JP7010254B2 - Production planning method and production planning system - Google Patents

Description

The present invention relates to a production planning method and a production planning system for planning the timing of processing in each processing facility when processing each of a plurality of objects in a plurality of processing facilities on a production line.

The processing process of the product is sequentially performed using a plurality of processing facilities in the production line. In order to maximize product productivity, it is important to optimize the production plan that defines the product input schedule to the processing equipment. In recent years, there are a wide variety of product types, and processing conditions such as processing time in each processing facility differ for each product type. Therefore, the number of possible production plan candidates increases exponentially with the increase in the number of products to be introduced. Therefore, when calculating the optimum production plan, it is not realistic to examine all the production plan candidates and extract the optimum production plan from the examined candidates.

Therefore, a method has been proposed in which an optimization problem is mathematically modeled and solved by a solver that implements a mathematical programming method (see, for example, Patent Documents 1 to 4). In Patent Documents 1 to 4, it is proposed to use a spatiotemporal network model as one of the representation methods of a mathematical model, and to plan a ship allocation plan, an operation plan of a car sharing system, or charging / discharging by the spatiotemporal network model. ing.

Japanese Unexamined Patent Publication No. 2017-333378 Japanese Unexamined Patent Publication No. 2016-151940 Japanese Unexamined Patent Publication No. 2012-175722 Japanese Unexamined Patent Publication No. 2018-106621

The methods of Patent Documents 1 to 4 have high expressive power and can be flexibly modeled even for complicated problems. However, in the methods of Patent Documents 1 to 4, there are many variables to be determined, and as the scale of the problem increases, it takes time to calculate, and it takes time to find the optimum production plan that maximizes productivity. It ends up.

Therefore, an object of the present invention is to provide a production planning method and a production planning system capable of creating a production plan that maximizes productivity at high speed.

The present invention has the following configurations in order to solve these problems.
[1] When processing a plurality of objects in a production line having a plurality of processing facilities, a production plan showing the start time and end time of the processing in each of the processing facilities is created for each of the plurality of objects. It ’s a production planning method.
A data acquisition process for acquiring the processing time in each processing facility for each object as processing condition data, and
Based on the acquired processing condition data, a formulation process for formulating the processing content to be applied to each object and the processing time as a QUABO model or Ising model via a spatiotemporal network model, and a formulation process.
The acquisition process to acquire the solution derived based on the formulated QUABO model or Ising model, and
A production planning method characterized by having.
[2] In the formulation step, the constraint condition indicating that the number of the objects to be processed at the same time in each of the processing facilities is one or less is formulated as an equal sign equation provided with a dummy variable. The production planning method according to [1].
[3] In the formulation step, an evaluation function is determined based on a term obtained by multiplying a variable related to an edge of the spatiotemporal network model by a weight that increases with the passage of time [1] or [2]. ] The production planning method described in.
[4] In the formulation process, a constraint condition indicating that processing can be replaced by two or more different processing facilities is set for one representative facility among the two or more processing facilities and the other alternative facility. The production planning method according to any one of [1] to [3], wherein the processing capacity ratio is formulated by using it as a weight of a variable related to an edge entering a node of the spatiotemporal network model.
[5] When processing a plurality of objects in a production line having a plurality of processing facilities, a production plan showing the start time and end time of the processing in each of the processing facilities is created for each of the plurality of objects. It is a production planning device
A data acquisition means for acquiring the processing time in each processing facility for each object as processing condition data, and
Based on the acquired processing condition data, a formulation means for formulating the processing content to be applied to each object and the processing time as a QUABO model or Ising model via a spatiotemporal network model.
A solution acquisition means for acquiring a solution when a formulated QUABO model or Ising model is solved by an annealing machine,
A production planning system characterized by having.

According to the present invention, in the processing process of a product having a plurality of processing facilities, the objective function and the constraint condition related to the production planning problem of the product are formulated into a QUAO model or an Ising model by utilizing the concept of a spatiotemporal network model. Since the optimum solution can be obtained using the annealing machine, the optimum solution can be derived at high speed even if the number of products having different processing contents increases.

It is a schematic diagram which shows an example of the rolling line which rolls a slab. It is a Gantt chart which shows the processing outline of one slab in the rolling line of FIG. It is a Gantt chart which shows an example of the case where two slabs A and B are rolled one by one. It is a Gantt chart which shows the rolling processing pattern of a plurality of slabs A, B in a rolling line. It is a Gantt chart which shows the rolling processing pattern of a plurality of slabs A to D in a rolling line. It is a schematic diagram which shows the processing outline of the overtaking rolling. It is a block diagram which shows the preferable embodiment of the production planning system of this invention. It is a schematic diagram which shows an example of the processing condition data SD acquired by the data acquisition means of FIG. It is a schematic diagram which shows an example of a space-time network model. It is a flowchart which shows the preferable embodiment of the production planning method of this invention.

First, a case where the production line showing an example of the embodiment of the production planning system of the present invention is, for example, a rolling line of a steel material in the steel industry, and the production planning of the rolling line is performed will be illustrated below. FIG. 1 is a block diagram showing an example of a rolling line for rolling a slab, which is an object of processing. The rolling line 100 of FIG. 1 includes a heating furnace 101 for heating the slabs, a rolling equipment 103 for rolling the slabs supplied from the heating furnace 101, and a cooling equipment 104 for cooling the slabs rolled in the rolling equipment 103. And the standby / overtaking equipment 102, which is provided between the heating furnace 101 and the rolling equipment 103 and makes the heated or rolled slabs stand by. Further, the rolling line 100 is provided with a transport facility 105 for transporting the slabs between the processing facilities.

The heating furnace 101 has a plurality of extraction ports for extracting the heated slabs, and the slabs s are extracted one by one from the extraction ports. The rolling equipment 103 rolls the slabs transferred from the heating furnace 101 via the transfer equipment 105 to the target plate thickness. The cooling equipment 104 has a function of performing controlled cooling (accelerated cooling) to the slabs after rolling by using, for example, a shower. It should be noted that air cooling may be performed by allowing the cooling equipment 104 to stand by without performing controlled cooling using a shower.

The standby / overtaking equipment 102 is equipment that makes the slabs stand by on the upstream side before being supplied to the rolling equipment 103. At the same time, the standby / overtaking equipment 102 has a function of lifting the slabs when overtaking in order such as supplying the slabs extracted from the heating furnace 101 later to the rolling equipment 103 first. The standby / overtaking equipment 102 functions as a cooling equipment for cooling the slabs by air cooling. The cooling process by air cooling process requires a longer time to cool down to the target temperature than the cooling process by water cooling process.

FIG. 2 is a Gantt chart showing an outline of processing of one slab in the rolling line of FIG. 1. In addition, in FIG. 2 and FIGS. As shown in FIGS. 1 and 2, the slabs extracted from the heating furnace 101 are rolled in the rolling equipment 103 until the plate thickness is required to start the cooling process (rolling time T1). After that, the slabs that need to be cooled during the rolling process are conveyed to the cooling facility 104 via the transport facility 105. After being cooled to the target temperature in the cooling equipment 104 (cooling time T2), it is returned to the rolling equipment 103 and subjected to a second rolling until the target plate thickness is reached (rolling time T3). Then, the rolling equipment 103 rolls until the plate thickness requires cooling, and when further cooling is required, the cooling equipment 104 cools the rolled slabs transported via the transport equipment 105.

FIG. 3 shows a Gantt chart focusing on one slab, but in the rolling line 100, a plurality of slabs are sequentially rolled. FIG. 3 is a Gantt chart showing an example of a case where two slabs A and B are rolled one by one. Note that FIG. 3 illustrates a case where the next slab B process is not performed until the process of one slab A is completed. That is, in FIG. 3, the rolling equipment 103 is in the standby state during the period in which the slab A is being cooled, and the cooling equipment 104 is in the standby state during the period in which the rolling process is being performed.

In this case, the time required to complete both rolling processes of the two slabs A and B is the first rolling time TA1 of the slab A, the cooling time TA2, the second rolling time TA3, and the first rolling time of the slab B. When the rolling time TB1, the cooling time TB2, and the second rolling time TB3 are set to (TA1 + TA2 + TA3) + (TB1 + TB2 + TB3). In this way, when the waiting time when nothing is done in the processing equipment occurs, the required total rolling time is extended and the productivity is lowered. In order to prevent this, it is conceivable to shorten the waiting period of the processing equipment such as the rolling equipment 103 or the cooling equipment 104 to shorten the rolling process of the plurality of slabs A and B.

FIG. 4 is a Gantt chart showing rolling processing patterns of a plurality of slabs A and B in a rolling line. In FIG. 4, in the cooling time TA2 in which the slab A after the completion of the first rolling is controlled and cooled by the cooling equipment 104, the next slab B is rolled in the rolling equipment 103 until the plate thickness is required to start the cooling process. (Rolling time TB1). At this time, the rolling process of the slab B is completed by the start of the second rolling process of the slab A.

At the end of the rolling process of the slab B, the slab A is controlled and cooled by the cooling equipment 104. Therefore, the slab B is transported to the standby / overtaking equipment 102 in order to wait until the control cooling of the slab A on the upstream side of the line and the completion of the second rolling process, and is cooled by the air cooling process while waiting (cooling). Time TB2a). Then, when the rolling process of the slab A (rolling time TA3) is completed, the slab B passes through the rolling equipment 103, is conveyed to the cooling equipment 104, and is cooled to a target temperature (cooling time TB2b).

As described above, between the first rolling time TA1 and the second rolling time TA3 for the slab A, the rolling treatment for the slab B (rolling time TB1) and the cooling treatment by air cooling (cooling time TB2a) are carried out. Therefore, the time required for the rolling process of both the slabs A and B is shortened to (TA1 + TA2 + TA3) + (TB2b + TB3).

FIG. 5 is a Gantt chart showing rolling processing patterns of a plurality of slabs A to D in a rolling line. As shown in FIG. 5, in the rolling process of the four slabs A to D, as in FIG. 4, the rolling process of the subsequent slab is performed during the cooling period of the preceding slab. Only one slab can be processed at the same time by each processing facility. Therefore, for example, while the preceding slab is rolling, the succeeding slab is not rolled. Further, while the preceding slab is controlled and cooled by the cooling equipment 104, the succeeding slab is not cooled by the cooling equipment 104.

FIG. 6 is a Gantt chart showing an outline of the overtaking rolling process in which the rolling processes of the slabs B and C, which do not require the cooling process, are performed during the cooling time of the slab A, which requires the cooling process during the rolling process. As shown in FIG. 6, after the slab A is rolled by the rolling equipment 103, it is transported to the standby / overtaking equipment 102 and air-cooled while being lifted from the transport equipment 105. Then, the slabs B and C extracted from the heating furnace 101 after the slab A are conveyed by the transfer equipment 105 and rolled (rolling time TB, TC).

By this overtaking rolling, the total rolling time required for the rolling process of the three slabs A to C can be further shortened. For example, if the slab A can be cooled by air cooling and the slab B needs to perform controlled cooling, it is better to perform further controlled cooling after rolling the slab B while the slab A is air-cooled. The processing time for the two slabs A and B is shortened. That is, in the rolling line 100, if the processing in which one rolling mill and all the two cooling facilities are operated is performed, the rolling processing will be performed most efficiently.

In FIGS. 2 to 6 described above, a case where the first rolling process, the cooling process, and the second rolling process are performed under the same processing conditions for all the slabs is illustrated. On the other hand, there are a wide variety of product types, and different product types have different processing conditions such as processing time at each processing facility. That is, the rolling time in the rolling equipment 103 is different, and the cooling time or the cooling speed in the cooling equipment 104 is also different depending on the required performance of the product. When slabs with different processing conditions are introduced in sequence, the number of possible production plan candidates increases exponentially, and it is hoped that the production plan that maximizes productivity will be extracted from them. It is rare.

FIG. 7 is a block diagram showing a preferred embodiment of the production planning system of the present invention, and the production planning system 1 will be described with reference to FIG. 7. The production planning system 1 of FIG. 7 formulates a production plan with a spatiotemporal network as a cost function (objective function) or a constraint condition, converts the cost function and the like into a QUABO model, and solves them with an annealing machine. It has a device 10 and an annealing machine 20. The modeling device 10 is, for example, a Neumann computer, which constructs a configuration as shown in the figure by executing a program on a computer. On the other hand, the annealing machine 20 includes, for example, a quantum annealing device or a digital annealing device using a dedicated circuit such as FPGA.

Models that can be handled by the annealing machine 20 include an Ising model or a QUADratic unconstrained quadratic optimization (QUAD) model. Of these, the QUABO model is represented by variables xi and xj that take a value of 0 or 1 and a matrix Q as in the above equation (1).

The Ising model takes variables +1 and -1 as spins, and the QUAO model only takes two values of variables 0 and 1 instead of spins. Both models are equivalent and can be converted to each other. Does not change.

When obtaining the optimum solution using the annealing machine, it is necessary to convert the combinatorial optimization problem into the QUABO model of the above equation (1). On the other hand, a production line having a plurality of processing facilities can be represented as a spatiotemporal network in which the spatial coordinates of the processing process in each processing facility are expanded in the time direction. Therefore, the modeling device 10 formulates the processing for each of a plurality of objects (slabs) using a space-time network, and QUAO as a combinatorial optimization problem for each of the formulated objects (slabs). Convert to a model.

The modeling device 10 includes a data acquisition means 11 and a formulation means 12. The data acquisition means 11 acquires the processing time of each object in each processing facility as the processing condition data SD. The processing condition data SD may be input from a keyboard or the like, may be acquired from a storage means (not shown), or may be acquired via a network.

FIG. 8 is a schematic diagram showing an example of processing condition data. As shown in FIG. 8, in the processing condition data SD, the first rolling time, the second rolling time, and the cooling time when the cooling equipment 104 is used are set for each slab s1 to s4, respectively. ing.

Here, in the rolling line shown in FIG. 1, the cooling process can be performed by either the standby / overtaking equipment 102 or the cooling equipment 104. When there are a plurality of processing equipments that can be substituted for one processing, the processing condition data SD in FIG. 8 contains alternative condition information indicating whether the processing by the alternative equipment is possible, and the processing when the substitution is performed. Ability ratio and is included. The processing capacity ratio means the capacity when any one of the processing equipments that can be replaced with each other is used as the representative equipment. In FIG. 8, the capacity ratio of the standby cooling process or the overtaking cooling process in the standby / overtaking facility 102 when the cooling facility 104 is used as the representative facility is input.

The formulation means 12 of FIG. 7 determines the processing content and the processing time to be applied to each slab based on the processing condition data SD acquired by the data acquisition means 11 via a spatiotemporal network model, a QUAO model or an Ising model. It is formulated as. FIG. 9 is a schematic diagram showing an example of a spatiotemporal network model. The spatiotemporal network model is an extension of the network of spatial coordinates in the time axis direction, and is represented by a node i and an edge e connecting the nodes i.

In other words, the spatial coordinate network means the processing facility (processing process) applied to the slab in each processing facility of the rolling line, and the time t to which this spatial coordinate network was processed is expanded in the time axis direction. It is a thing. The rolling process of the slabs corresponds to tracing the edge e from the start node to the end node on the spatiotemporal network. Therefore, the passing process of the slabs and the processing time (t) can be known from the passed edge e.

In a spatiotemporal network, constraints are formulated when tracing each node from the start node to the end node and selecting an edge. First, let xse be a variable that becomes "1" when the slab s passes through the edge e and becomes "0" when it does not pass through. The set of edges e entering the node i is Ein (i), the set of edges e'exiting the node i is Eout (i), the set of slabs is S, and the set of nodes i of the slabs is I (s). , Let P be the set of edges e. Then, the first rolling process by the rolling equipment 103, the cooling process by the cooling equipment 104 (or the standby / overtaking equipment 102), and the second rolling process by the second rolling equipment 103 are sequentially performed on a certain slab s. Is expressed by the following equation (2) on the spatiotemporal network.

In the equation (2), the node i belonging to the start node set I (s) S and the end node set I (s) e is not considered. The constraint on the start node set I (s) S is expressed by the following equation (3), and the constraint on the end node set I (s) e is expressed by the following equation (4).

Among the treatments applied to the slabs, there are irreplaceable treatments that can be performed only by a predetermined facility and treatments that can be replaced by other equipment. The rolling process is an irreplaceable process that can only be performed by the rolling equipment 103. On the other hand, the cooling process is an alternative process that can be performed not only in the cooling facility 104 but also in the standby / overtaking facility 102.

For the processing that cannot be replaced in other facilities, the constraint condition for selecting the edge e is formulated so that the processing in the equipment that cannot be replaced is performed for a predetermined time. Assuming that the set of non-substitutable processing p is P, the processing time in the non-substitutable processing p is Tsp, and the set of edges corresponding to the processing p of the slabs is Esp, it can be expressed by the following equation (5).

On the other hand, for processing that can be replaced by a plurality of facilities, the constraint condition is that the processing time at the plurality of facilities satisfies the processing time of the processing condition data SD. That is, for the processing that can be replaced by other processing, the constraint condition for selecting the edge so that the processing is performed for a predetermined time in each facility is formulated. For a certain slab s, if the set of substitutable processing ps is g (s) and the set of edges corresponding to the set g (s) is Esg (s), it can be expressed by the following equation (6).

In the formula (6), one representative of the alternative treatments for the slabs is selected (cooling equipment 104 in this example), the treatment time when the treatment is performed alone is Tsg, and the other alternative to the representative treatment. The ratio of the cooling rate of possible processing is defined as the processing capacity ratio Vsp. When the cooling process is performed by the cooling equipment 104, Vsp = 1. Further, let f be a function that returns the process p corresponding to the edge e. Although the case where the data acquisition means 11 acquires the processing capacity ratio Vsp as the processing condition data SD is illustrated in FIG. 8, it may be stored in advance in the formulation means 12.

The above equations (2) to (6) are formulations of constraint conditions and the like in each slab s, but it is necessary to consider equipment constraints and the like related between different slabs. That is, only one slab s can be processed by each processing facility at the same time. Here, the time is t, the set of edges corresponding to the equipment m is Emt, the dummy is "0" when the equipment m is not processing any slab at the time t, and is "1" when the equipment m is processing. If dmt is provided as a variable of, it can be expressed by the following equation (7).

Further, from the viewpoint of maximizing productivity, the processing end time of the slabs to be planned may be the shortest. Therefore, in the spatio-temporal network model, an evaluation function Wt whose value increases as the time is slower is provided as a weight for the edge e entering the end point node, and the problem is to minimize the following equation (8). Specifically, the elapsed time from the start of production is t, and the evaluation function becomes larger as the elapsed time becomes longer. Here, the set of edges entering the end node of the slab s is Ese, and the function that returns the time t corresponding to the edge e is Tf (e). Further, here, the formulation is made focusing on the edge e that enters the end point node, but it does not exclude the targeting of other edges, and it is sufficient if the elapsed time can be evaluated.

Here, the evaluation function Wt is a function such as Wt = ab ^t (a> 0, b> 1). The evaluation function Wt is not limited to this, and the evaluation value with respect to the time t may be stored as a table.

Further, the above-mentioned equation (7) can be expressed by the constraint equation of the following equation (9) without using a dummy variable.

However, in quantum annealing, it is necessary to convert to an Ising model or a QUA model and solve it, but these models make it difficult to handle the constraint of the inequality sign that appears in the expression of the resource constraint. Therefore, by using a dummy constraint as in Eq. (7), it can be formulated as a constraint expression with an equal sign that can be converted into a QUABO model.

The above-mentioned equations (2) to (8) are stored in advance in the formulation means 12 of FIG. 7. Then, the formulation means 12 formulates as a combinatorial optimization problem using the spatiotemporal network model by substituting the processing condition data SD acquired by the data acquisition means 11 into the equations (2) to (8). To go.

[Conversion to QUABO model]
The formulation means 12 of FIG. 7 formulates the functions shown in the above equations (2) to (8) into a QUABO model.

First, regarding equation (2), the right side of equation (2) is moved to the left side for the purpose of model transformation so that the value of the function increases when the constraint condition is violated. Further, when squared so that a negative term does not appear, the following equation (10) is obtained.

By expanding this, it is possible to convert it into a quadratic expression.

Similarly, when the equations (3) and (4) are expanded into quadratic equations, they become quadratic equations as shown in the following equations (12) and (13). In the equations (12) and (13), it is used that Xse is a value of 0 or 1 and Xse = xse ² . Also, the constant part is ignored because it does not affect the minimization.

Similarly, when the equations (4) to (7) are expanded and expressed by a quadratic equation, the following equations (14) to (17) are obtained.

The H of the QUABO model is as follows using the above equation (18).

It should be noted that A1 to A5 in the equation (18) are constants preset in the formulation means 12. Further, in the formulation means 12, the combination of the slab s and the edge e which are the subscripts in the variable xse and the combination of the equipment m and the time t which are the subscripts of the dummy variable d are the variables xij of the QUABO model in the equation (1). It is associated with the subscripts i and j of. Further, in the Hamiltonian H of the equation (18), the coefficient that appears when the variable xi and the variable xj are bound by the quadratic product is the Qij of the QUABO model in the above equation (1). In this way, the formulation means 12 converts the functions shown in the above equations (2) to (8) into the QUABO model shown in the equation (18).

The modeling device 10 of the production planning system 1 of FIG. 7 further includes a transmission / reception means 13 and an information output means 14. The transmission / reception means 13 transmits data to and from the annealing machine 20 via a network, for example. The transmission / reception means 13 may be any as long as it transmits data to the annealing machine 20 via wire or wireless. Then, the transmission / reception means 13 transmits the QUABO model converted as in the equation (18) in the formulation means 12 to the annealing machine 20.

The annealing machine 20 searches for the optimum solution by changing the Hamiltonian over time, and tries to select the value of the variable that minimizes H represented by the equation (18). Further, the transmission / reception means 13 functions as a solution acquisition means for acquiring a solution when the converted QUABO model or Ising model is solved by the annealing machine. The information output means 14 is composed of, for example, a display or a printer device, and outputs the optimum solution received by the transmission / reception means 13.

FIG. 10 is a flowchart showing a preferred embodiment of the production planning method of the present invention, and the production planning method will be described with reference to FIGS. 1 to 10. First, in the data acquisition means 11, the processing step and the processing time thereof are acquired for each slab s which is an object (see FIG. 8, step ST1). Then, based on the acquired processing condition data SD, a function using the spatiotemporal network model is generated as in equations (2) to (8) (see FIG. 9, step ST2).

Then, in the formulation means 12, the functions of equations (2) to (8) are converted into QUAO models such as equations (10) to (18) (step ST3). This QUAO model is transmitted from the transmission / reception means 13 to the annealing machine 20, and the optimum solution is obtained in the annealing machine 20 (step ST4). After that, in the transmission / reception means 13, the optimum solution is acquired from the annealing machine 20, and the optimum solution is output from the information output means 14 such as a monitor (step ST5).

Here, steps ST2 and ST3 need only be performed once in the formulation of the problem, and need not be performed when the case study is performed without changing the problem structure. In addition, the annealing machine does not necessarily guarantee that a global optimum solution can be obtained at this time, but here, acquiring a feasible semi-optimal solution is also considered to be a solution acquisition, and is treated as an optimum solution in a broad sense.

According to the above embodiment, all the candidates are selected once by converting the combinatorial optimization problem in which the production plan in the production line is formulated by the spatiotemporal network model into the QUABO model or the Ising model and deriving the optimum solution. Since it can be investigated by processing, the optimum solution can be derived at high speed even if the number of objects with different processing conditions on the production line increases. In other words, the quantum annealing technology is capable of high-speed calculation unlike the conventional Neumann computer. Also, the calculation time does not change as the scale of the problem increases.

The embodiment of the present invention is not limited to the above embodiment, and various modifications can be made. For example, in the above embodiment, a rolling line is exemplified as a production line, and it can be applied not only to a rolling line but also to various production plans. Further, as the processing step of the production line, the case where there are three processing steps of two rolling steps and the cooling step is illustrated, but the case where there are three or more processing steps can also be applied. Further, in FIG. 1, the case where the formulation means 12 is provided in the modeling device 10 is illustrated, but it may be provided on another device such as a cloud.

1 Production planning system 10 Modeling device 11 Data acquisition means 12 Formulation means 13 Model transformation means 13 Transmission / reception means (solution acquisition means)
14 Information output means 20 Annealing machine 100 Rolling line 101 Heating furnace 104 Standby / overtaking equipment 103 Rolling equipment 104 Cooling equipment 105 Transfer equipment AD, s slab (object)
SD processing condition data

Claims (4)

A production planning method for creating a production plan showing the start time and end time of processing in each of the processing facilities for each of the plurality of objects when processing a plurality of objects in a production line having a plurality of processing facilities. And,
A data acquisition process for acquiring the processing time in each processing facility for each object as processing condition data, and
Based on the acquired processing condition data, a formulation process for formulating the processing content to be applied to each object and the processing time as a QUABO model or Ising model via a spatiotemporal network model, and a formulation process.
The acquisition process to acquire the solution derived based on the formulated QUABO model or Ising model, and
Have,
In the formulation process, the constraint condition indicating that processing can be replaced by two or more different processing facilities is the processing capacity ratio of one representative facility among the two or more processing facilities to the other alternative facility. Is a production planning method, which is characterized by using as a weight of a variable related to an edge entering a node of the spatiotemporal network model . The claim is characterized in that, in the formulation step, the constraint condition indicating that the number of the objects to be processed at the same time in each of the processing facilities is one or less is formulated as an equal sign equation provided with a dummy variable. The production planning method according to 1. The production according to claim 1 or 2, wherein in the formulation step, an evaluation function is determined based on a term obtained by multiplying a variable related to an edge of the spatiotemporal network model by a weight that increases with time. Planning method. A production planning device that creates a production plan showing the start time and end time of processing in each of the processing equipments for each of the plurality of objects when processing a plurality of objects in a production line having a plurality of processing equipments. And,
A data acquisition means for acquiring the processing time in each processing facility for each object as processing condition data, and
Based on the acquired processing condition data, a formulation means for formulating the processing content to be applied to each object and the processing time as a QUABO model or Ising model via a spatiotemporal network model.
A solution acquisition means for acquiring a solution when a formulated QUABO model or Ising model is solved by an annealing machine,
Have,
The formulation means sets a constraint condition indicating that processing can be replaced by two or more different processing facilities, and the processing capacity ratio of one representative facility among the two or more processing facilities to the other alternative facility. Is a production planning system, which is characterized by using as a weight of a variable related to an edge entering a node of the spatiotemporal network model .

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