying out the steel material from the yard, Storage space is limited. For this reason, it is required to perform the transshipment work of the steel material efficiently and in a space-saving manner.
Therefore, due to various circumstances before and after the arrival at the yard, the work of reloading the piles that are no longer in the order of dispensing at the time of arrival at the yard in the order of dispensing can be performed efficiently (ie, with the smallest possible number of transports) and in the final amount as small as possible. The need to increase the number of mountains is extremely high.

Patent Documents 1 to 3 disclose inventions described in Patent Documents 1 to 3 as prior arts for the problem of reloading a steel material from an initial peak to a final peak.
First, Patent Literature 1 discloses that when reloading the steel materials of the former mountain already in the yard in the order of dispensing, the optimum stacking shape of the final mountain is optimized by taking into account the necessary rearrangement load and the stacking shape constraint. A technique of formulating a problem and calculating using a tab search technique is disclosed. However, in the invention described in Patent Literature 1, the method of obtaining the stacked shape of the final mountain is shown, but how to determine the transport order from the initial mountain to the final mountain is clearly shown. Not.

Next, Patent Literature 2 discloses an initial mountain when the state of the initial mountain and the state of the final mountain at that time are given in a situation where steel materials arriving at the yard and unarrived materials are mixed. In order to solve the problem of transfer and transfer of steel materials from the state of the last pile to the state of the last pile, a method of formulating as a mixed integer programming problem using the initial transfer time variable and the final transfer time variable on the assumption that each steel material is transported at most twice. It has been disclosed.
Finally, Patent Literature 3 discloses a method of reducing the mathematical programming problem that satisfies the constraint conditions related to the hill setting and the transport, and simultaneously optimizing the hill sorting and the transport order.

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

  However, in the techniques described in Patent Literatures 1 to 3, when the piles are transshipped, the problem is set on the assumption that all the steel materials are moved or the non-moved (fixed) steel materials are given in advance.

  When transshipping a pile already piled up in the yard, in actual operation, unless there is a request to change the pile storage itself, it is possible to move the piles together and not to transship the piles. In order to reduce the number of transshipments only, a method of avoiding unnecessary movement of steel materials is adopted. In other words, in the case of such transshipment, it is required that the steel material that does not need to be moved in the initial pile is transshipped with the minimum number of transports as it is. To achieve this, it is not always best to use a method that does not move all steel materials that can be non-movable (fixed). This is because a steel material that can be made non-movable (fixed) is not moved, and thus the number of final mountains may increase. Therefore, as in the techniques described in Patent Documents 1 to 3, unless the necessity of moving the steel material to minimize the number of final peaks is considered, the number of final peaks may increase. In addition, in order to guarantee that the number of final hills determined in consideration of the necessity of moving the steel material to minimize the number of final hills is the feasible number of hills, It is necessary to consider the figure.

  The present invention has been made in view of the above problems, and minimizes the total number of final peaks when creating a metal material transfer plan for reloading metal materials from an initial mountain to a final mountain. And minimizing 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 mountain made of the metal material piled up in the yard, which is a storage space between the processes, by a transport device, and stacks the metal material according to the order of dispensing to the subsequent process of the yard. When creating a final mountain made of metal materials piled up in order, a moving metal material that is a metal material transported from the initial mountain to the final mountain in the depot, and the final mountain in a place of the initial mountain as it is. Non-movable metal material fixed to the location of the initial mountain to create a, the yard management device for determining at least the metal material constituting the final mountain, the metal constituting the initial mountain In the initial mountain, a non-moving uppermost metal material discriminating variable indicating whether or not the metal material is the uppermost metal material in the non-moving metal material, and the moving metal material is arranged in the final mountain. Whether or not moving metal A final mountain allocation variable, an allocation mountain identification variable indicating whether or not the last mountain candidate mountain, the original mountain and the new mountain, is to be the final mountain, as a decision variable, and the identification information of the initial mountain, Metal material information acquisition means for acquiring metal material information including 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 movement that can be arranged at the base mountain A first constraint equation expressing the condition of the metal material using the decision variable, and a second constraint equation expressing the condition of the moving metal material that can be arranged in the new mountain using the decision variable A constraint function including a constraint expression setting means for setting based on the metal material information, a term for evaluating the total number of the moving metal materials, and an objective function including a term for evaluating the total number of the final peaks, Objective function setting based on the metal material information Means for deriving, as an optimal solution, the value of the decision variable when the value of the objective function is minimum or maximum within a range satisfying the constraint expression, by performing optimization calculation by mathematical programming. Optimizing calculation means, wherein the source mountain is a mountain that is a candidate for the final mountain, and at least a part of the mountain formed in the yard at the time the metal material information is created. 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.

  According to the yard management method of the present invention, the metal material of the initial mountain made of the metal material piled up in the yard, which is the storage space between the processes, is transported by the transport device, and the yard is stacked according to the payout order to the subsequent process of the yard. When creating a final mountain made of metal materials piled up in order, a moving metal material that is a metal material transported from the initial mountain to the final mountain in the depot, and the final mountain in a place of the initial mountain as it is. Non-movable metal material fixed to the location of the initial mountain to create a, the yard management method for at least determining the metal material constituting the final mountain, the metal constituting the initial mountain In the initial mountain, a non-moving uppermost metal material discriminating variable indicating whether or not the metal material is the uppermost metal material in the non-moving metal material, and the moving metal material is arranged in the final mountain. Whether or not moving metal A final mountain allocation variable, an allocation mountain identification variable indicating whether or not the last mountain candidate mountain, the original mountain and the new mountain, is to be the final mountain, as a decision variable, and the identification information of the initial mountain, A metal material information obtaining step of obtaining metal material information including identification information of the metal material at each stacking position of the initial mountain and the payout order of the metal material; and the movement that can be arranged at the base mountain. A first constraint equation expressing the condition of the metal material using the decision variable, and a second constraint equation expressing the condition of the moving metal material that can be arranged in the new mountain using the decision variable A constraint expression including a constraint expression setting step of setting based on the metal material information, a term for evaluating the total number of the moving metal materials, and an objective function including a term for evaluating the total number of the final peaks, Eye set based on the metal material information Performing an optimization calculation by a mathematical programming method, wherein a function setting step and deriving, as an optimal solution, the value of the decision variable when the value of the objective function is minimum or maximum within a range satisfying the constraint expression. Wherein the base mountain comprises at least a part of the mountain formed in the yard at the time 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.

  A program according to the present invention causes a computer to function as each unit of the yard management device.

  According to the present invention, when creating a metal material transfer plan for reloading a metal material from an initial mountain to a final mountain, minimizing the total number of final mountains and minimizing the number of metal materials moving from the initial mountain Can be balanced with

It is a figure showing an example of functional composition of a yard management device. It is a flowchart explaining an example of a yard management method. FIG. 9 is a diagram showing calculation results in the invention example and comparative example 1. It is a figure which shows the calculation result in the invention example and the comparative example 2. It is a figure showing an example of a 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 initial pile pile, given the initial pile, the steel material that should be moved (transported) and the steel material that should not be moved (transported) are determined from the steel material that constitutes the initial mountain. At the same time as determining the total number of piles and the final pile. Then, assuming that only the steel material to be moved is moved, the transfer order of each steel material when transferring from the initial mountain to the final mountain is derived by a known method. In addition, it is assumed that, at least in part of the initial mountain, the steel materials (slabs) manufactured in the steelmaking process are not stacked in the order of transportation to the rolling process. In the following description, the order in which the steel materials are transported to the rolling process will be referred to as a payout order as necessary. Further, a steel material determined to be moved according to the present invention is referred to as a moving steel material as necessary, and a steel material determined not to be moved is referred to as a non-moving steel material as necessary. Further, in the following description, the “moving steel material” and the “non-moving steel material” may be referred to as “moving steel material” and “non-moving steel material”, respectively.

First, points of interest in implementing the present embodiment will be described.
In the present embodiment, a problem of simultaneously minimizing the total number of the final peaks and the total number of the moving steel materials is considered. Here, all steel materials can be identified as either moving steel materials or non-moving steel materials. Further, a steel material that can be a non-moving steel material can be determined from the pile shape of the initial mountain. The steel material that can be a non-moving steel material is a portion in which the product order from the bottom of the initial mountain is the payout order (the payout order is descending from bottom to top). In addition, in each initial mountain, if a steel material is a non-migrating steel material, a group of steel materials below the steel material must also be a non-migrating steel material. This is because, in order to move a group of steel materials below the non-moving steel material, the non-moving steel material must be moved. Therefore, among the non-migrating steel materials in each initial mountain, all the steel materials above the uppermost non-migrating steel material are the moving steel materials.

  In order to simultaneously minimize the total number of the final peaks and the total number of the moving steel materials, it is necessary to determine the moving steel material in consideration of the feasibility of the final mountain. Therefore, not only the moving steel material, but also the appearance of the final pile after the transshipment (the constituent steel material constituting each final pile) is specified from the decision variables. The stacking constraint on the final mountain can be realized by a constraint that prohibits the specific two steel materials from being arranged on the same final mountain. Further, there is no guarantee that the minimum value of the total number of the last peaks is determined by ceil (n / h). Therefore, the total number of the last 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 last peak, and ceil (n / h) represents a ceiling function (the minimum integer value of n / h or more).

From these requests, in the present embodiment, in the present embodiment, the moving steel material final mountain allocation variable z _ij (1 is set when the steel material i is moved and placed on the original mountain or the new mountain j, and is 0 (zero) otherwise. (1 variable) is introduced as a decision variable. Further, an assigned mountain identification variable q _j (0-1 variable which becomes 1 when the mountain j which is a candidate for the final mountain as the final mountain and becomes 0 (zero) otherwise) is introduced as a decision variable. The non-moving uppermost steel discrimination variable x _i (1 if the steel i constituting a certain initial mountain is the uppermost non-moving steel among the non-moving steels, and 0 (zero) otherwise. Are introduced as decision variables. A 0-1 variable that becomes 0 and a movement presence / absence determination variable y _i (a 0-1 variable that becomes 1 when the steel material i is a moving steel material and becomes 0 (zero) otherwise).

  In the present embodiment, using these decision variables, the total number of final peaks, the objective function aiming at minimizing the total number of moving steel materials, the decision variables, the moving steel materials, and the constraint formulas related to the final mountain, Construct and derive a decision variable that minimizes or maximizes the value of the objective function within a range that satisfies the constraint equation. Hereinafter, an example of the details will be described.

(Premise of the problem)
In the present embodiment, it is assumed that the initial pile shape and the payout order (rolling order) of each steel material are given.
Here, a set of steel materials is denoted as N = {1, 2,..., N}.

  The initial mountain includes a Motoyama and a virtual mountain. The original mountain as the initial mountain is the mountain itself 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 for which the final mountain is created. Thereafter, even if some of the steel materials constituting the initial mountain are piled on another mountain, if some of the steel materials constituting the initial mountain remain in the initial mountain, the mountain is also a former mountain. And In this way, the original mountain is at least a part of the mountain formed in the yard at the time when the steel material information is created (that is, when the final mountain is created), and is a mountain whose location does not change from the mountain. is there. The virtual mountain is a steel material which is not yet piled 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 for which the final mountain is to be created. This is a mountain assuming that the earlier the mountain, the higher the pile. In the present embodiment, it is assumed that all steel materials that have not arrived at the yard and have not yet been piled up are piled up in one virtual mountain among the steel materials for which the final mountain is to be created. As described above, in the present embodiment, it is assumed that steel materials that have not arrived at the yard and have not yet been piled up are also piled up as virtual piles (that is, all steel materials for which the final pile is to be created are piled up at the yard). ), And its appearance is given. In addition, it is assumed that there is no non-moving steel material with respect to the steel material (unarrived material) constituting the virtual mountain, and all of the steel material is a moving steel material. Therefore, the steel material constituting the virtual mountain 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 appearance of the initial mountain is known, but the appearance of the final mountain is unknown. It is assumed that the last mountain is a mountain piled up from the top in the order of payout, and that the total number of the last mountain is also unknown.
In addition, the number of times of transfer from the initial mountain (initial yard) to the final mountain (final yard) is a maximum of two times for any steel material. That is, the steel material transported twice is temporarily placed, but the steel material transported to the temporary mountain (temporary storage) is always transported to the final mountain (final storage) at the next transport, and a different temporary material is used. It shall not be transported between mountains (temporary storage).
Further, the storage area of the initial mountain having the non-moving steel material is the storage area of the final mountain including the non-moving steel material. The final mountain (new mountain) composed only of the moving steel material is placed in a different yard from the yard of the initial mountain including the moving steel material.

Further, in the present embodiment, the following width constraint, length constraint, and height constraint are taken as stacking constraint.
Width restriction If the width of a steel material is smaller than the width of any steel material located under the steel material, the steel material can be unconditionally placed on the steel material located under the steel material. If 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) is reduced. If the difference is less than a reference value (for example, 200 [mm]) determined by the work constraint, the certain steel material can be placed on the steel material located below, but cannot be placed beyond that.

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

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

  That is, the length constraint is satisfied when the length of a certain steel material is shorter than the length of a steel material located under the certain steel material, and when the length of a certain steel material is below the certain steel material. And the difference between the certain steel material and each of the widths of all the steel materials located under the certain steel material is less than a reference value (for example, 2000 [mm]). Is the case.

-Height restriction The number of steel materials that can be piled up as one final mountain must be not more than the upper limit value h of the final mountain. The upper limit value h of the height of the last peak is, for example, 10.

  The storage area of the initial mountain (Mt. Motoyama) where the non-moving steel material is located is the storage area of the final mountain. The last mountain consisting only of mobile steel is Shinzan. As mentioned above, the yard of the new mountain is different from the yard of the initial mountain.

(Decision variables)
<Determining variables used in determining non-moving steel and moving steel, and determining the total number of piles and the final appearance>
In this embodiment, for any steel i, immobile and uppermost steel discriminatory variable x _i, the decision variable and the movement whether the discriminatory variable y _i. The non-moving uppermost steel material discriminating variable x _i is defined as in the following equation (1), and the movement presence / absence discriminating variable y _i is defined as in the following equation (2). It is assumed that the variable i is numbered in the order of payout of the steel materials (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 mountain is the uppermost non-moving steel material among the non-moving steel materials, and 0 (zero) otherwise. 0-1 variables. Thus, the initial mountain, if non-moving steel is not even one, non moving uppermost steel discriminatory variable x _i for all steel i constituting the initial mountain becomes 0 (zero). On the other hand, the initial mountain, if non-moving steel has one or more, only the non-moving top steel discriminatory variable x _i with respect to the non-moving steel i in top of the non-moving steel becomes 1. In this case, the non-moving top steel discriminatory variable x _i with respect to other steel i constituting the initial mountain will (also the steel i is a non-moving steel) 0 (zero). That is, for one initial peaks, the number of non-moving steel top steel discriminatory variable x _i is 1 is 1 at a maximum.
The movement presence / absence determination 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) otherwise.

Further, in the present embodiment, the moving steel material final mountain assigned variable z _ij and the assigned mountain identification variable q _j are determined variables. The moving steel material final mountain allocation variable z _ij is defined as in the following equation (3), and the allocated mountain identification variable q _j is defined as in the following equation (4). Here, j is identification information (ID) for uniquely identifying each mountain. For example, the identification number of the steel yard in the yard can be adopted as j.

The moving steel material final mountain allocation variable z _ij is obtained by converting the steel material i that is the moving steel material to the original mountain j (= 1,..., P (p> 1)) or the new mountain j (= p + 1,..., P + m (m = n)) is a 0-1 variable that is 1 if placed in, and 0 (zero) otherwise. When the steel material i is a non-moving steel material (that is, a steel material i in which the movement presence / absence determination variable y _i is 0 (zero)), the moving steel material final mountain allocation variable z _ij is 0 for an arbitrary final mountain j. (Zero).
The assigned mountain identification variable q _j (j = 1,..., P, p + 1,..., P + m) is the original mountain j (= 1,..., P) or the new mountain j (= p + 1, .., P + m) are 1 if they are assigned, and 0 (zero) otherwise. Note that, as described above, Motoyama j and New mountain j are mountains that are candidates for the final mountain.

<Decision variables used when determining the transport order>
In the present embodiment, after determining the non-moving steel material and the moving steel material and determining the appearance of the final mountain, only the moving steel material is moved (conveyed). The transfer order of each steel material i is determined. The method of determining each steel material i when transferring 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 Literature 2, the initial transfer time k_it [i] of the transfer target steel material i and the final transfer time k_ft [i] of the transfer target steel material i are determined variables. Since the details of these decision variables are described in Patent Document 2, their detailed description is omitted here, and only the outline is described.

  For unarrived materials, the time at which transport to the yard is first started after arriving at a receiving entrance such as a receiving table is the initial transport time k_it [i] of the steel material i to be transported. In the already arrived material, the time at which transport is first started from the storage site at the current time is the initial transport time k_it [i] of the steel material i to be transported. The time at which the transfer of the transfer target steel material i to the final mountain is started is the final transfer time k_ft [i] of the transfer target steel material i.

(Functional configuration of the yard management device 100)
FIG. 1 is a diagram illustrating an example of a functional configuration of the yard management device 100. The hardware of the yard management device 100 is realized by using, for example, an information processing device including a CPU, a ROM, a RAM, an HDD, and various interfaces, or dedicated hardware. FIG. 2 is a flowchart illustrating an example of the 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 on steel materials to be piled up. The steel material information includes basic steel material information, information for specifying the initial pile shape of each steel material, information for specifying the upper limit value h of the final mountain height, and weighting factors k ₁ and k ₂ .

The steel basic information includes identification information, a payout order, the number of steels, a width, and the like for each steel (the set of steels N = {1, 2,..., N}) for which the final mountain is to be created. , Length information is included. Here, for simplicity of description, it is assumed that all steel materials have the same thickness.
The identification information is identification information (steel material ID) for uniquely identifying each steel material.
The order of payout is the order of payout of each steel material (the order of transport to the rolling process). In the present embodiment, since the identification information is in the order of payout, the order of payout does not need to be included in the basic steel material information.

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

  Examples of the form of acquiring the steel material information include an input operation of a user interface of the yard management device 100, transmission from an external device, and reading from a portable storage medium.

[Constraint equation / objective function setting unit 102, constraint equation setting step S202, objective function setting step S203]
The constraint expression / objective function setting unit 102 sets a constraint expression that expresses the above-mentioned constraint by an expression and an objective function that expresses the above-mentioned purpose by an expression.
<< Constraint formula >>
First, a constraint expression will be described.

(A) Restriction on Moving Steel Material A set of steel material subsets S _k ({N) _obtained by dividing the steel material set N is denoted as S = {S ₁ , S ₂ ,..., S _r }. Each subset S _k of this steel is the initial mountain. Further, as described above, 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) hold.

In each initial mountain S _k , a partial mountain obtained by extracting from the initial mountain S _k all the steel parts whose product order is the order of payout from the bottom row (the order of payout is descending from bottom to top). max (S _k ). Here, the partial mountain is a mountain formed by stacking all the steel materials below a certain steel material of the given mountain in the same order as the given mountain. At this time, a steel material not in max (S _k ) is always a moving steel material. This is represented by the following equations (7) and (8).

The expression (7) indicates that the steel material i in the portion excluding max (S _k ) from the initial mountain S _k moves (becomes a moving steel material). (8) are steel i in the initial mountain S _k to the portion excluding the max (S _k) denotes that the initial in mountain S _k, does not become steel in top of the non-moving steel . (7) and Equation (8), in each initial mountain S _k, steel i the product order from the lowermost payout order (payout order from bottom to top is descending) not in the be moved expressed.

(B) limited in the early mountain S _k for the non-moving top steel discriminatory variable x _i, the maximum value of the number of steel i of immobile uppermost steel discriminatory variable x _i is 1 (x _i = 1) is 1 is there. Therefore, the following equation (9) holds.

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

(C) restrictions on the movement whether the discriminatory variable y _i in each initial mountain S _k, steel is above the moving steel i moves all. Accordingly, when the payout order (= i (identification number of steel material)) when viewed from the bottom to the top at each initial mountain S _k is k ₁ , k ₂ ,..., The following (11) The formula holds.

(D) all steel i constraint defines the relation of the non-moving and the uppermost steel discriminatory variable x _i and the mobile whether discriminatory variable y _i is identified uniquely to one of the moving steel and non-moving steel. In the initial mountain _Sk , the number of stacked stages counted from the lowest stage of the steel member i (the number of steel plates including the steel member and located below it and the number of stacked stages at the lowest stage is set to 1) is represented by b. When _i, the total number of non-moving steel, non-migrating with the uppermost steel discriminatory variable x _i, it can be expressed as _Σ i∈N b _i · x _i. Also, the total number of moving steel materials can be expressed as _{∈ i N} y _i using the movement presence / absence determination 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 the steel materials constituting the initial mountain (the original mountain and the virtual mountain).

If the movement whether the discriminatory variable y _i is 1 (y _i = 1) for the steel i, the initial mountain in S _k, the steel i and non-moving top steel discriminatory variable x _i for all the steel i above it Becomes 0 (zero, x _i = 0). Conversely, movement whether the discriminatory variable y _i is 0 (zero, y _i = 1) for the steel i If, in the initial mountain S _k, and the steel i, among the steel i above it, one steel i , Only the non-moving uppermost steel material discriminating variable x _i becomes 1 (x _i = 1). Therefore, for a steel material i∈S _k , at the initial mountain S _k , a set of the steel material i and the steel material i above it is defined as S _k ^↑ (i) (see the following equation (14)). ) And the following equation (13) is satisfied.

(13), for any steel i initial mountain S _k, if the steel material i is a mobile steel, rather motionless steel above it, if the steel i is not moving steel, the steel i or one of the steel materials above the steel material i is the non-migrating steel material located at the top of the non-migrating steel materials (that is, there is only one non-migrating steel material where x _i = 1).

(E) Constraint defining relationship between moving steel material final mountain allocation variable z _ij and movement presence / absence determination variable y _i Arbitrary steel material i is a source mountain j (= 1,..., P (p> 1)) or It must be located at the new mountain j (= p + 1,..., P + m (m = n)). Further, as described above, the moving steel material final mountain allocation variable z _ij for the steel material i that is a non-moving steel material (that is, the steel material i for which the movement presence / absence determination variable y _i is 0 (zero)) is 0 for any mountain j. (Zero, z _ij = 0). Therefore, the following equations (15), (15 ′), and (15 ″) hold.

The expression (15) indicates that if the steel material i is a moving steel material, the steel material i is a steel material that moves to one of the original mountain j and the new mountain j, and if the steel material i is a non-moving steel material, This indicates that the steel material i does not move to any of the former mountain j and the new mountain j. The expression (15 ′) indicates that the steel material i in the portion excluding the max (S _k ) from the initial mountain S _k is a steel material that moves to any one of the original mountain j and the new mountain j. Equation (15 ″) indicates that the steel material i in the portion of max (S _k ) in the initial mountain S _k moves to any one of the original mountain j and the new mountain j, and the original mountain j and the new mountain j (That is, it may be a moving steel material or a non-moving steel material).

(F) Motoyama constraints upon reloading to (constraint that defines the moving steel final mountain assigned variable z _ij, and the non-moving top steel discriminatory variable x _i, the mobile steel final mountain assignment variables z _ij and allocation mountain identification variable q constraint that defines the relationship with _j )
For the steel material i_k (∈max (S _k )) constituting the original mountain (initial mountain) k (= 1,..., P), a set of steel materials i that can be placed on the steel material i_k is represented by U (i_k ). Steel i_k is, when a non-moving steel in top of the non-moving steel in Motoyama k (i.e., if the non-moving top steel discriminatory variable x _i is _{1 (x i = 1))} , the steel i_k The steel material i that cannot be loaded cannot be placed on the base mountain k to which the steel material i_k belongs. This is expressed by the following equation (16). According to the expression (16), it is possible to suppress the unrealizable final mountain from being obtained.

  Here, in the present embodiment, a set U (i_k) of steel materials i that can be placed on the steel material i_k is specified by the same mountain-forbidden steel material set F. The same mountain-forbidden steel material pair set F is a set of arbitrary two steel material pairs {i, j} N as shown in the following equation (17), and at least one of the width condition and the length condition described above. It is a set of two pairs of steel materials that do not satisfy one of them. In addition, 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 below the steel material i and the candidate steel material to be put on the steel material i_k is not included in the same mountain-forbidden steel material pair set F, the steel material i_k is included in the steel material i_k. The steel material that is a candidate to be mounted is included in a set U (i_k) of steel materials i that can be mounted on the steel material i_k.

In addition, the number of steel materials that can be arranged on the steel material i_k in the last mountain is limited by the height constraint described above. Product number when counted from the bottom in the steel i_k belonging to Motoyama k a b _i (including the steel product number in the case of it from the 1 to the bottom of the product number is a number of steel below) If it _ _k, holds the following equation (18).

  Equation (18) indicates that the total number of steel materials i moving to the original mountain k is the number of steel materials that can be arranged on the uppermost non-movable steel material among the non-migrating steel materials belonging to the original mountain k (initial mountain). Must be less than or equal to the upper limit of. The right side of the expression (18) represents an empty space (the number of steel materials) formed on the steel material i_k at the Motoyama k. According to the expression (18), it is possible to suppress the unrealizable final mountain from being obtained.

The initial mountain k (= 1, ···, p ) steel i_k belonging to is a non-moving steel in top is (non-moving top steel discriminatory variable x _i of the non-moving steel material 1 (x _i = 1)), the initial mountain (original mountain) k is the last mountain, and therefore the following equation (19) holds.

(G) Mountain height constraint on the last mountain other than Motoyama (new mountain) The constraint on the height of the new mountain j (= p + 1,..., P + m), which is the last mountain other than Motoyama, is expressed by 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 expression (20), it is possible to suppress the unrealizable final mountain from being obtained.
In addition, as for the new mountain j, it is preferable to limit the solution space so that the one with the smaller identification information is preferentially constructed as in the following equation (20 ′).

The expression (20 ′) is not applied to Motoyama ({j∈ ｛1,..., P｝).
(H) Same last mountain prohibition constraint (width, length constraint)
When the moving steel material is placed on the last mountain, the last mountain satisfies the stacking constraint (width constraint, height constraint), so that the pair of two steel materials i1 and i2 belonging to the same mountain-forbidden steel material pair set F is replaced with the same final material. A constraint that prohibits placement at the mountain j is determined as in the following equation (21).

  Note that 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 formula (17). According to the expression (21), it is possible to suppress the unrealizable final mountain from being obtained.

The constraint expression / objective function setting unit 102 converts the expressions (7) to (13), (15), (15 ′), (15 ″), (16) to (21) into, for example, On the other hand, by setting i, j, S, S _k , p, n, F, h, b _i , and m, the expressions (7) to (13), (15), (15 ′), (15 ″) and the constraint equations (16) to (21) are set.

<< Objective function >>
Next, the objective function will be described.
As described above, the present embodiment aims at minimizing the total number of moving steel materials (or maximizing the total number of non-moving steel materials) and minimizing the total number of final hills. The objective function J is used.

In the present embodiment, as shown in Expression (22), a weighted linear sum of the total number of moving steel materials (Σy _{i in} Expression (22)) and the total number of final hills (Σq _{j in} Expression (22)) is obtained. Function. The weighted linear sum is obtained by adding a value obtained by multiplying a weight coefficient k ₁ for the total number of moving steel materials and a weight coefficient k ₂ for the total number of final mountains to the total number of moving steel materials and the total number of final mountains, respectively. . Weight coefficient k ₁ to the total number of mobile steel, the evaluation of the total number of mobile steel is a coefficient representing a balance between the evaluation of the total number of final mountain. Weight coefficient k ₂ to the total number of final mountain, the evaluation of the total number of final mountain is a coefficient representing a balance between the evaluation of the total number of final mountain. If the weight coefficient k ₁ to the total number of mobile steel than the weight coefficient k ₂ to the total number of final mountain value larger, for example, towards the total number of mobile steel than the total number of final mountain one less that reduced one However, the amount by which the value of the objective function J decreases is large. Therefore, the objective function J in this case is an objective function that emphasizes evaluation on the total number of moving steel materials rather than evaluation on the total number of final peaks. Conversely, when a value larger the weighting coefficient k ₂ of the total number of final mountain than the weight coefficient k ₁ to the total number of mobile steel, for example, one the total number of final mountain than one less the total number of mobile steel As the number decreases, the amount of decrease in the value of the objective function J increases. Therefore, the objective function J in this case is an objective function that emphasizes evaluation on the total number of final hills rather than evaluation on the total number of moving steel materials. As described above, in the objective function J of the equation (22), it is possible to balance the evaluation with respect to the total number of moving steel materials and the evaluation with respect to the total number of final hills by the weight coefficients k ₁ and k ₂ . That is, the equation (22) is based on the balance of such evaluations (under the condition of such evaluation balance), the minimum value of the total number of moving steel materials and the minimum value of the total number of final peaks are obtained. Is the objective function for which As described above, by using Equation (22) having the total number of the moving steel materials and the total number of the final hills as the decision variables as the objective function J, it is possible to minimize the total number of the moving steel materials and the total number of the final hills. You will be able to balance.

The constraint equation / objective function setting unit 102 sets the objective function J of the equation (22) by, for example, 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). In the range, the decision variables (the non-moving uppermost steel material discriminating variable x _j , the moving existence discriminating variable y _i , the moving steel material final mountain assigning variable z _ij , and the assigning variable when the value of the objective function J in Equation (22) is minimized) The mountain identification variable q _j ) is calculated as the optimal solution. The calculation of the optimal 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 such as a mixed integer programming.

[Post-processing unit 104, post-processing step S205]
As described above, the optimal solution of the non-moving uppermost steel material discriminating variable x _j , the moving presence / absence discriminating variable y _i , the moving steel material final mountain allocation variable z _ij , and the allocated mountain identification variable q _j is derived. It is possible to determine whether or not to move each steel material included in N (that is, whether to move the steel material or the non-movable steel material), the total number of the final hills, and the stacked shape of the final hills. Note that, as described in (Premise of Problem), the pile shape of the final mountain is determined by arranging the steel materials from the top in the order of dispensing. The final mountain is either a fixed mountain or a new mountain. The fixed mountain is a mountain including a non-moving steel material among the original mountains, and the new mountain is a mountain consisting only of the moving steel material. In this way, the non-moving steel material and the steel material constituting each final mountain are determined.

  Then, assuming that the non-moving steel material is not moved (transported) but is moved (transported) only with respect to the moving steel material, the transfer order of each steel material when reloading the steel material from the initial mountain to the final mountain is determined as post-processing. Is also good. In such a case, the post-processing unit 104 is activated. The post-processing unit 104 determines the order in which the steel materials are transported when the steel materials are reloaded from the initial mountain to the final mountain. This determination can be realized by a known technique. As described above, in the present embodiment, the transfer order of the steel materials when the steel materials are reloaded from the initial mountain to the final mountain is determined using the method described in Patent Document 2. As shown in Patent Document 2, the post-processing unit 104 determines the value of the transfer time objective function as a minimum within a range that satisfies the transfer constraint equation (the initial transfer time k_it [i] and the final transfer time of the transfer target steel i). The transfer order of each steel material is determined by deriving the time k_ft [i]). However, as a transport constraint equation, a constraint equation indicating that a non-movable steel material is not moved (transported) is added to the constraint equation described in Patent Document 2. Note that, in Patent Document 2, the initial peak in this specification is referred to as Motoyama, and the final peak is referred to as Motoyama. Since the specific contents of the transfer constraint equation and the transfer time objective function are described in Patent Document 2, their detailed description is omitted here. Further, as described in Patent Literature 2, the post-processing unit 104 determines what kind of steel material is determined to be temporarily placed when determining the transfer order of the steel material when the steel material is reloaded from the initial mountain to the final mountain. Alternatively, it may be determined whether the pile is to be loaded on a temporary mountain (a mountain where temporary placement is unavoidable when transferring from the initial mountain to the final mountain after the present time). Such determination of the pile shape of the temporary mountain can also be realized by a known technique. If there is enough room, for example, the steel material determined to be temporarily placed may be placed flat in an empty storage space (only one piece may be placed), and it is not essential to create a temporary mountain. Absent.

[Output unit 105, output step S206]
The output unit 105 outputs the information derived from the post-processing unit 104 and indicating the transport order of the steel materials included in the steel material set N from the initial mountain to the final mountain. The output unit 105 may output, in addition to or in place of this information, identification information of the moving steel material and the non-moving steel material, information on the total number of the final mountains, and information on the appearance of the final mountains. The output form includes at least one of display on a computer display, storage in a storage medium inside or outside the yard management device 100, and transmission to an external device. Examples of the external device include a crane or a control device that controls the operation of the crane.

(Summary)
As described above, in the present embodiment, the yard management device 100 sets the constraint indicating the condition of the moving steel material that can be placed on the base mountain as the determination variable (the non-moving uppermost steel material discriminating variable x _i and the moving steel material last mountain allocation variable). z _ij ) and constraints indicating the conditions of the moving steel material that can be placed on the new mountain using decision variables (moving steel material final mountain allocation variable z _ij and allocation mountain identification variable q _j ). In order to satisfy the formula, a decision variable for minimizing the value of the objective function J for the purpose of minimizing the total number of moving steel materials and the total number of final peaks is derived, and non-moving steel materials and moving steel materials are determined. , The total number of the final mountains, and the appearance of the final mountains. Therefore, when creating a steel material transfer plan for transferring the steel material from the initial mountain to the final mountain, when creating a metal material transfer plan for transferring the metal material from the initial mountain to the final mountain, Can be balanced with minimizing the total number of metal materials moving from the initial mountain.

<Example of calculation>
Next, a calculation example will be described. In the present embodiment, the total number of the final peaks and the total number of the moving steel materials are minimized by appropriately selecting the non-moving steel materials. Therefore, in the technique described in Patent Literature 3, a 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 bottom to top) is not moved. By comparing the method of deriving the stacked shape of the final mountain without moving as a steel material with the method of the present embodiment, it is shown that the method of the present embodiment can reduce the total number of final mountains. In the method according to the present embodiment, the transfer order of each steel material is determined by the method described in Patent Document 2 in the post-processing.
In addition, in the technology described in Patent Document 3, a method of deriving the stacked shape of the final mountain using all the moving steel material is compared with the method of the present embodiment, and it is shown that the total number of the final mountains does not change in both methods. .

Here, an 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 is omitted here.
In Patent Document 3, the mountain sorting / transport order variable x [i] [m] [s], the temporary placement judgment variable y [p] [s ₁ ] [s ₂ ], and the optimum mountain existence judgment variable δ [m] Are determined variables. As a constraint expression, there is a constraint that one steel material i is not assigned to a plurality of transport orders and a plurality of final hills (unique constraint of a transport lot), and a plurality of steel materials i or final A constraint that the mountain m is not assigned (unique constraint in the transport order) and a stacking constraint (length constraint, width constraint, height constraint) are used. The objective function as J ', as shown in the following equation (23), using a weighted linear sum of the objective function J ₂ for evaluating the total transport times as the objective function J ₁ to evaluate the total number of peaks in the final mountain .

  In equation (23), the weighting factors Weight1 and Weight2 are set in advance depending on how much importance is placed on each evaluation item. Shows the balance of evaluation. For example, when the number of final hills is an important evaluation item rather than the total number of times of transfer of the steel material, the magnitude of the weight coefficient Weight1 is made larger than the magnitude of the weight coefficient Weight2.

In Patent Document 3, a decision variable (a mountain sorting / transport order variable x [i] [m] [s] and a temporary placement judgment variable y [ p] [s ₁ ] [s ₂ ] and the optimum mountain existence determination variable δ [m]) are obtained. From these determined variables, it is possible to obtain the transport order of each steel material i and the appearance of the final pile. Here, among the variables in which the optimal solution y _opt [p] [s ₁ ] [s ₂ ] of the provisional judgment variable becomes 1, if there is a variable satisfying s ₁ > s ₂ , among the steel material pair p, , The steel material above is the target for temporary placement. In this manner, the steel material i to be temporarily placed can be obtained.

Patent Document 3 assumes that all steel materials are moved. Therefore, when the method described in Patent Document 3 is applied assuming that only the moving steel material is moved (transported) without moving (transporting) the non-moving steel material as in the present embodiment, the following is necessary. There is.
First, a mountain sorting / transport order variable x [i] [m] [s] for the final mountain m of the steel material i that 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 mountain m in the transport order s, and is 0 (zero) otherwise. 0-1 variables.

For example, additional When allocating initial mountain comprising two steel steel i _1, i ₂ as a non-moving steel to final Mountain m _1, as Sekisugata constraints on the final Mountain m _1, the following equation (24) Constraints There is a need to. Note that F (i ₁ ) represents a set of steel materials that cannot be the same final mountain as the steel material i ₁ .

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

Here, _Hf 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 last peak described by the thickness and the number, respectively. The thickness [i] is the thickness of the steel material i.

(Calculation condition)
In the invention example, the initial pile shape is given based on the operation data, and the non-moving steel material and the moving steel material and the total number and the final shape of the final mountain are determined by the algorithm described in the present embodiment. Then, on the premise of this, the post-processing based on Patent Document 2 is executed to determine the transfer 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 bottom to top) is a non-moving steel material, With the method described in Patent Document 3, the pile shape of the final mountain and the order of transport of the steel materials are determined at the same time. Further, in Comparative Example 2, all steel materials are assumed to be moving steel materials, and on the premise of this, the appearance of the final mountain and the order of transport 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 last peak was set to 10 steps (h = 10). In equation (22), the weighting factor k ₁ for the total number of moving steel materials and the weighting factor k ₂ for the total number of final hills were respectively set to 1 and 10 (k ₁ = 1, k ₂ = 10). Further, the weighting coefficients Weight1 and Weight2 in the equation (23) are set to 10, 1 (Weight1 = 10, Weight2 = 1), respectively.

The computing environment is as follows.
Processor: Intel (registered trademark) Xeon (registered trademark) CPU E5-2687W @ 3.1GHz (2 processors)
Mounting memory (RAM): 128 GB
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 the moving steel materials and the total number of the final peaks were derived for each piece of the steel material information by the method of the above-described invention example, comparative example 1, and comparative example 2. The results are shown in FIGS.

FIG. 3 is a diagram showing calculation results in the invention example and the comparative example 1 in a table 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 bottom to top) is the non-movable steel material. Based on this, the appearance of the final pile and the order of transport of the steel materials are determined simultaneously by the method described in Patent Document 3. 3 and 4, the number of SLs is the total number of slabs (steel materials) constituting the initial mountain. The number of fixed peaks is the number of Motoyama that became the last peak.
As shown in FIG. 3, in the example of the invention, as compared with the comparative example 1, the total number of moving steel materials is increased by only about 3 on average (about 12%), and the total number of final peaks is increased from 5.5 to 3.7. It can be seen that it can be reduced by about 33%.

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

In the yard, when carrying out the work (rearrangement) of reloading the steel materials of the initial piles that are not in the order of dispensing from the top in the order of dispensing from the top, the steel materials are moved for each mountain and a new storage area If there is a part at the bottom of the initial mountain where the payout order is descending from bottom to top, make use of this as much as possible and only transfer the upper part of the initial mountain. May reduce the total number of transports. In the present embodiment, for the latter case, an algorithm for solving the problem of minimizing the total number of moving steel materials while maintaining the total number of final mountains at a minimum (this algorithm) has been developed. Then, in the calculation example, it was shown by a verification test based on actual data that the minimum number of peaks obtained under the condition without the non-moving steel material can be realized while securing the maximum total number of non-moving steel materials.
As described above, given the initial pile pile shape, when the steel material of the initial pile is transshipped from the top to the final pile piled up in the order of dispensing, while minimizing the total number of the final pile, A transfer transfer plan for maximizing the total number (minimizing the total number of moving steel materials) can be created.

(Modification)
In the present embodiment, the minimization problem for minimizing the value of the objective function J in Expression (22) has been described as an example. However, a maximization problem may be obtained by, for example, multiplying each term on the right side of the equation (22) by (−1).

Further, in the present embodiment, the case where the steel material is moved (conveyed) one by one has been described as an example. However, the method of the present embodiment can be applied even when the movement (conveyance) 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 (a 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 smaller than the minimum width of a steel group located below the certain steel group, or when a certain steel group is This is the case where the maximum width is wider than the minimum width of the steel group located below the certain steel group, and the difference between the two widths is less than a reference value (for example, 200 [mm]). The length constraint is satisfied, for example, when the maximum length of a certain steel group is shorter than the minimum length of a steel group located below the certain steel group, and when the maximum length of a certain steel group is In this case, the length is longer than the minimum length of the steel group located below the certain steel group, and the difference between the lengths is smaller than a reference value (for example, 2000 [mm]). Further, for example, the number of steel materials can be expressed using the number w _i of steel materials included in (one) steel material group i.

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

  In addition, as a place between processes, a place between two manufacturing processes is targeted, and as a metal material, a semi-finished product may be targeted, or as a place between processes, a place between a manufacturing process and a shipping process is targeted. Alternatively, a final product may be used as a metal material. In this case, when a plurality of metal materials are housed in a container for transportation and arrangement, the container housing the metal materials may be handled as one metal material. Further, the storage space between the steps is not limited to the storage space in the metal manufacturing process, but may be a general distribution and transportation between the processes. In the logistics field, the present invention is not limited to the contents but can be applied 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 modifications>
The embodiment of the present invention described above can be realized by a computer executing a program. 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 nonvolatile memory card, a ROM, and the like can be used.
In addition, the embodiments of the present invention described above are merely examples of specific embodiments for carrying out the present invention, and the technical scope of the present invention should not be interpreted in a limited manner. Things. That is, the present invention can be implemented in various forms without departing from the technical idea or the main features.

(Relationship with claims)
An example of the relationship between the claims and the embodiment will be described below. It should be noted that the description of the claims is not limited to the description of the embodiment, as described in the modified examples.
<Claims 1 and 8>
Immobile uppermost metal material determining variables, for example, correspond to the non-moving top steel discriminatory variable x _i.
The moving metal material final mountain allocation variable corresponds to, for example, the moving steel material final mountain allocation variable z _ij .
The assigned mountain identification variable corresponds to, for example, the assigned 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 by using, for example, steel material information. The identification information of the initial mountain and the identification information of the metal material at each stacking position of the initial mountain are, for example, information for identifying the appearance of the initial mountain of each steel material (identified by the initial mountain ID and the initial mountain ID). This is realized by using a steel material ID located at each stack of the initial mountain.
The constraint equation setting means (step) is realized by using, for example, the constraint equation / objective function setting unit 102 (constraint equation setting step S202).
The first constraint expression is realized, for example, by using at least one of the expressions (16) and (18).
The second constraint expression is realized, for example, by using at least one of the expressions (20) and (21).
The objective function setting means (step) is realized, for example, by using the constraint equation / objective function setting unit 102 (constraint equation / objective function setting step S203).
An objective function including a term for evaluating the total number of the moving metal materials and a term for evaluating the total number of the final peaks is realized by using, for example, Equation (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 last peaks is, for example, the second term on the right side of the equation (22). Corresponding.
The optimization calculation means (step) is realized, for example, by using the optimization calculation unit 103 (optimization calculation step S204).
<Claim 2>
The movement presence / absence determination variable is realized, for example, by using the movement presence / absence determination variable y _i .
The third constraint equation is realized by using, for example, equation (15).
<Claim 3>
The fourth constraint equation is realized, for example, by using 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 Expression (12). The total number of the metal materials forming the initial mountain corresponds to, for example, the right side of Expression (12).
<Claim 4>
The fifth constraint equation is realized by using, for example, equation (13).
When the metal material is the moving metal material, the metal material located above the metal material in the initial mountain does not become the non-moving metal material. This 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 peak is located at the top of the non-moving metal material. Being a certain metal material corresponds to, for example, a case where the value of the movement presence / absence determination variable y _i is 0 (zero) in the equation (13).
<Claim 5>
The stack figure constraint corresponds to, for example, a width constraint and a length constraint.
The set of metal materials that can be mounted on the metal material corresponds to, for example, a set U (i_k) of steel materials i that can be mounted on the steel material i_k.
The Motoyama placement constraint equation corresponds to, for example, equation (16).
When the metal material is the uppermost non-moving metal material among the non-moving metal materials in the initial mountain, for example, in the expression (16), the moving uppermost steel material discriminating variable x _{i — k} is 1 This 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 arranged on the base mountain to which the metal material belongs, for example, means that, in Expression (16), the moving uppermost steel material discrimination variable x _{i — k} is 1 ( In the case of x _{i — k} = 1), it corresponds to the moving steel material final mountain allocation variable z _ij becoming 0 (zero).
The Motoyama height constraint equation corresponds to, for example, equation (18).
The number of the metal materials determined based on a preset upper limit of the height of the final mountain, which is disposed on the uppermost non-moving metal material among 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 Expression (18). The total number of the moving metal materials that move to the base mountain to which the non-moving metal material belongs corresponds to, for example, the left side of Expression (18).
<Claim 6>
The stack figure constraint corresponds to, for example, a width constraint and a length constraint.
The new mountain height constraint equation corresponds to, for example, equation (20).
The total number of the moving metal materials forming the new mountain corresponds to, for example, the left side of Expression (20). The number of the metal materials determined based on the preset upper limit value of the height of the last peak corresponds to, for example, the right side of Expression (20).
The moving metal material appearance constraint equation corresponds to, for example, equation (21).
The fact that the two moving metal members that do not satisfy the stacked figure constraint cannot be arranged on the same final mountain is that both the first and second terms on the left side of Expression (21) cannot take a value of 1. Corresponding.

  100: yard management device, 101: steel material information acquisition unit, 102: constraint expression / objective function setting unit, 103: optimization calculation unit, 104: post-processing unit, 105: output unit

Claims (10)

The metal material of the initial pile made of metal material piled up in the yard which is a storage space between processes is transported by the transport device, and the metal material piled up in the stacking order according to the order of dispensing to the subsequent process of the yard. When creating the final mountain, a moving metal material that is a metal material transported from the initial mountain to the final mountain in the depot, and the initial mountain to create the final mountain in the same place as the initial mountain. Non-movable metal material fixed to the place, and a yard management device for at least determining the metal material constituting the final mountain,
A non-moving uppermost metal material discriminating variable indicating whether or not the metal material constituting the initial mountain is the uppermost metal material among the non-moving metal materials in the initial mountain; A moving metal material final mountain allocation variable indicating whether or not to place the material on the final mountain, and an allocation mountain identification indicating whether or not Motoyama and New Mountain, which are candidate mountains for the final mountain, are to be the final mountain. Variables and are decision variables,
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 product position of the initial mountain, and the payout order of the metal material,
The conditions of the moving metal material that can be arranged on the base mountain are represented by a first constraint expression expressed by using the decision variables, and the conditions of the moving metal material that can be arranged on the new mountain are determined by the determination. A constraint expression including a second constraint expression expressed using a variable, a constraint expression setting unit configured to set the constraint expression based on the metal material information;
An objective function including a term for evaluating the total number of the moving metal materials, and an objective function including a term for evaluating the total number of the final peaks, based on the metal material information,
Deriving, as an optimal solution, the value of the decision variable when the value of the objective function is minimum or maximum within a range satisfying the constraint expression, by performing an optimization calculation by mathematical programming Calculation means;
Has,
The source mountain is a mountain that is a candidate for the final mountain, and is at least a part of a mountain formed in the yard at the time the metal material information is created, and a mountain whose location does not change from the mountain. And
The yard management device, 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. The determination variable further includes a movement presence / absence determination variable indicating whether the metal material is a moving metal material,
The constraint formula further includes a third constraint formula expressing, using the decision variable, that any metal material must be arranged on any one of the original mountain and the new mountain. The yard management device according to claim 1, wherein:   The constraint formula, the sum of the total number of the moving metal material, the total number of the non-moving metal material, the constraint formula expressing using the decision variable that the total number of the metal material constituting the initial mountain is equal. 3. The yard management device according to claim 2, further comprising a fourth constraint expression:   The constraint formula is that, when the metal material is the moving metal material, the metal material above the metal material in the initial peak 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 is the metal material at the top of the non-moving metal material. 4. The yard management device according to claim 2, further comprising a fifth constraint expression expressed by using the decision variable. The constraint equation setting means is a constraint that is set in advance 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 on the same final mountain. Identify the set of metal materials that can be placed on the metal material,
The first constraint expression is that, when the metal material is the uppermost non-moving metal material of the non-moving metal materials in the initial mountain, the metal material belongs to the base mountain to which the metal material belongs. The non-movable top metal material discriminating variable and the moving metal material final mountain allocation variable express the fact that the metal material that cannot be placed on the vehicle cannot be arranged, is set in advance, and The number of the metal materials determined based on the upper limit of the height of the final mountain, which can be arranged on the uppermost non-moving metal material among the non-moving metal materials in the initial mountain. The non-moving top metal material discriminating variable and the moving metal material final variable indicate that the number of the metal materials must be equal to or greater than the total number of the moving metal materials moving to the base mountain to which the non-moving metal material belongs. Use mountain assignment variables Include the Motoyama height constraint represents Te yard management device according to any one of claims 1 to 4, characterized in. The constraint equation setting means is a constraint that is set in advance 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 on the same final mountain. Identifying the metal material that cannot be placed on the last mountain of
The second constraint formula is 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 a preset upper limit of the height of the final mountain. A new mountain height constraint expression expressed using the moving metal material final mountain allocation variable and the allocated mountain identification variable, and the two moving metal materials that do not satisfy the stacked figure constraint cannot be arranged on the same final mountain. 6. The yard management device according to claim 1, further comprising: a moving metal material stacking constraint expression expressed by using the moving metal material final mountain allocation variable. 7. The movement is performed in units of a metal material group,
The yard according to any one of claims 1 to 6, wherein the metal material group includes 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 space between a steel making process and a rolling process in a steel manufacturing 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 made of metal material piled up in the yard which is a storage space between processes is transported by the transport device, and the metal material piled up in the stacking order according to the order of dispensing to the subsequent process of the yard. When creating the final mountain, a moving metal material that is a metal material transported from the initial mountain to the final mountain in the depot, and the initial mountain to create the final mountain in the same place as the initial mountain. Non-movable metal material fixed to the location of, the yard management method for at least determine the metal material constituting the final mountain,
A non-moving uppermost metal material discriminating variable indicating whether or not the metal material constituting the initial mountain is the uppermost metal material among the non-moving metal materials in the initial mountain; A moving metal material final mountain allocation variable indicating whether or not to place the material on the final mountain, and an allocation mountain identification indicating whether or not Motoyama and New Mountain, which are candidate mountains for the final mountain, are to be the final mountain. Variables and are decision variables,
Identification information of the initial mountain, identification information of the metal material at each product position of the initial mountain, and metal material information acquisition step of acquiring metal material information including the payout order of the metal material,
The conditions of the moving metal material that can be arranged on the base mountain are represented by a first constraint expression expressed by using the decision variables, and the conditions of the moving metal material that can be arranged on the new mountain are determined by the determination. A constraint expression including a second constraint expression expressed using a variable, and a constraint expression setting step of setting the constraint expression based on the metal material information;
An objective function setting step of setting an objective function including a term for evaluating the total number of the moving metal materials and a term for evaluating the total number of the final peaks based on the metal material information,
Deriving, as an optimal solution, the value of the decision variable when the value of the objective function is minimum or maximum within a range satisfying the constraint expression, by performing an optimization calculation by mathematical programming Calculation step;
Has,
The source mountain is a mountain that is a candidate for the final mountain, and is at least a part of a mountain formed in the yard at the time the metal material information is created, and a mountain whose 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 causing a computer to function as each unit of the yard management device according to claim 1.

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