JP2018012559A - Yard management apparatus, yard management method, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To quickly and appropriately obtain an order in which a metal material is transferred when the metal material is moved from an initial mountain to a final mountain.SOLUTION: Used are an initial transfer order variable y (s, s') which is a binomial variable to define a relative order of initial transfer of any two steel materials and a temporary placement occurrence variable x (s) to define whether or not the initial transfer is a transfer to a temporary mountain. If a steel material above underlying steel materials in the same final mountain is initially transferred earlier, a constraint equation is set which includes a linear inequality expressing that temporary placement is required for the steel material to be transferred earlier. Then, in order to satisfy the set constraint equation, the initial transfer order variable y (s, s') and the temporary placement occurrence variable x (s) are derived when the value of an objective function J aiming at minimizing the occurrence of temporary placement becomes minimum, and on the basis of these variables, a transfer order in which each steel material contained in a steel material set N is transferred from the initial mountain to the final mountain is derived.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a yard management device, a yard management method, and a program, and in particular, in a metal manufacturing process, the metal material is sorted in a yard provided to smoothly supply a metal material such as a slab or a coil to the next process. It is suitable for use in sorting containers in the logistics field and the like.

  In the iron making process that is an example of a metal manufacturing process, for example, when transporting a steel material that is an example of a metal material from the steel making process to the next rolling process, the steel material is once placed in a temporary storage place called a yard, It is unloaded from the yard in accordance with the processing time of the next rolling process. An example of the yard layout is shown in FIG. As shown in FIG. 6, the yard is storage spaces 601 to 604 that are partitioned vertically and horizontally as a buffer area for supplying a steel material such as a slab discharged from the upstream process to the downstream process. The vertical division is often referred to as “building” and the horizontal division is referred to as “row”. That is, the cranes (1A, 1B, 2A, 2B) can move in the building and transfer steel materials between different rows in the same building. In addition, steel materials are transferred between buildings using a transfer table. When creating the transport command, by specifying the “building” and “row”, indicate where the steel material is transported (number (11) in parentheses in the locations 601 to 604 in FIG. 6, (See (12), (21), (22)).

Next, FIG. 6 is used as an example to show the basic work flow in the yard. First, the steel material carried out from the continuous casting machine 610 in the steelmaking process, which is the previous process, is transported to the yard by the receiving table X via the pillar 611 and partitioned by the cranes 1A, 1B, 2A, and 2B. ˜604 is transported and placed in piles. And according to the manufacturing schedule of the rolling process which is a post process, it is mounted on the delivery table Z again by the cranes 1A, 1B, 2A and 2B, and conveyed to the rolling process. Generally, in the yard, steel materials are placed in a piled state as described above. This is to effectively utilize the limited yard area.
In the present specification, claims, and drawings, “initial mountain”, “final mountain”, and “temporary mountain” are used in the following meanings.
Early mountain: A mountain that has already been formed in the yard.
Final mountain: The final mountain (also called the “payout mountain”) that has been piled up for the subsequent process.
Temporary mountain: A mountain that is unavoidably temporarily placed when it is transferred from the initial mountain to the final mountain after the present time.

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

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

  Furthermore, the rolling order in the hot rolling process, which is the subsequent process, of the steel products stacked in the order in which they are discharged from the yard to the hot rolling process, which is the subsequent process, is changed after the steel material arrives at the yard. As a result, the piles may not be stacked in the order of payout, and the case where the steel materials are forced to be transposed according to the changed rolling order may frequently occur. Here, the steel materials are stacked on the mountain in the order of paying out. At any stack position of the mountain, one steel or a plurality of steel materials that are conveyed at the same time are lower than the steel materials. It means paying out to a later process earlier than a certain steel material.

However, since the transshipment work required here must be performed in parallel with the work of receiving steel from the yard and the work of paying out steel from the yard, the time zone in which the steel can be transshipped is limited. Therefore, it is required to efficiently transship steel materials.
Therefore, due to various circumstances before and after arrival at the yard, there is an extremely high need for efficiently (i.e., using as few transports as possible) the task of reloading the piles that are no longer in the delivery order upon arrival at the yard in the order of delivery. .

  There are inventions described in Patent Documents 1 to 7 regarding a yard management method in which these are required. The inventions described in Patent Documents 1 to 5 are inventions for a case in which a mountain sorting plan is made for steel materials that are scheduled to arrive at the yard (so-called unarrived materials), and the mountain shape of the final mountain, that is, the target steel material Consideration has been made on how to properly perform the mountain sorting. However, in the inventions described in Patent Documents 1 to 5, steel materials are stacked in the order of payout in the final pile when the steel materials that have been received are not yet stacked on the piles in the payout order while being accepted into the yard. Thus, the subject which performs the transshipment of steel materials efficiently is not made | formed.

The invention corresponding to this problem is the invention described in Patent Documents 6 and 7.
First, the invention described in Patent Document 6 is a technique that results in a mathematical programming problem that satisfies the constraints on mountain setting and conveyance, and simultaneously optimizes the mountain sorting and the conveyance order. However, in the invention described in Patent Document 6, the occurrence of temporary placement, which is a factor that increases the conveyance order, can be considered only for a steel material pair having the same initial mountain. That is, the temporary placement does not occur only between pairs of steel materials having the same initial mountain, but can sufficiently occur between steel materials in different initial mountains depending on which steel material is transported first. Therefore, in the invention described in Patent Document 6, it is not possible to consider every conveyance order of steel materials, and it is impossible to obtain an optimal conveyance order of steel materials when making the final pile.

  Next, in Patent Document 7, in the situation where steel materials that have arrived at the yard and unarrival materials are mixed, the initial mountain state at the time of the initial mountain state and the final mountain state is given. For the problem of transshipment transport of steel materials from the state of the last to the state of the final mountain, there is a method formulated as a mixed integer programming problem using the initial transport time variable and the final transport time variable on the assumption that each steel transport is at most twice. It is disclosed. Unlike the invention described in Patent Document 6, the invention described in Patent Document 7 also considers temporary placement that occurs between steel materials in different initial mountains. However, in the invention described in Patent Document 7, since the initial transport time variable and the final transport time variable are used, when the number of steel materials is 50 or more which is an actual scale, it is requested at the time of recalculation accompanying information update in the yard. There is a possibility that the calculation will not be completed within a certain time (about 30 seconds to 1 minute).

JP-A-6-179525 JP 2000-226123 A JP-A-11-255336 JP 2007-84201 A JP 2008-260630 A JP 2010-269929 A Japanese Patent No. 5365759

  This invention is made | formed in view of the above problems, and it aims at calculating | requiring the conveyance order of a metal material at the time of transshipment of a metal material from an initial mountain to the last mountain appropriately at high speed.

  The yard management device according to the present invention uses the metal material of the initial mountain made of a metal material piled up in a yard in which a metal material including any one of a semi-finished product, a final product, and a container is placed as a place between processes. A yard management device for creating a final pile made of metal materials that are transported by a transporting device and stacked in a stacking order according to a delivery order to a subsequent process of the yard, and any two of the metal materials An initial transfer sequence variable that is a binomial variable that defines a relative order of initial transfer that is transfer from the initial mountain, and initial transfer of the metal material from the initial mountain to the temporary storage area of the yard. The initial placement identification information, the identification information of the metal material at each product position of the initial mountain, and the identification of the final mountain Information and relevant The metal material information acquisition means for acquiring the metal material information including the identification information of the metal material at each product position of the final mountain, and in the same final mountain, the metal material above the metal material below is first In the case of the initial transport, the metal material to be initially transported first is expressed by using the determination variable, which indicates that it is necessary to temporarily place the metal material in the temporary storage place before the transport to the final mountain. A constraint equation setting means for setting a constraint equation including a constraint equation of the following based on the metal material information, and an objective function for minimizing the number of the metal materials in which the temporary placement occurs, An objective function setting means for setting based on the material information, and deriving the value of the decision variable when the value of the objective function is minimum or maximum as long as the constraint equation is satisfied as an optimal solution. By performing optimization calculation by the method And having an optimization calculating means for lines.

  In the yard management method of the present invention, as a place between processes, the metal material of the initial mountain composed of metal materials stacked in a yard where a metal material including any one of a semi-finished product, a final product, and a container is arranged. A yard management method for creating a final pile made of a metal material that is transported by a transport device and stacked in a stacking order according to a delivery order to a subsequent process of the yard, wherein any two of the metal materials An initial transfer sequence variable that is a binomial variable that defines a relative order of initial transfer that is transfer from the initial mountain, and initial transfer of the metal material from the initial mountain to the temporary storage area of the yard. The initial placement identification information, the identification information of the metal material at each product position of the initial mountain, and the identification of the final mountain Information and relevant The metal material information acquisition step for acquiring the metal material information including the identification information of the metal material at each product position of the final mountain, and the metal material that is higher than the lower metal material in the same final mountain first In the case of the initial transport, the metal material to be initially transported first is expressed by using the determination variable, which indicates that it is necessary to temporarily place the metal material in the temporary storage place before the transport to the final mountain. A constraint equation setting step that sets a constraint equation including the constraint equation of the following, and an objective function that aims to minimize the number of the metal materials in which the temporary placement occurs, An objective function setting step that is set based on material information, and deriving the value of the decision variable when the value of the objective function is minimum or maximum within a range that satisfies the constraint formula as an optimal solution. By performing optimization calculation by the method And having an optimization calculation step of rows.

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

  ADVANTAGE OF THE INVENTION According to this invention, the conveyance order of a metal material at the time of transshipment of a metal material from an initial mountain to the last mountain can be calculated | required rapidly and appropriately.

It is a figure which shows an example of a functional structure of a yard management apparatus. It is a flowchart explaining an example of a process of the yard management apparatus. It is a figure which shows an example of the form of conveyance of the steel materials in case there exists a fixing part in an initial mountain. It is a figure which shows the result of Example 1 in a table format. It is a figure which shows the result of Example 2 in a table format. It is a figure which shows an example of the layout of a yard.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings. In the following embodiments, in the steel manufacturing process, the steel materials (slabs) manufactured in the steel making process are piled up from the top in the order of transport to the rolling process. The case where the conveyance order of each steel material is determined will be described as an example.
(First embodiment)
First, the first embodiment will be described.
<Assumptions and problem settings>
In the present embodiment, an example will be described in which the transport order of steel materials when transferring steel materials from the initial mountain to the final mountain is obtained under the following assumptions.
(1) The mountain shape of the initial mountain, the mountain shape of the final mountain, and the delivery order (rolling order) of each steel material are given. The last mountain shall be loaded with steel from the top in the order of delivery. The delivery order (rolling order) is specified from the mountain shape of the final mountain, and is not necessarily given. Here, a set of steel materials is represented as N = {1, 2,..., N}.
(2) No new steel will arrive at the yard (ie, steel will be added to the initial mountain).

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

Moreover, in this embodiment, the optimization problem aiming at minimizing the frequency | count of conveyance of steel materials is solved under the following restrictions.
(I) The steel material of each initial mountain can be conveyed only in order from the top of the initial mountain.
(Ii) When creating the final mountain, it can only be stacked in order from the bottom.
(Iii) The number of steel materials that can be transported simultaneously depends on the number and capacity of the cranes that can be used. In the present embodiment, in order to simplify the description, the case where the number of usable cranes is “1” and the number of steel materials that the crane can carry at one time is described as an example. To do.
As described above, since the number of conveyances from the initial mountain (initial storage site) to the final mountain (final storage site) is a maximum of 2 times for any steel material (refer to the premise of (3) above), the number of steel material conveyance times is as follows. Minimizing is equivalent to minimizing the number of temporary placements.

<Decision variable>
In this embodiment, a variable that determines only the order in which the steel materials are removed from the initial mountain is an independent variable, and whether or not each steel material needs to be temporarily placed is determined based on the mountain shape of the final mountain. The reason why only the order in which the steel material is removed from the initial mountain is set as an independent variable is to reduce the variable by paying attention to the fact that the mountain shape of a given final mountain has information on the final conveyance order. Moreover, unlike the patent document 7, about the initial conveyance order variable which is a variable which shows the order which removes steel materials from an initial mountain, the order restriction between two steel materials is simplified by making it a relative order variable instead of an absolute order variable. And be able to express it clearly. By using such an initial transport order variable, the scale of the independent variable can be reduced from _n ² to _n C ₂ with respect to Patent Document 7.

  For an arbitrary steel pair (two steel materials), an initial transport sequence variable y (s, s') that determines the order in which the steel materials are removed from the initial mountain, and temporary placement occurrence that indicates whether temporary placement has occurred for any steel material The presence / absence variable x (s) is defined as follows. The latter becomes the former dependent variable, and the independent variable is only the former.

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

Here, initial conveyance means conveyance of the steel material in the initial mountain to the final mountain (final storage site) or temporary mountain (temporary storage site). On the other hand, final conveyance means conveying the steel materials in an initial mountain or a temporary mountain (temporary storage place) to the final mountain (final storage place). s is a variable that specifies the initial conveyance of each steel material, and a different value is set for each steel material (s ′ is described so as to be distinguishable from s, and s ′ and a formula (4) described later) s ″ is also a variable that specifies the initial conveyance of each steel material).
(B) Temporary placement occurrence variable x (s): Number of variables = n
The temporary placement occurrence variable x (s) indicates whether the initial transport is transport to the temporary mountain (temporary storage site) or the final mountain (final storage site) when the steel material is initially transported from the initial mountain to the final mountain. It is a 0-1 variable that represents whether or not it is transported. Accordingly, the temporary placement occurrence variable x (s) is defined as in the following equation (2).

The total number of decision variables in this embodiment is ( _n C ₂ + n).
<Functional Configuration of Yard Management Device 100>
FIG. 1 is a diagram illustrating an example of a functional configuration of the yard management apparatus 100. The hardware of the yard management device 100 is realized by using, for example, an information processing device including a CPU, ROM, RAM, HDD, and various interfaces, or dedicated hardware. FIG. 2 is a flowchart for explaining an example of processing of the yard management apparatus 100.

[Steel Information Acquisition Unit 101, Step S201]
The steel material information acquisition unit 101 acquires steel material information. The steel material information includes a steel material ID that is identification information for uniquely identifying the steel material, information for specifying the mountain shape of the initial mountain, and information for specifying the mountain shape of the final mountain.
As described above, the number of steel materials is n. A variable s that specifies initial conveyance is set for each of these steel materials. In the present embodiment, a case where the variable s is a steel material ID will be described as an example.

The information specifying the mountain shape of the initial mountain includes an initial mountain ID that is identification information for uniquely identifying the initial mountain, and a steel material ID in each product stage of the initial mountain identified by the initial mountain ID. In the following description, information specifying the initial mountain shape is referred to as initial mountain shape specifying information as necessary.
The information for specifying the mountain shape of the final mountain includes a final mountain ID that is identification information for uniquely identifying the final mountain, and a steel material ID in each product stage of the final mountain identified by the final mountain ID. In the following description, information specifying the final mountain shape is referred to as final mountain shape specifying information as necessary.

[Constraint Expression / Objective Function Setting Unit 102, Steps S202 and S203]
The constraint equation / objective function setting unit 102 sets a constraint equation that expresses the above-described constraint in a mathematical expression and an objective function that expresses the above-described objective in a mathematical equation.
<< constraint expression >>
First, the constraint equation will be described.
(A) Definition restriction of initial conveyance order variable y (s, s') The order of removing any two steel materials from the initial pile is the total order of steel material set N (transition (the following (4) formula)). Since it is an anti-symmetric and complete (refers to the following binary relationship (Equation (3))), an initial transfer forward variable y (s, s ′) that determines the relative order of removing any two steel materials from the initial pile. ) Satisfies the perfect law (comparable) represented by the following expression (3) and the transition law represented by the following expression (4). Moreover, the initial conveyance order variable y (s, s ′) satisfying the following expressions (3) and (4) corresponds to the entire order of the steel materials.

The expression (3) indicates that one of the initial conveyance of the steel material specified by the variable s and the initial conveyance of the steel material specified by the variable s ′ are always ahead and the other is behind. Note that these two steel materials are different steel materials.
In the equation (4), the initial conveyance of the steel material specified by the variable s is ahead of the initial conveyance of the steel material specified by the variable s ′, and the initial conveyance of the steel material specified by the variable s ′ is the variable s. If it is ahead of the initial conveyance of the steel material specified by ″, it indicates that the initial conveyance of the steel material specified by the variable s is ahead of the initial conveyance of the steel material specified by the variable s ″. These three steel materials are different steel materials.

  Moreover, it is necessary to perform the operation | work which removes steel materials from an initial mountain in order from the top of each initial mountain. Therefore, in the same initial mountain, when the steel material to be subjected to the initial conveyance specified by the variable s' is lower than the steel material to be subjected to the initial conveyance specified by the variable s, (5) is established. As described above, the variable s for specifying the initial conveyance is set for each steel material.

Equation (5) indicates that in the same initial mountain, the steel material that is above the steel material that is below must be initially transported first.
(B) Temporary placement restrictions that occur with transport to the final mountain The final transport order of the steel materials follows the order of the product from the lowest level of the mountain in the mountain shape of a given final mountain. Therefore, when the final transport order (the last pile stacking order) and the initial transport order are different, the steel material initially transported first needs to be temporarily placed. That is, in the same final mountain, when the initial conveyance order of the steel material above is ahead of the initial conveyance order of the steel material below, the steel material initially conveyed first needs to be temporarily placed. Therefore, in the same final mountain, when the steel material that is initially transported specified by the variable s ′ is lower than the steel material that is initially transported specified by the variable s, Equation (6) is established.

Equation (6) indicates that, in the same final mountain, when the steel material that is above the steel material below is initially transported first, the steel material that is initially transported first needs to be temporarily placed.
The constraint expression / objective function setting unit 102 sets the constraint expressions of the expressions (3) to (6) by setting the variables s, s ′, and s ″ for the expressions (3) to (6). To do.

When setting the formula (5), from the initial mountain shape identification information, the steel material relatively below and the steel material above are specified in the same initial mountain, and the upper of the two steel materials is identified. Let s be the set variable and s' be the variable set for the bottom.
(6) When setting the equation, from the final mountain figure specifying information, the steel material relatively below and the steel material above are specified in the same final mountain, and the upper of the two steel materials Let s be the set variable and s' be the variable set for the bottom.

  As for the expression (3), s and s ′ are set for each of the combinations of two arbitrary steel materials in the steel material set N. As for the expression (4), s, s ′, and s ″ are set for each of the combinations of arbitrary three steel materials of the steel material set N.

<< Objective function >>
Next, the objective function will be described.
As described above, in the present embodiment, the objective is to minimize the number of times the steel material is conveyed, that is, to minimize the number of temporary placements. Therefore, the objective function J shown in the following equation (7) is used.

  The constraint equation / objective function setting unit 102 sets the objective function J of (7) by setting the variable s to the equation (7).

[Optimization calculation unit 103, step S204]
The optimization calculation unit 103 sets the initial transport forward variable y (s, s) when the value of the objective function J in the expression (7) is minimized within a range satisfying the constraint expressions in the expressions (3) to (6). ') And the temporary placement occurrence variable x (s) are calculated as optimum solutions. As described above, the temporary placement occurrence presence / absence variable x (s) is a dependent variable of the initial transport order variable y (s, s ′). The calculation of the optimal solution can be realized by using a known algorithm (solver) for solving the optimization problem by mathematical programming such as mixed integer programming.

[Post-Processing Unit 104, Step S205]
When the initial transport order variable y (s, s ′) is derived as described above, the initial transport order (the order of removal from the initial mountain) of each steel material included in the steel material set N can be determined. However, from the final conveyance order (temporary mountain (temporary placement)) to the final mountain (temporary mountain (temporary placement)) of the steel material that is determined to be temporarily placed (the steel material in which the variable s where the temporary placement occurrence variable x (s) is “1”) is set. Since the transport order) to the final place) is not fixed, it is necessary to determine this. That is, it is necessary to determine where in the initial conveyance order determined as described above, the final conveyance order of the steel material determined to cause temporary placement is to be interrupted. Therefore, in the present embodiment, the post-processing unit 104 determines the final conveyance order of each steel material as follows.

  The steel material determined to be temporarily placed needs to be transported twice, that is, the initial transport and the final transport. On the other hand, the initial conveyance and the final conveyance coincide with each other for steel materials that are determined not to be temporarily placed. Accordingly, for the steel material determined to be temporarily placed, the ID for these two transports is set as the variable s. That is, for the steel material, two variables s are set as if there are two virtually different steel materials. Accordingly, the number of steel materials to be transported here is a value obtained by adding the number of steel materials determined to be temporarily placed to the actual number of steel materials to be transported. In this way, by changing the information given to the algorithm described above, all steel materials to be transported can be transshipped from the initial mountain to the final mountain by initial conveyance, and the final conveyance order of each steel material can be obtained. it can. Specifically, the following modifications are performed on the algorithm described above. In the following description, a steel material that is determined to be temporarily placed is referred to as a temporarily placed steel material as necessary.

  The variable s is a variable that specifies the initial conveyance, and is set for each steel material included in the steel material set N. Moreover, two variables s are set for the temporary placement target steel material. As described above, in this embodiment, the variable s for each steel material is the steel material ID of the steel material. Accordingly, an ID different from the steel material ID is set for each temporary placement target steel material as a virtual steel material ID. Then, the steel material ID of the temporary placement target steel material and the virtual steel material ID set for the temporary placement target steel material are set as two variables s for the temporary placement target steel material. When the number of temporarily placed steel materials is t, the number of variables s is (n + t). As described above, two variables s for specifying initial conveyance are set for the temporarily placed steel material. One of these two variables s is a variable that specifies the initial conveyance from the initial mountain, and the other is a variable that specifies the initial conveyance from the temporary mountain. As described above, the steel materials determined to be temporarily placed are regarded as two steel materials, so that the steel materials are transported twice (initial transport from the initial mountain to the temporary mountain and final from the temporary mountain to the final mountain. Transport) can be treated as initial transports.

  Next, the mountain shape of the initial mountain for the temporary placement target steel material specified by the variable s that specifies the initial conveyance from the initial mountain is a steel material whose initial conveyance order is determined by the initial conveyance order variable y (s, s ′). It is assumed that one virtual mountain is stacked in order from the top. The number of product stages of this initial mountain (virtual mountain) is n. Further, each product stage of the initial mountain (virtual mountain) is assigned a steel material ID of the corresponding steel material from above according to the initial conveyance order calculated by the optimization calculation unit 103. On the other hand, the initial mountain for the steel material determined to be temporarily placed by the optimization calculating unit 103 is an initial mountain having two product stages. The second level is s which is the steel material ID of the steel material, and the first level is n + s which is the steel material ID corresponding to the final conveyance of the steel material (conveyance from the temporary mountain to the final mountain).

Here, as the initial mountain, the virtual mountain having the number n of product stages is created by the post-processing unit 104 (step S205) in accordance with the initial conveyance order of all the steel materials determined by the optimization calculation unit 103 (step S204). This is to maintain the order of conveyance. Moreover, the reason why the virtual pile of the number of product stages 2 corresponding to the temporary placement target steel material is created is to define the order of the initial conveyance and the final conveyance for the temporary placement target steel material. The steel material ID corresponding to the initial conveyance of the temporary placement target steel material is assigned to both the virtual pile of the product stage number n and the virtual pile of the product stage number 2 so that the initial conveyance of the temporary placement target steel material goes straight to the final pile. The post-processing unit 104 (step S205) simultaneously determines the order relationship between the initial conveyance of the steel material to be performed and the order relationship between the initial conveyance and the final conveyance of the temporarily placed steel material.
Next, the mountain shape of the last mountain is replaced with the virtual steel material ID given to the temporary placement target steel material, with respect to the final mountain shape identification information included in the steel material information, the steel material ID of the steel material that is the temporary placement target steel material. It will be a thing.
Further, the following constraint formula (8) is set for each temporarily placed steel material.

In the equation (8), s is a variable (steel ID of the temporary placement target steel material) that specifies initial conveyance from the initial pile of the temporary placement target steel material, and n + s is an initial value from the temporary pile of the temporary placement target steel material. It is assumed that it is a variable (virtual steel material ID of the temporary placement target steel material) that specifies the conveyance. Equation (8) indicates that the initial conveyance order (initial conveyance from the initial mountain) of the temporarily placed steel material is ahead of the final conveyance order (initial conveyance from the temporary mountain).
The post-processing unit 104 sets the variables s, s ′, s ″, and n for the equations (3) to (6) and (8), and sets the variable s for the equation (7). Then, the post-processing unit 104 performs the initial transport order when the value of the objective function J in the equation (7) is minimized within the range satisfying the constraint equations in the equations (3) to (6) and (8). The variable y (s, s ′) is calculated as the optimal solution. Based on the optimal solution of the initial transfer forward variable y (s, s ′) calculated in this way, the post-processing unit 104 determines all the steel materials included in the steel material set N from the initial mountain to the final mountain. The order of transport (transport order) is derived.

[Output unit 105, step S206]
The output unit 105 outputs information indicating the conveyance order from the initial mountain to the final mountain of each steel material included in the steel material set N derived by the post-processing unit 104. The form of output includes at least one of display on a computer display, storage on a storage medium inside or outside the yard management apparatus 100, and transmission to an external apparatus. Examples of the external device include a crane or a control device that controls the operation of the crane.

<Summary>
As described above, in this embodiment, the initial transfer order variable y (s, s ′), which is a binary variable that determines the relative order of the initial transfer of any two steel materials, and the initial transfer to the temporary mountain are transferred. In the case of initially transporting the steel material above the steel material below in the same final mountain using the temporary occurrence occurrence variable x (s) that is a variable that determines whether or not A constraint equation including a linear inequality representing that the steel material initially transported first needs to be temporarily placed is set. Then, the initial transfer order variable y (s, s ′) and the temporary placement when the value of the objective function J for the purpose of minimizing the occurrence of the temporary placement is minimized so as to satisfy the set constraint equation. The occurrence / non-occurrence variable x (s) is derived, and based on these, the conveyance order from the initial mountain to the final mountain of each steel material included in the steel material set N is derived. Therefore, the conveyance order of the steel materials when the steel materials are reloaded from the initial mountain to the final mountain can be obtained at high speed and appropriately.

<Modification>
In the present embodiment, the problem of minimizing the objective function J has been described as an example. However, for example, the objective function may be obtained by multiplying the right side of equation (7) by (−1), and the objective function may be maximized.

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

(Second Embodiment)
Next, a second embodiment will be described. In the first embodiment, the initial mountain and the final mountain are different from each other, and it is assumed that all steel materials must be transported from the initial mountain (initial storage) to the final mountain (final storage). Explained with an example. However, in the initial mountain, there is a case where the product order from the lowest stage is already the payout order (the payout order is descending from bottom to top). In such a case, in the initial mountain, it is not necessary to reload the portion in which the product order from the lowest level is the payout order (the payout order is descending from the bottom to the top). Therefore, in the present embodiment, a description will be given of a case where, for such a portion, the initial mountain and the final mountain are allowed to be the same (that is, the initial mountain is not moved). As described above, the present embodiment and the first embodiment mainly differ in processing due to the difference in the premise (4) described in the first embodiment. Therefore, in the description of the present embodiment, the same parts as those in the first embodiment are denoted by the same reference numerals as those in FIGS.

In the present embodiment, the following premise (5) is adopted instead of the premise (4) described in the first embodiment.
(5) The initial mountain and the final mountain are allowed to be in the same place, and the part of the initial mountain where the product order from the lowest level is the delivery order (the delivery order is descending from bottom to top) is transported. (I.e., some steel materials of the initial mountain (a plurality of steel materials continuous from the lowest level) may not be transported). Therefore, it is assumed that whether or not the steel material is conveyed in this way is included in the steel material information.

  The difference between the premise of (4) described in the first embodiment and the premise of (5) is the same place (mountain) that cannot occur under the premise of (4) under the premise of (5) The upper steel material is allowed to be replaced. In order to replace such steel materials, the steel material existing at the upper part of the initial mountain is conveyed to the temporary mountain or the final mountain, and another steel material is conveyed onto the remaining part (lower part) of the initial mountain. It will be. Steel materials transported over the lower part of the initial mountain include steel materials in an initial mountain different from the initial mountain, and steel materials temporarily placed in the temporary mountain among the steel materials in the upper part of the initial mountain. Is included.

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

This algorithm can be realized by making the following changes to the constraint equations (3) to (6) in the first embodiment.
First, a constraint equation added to the constraint equations (3) to (6) described in the first embodiment will be described.
If all steel materials are not subject to transportation and a part of the initial mountain is used as the final mountain as it is, the following cases are assumed that are not intended for transportation of all steel materials. Need to add constraints.
FIG. 3 is a diagram illustrating an example of a form of transporting a steel material when there is a fixed portion on the initial mountain.
In the initial mountain shown in FIG. 3, it is assumed that the steel materials I and II in the two stages from the bottom are fixed portions, and the steel materials III, IV, and V thereon are moving portions. In this case, the steel materials I and II of the fixed portion remain as they are at the final mountain. In addition, among the steel materials III, IV, and V of the moving portion of the initial mountain, the steel materials III and V are conveyed to another final mountain, and the steel material IV is conveyed to the temporary mountain and then the initial mountain (that is, the final mountain) again. The steel materials VI and VII are transported from another initial pile onto the steel material IV. Even in such a case, in order to appropriately calculate the transport order, it is necessary to provide a restriction on the initial transport order.

When steel material is transported from another initial mountain or temporary mountain to an initial mountain having a fixed part (that is, the final mountain), the steel materials III, IV, V of the moving part at the upper part of the fixed part are initially transported. Otherwise, the final transport of steel materials IV, VI and VII is not possible. Therefore, it is necessary to set a restriction that the final conveyance of the steel materials IV, VI, and VII must be performed after the initial conveyance of the slabs III, IV, and V. Therefore, the initial conveyance order of the steel materials at the upper part of the fixed part such as the steel materials III, IV, V is the steel material conveyed to the upper part of the fixed part from another initial mountain or temporary mountain such as the steel materials IV, VI, VII. It is a necessary and sufficient condition to be ahead of the final transport order. However, in the algorithm described in the first embodiment, the only independent variable is the initial transport order variable y (s, s ′) (there is no variable that determines the final transport order). Therefore, in this embodiment, a constraint expression that gives sufficient conditions is added as follows.
That is, the variable that specifies the initial conveyance of the steel material of the moving part of the initial mountain l is i _U, and the initial conveyance of the steel material conveyed from the mountain different from the initial mountain l (initial mountain or temporary mountain) to the initial mountain l is The variable to be identified is i _T , and the following constraint expression (9) is added.

When the initial conveyance specified by the variable i _T is the conveyance to the final mountain, Equation (9) satisfies the above-mentioned necessary and sufficient conditions, but the initial conveyance specified by the variable i _T is the conveyance to the temporary mountain. If this is the case, equation (9) becomes a sufficient condition and becomes excessively restrictive.
Further, in the case of a steel material that is initially transported from the initial mountain l and returns to the initial mountain l again (that is, i _U and i _T ), such as the steel material IV in the example of FIG. However, the following equation (10) is set for such a steel material.

Next, the part changed with respect to the constraint expressions of the expressions (3) to (6) described in the first embodiment will be described.
As described above, since the steel material of the fixed portion of the initial mountain is given, the steel material on which the initial conveyance is not performed is known. Therefore, in the formula (5), when at least one of the variables s and s ′ for specifying the initial conveyance is a variable set for the steel material of the fixed portion of the initial mountain, those variables are set. For the initial transfer order variable y (s, s ′) by s, s ′, the constraint equation of equation (5) is not set. For the other initial transporting order variable y (s, s ′), the constraint equation (5) is set.

  Further, if the initial conveyance is not performed, temporary placement does not occur. Therefore, in the equation (6), when at least one of the variables s and s ′ for specifying the initial conveyance is a variable set for the steel material of the fixed portion of the initial mountain, those variables are set. It is assumed that the constraint equation (6) is not set for the initial transport order variable y (s, s ′) by s and s ′. For the other initial transporting order variable y (s, s ′), the constraint equation (6) is set.

  When at least one of the variables s, s ′, and s ″ that specify the initial conveyance is a variable set for the steel material of the fixed portion of the initial mountain, these variables s and s ′ , S ″, the initial transfer order variables y (s, s ′), y (s ′, s), y (s ′, s ″), y (s, s ″) In addition, the constraint equation (4) is not set. Alternatively, by expanding equation (5) as follows, all the constraint equations other than equation (5) may be set in the same manner as the steel material of the moving portion (non-fixed portion) for the steel material of the fixed portion.

  That is, the above formula (5) is for the steel part of the moving part (non-fixed part), but when one steel material is a fixed part and the other steel material is a non-fixed part, the following ( If the constraint equation of 11) is set and both steel materials are fixed parts and they are in the same initial mountain, the constraint equation of the following equation (12) is set.

  In the present embodiment, the constraint equation / objective function setting unit 102 sets the constraint equations (3) to (6), (9), and (10) as described above. Note that, as described above, the constraint equations (11) and (12) may be set. And the optimization calculation part 103 is (3) Formula-(6) Formula, (9) Formula and (10) Formula (or (3) Formula-(6) Formula and (9) Formula-(12) Formula ) Within the range satisfying (), the initial transfer order variable y (s, s ′) and the temporary placement occurrence variable x (s) when the value of the objective function J in equation (7) is minimized are calculated.

  As described above, in the present embodiment, when at least one of the steel materials is the steel material of the fixed portion of the initial mountain, the equation (5), which is a constraint equation representing a constraint when conveying the steel material, is not set, or The constraint formulas of formulas (11) and (12) are set. Moreover, the initial conveyance of the steel material of the moving part of the initial mountain is ahead of the initial conveyance of the steel material conveyed to the initial mountain having the moving part using the initial conveyance order variable y (s, s ′). A constraint expression (Expression (9)) is added. Therefore, in addition to the effects described in the first embodiment, the steel material transport sequence when the metal material is reloaded from the initial mountain to the final mountain so as not to convey the steel material of the fixed portion of the initial mountain that does not need to be conveyed. Can be requested.

<Modification>
As described above, since the expression (9) expresses the constraint condition for replacement with sufficient conditions, the solution obtained in this way is not guaranteed to be an optimal solution, and cannot be realized even though there is an optimal solution. May be calculated as (no solution). Therefore, instead of the equation (9), the following constraint equation (13) that expresses the constraint condition for replacement as a necessary condition may be used.

  When the steel material conveyed to the initial mountain having the moving part of the initial mountain is temporarily placed, the order of the initial conveying of the steel material and the initial conveying of the steel material of the moving part is not limited. Otherwise, as in equation (9), it indicates that the initial conveyance of the steel material in the moving part of the initial mountain is ahead of the initial conveyance of the steel material conveyed to the initial mountain having the moving part. In the equation (13), when the steel material to be transported to the initial pile having the moving part is temporarily placed, there is no restriction, so it becomes only a necessary condition, and the obtained solution becomes an unrealizable solution (that is, obtained) It may not be possible to transport the solution).

For example, when it is desired to reliably prevent a solution that cannot be realized, the equation (9) is used. When the steel material to be transported to the initial mountain having the moving part is rarely placed ( The constraint equation to be adopted may be selected by using the equation (13).
Also in the present embodiment, the modification described in the first embodiment can be employed.

(Third embodiment)
Next, a third embodiment will be described. In the second embodiment, since the independent variable is only the initial transfer sequence variable y (s, s ′), the above-described constraint condition for replacement cannot be expressed by the necessary and sufficient condition, and the sufficient condition (or the necessary condition). The case where the constraint expression expressed in () is used has been described as an example. On the other hand, in this embodiment, the relative order between the 2N pieces of conveyance of the initial conveyance and the final conveyance of arbitrary steel materials included in the steel material set N is determined, and the constraint condition for replacement is expressed as a necessary and sufficient condition. The case where it does is demonstrated. As described above, the present embodiment and the second embodiment are mainly different in processing by expressing the constraint conditions for replacement as necessary and sufficient conditions. Therefore, in the description of the present embodiment, the same parts as those in the first and second embodiments are denoted by the same reference numerals as those in FIGS.

  Similarly to the second embodiment, in this embodiment, instead of the premise of (4) described in the first embodiment, the premise of (5) described in the second embodiment (that is, the first embodiment). Under the assumptions (1) to (3) described in the embodiment and (5) described in the second embodiment), the conveyance order of the steel materials when the steel materials from the initial mountain to the final mountain are transshipped is obtained.

<Decision variable>
In this embodiment, variables that define both the order in which the steel material is removed from the initial mountain and the order in which the steel material is conveyed to the final mountain are prepared as independent variables. Let G ₂ = (N + N ₂ , E) be a fully effective graph in which each element of the steel material set N has two vertices. Here, N ₂ has the same number of elements as N, and an arbitrary sεN is a set having s + nεN ₂ as an element. Therefore, both sets N and N ₂ do not have a common set. At this time, E = {(s, s ′) ∈ (N + N ₂ ) ² | s ≠ s ′}.

Here, s satisfying s ≦ n (s∈N) represents a variable for specifying the initial conveyance of the steel material. On the other hand, s satisfying s> n (sεN ₂ ) represents a variable that specifies the final conveyance of the steel material on which the initial conveyance specified by (s−n) is performed. In the first embodiment, the vertices of the fully directed graph G correspond to the initial conveyance, but in the present embodiment, the vertices of the fully effective graph G ₂ correspond to the initial conveyance or the final conveyance.

  For any steel pair (two steels), the overall order of removing steel from the initial pile and transporting steel to the final pile (initial transfer from the initial pile to the final pile and temporary storage from the initial pile) The initial and final transport sequence variable z (s, s') that determines the initial transport to and the final transport from the temporary storage to the final mountain), and whether or not temporary storage has occurred for any steel material The temporary placement occurrence presence / absence variables x (s) to be expressed are respectively defined as follows. The latter becomes the former dependent variable, and the independent variable is only the former.

(A) Initial / final transport order variable z (s, s ′): number of variables = _2n C ₂
The 0-1 variable z (e) (∀e∈E: (s, s ′)) defined on the effective branch set E of the complete effective graph G ₂ defined as described above is introduced, and the following (14 ) Define the initial and final transport order variables z (s, s ′) as in the equation

Here, the conveyance includes an initial conveyance and a final conveyance.
(B) Temporary placement occurrence variable x (s): Number of variables = n
As described in the first embodiment, the temporary placement occurrence variable x (s) is transferred when the steel material is initially transported from the initial mountain to the final mountain. Or 0-1 variable indicating whether the transfer is to the last mountain (final parking lot). Therefore, a temporary placement occurrence variable x (s) is defined as in the following equation (15).

Here, the conveyance includes an initial conveyance and a final conveyance. Since the final transport is always transported to the final mountain, the value of the temporary placement occurrence variable x (s) is “0 (zero)”.
The total number of decision variables in the present embodiment is ( _2n C ₂ + n).

<Functional Configuration of Yard Management Device 100>
An example of a functional configuration of the yard management apparatus 100 according to the present embodiment is a configuration in which the post-processing unit 104 is eliminated from the configuration illustrated in FIG. That is, the calculation result by the optimization calculation unit 103 is given to the output unit 105.

[Steel Information Acquisition Unit 101, Step S201]
The steel material information acquisition unit 101 is the same as that in the first embodiment.

[Constraint Expression / Objective Function Setting Unit 102, Steps S202 and S203]
The constraint equation / objective function setting unit 102 sets a constraint equation and an objective function, as in the first embodiment. However, in the present embodiment, the following constraint equations are used in place of the constraint equations (3) to (6).
<< constraint expression >>
(A) Definition Restriction of Initial / Final Transfer Order Variable z (s, s ′) In order to set the initial / final transfer order variable z (s, s ′) as the total order, it has been described in the first embodiment (3). Similar to the equations (4) and (4), the following constraint equations (16) and (17) indicating the definition constraints on the initial / final transport sequence variable z (s, s ′) are used.

In general, since the final transport is performed after the initial transport, the order of the set N + N ₂ is set to the total order (in order to satisfy the completeness (comparability), it is necessary to determine the relative order between different elements. Therefore, the following constraint equation (18) is used.

  Further, similarly to the equation (5) described in the first embodiment, the initial conveyance specified by the variable s ′ is performed on the same initial mountain, rather than the steel material on which the initial conveyance specified by the variable s is performed. When the steel material is lower, the initial / final transport sequence variable z (s, s ′) is constrained by the following equation (19).

  In the present embodiment, the initial / final conveyance order variable z (s, s ′) also represents the relative final conveyance order of any two steel materials, so the initial / final conveyance order variable z (s, s ′) is , Get the restraint of the final mountain. Therefore, in the same final mountain, when the steel material for which the final conveyance specified by the variable n + s is performed is lower than the steel material for which the final conveyance specified by the variable n + s ′ is performed, for the steel material, the following Equation (20) holds.

The equation (20) indicates that, in the same final mountain, the steel material below the steel material above needs to be finally conveyed first.
(B) Temporary placement restrictions that occur with conveyance to the final pile As described in the first embodiment, the initial conveyance order of the steel materials above is the initial conveyance order of the steel materials below in the same final pile. If it is earlier, the steel material initially transferred first needs to be temporarily placed. Therefore, by replacing the initial transport sequence variable y (s, s ′) in equation (6) with the initial / final transport sequence variable z (s, s ′), it is higher than the steel material below in the same final mountain. It can be expressed that the steel material initially transferred first needs to be temporarily placed when the steel material initially transferred is first transferred. That is, in the same final mountain, when the steel material that is subjected to the initial conveyance specified by the variable s ′ is lower than the steel material that is subjected to the initial conveyance specified by the variable s, for the steel material, The following equation (21) holds.

  Moreover, when the initial conveyance order and final conveyance order differ between two steel materials, the steel material initially conveyed initially among the said two steel materials needs temporary placement. That is, the initial transport order specified by the variable s is ahead of the initial transport order specified by the variable s ′, and the final transport order specified by the variable n + s ′ is specified by the variable n + s. In the case where it is ahead of the order of the final conveyance, the steel material to be subjected to the initial conveyance specified by the variable s needs to be temporarily placed. Therefore, instead of or in addition to the equation (21), the following equation (22) It is also possible to use the constraint equation.

(C) Constraint when the lower part of the initial mountain is fixed and only the upper part is replaced Under the premise of (5) described in the second embodiment, the upper part of the initial mountain (the moving part shown in FIG. 3) In order to replace, the steel material that was present in the initial mountain in the initial state is transported to another mountain (final mountain or temporary mountain), and the steel material is transported from the other mountain (initial mountain or temporary mountain) to that stage. It is necessary to Therefore, the “initial conveyance order” of the steel members of the moving part that was in the initial mountain must be ahead of the “final conveyance order” of the steel materials that are conveyed from the other mountain to the place where the steel material is located. This constraint can be expressed as follows:
That is, the s _o, (steel in the example shown in FIG. 3 III, IV, V) steel transport target of the initial mountain as a variable to identify the initial transport of the s _i, are transported from another mountain to the initial mountain Steel material or steel material conveyed from the initial mountain via the temporary mountain to the initial mountain (in the example shown in FIG. 3, assuming that the initial conveyance of the steel material (IV, VI, VII) is a variable, the following (23 ) Formula holds.

Constraints, objective function setting unit 102, (16) to (23) with respect to the variable s, s', n, s o, by setting the s _i, (16) to (23) of Set constraint expressions.
When setting the equation (19), from the initial mountain shape identification information, the steel material relatively below and the steel material above are identified in the same initial mountain, and the upper of the two steel materials is identified. Let s be the set variable and s' be the variable set for the bottom.
When setting the equation (20), from the final mountain figure specifying information, the steel material relatively below and the steel material above in the same final mountain are specified, and the upper of the two steel materials is specified. Let s' be the set variable and s be the variable set below.

When setting the formula (21) and (22), from the final mountain shape identification information, the steel material relatively below and the steel material above are identified in the same final mountain, and the two steel materials The variable set for the top is s, and the variable set for the bottom is s'.
(23) of the s _o, the s _i, is identified from the initial mountain shape specific information, given the variables are set for steel of the moving portion of the initial mountain.

<< Objective function >>
In the present embodiment, as in the first embodiment, the objective is to minimize the number of times the steel material is conveyed, that is, to minimize the number of temporary placements. Use.

[Optimization calculation unit 103, step S204]
The optimization calculation unit 103 sets the initial / final transport forward variable z (s) when the value of the objective function J in the equation (7) is minimized within a range satisfying the constraint equations (16) to (23). , S ′) and temporary placement occurrence variable x (s) are calculated as optimum solutions. The temporary placement occurrence presence / absence variable x (s) is a dependent variable of the initial / final transport order variable z (s, s ′).
Based on the calculated initial / final transport sequence variable z (s, s ′), the optimization calculation unit 103 performs the transport of all the steel materials included in the steel material set N from the initial mountain to the final mountain. The order (conveyance order) is derived. In the present embodiment, both the initial transport order and the final transport order of any two steel materials are specified by the initial / final transport order variable z (s, s ′). Therefore, after the description in the first embodiment, The processing in the processing unit 104 (the processing in step S205) is not necessary.

[Output unit 105, step S206]
The output unit 105 outputs information indicating the conveyance order from the initial mountain to the final mountain of each steel material included in the steel material set N, which is derived by the optimization calculation unit 103.

<Summary>
As described above, in the present embodiment, the initial / final transport order variable z (s, s ′), which is a binary variable that determines the relative order of both the initial transport and the final transport of any two steel materials, and the initial Using the temporary placement occurrence variable x (s), which is a variable that determines whether or not the conveyance is to a temporary mountain, the “initial conveyance order” of the steel material of the moving part in the initial mountain is the steel material. A constraint formula indicating that the steel materials to be transported from other piles to a certain location must be ahead of the "final transport order", and in the same final mountain, the steel materials that are above the steel materials below are placed first. In the case of initial conveyance, a constraint equation including a constraint equation indicating that temporary placement is necessary for the steel material initially conveyed first is set. Then, the initial and final transport order variables z (s, s ′) when the value of the objective function J for the purpose of minimizing the occurrence of temporary placement is minimized so as to satisfy the set constraint equation and The temporary placement occurrence variable x (s) is derived, and based on these, the conveyance order from the initial mountain to the final mountain of each steel material included in the steel material set N is derived. Therefore, the constraint conditions for replacement can be expressed as necessary and sufficient conditions. Therefore, the conveyance order of the steel materials when the steel materials are reloaded from the initial mountain to the final mountain can be appropriately derived so as not to convey the steel material of the fixed portion of the initial mountain that does not need to be conveyed. That is, it is possible to prevent an optimal solution from being calculated as an infeasible (no solution) or an obtained solution from being an infeasible solution (a solution that cannot be conveyed).
Also in this embodiment, the modification described in the first embodiment can be adopted.

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

<Example 1>
In this example, the method (invention example) described in the first embodiment and the method (comparative example) described in Patent Document 7 are used for each of the steel material information (input data) in the eight cases shown in FIG. Thus, the transport order from the initial mountain to the final mountain of each steel material was obtained.

  As shown in FIG. 4, in any case, the number of transported steel materials (temporary number, that is, the optimum solution) obtained in the invention example and the comparative example is the same. In both the invention example and the comparative example, the number of times the steel material is conveyed from the initial mountain (initial storage site) to the final mountain (final storage site) is two times maximum. The number of steel materials that are temporarily placed is two times, and the number of steel materials that are not temporarily placed is one time. Therefore, in FIG. 4, the total number of conveyance is the sum of the number of steel materials and the temporary number. And as shown in FIG. 4, in any case, it turns out that the solution time of the invention example is shorter than that of the comparative example, and the solution can be solved at high speed (see the column of solution time shown in FIG. 4). Comparing the average solution times of the eight cases, it can be seen that the comparative example required 99 seconds and the invention example can solve in 1.5 seconds.

<Example 2>
In the present example, the lower stage part of the initial mountain (the upper stage part (moving part) is replaced without moving the fixed part and the steel material is reloaded, which cannot be realized by the invention described in Patent Document 7). The transport order from the initial mountain to the final mountain was determined using the method described in the third embodiment, and Fig. 5 is a diagram showing the results in a tabular form. In the description, the final mountain whose final mountain ID is “n” (n is a positive integer) is referred to as final mountain n, and the initial mountain whose initial mountain ID is “n” is referred to as initial mountain n. An initial transport order of “0” indicates that the initial transport is not performed (that is, a fixed portion), and a final transport order of “/” indicates that the initial transport is the final transport (temporary transport). This means that there is no placement, or that initial conveyance is not performed. It is a / "indicates that the temporary placement does not occur.

In the example shown in FIG. 5, the final mountain 1 and the final mountain 2 are formed in such a manner that the lower part of the initial mountain 1 and the initial mountain 3 are used as fixed parts and the upper part thereof is replaced.
First, with respect to the final mountain 1, the first to third stages from the bottom remain the initial mountain 1, and the steel materials in the upper stages from the fourth stage are replaced. The initial mountain 1 is a mountain composed of 8 steps, and the steel material existing in the 4th to 8th steps from the bottom of the initial mountain 1 is transferred to another mountain, and a new 4th step from the bottom of the initial mountain 1 The steel material with the steel material ID “83” is transported in the fifth stage, and the steel material with the steel material ID “195” is conveyed in the fifth stage.

  In this case, after the initial conveyance of the steel material with the steel material ID “160” that was present in the fourth stage from the bottom transported last from the initial mountain 1, 4 from the bottom of the initial mountain 1 vacated thereby. At the stage, the steel material whose steel material ID is “83” must be finally conveyed. Since the initial conveyance order of the steel material with the steel material ID “160” is the 14th and the final conveyance order of the steel material with the steel material ID “83” is the 26th, the initial mountain 1 of the steel material with the steel material ID “83” (that is, the final Transport to mountain 1) becomes possible. As shown in FIG. 5, in the initial mountain 1, the steel materials present in the eighth, seventh, sixth, fifth, and fourth stages from the bottom are initially conveyed in this order. (Refer to the initial conveyance order column of steel materials with steel material IDs “87”, “126”, “101”, “120”, “160”).

  As for the other final mountain 2, the steel material in the upper level from the fourth level is replaced with the initial level 3 remaining from the first to the third level. The initial mountain 3 is also a mountain composed of 8 steps, and the steel material that was present in the 4th to 8th steps from the bottom of the initial mountain 3 is transferred to another mountain, and a new 4th step from the bottom of the initial mountain 3 The steel material with the steel material ID “136” is transferred to the fifth stage, and the steel material with the steel material ID “126” is conveyed to the fifth stage.

Also in this case, after the initial conveyance of the steel material having the steel material ID “189” that was present in the fourth stage from the bottom that is finally conveyed from the initial mountain 3, 4 from the bottom of the initial mountain 3 that is vacant thereby. At the stage, the steel material having the steel material ID “136” must be finally conveyed. Since the initial conveyance order of the steel material with the steel material ID “189” is ninth and the final conveyance order of the steel material with the steel material ID “136” is eleventh, the initial pile 3 of the steel material with the steel material ID “136” (that is, the final Transport to the mountain 2) becomes possible. As shown in FIG. 5, in the initial mountain 3, the steel materials present in the eighth, seventh, sixth, fifth, and fourth stages from the bottom are initially conveyed in this order. (Refer to the initial conveyance order column for steel materials having steel material IDs “156”, “142”, “99”, “192”, and “189”).
Further, in this case, the steel material with the steel material ID “189” has the same initial mountain and final mountain, and the stacking stage is changed from the fourth stage to the tenth stage from the bottom. Such a steel material becomes a temporary placement target steel material as shown in the equations (21) and (22).

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

(Relationship with claims)
Below, an example of the relationship between a claim and embodiment is shown. It should be noted that the description of the claims is not limited to the description of the embodiment, as described in the modification.
<Claim 1>
A metal material information acquisition means is implement | achieved by using the steel material information acquisition part 101, for example. The metal material identification information is realized by using, for example, a steel material ID, and the metal material information is realized by using, for example, steel material information.
The constraint equation setting means is realized by using, for example, the constraint equation / objective function setting unit 102. The first constraint expression is realized by using, for example, the expression (6).
The objective function setting means is realized, for example, by using the constraint equation / objective function setting unit 102. The objective function is realized, for example, by using equation (7).
The optimization calculation means is realized by using the optimization calculation unit 103, for example.
<Claim 2>
The second constraint expression is realized by using, for example, the expression (3).
The third constraint equation is realized, for example, by using equation (4).
<Claim 3>
The fourth constraint expression is realized by using, for example, Expression (5).
<Claim 4>
The derivation means is realized by using the post-processing unit 104, for example.
The fifth constraint equation is realized, for example, by using equation (8).
<Claim 5>
The sixth constraint equation is realized by using, for example, equation (9).
<Claim 6>
The seventh constraint expression is realized by using, for example, Expression (18). When the initial and final transport order variables are used instead of the initial transport order variables, the first constraint expression is realized by using at least one of the expressions (21) and (22), for example. The second constraint expression is realized by using, for example, Expression (16). The third constraint expression is realized by using, for example, Expression (17). The fourth constraint equation is realized by using, for example, equation (19).
<Claim 7>
The eighth constraint equation is realized by using, for example, equation (23).
<Claim 8>
The ninth constraint expression is realized by using, for example, Expression (20).

  DESCRIPTION OF SYMBOLS 100: Yard management apparatus, 101: Steel material information acquisition part, 102: Constraint formula and objective function setting part, 103: Optimization calculation part, 104: Post-processing part, 105: Output part

Claims (12)

As a place between the processes, the metal material of the initial mountain made of metal material piled up in a yard where the metal material including any one of the semi-finished product, the final product, and the container is arranged is conveyed by a conveying device, A yard management device for creating a final pile made of metal materials piled in a stacking order according to a payout order to the subsequent process of the yard,
For any two of the metal materials, an initial transport sequence variable that is a binomial variable that defines a relative order of initial transport that is transport from the initial mountain, and an initial transport of the metal material from the initial mountain, A temporary variable occurrence presence / absence variable, which is a variable that determines whether or not the yard is temporarily transported to a temporary storage place, is a decision variable,
Metal material information including identification information of the initial mountain and identification information of the metal material at each product position of the initial mountain, and identification information of the final mountain and identification information of the metal material at each product position of the final mountain Metal material information acquisition means for acquiring
In the same final mountain, when the metal material that is above the metal material below is initially conveyed first, the metal material that is initially conveyed first is transferred to the temporary mountain before the conveyance to the final mountain. Constraint equation setting means for setting a constraint equation including a first constraint equation that represents that it is necessary to temporarily place it in a storage site using the decision variable based on the metal material information;
Objective function setting means for setting an objective function aimed at minimizing the number of the metal materials where the temporary placement occurs based on the metal material information;
Deriving the value of the decision variable as an optimal solution when the value of the objective function is minimum or maximum within a range satisfying the constraint equation is performed by performing optimization calculation by mathematical programming A yard management device comprising a calculation means. The initial transfer order variable is a two-term parameter that defines the relative order of the initial transport of the two metal materials from the initial peak, considering the order of the initial transport of the metal material from the initial peak as a total order. Variable,
The constraint expression is such that the initial transport forward variable is comparable, the second constraint expression is an expression expressed using the initial transport forward variable, and the initial transport forward variable is transitive. The yard management device according to claim 1, further comprising: a third constraint expression that is an expression expressed by using the initial transport order variable.   The constraint equation is that, using the initial transfer forward variable, the metal material that is above the metal material underneath must be initially transported from the initial mountain first in the same initial mountain. The yard management device according to claim 1, further comprising a fourth constraint equation that is an expressed equation. In addition to the identification information of the metal material, in addition to the identification information of the metal material, the identification information of the metal material is determined based on the temporary placement occurrence presence / absence variable derived by the optimization calculation unit. Giving another identification information, considering the final transport of the metal material from the temporary storage site to the final mountain as an initial transport of the virtual metal material given the other identification information;
Changing the identification information of the metal material at the stack position of the metal material where the temporary placement in the final mountain occurs to the other identification information given to the metal material;
One pile piled according to the initial conveyance order from the initial pile of the metal material, which is determined based on the initial conveyance order variable derived by the optimization calculation means, and the metal material where the temporary placement occurs Considering the virtual piles arranged in the upper stage and each of the two stacking stages in which the virtual metal material corresponding to the final conveyance of the metal material in which the temporary placement occurs is arranged in the lower stage as the initial pile,
Setting the initial transport sequence variable as a binary variable that defines the relative order of the initial transport from the initial mountain or the temporary storage of any two of the metal materials including the virtual metal material;
The initial transport order variable that has been set is that the order of initial transport of the metal material from which the temporary placement occurs from the initial mountain is ahead of the order of initial transport of the metal material from the temporary storage site. Further setting as the constraint equation a fifth constraint equation that is an expression expressed using
After setting the objective function,
Deriving the set initial transport forward variable when the value of the objective function is minimum or maximum within a range satisfying the constraint equation, and based on the derived initial transport forward variable, for each of the metal materials, The yard management device according to any one of claims 1 to 3, further comprising a derivation unit that derives an order of conveyance from the initial mountain to the final mountain.   The constraint equation is present above the portion of the metal material constituting the initial mountain where the product order from the lowest level of the initial mountain coincides with the product order from any of the lowest levels of the final mountain. The initial transport order of the metal material from the initial mountain to the initial mountain is the initial transport of the metal material transported from the initial mountain different from the initial mountain or the temporary storage to the initial mountain. The yard according to any one of claims 1 to 4, further comprising a sixth constraint expression that is an expression expressing the order of the first order by using the initial conveyance order variable. Management device. Instead of the initial transfer order variable, the initial transfer of any two of the metal materials from the initial mountain to the final mountain, the initial transfer from the initial mountain to the temporary storage site, and from the temporary storage site to the final Using the initial and final transport sequence variables, which are binary variables that define the relative order of final transport to the mountain,
The constraint equation indicates that the initial conveyance of the metal material from the initial mountain to the temporary storage is ahead of the final conveyance of the metal material from the temporary storage to the final mountain. The yard management device according to any one of claims 1 to 4, further comprising a seventh constraint expression that is an expression expressed using an order variable.   The constraint equation is present above the portion of the metal material constituting the initial mountain where the product order from the lowest level of the initial mountain coincides with the product order from any of the lowest levels of the final mountain. The order of the initial transport of the metal material from the initial mountain is the transport of the metal material transported from the initial mountain different from the initial mountain or the temporary storage to the initial mountain to the initial mountain. 8. The eighth constraint expression according to claim 6, further comprising an eighth constraint expression that is an expression expressing that the order is ahead of the order using the initial / final transport order variable and the temporary placement occurrence variable. Yard management device.   The constraint equation indicates that, in the same final mountain, it is necessary to first transport the metal material below the metal material above to the final mountain first, and the initial and final transport order variables. The yard management device according to claim 6, further comprising a ninth constraint expression that is an expression expressed by using the ninth constraint expression.   The yard management device according to claim 1, wherein the first constraint equation is represented by at least one of a linear inequality and an equation. The yard is a place between a steel making process and a rolling process in a steel manufacturing process,
The yard management device according to claim 1, wherein the metal material is a steel material. As a place between the processes, the metal material of the initial mountain made of metal material piled up in a yard where the metal material including any one of the semi-finished product, the final product, and the container is arranged is conveyed by a conveying device, A yard management method for creating a final pile made of metal materials piled up in a stacking order according to a payout order to a subsequent process of the yard,
For any two of the metal materials, an initial transport sequence variable that is a binomial variable that defines a relative order of initial transport that is transport from the initial mountain, and an initial transport of the metal material from the initial mountain, A temporary variable occurrence presence / absence variable, which is a variable that determines whether or not the yard is a temporary storage,
Metal material information including identification information of the initial mountain and identification information of the metal material at each product position of the initial mountain, and identification information of the final mountain and identification information of the metal material at each product position of the final mountain Metal material information acquisition process to acquire,
In the same final mountain, when the metal material that is above the metal material below is initially conveyed first, the metal material that is initially conveyed first is transferred to the temporary mountain before the conveyance to the final mountain. A constraint equation setting step for setting a constraint equation including a first constraint equation that represents that it is necessary to temporarily place it at a storage location using the decision variable based on the metal material information;
An objective function setting step for setting an objective function aimed at minimizing the number of the metal materials in which the temporary placement occurs based on the metal material information;
Deriving the value of the decision variable as an optimal solution when the value of the objective function is minimum or maximum within a range satisfying the constraint equation is performed by performing optimization calculation by mathematical programming A yard management method comprising: a calculation step.   A program that causes a computer to function as each unit of the yard management device according to any one of claims 1 to 10.

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