Processing plan development method, processing resource allocation method, processing plan development device, processing resource allocation device, processing plan development program, and processing resource allocation program

Abstract

To improve production efficiency in a parallel distribution type production form.SOLUTION: The processing plan formulation method includes a solving step of solving an optimization problem having a configuration unit to which each job is allocated and a processing order of the job allocated to each configuration unit as a solution by using an objective function representing a cost or a benefit of the processing plan derived from the solution, wherein the processing plan includes an exchange between configurations for processing a job included in the job by a configuration different from the configuration to which the job is allocated, and the objective function includes a term representing a cost of the exchange between the configurations.SELECTED DRAWING: Figure 5

Description

[Technical Field]

[0001] The present invention relates to a processing plan development method, a processing resource allocation method, a processing plan development device, a processing resource allocation device, a processing plan development program, and a processing resource allocation program for processing involving multiple entities and multiple steps. [Background technology]

[0002] In recent years, in the manufacturing industry, as a countermeasure against the risk of production stoppage due to disasters and other reasons, distributed production across multiple factories has become more common, rather than production at a single factory. Also, the so-called parallel distributed production model, in which the same item is produced across multiple factories, is becoming increasingly common. Indeed, with a parallel distributed production model, even if one factory stops, production of the same product can continue at other factories. This allows for better dispersion of the risk of a factory or manufacturing equipment shutdown compared to production at a single factory. However, in terms of production efficiency, a parallel distributed production model is not necessarily desirable, as it often requires more time for setup, transportation, etc. than production at a single factory or with dedicated production resources.

[0003] It goes without saying that it is desirable to improve production efficiency even in a parallel distributed system. For example, Patent Document 1 describes a multi-subject collaborative planning system that, when formulating an operation plan including multiple subjects, generates multiple plan proposals that satisfy constraint conditions and evaluates the generated plan proposals based on an objective function calculated from a self-evaluation value, an estimated evaluation value of a collaborative partner, and a collaborative partner rate. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Patent Publication No. 2021-117851 Summary of the Invention [Problem to be solved by the invention]

[0005] Various methods have been studied to improve production efficiency in parallel distributed production systems, but there is still room for improvement, including the conventional technologies mentioned above.

[0006] An object of one aspect of the present invention is to realize a process planning method and the like that contributes to improving production efficiency in a parallel-distributed production format. [Means for solving the problem]

[0007] In order to solve the above-mentioned problems, a processing plan formulation method according to one embodiment of the present invention is a processing plan formulation method for formulating a processing plan for processing a plurality of jobs by a plurality of constituent units, and includes a solution process for solving an optimization problem whose solution is the constituent units to which each job is allocated and the processing order of the jobs allocated to each constituent unit, using an objective function that represents the cost or benefit of the processing plan derived from the solution, wherein the processing plan includes interactions between constituent units for processing the steps that make up a job by constituent units different from the constituent units to which the job is allocated, and the objective function includes a term that represents the cost of interactions between the constituent units.

[0008] In order to solve the above-mentioned problems, a processing resource allocation method according to one embodiment of the present invention is a processing resource allocation method for allocating each of a plurality of processes for producing each of a plurality of product types to each of one or more pieces of equipment provided in each of one or more factories, and includes a solution process for solving an optimization problem whose solution is at least one of whether or not to allocate each process to each piece of equipment and the amount of time that can be allocated, using an objective function that represents the cost or benefit of the solution, and the objective function includes a term that represents the constraint violation risk that takes into account the transportation time that occurs when the factory equipped with the equipment that allocates the current process according to the solution is different from the factory equipped with the equipment that allocates the previous process according to the solution.

[0009] In order to solve the above-mentioned problems, a processing plan development device according to one embodiment of the present invention is a processing plan development device that develops a processing plan for processing multiple jobs at multiple constituent units, and includes a first solution unit that solves an optimization problem whose solution is the constituent units to which each job is allocated and the processing order of the jobs allocated to each constituent unit, using an objective function that represents the cost or benefit of the processing plan derived from the solution, and the processing plan includes interactions between constituent units for processing steps that make up a job at constituent units other than the constituent units to which the job is allocated, and the objective function includes a term that represents the cost of interactions between the constituent units.

[0010] In order to solve the above-mentioned problems, a processing resource allocation device according to one embodiment of the present invention is a processing resource allocation device that allocates each of a plurality of processes for producing each of a plurality of varieties to each of one or more pieces of equipment provided in each of one or more factories, and is equipped with a second solution-finding unit that solves an optimization problem whose solution is at least one of whether or not to allocate each process to each piece of equipment and the amount of time that can be allocated, using an objective function that represents the cost or benefit of the solution, and the objective function includes a term that represents the constraint violation risk that takes into account the transportation time that occurs when the factory in which the equipment that allocates the current process according to the solution is installed is different from the factory in which the equipment that allocates the previous process according to the solution is installed.

[0011] The device according to each aspect of the present invention may be realized by a computer. In this case, the control program for the device, which causes the computer to operate as each part (software element) of the device, thereby realizing the device on the computer, and the computer-readable recording medium on which the control program is recorded, also fall within the scope of the present invention. [Effects of the Invention]

[0012] According to one aspect of the present invention, a production plan with high production efficiency can be formulated in a parallel distributed production configuration. [Brief explanation of the drawings]

[0013] [Figure 1] 1 is a functional block diagram illustrating an example of a production plan formulation device according to a first embodiment of the present invention. [Figure 2] FIG. 1 is a diagram for explaining the operation of the multipurpose DABC used in the production planning method. [Figure 3] FIG. 1 is a diagram showing a multi-factory model that is the subject of the production planning method. [Figure 4] FIG. 1 is a diagram showing transport routes between factories. [Figure 5] 1 is a flowchart showing the flow of a production planning method. [Figure 6] It is a single common hybrid flow that integrates the flows for all target product types. [Figure 7] 1 is a graph showing the characteristics of the reliability function R(t) and the failure probability distribution function F(t). [Figure 8] FIG. 10 is a diagram showing a comparison of H and QTC compliance rates included in the objective function. [Figure 9] FIG. 10 is a functional block diagram showing an example of a production resource allocation device according to a second embodiment of the present invention. [Figure 10] FIG. 1 is a diagram showing transport routes between and within two factories. [Figure 11] FIG. 10 is a functional block diagram showing an example of a production plan formulation device according to a third embodiment of the present invention. [Figure 12] FIG. 2 is a diagram illustrating an example of the physical configuration of each device. DETAILED DESCRIPTION OF THE INVENTION

[0014] In the following, a factory will be used as an example of a structural unit processed by the processing planning method. In this case, processing refers to production in the factory, and the processing planning method can be referred to as a production planning method in the factory. Furthermore, the processing planning device can be referred to as a production planning device. Furthermore, the processing resource allocation method can be referred to as a production resource allocation method in the factory, and the processing resource allocation device can be referred to as a production resource allocation device. [Embodiment 1] An embodiment of the present invention will be described in detail below. The production planning method according to this embodiment realizes integrated scheduling of a parallel, distributed, multi-factory production system that handles a wide variety of products. FIG. 1 is a functional block diagram showing an example of a production planning device 10 that realizes the production planning method according to this embodiment. As shown in FIG. 1, the production planning device 10 includes a first solution-finding unit 11 and a first model 12. The production planning method described below is realized by the first solution-finding unit 11 and the first model 12.

[0015] [Multi-objective DABC algorithm] This paper explains the multi-objective DABC (Discrete Artificial Bee Colony) algorithm, which is the premise of the production planning method.

[0016] The multi-objective DABC algorithm applies the DABC algorithm to the Distributed Hybrid Flow-shop Problem (DHFSP), a multi-factory scheduling problem that does not consider inter-factory transportation, by expanding its objective function and taking into account multiple factors such as process efficiency and on-time delivery. After generating an initial solution using the Intelligent Nawaz, Enscore, and Ham (INEH) rules, DABC attempts to improve the solution using ABC, which employs two types of exchange operations: (1) "job exchange within a factory (changing the processing order)" and (2) "job exchange between factories" (Figure 2). ABC's unique feature is its ability to forcibly update solutions that are difficult to improve, enabling global search while maintaining solution diversity. Numerical experiments have shown that it outperforms methods such as Genetic Algorithm (GA) and Iterated Greedy (IG). The multi-objective function used in the multi-objective DABC algorithm is as follows:

number

[0017] The multi-objective DABC algorithm is broadly divided into three stages: initial solution generation, solution search (search by worker bees and spectator bees), and forced solution update (search by scout bees). Initial solution generation is based on a method called INEH (Intelligent Nawaz, Enscore, Ham)1. In INEH1, an ordered set of jobs is created in descending order of total processing time, and then jobs are assigned, starting with the first job, to the factory with the smallest objective function value (hereafter referred to as the evaluation value) for each factory at that time. At this time, the position with the smallest evaluation value is identified from among the possible insertion positions in the processing order list of the factory for which the assignment has been determined, and the job is inserted into that position.

[0018] In the second stage, solution search (search by worker bees and spectator bees), the solution generated by INEH1 is improved by two neighborhood search operations: ·Important Factory Insertion Operation: Randomly select one job from the processing order list of the factory with the highest evaluation value and move it to a different random position within that list. ·Important factory swap operation: Randomly select one job each from the processing order list of the factory with the highest evaluation value and another randomly selected factory, and swap them.

[0019] In the third stage, forced solution updating (search by scout bees), a critical factory exchange operation is applied to solutions that have not been updated consecutively for a certain number of times during the solution search stage, and the solution is forcibly updated. This prevents the system from falling into a local solution and enables global search.

[0020] In this embodiment, we use IINEH1 (Improved-INEH1), an improved version of INEH1. IINEH1 randomly selects √J' possible insertion locations using the total number of jobs J' already assigned to a factory at the time the factory to which the next job will be assigned is determined by comparing evaluation values ​​between factories, and inserts the job into the location with the lowest evaluation value.

[0021] [Production planning method] First, we will describe the problem setting for a multi-factory that is the target of the production planning method of this embodiment. Here, we focus on a parallel, distributed multi-factory that can process and transport jobs across multiple different factories. Figure 3 shows the target multi-factory model. In Figure 3, a device executes job processing. A device group is a collection of devices belonging to the same device group, grouped by their function or location within the factory. A stock is a job that is temporarily stored while waiting to be processed or transported. The subscript before the stock indicates the location of the stock, and the subscript after the stock indicates the job status (I: waiting for processing, O: waiting for transport). For example, "device-stock (I)" indicates the stock of jobs waiting to be processed by the device, and "device group-stock (O)" indicates the stock of jobs waiting to be transported from the device group.

[0022] The multi-factory model shown in Figure 3 has multiple parallel factories, each with multiple parallel equipment clusters composed of multiple parallel machines with similar functions. Each factory, equipment cluster, and machine has two types of stock: waiting for processing (In) and waiting for transport (Out). Taking "equipment-to-stock" as an example, "equipment-to-stock (I)" is the stock where jobs waiting to be processed at that machine are stored, and "equipment-to-stock (O)" is the stock where jobs waiting to be transported from that machine to another equipment cluster, etc. As shown in Figure 3, there are transports between each stock. Transports include intra-factory transports and inter-factory transports. In actual job transport, both of these occur as transport tasks for the job, which contribute to increasing the job cycle time. When processing is completed on a machine in one equipment cluster and the next process is to be processed on a machine in another equipment cluster, the job is transported from the equipment's stock to the current equipment cluster's stock, then to the next equipment cluster's stock, and so on. However, if the next process is to be carried out by a group of equipment in another factory, transportation from the group of equipment to the factory stock and transportation between the factory stocks are required. The information added regarding transportation mainly includes transportation conditions such as transportation time and transportation capacity.

[0023] Generally, inter-factory transport time is much longer than intra-factory transport time. Furthermore, while insufficient transport capacity can result in waiting times, this is not a substantial constraint when the transport capacity is sufficient. Furthermore, transport time can be asymmetric. In other words, reverse transport does not necessarily require the same transport time. In fact, transport between buildings may involve different physical routes and paths. Furthermore, inter-factory transport can be divided into two types: direct and indirect. As shown in Figure 4 (described later), there are multiple transport routes between factories. For example, when transporting from Factory 1 to Factory 3, direct transport uses a single route connecting the two factories. Indirect transport involves a detour, such as Factory 1 → Factory 2 → Factory 3, and then an indirect transport via another factory. While direct transport typically requires less effort and time, indirect transport may be used when the direct route is congested (maximizing transport capacity) and waiting times occur. Therefore, appropriate route selection is required for inter-factory transport.

[0024] When such a system exists across all factories and between all factories, in addition to the traditional issues of "which factory should handle each job" and "in what order should jobs be processed at each factory," one must also consider "which factory should process a certain process." Inter-factory transport is something that should be avoided unless absolutely necessary, as it increases the amount of time and energy required and greenhouse gas emissions. However, if the reliability of a factory or manufacturing equipment drops below a certain level, the quality assurance period may be exceeded depending on the time required for recovery. Therefore, inter-factory transport is necessary when conditions arise that make it impossible to meet the target quality or demand volume. However, as mentioned above, it results in various losses, so it is desirable to minimize inter-factory transport.

[0025] As an example, consider a case where parallel distributed production is performed in multiple factories (buildings) in the same area, with inter-factory (inter-building) transportation being performed as needed, as shown in Figure 3. Generally, in the current corporate environment, the priority is placed on meeting quality assurance time constraints between processes, and jobs are transported to the factory that can start processing the next process earliest. However, this method considers each process independently, resulting in frequent job transfers between factories, resulting in time and energy losses. Furthermore, there are doubts about the overall efficiency and adherence to delivery deadlines. Therefore, this embodiment realizes a production planning method that takes into account production efficiency, adherence to delivery deadlines, adherence to quality assurance times, and inter-factory transportation, and is capable of scheduling certain sections together.

[0026] In this method, the above-mentioned multi-objective DABC algorithm is expanded to a form that can be used in multiple factories, and is applied to realistic semiconductor front-end process scheduling problems to realize production scheduling that accommodates inter-factory transportation and QTC (Q-time constraint, a time constraint for guaranteeing job quality).

[0027] [Flow of production planning method] Figure 5 shows the flow of the production planning method proposed in this method. Figure 5 is a flowchart showing the flow of the production planning method. In the flowchart shown in Figure 5, the target section is assumed to be a certain number of processes for each product type, starting from an arbitrary equipment group among all processes, and to be scheduled collectively. The scheduling target section is specified, and the capacity and flow used in that section are optimized before calculations using the DABC algorithm.

[0028] The production planning method described below is realized as a solution-finding step by the first solution-finding unit 11 in the production planning device 10, as an example.

[0029] (Step S101) First, in the production planning method according to this embodiment, a certain number of processes for each product type are scheduled at one time, starting from a bottleneck or other arbitrary equipment group among all processes. The number of processes to be calculated is determined based on the number of processes, the time length, etc. As an example, a process that can be reached within an arbitrary time T2 is considered as a single scheduling target section. Note that T2 may be determined based on the schedule review cycle or other factors, and may be arbitrary. After determining the target section, all equipment groups used by each product type are lined up within the target section, taking into account the order in which each product type's equipment group is used. This creates a single common hybrid flow (CHF) that integrates the flows for all product types (Figure 6). In this case, to express the CHF, if there are any unused equipment groups in the flow, those equipment groups are skipped with a processing time of zero (e.g., equipment group C for product type 3 in Figure 6).

[0030] (Step S102) Next, we calculate the expected in-process and arrival quantities of jobs for each product type at the target equipment group. This method divides production into sections and schedules them in stages, so we need to estimate the in-process and arrival quantities of jobs from the evaluation time to the target period (T2). Therefore, this method assumes that the in-process quantities and arrival quantities of jobs can be predicted using known forecasting techniques, including arrivals from distant times and processes. In other words, we assume that the in-process quantities and arrival quantities of jobs during the target period are known through some kind of information processing, such as forecasting, and then schedule the entire job. For primary numerical verification, this method uses data generated pseudo-Poisson arrivals, including the predicted quantities. Poisson arrivals are widely used to describe a random arrival sequence in which the number of arrivals per unit time follows a Poisson distribution and the job arrival interval follows an exponential distribution.

[0031] (Step S103) When there are groups of machines that require repeated processing, the conventional DABC algorithm, which is based on flow shops, cannot be applied directly because it lacks a function for allocating capacity to each process. Therefore, in this method, after estimating the in-process and arrival times of jobs, we calculate the number of machines (capacity) that can be allocated to process the corresponding process for each product type in each machine group and specify the capacity allocation. Scheduling is performed under the condition that only machines below this specified value are used. To calculate the number of machines to be allocated, this method uses a simple proportional allocation method. The proportional allocation method allocates processing capacity based on the ratio of demand for each type to the total demand, and can be used even when demand exceeds supply. The specific calculation method is shown in Equation (1.1). To achieve higher performance, such as maximizing good product throughput as a rectification effect, well-known optimization mechanisms can be applied. The number of machines can be expressed as a number of units or hours, allowing decimal values.

number

[0032] (Step S104) After determining the allocation of equipment capacity that can be used by each product type and process in each equipment group, the number of units of equipment required for each product type in each equipment group is calculated. This is not only intended to achieve scheduling that takes into account the trade-off between risk dispersion and efficiency improvement, but also to better streamline the flow from bottleneck equipment groups if the source equipment group is a bottleneck. Furthermore, the number of units of equipment required here is used to determine the factory and machine responsible for each product type when generating the initial solution later. The method for calculating the number of units of equipment required for a certain product type k in process s is shown below.

[0033] First, the number of jobs of product k that can be processed by the equipment of process s per unit time, that is, the service rate μ s,k Calculate (equation (1.2)).

number

[0034] Next, the number of jobs of product k arriving at process s per unit time, i.e., the arrival rate λ s,k Calculate (equation (1.3)).

number

[0035] Finally, the number of devices to be handled (required number of devices) is determined using the service rate and arrival rate, taking into consideration the reliability of the device group (equation (1.4)).

number

[0036] As described above, the production planning method further includes an allocation step of determining, for each process, the number of machines to be used in each machine group to process that process using a proportional allocation method, and a calculation step of calculating, for each process, the number of machines for each product type to be used in each machine group to process that process based on the service rate for that product type, the arrival rate for that product type, and the reliability of that machine group. In the solution step, an optimization problem is solved, the solution of which is a factory to which each job is allocated and the processing order of the jobs allocated to each factory, with the smaller of the number of machines determined in the allocation step and the number of machines for each product type calculated in the calculation step as a constraint.

[0037] (Step S105) After the constraints are met by optimizing the available capacity and flow, an initial solution is generated. The objective function used to calculate the base and evaluation value for the initial solution generation method here is IINEH1, as described above, and FC, as expressed in equation (1.5), as described below. However, to take into account the risk of the entire factory shutting down, the procedure is improved as follows. The improved procedure is called DI-INEH1.

[0038] <Improved procedure (DI-INEH1)> (1) Create an ordered set of jobs in descending order of total processing time. (2) Calculate the evaluation value of each factory at that time. Check the product type of the job at the top of the ordered set, and if the number of factories or devices responsible for that product type does not reach the total number of factories or the number of devices required for that product type, select the factory with the lowest evaluation value from among the factories that have not yet been assigned any jobs for that product type, and assign it to that factory. If the number of factories responsible for that product type reaches the total number of factories or the number of devices required for that product type, select the factory with the lowest evaluation value from among the factories that have already been assigned jobs for that product type, and assign it to that factory. (3) The evaluation values ​​when inserting into the beginning and end of the processing order list of the factory for which the allocation has been decided, and into randomly selected √J' positions (J' is the total number of jobs already assigned to the factory), are compared, and the job is inserted into the position with the lowest evaluation value. (4) Delete the job at the top of the ordered set. If the ordered set is empty, the process ends. If it is not empty, the process returns to (2).

[0039] Next, a solution search is performed using the multi-objective DABC algorithm based on the initial solution generated in the above procedure. In this search, the multi-objective function shown in equation (1.5) is used. This multi-objective function corresponds to the first objective function in the first model 12.

number

[0040] In equation (1.5), the term representing the cost of inter-factory transportation is the transportation time H taken to complete the processing of each job j.j Sum of Σ j H j The objective function is a term obtained by multiplying the due date of each job j by d j (1) The cycle time C of each job j j Sum of Σ j C j (2) The term obtained by multiplying the coefficient of each job j by E j =max{0,d j -C j} sum Σ j E j (3) The delayed due date of each job j, T j =max{0,C j -d j} sum Σ j T j It can be said that it further includes a term multiplied by a coefficient.

[0041] Furthermore, it can be said that the coefficient of each term included in the objective function is the product of a first coefficient set by the user and a second coefficient optimized in the solution-finding step.

[0042] The above objective function has two features. The first is that it adds transportation between buildings in a multi-factory. Specifically, in FC, the formula for calculating FA described above is improved, and the cumulative transportation time H taken for transportation between factories until job j is completed is added. j The second point is that each term is multiplied by a weight parameter that can be set arbitrarily. For example, if there is a margin in the delivery date, E j becomes relatively large, and T j and H j In addition, in the case of stock production, it is important to achieve the set throughput, and the size of the delivery time difference due to completion earlier than the deadline is not as significant as in made-to-order production. Furthermore, the cumulative transportation time H j is the cycle time C jSince the value level is low compared to other factors, it is difficult to improve without individual measures such as scaling, and the desired effect may not be expected. In light of this possibility, we have decided to allow room for arbitrary weighting of each term in advance. The setting of these weight parameters is automatically optimized by SETUP-BO. f , v f , w f , z f This is more intuitive and easier than setting the four weighting parameters, and does not significantly increase the user's difficulty in using it. Overall, the use of this objective function reduces unnecessary inter-factory transport while taking into consideration process efficiency and adherence to delivery dates.

[0043] Next, we explain how to calculate the objective function value (evaluation value). Metaheuristics such as the DABC algorithm use the objective function value to compare solutions during the solution search process. Each solution has its own objective function value. To calculate this objective function value from a solution, production must first be simulated according to the solution's job assignment to each factory and processing order at each factory. To account for inter-factory transportation and QTC, our method introduces two types of transportation mechanisms—a simplified transportation mechanism and a transportation optimization mechanism—to determine transportation within the simulation. First, the simplified transportation mechanism transports jobs for which the current factory does not have the equipment to process them and jobs for which QTC is expected to be exceeded if processed at the current factory. In situations where a factory's production capacity is insufficient, the excess production load at that factory can be allocated to other factories, allowing the production of the former jobs to continue uninterrupted and reducing the risk of QTC exceedance for the latter jobs. Specifically, inter-factory transportation is performed according to the following flow.

[0044] When deriving the production plan in the solution-finding process, for each process, the factory that will process each job is determined so as to optimize the risk of QTC violation, and then the processing start time and processing end time for each job are determined.

[0045] <Transportation between factories using a simple transport mechanism in process s> (1) Prepare an empty list (transport job list). Extract and insert jobs that require transportation from the expected queue of each factory in process s (the processing order list for the first process). Whether or not a QTC exceedance is expected is determined by simulating production according to the expected queue and determining whether or not the following formula (1.6) is satisfied for each job j (if it is not satisfied, transport is performed).

number

number

[0046] In this way, after the load of each factory is equalized by the simple transport mechanism, if there are still jobs that are expected to exceed the QTC, the second transport optimization mechanism transports the jobs in a way that optimizes the risk of exceeding the QTC. The specific mechanism of the transport optimization mechanism is shown below.

[0047] <Inter-factory transport using transport optimization mechanism in process s> (1) Select one job at a time from the top of the expected queue for each factory in the process. (2) Check whether the QTC of each job selected in (1) can be met when processed in the current factory. If all jobs can meet the QTC, proceed to (3). If there are jobs where the QTC is expected to be exceeded, proceed to (3)'. (3) Remove the currently selected job from the forecast queue and determine the processing start and end times at the current factory. (3)' Delete the currently selected job from the predicted queue. From the destination process and order patterns of all currently selected jobs, select the pattern that minimizes the sum of α(δ(j,s))·δ(j,s) for all selected jobs, as shown in the following equation (1.8), and determine the processing start time and processing end time of each job according to that pattern.

number

[0048] Here, the first and second terms in equation (1.8) represent the required time, while the third and fourth terms represent the grace period for complying with the constraints. δ(j,s), which is the difference between them, represents the amount of QTC exceeded, i.e., the QTC exceedance risk, and α(δ(j,s)) is a weighting parameter that changes depending on whether δ(j,s) is positive or negative. When δ(j,s) is positive, that is, when QTC is expected to be exceeded, α + , when δ(j,s) is negative, i.e., when compliance with QTC is expected, α - where 0<α - <α + By optimizing α(δ(j,s))·δ(j,s) as the number of jobs selected, it is possible to determine the destination process and order pattern that is less likely to cause the QTC of each selected job to exceed the QTC. + = 5, α - =1.

[0049] In this way, this method optimizes production capacity and flow, sets constraints, and then generates an initial solution and searches for a solution based on those conditions. This allows the target requirements to be considered without lengthening the calculation time required for algorithms such as the DABC algorithm. Initial solution generation uses an improved IINEH1 procedure to ensure that the number of factories responsible for each product meets the conditions, and solution search uses an objective function FC that takes inter-factory transportation into account. Furthermore, in the simulation performed to calculate the objective function value from the solution, transportation is determined according to a simple transportation mechanism and a transportation optimization mechanism, and transportation is implemented to optimize the risk of exceeding QTC. The initial solution generation and solution search portions are improved by automatically optimizing the weight parameters of the objective function FC using SETUP-BO.

[0050] As described above, when deriving the production plan in the solution-finding process, for each process, (1) only for jobs for which it is assumed that the assigned factory does not have equipment capable of processing the process, and jobs for which it is assumed that processing the process in the assigned factory would violate the QTC, the job is selected to be processed in a factory other than the assigned factory. Then, if all jobs still do not satisfy the QTC, (2) the factory for processing the process for each job is determined so as to optimize the degree of violation of the QTC, and the processing start time and processing end time for each job are determined.

[0051] As described above, the production planning method according to this embodiment is a production planning method executed by the production planning device 10 to formulate a production plan for processing multiple jobs at multiple factories. The first solution finding unit 11 executes a solution process to solve an optimization problem, the solution of which is a factory to allocate each job and the processing order of the jobs allocated to each factory, using an objective function that represents the cost or benefit of the production plan derived from the solution. The production plan includes inter-factory transportation for processing processes that make up a job at a factory other than the factory to which the job is allocated, and the objective function includes a term that represents the cost of the inter-factory transportation.

[0052] This makes it possible to quantitatively evaluate and improve processes using simulations in multiple factories that use parallel distributed processing.

[0053] [Example of Embodiment 1] Next, the results of numerical verification using the above-described production planning method will be described with reference to FIGS.

[0054] In the numerical verification, we extracted bottleneck equipment groups and their subsequent processes from the SMT2020 model and expanded it to a multi-factory. We then solved a multi-objective multi-factory scheduling optimization problem that considered the trade-off between improving the throughput of non-defective products at the bottleneck equipment groups and the deterioration of production efficiency across the entire target section due to the need for inter-factory transport in the subsequent processes. SMT2020 is a Semiconductor Manufacturing Testbed, a testbed that simulates an actual semiconductor production system. SMT2020 simulates an actual semiconductor front-end factory, and is a realistic model consisting of 10 types of products produced through hundreds of processes, more than 1,000 pieces of equipment, and more than 100 equipment groups. The computational environment shown in Table 1 below was used in this numerical experiment. [Table 1]

[0055] [Various settings for numerical experiments] The various settings used in this numerical experiment are described below. Regarding production capacity, the original SMT2020 model assumes single-factory production and does not incorporate the concepts of multiple factories or transportation. Therefore, in this experiment, SMT2020 is expanded to multiple factories. For example, when the number of factories is F=3, the SMT2020 model assumes three single factories. However, to properly evaluate performance, the number of machines in each machine group may not follow the settings in the original SMT2020 model. The settings are basically based on the job arrival rate. For example, to simulate situations where it is difficult to comply with QTC, the number of machines is reduced by 60% only for processes where QTC is set.

[0056] We assume that the transport capacity between factories is infinite. In reality, because transport vehicles and carts are used to transport jobs, there is an upper limit to the transport capacity that can be used at the same time. When transport capacity is fully utilized, transport queues occur. However, carrying out production with such low transport capacity that inter-factory transport becomes a bottleneck is inherently inappropriate, and transport capacity must be improved before scheduling can begin. This is because, while the unit cost of production equipment is extremely high, ranging from billions to tens of billions of yen, the investment required for an inter-factory transport system is orders of magnitude lower, less than a few tenths of that amount. Therefore, it is undesirable for inter-factory transport to become a bottleneck and result in idle production equipment. Based on this concept, in this experiment, we assume that job transport can begin at any time. While transport queues are not considered, transport time itself is considered. Next, we assume that transport times between factories are asymmetric, meaning that different settings can be made for the direction of the source and destination factories (even for the same combination of factories, transport times can differ if the transport directions are reversed). As shown in Figure 4, multiple transport routes, including indirect routes, are possible between factories. However, under the assumption that transport capacity is infinite, the route with the shortest transport time can be selected. Therefore, in this experiment, rather than solving the transport route selection as an internal problem, the minimum transport time is provided as input data from the beginning. However, in actual problems, if the direct transport route is congested, the goods are detoured and transported indirectly via another building. Similar to direct transport, this type of indirect transport is treated as an optimization problem, such as the shortest route, but the direct reduction of indirect transport is not expected. Generally, indirect transport cannot be avoided; routes tend to be either very short or very long, or moderate routes prevail. Therefore, it is desirable to achieve more computationally efficient and effective optimal planning and operation methods for transport systems through approaches such as robust optimization and modeling of new transport operations as external setup. However, in this experiment, we do not add such optimization, and as a first step, we examine a configuration in which indirect transport, which is the target to be reduced, is not considered in the optimization objective function.Furthermore, since the equipment stock and the equipment group stock are nearly identical in this experiment, only transport between stocks of different equipment groups within the same factory, between equipment group stock and factory stock, and between stocks in different factories are considered. The transport time from equipment group m to equipment group m' within the same factory is represented by Trm(m, m'), the transport time from equipment group m to the stock of factory f where that equipment group is located is represented by Tr(m, f), and the transport time from the stock of factory f to the stock of factory f' is represented by Trf(f, f').

[0057] Regarding equipment failures, we will consider a realistic repair system and think about it as follows: When a machine breaks down, a certain amount of time is required for repairs, and during that time no jobs will be processed. Also, if a machine breaks down while a job is being processed, the job that was being processed will be restarted from the beginning after production resumes.

[0058] Below, we explain how to generate data related to failures. In this experiment, failures are simulated at the factory and equipment level, and data for numerical verification is generated based on knowledge of reliability engineering. Specifically, failures are assumed to occur when production resumes after repairs, and a repairable system is assumed to occur as a result of partial or complete deterioration of the machine over time. First, each machine is given a reliability R(t) as shown in equation (2.1), with t=0 as the time when repairs are completed.

number

number

[0059] To determine the start time of a machine failure, a sequence of failure intervals is created by substituting a sequence of random numbers obtained by uniform random numbers [0,1] into the inverse function of the distribution function F(x) = 1-exp(-Λx) shown in equation (2.3).

number

[0060] Next, the repair time is determined based on the average value of the sequence of failure intervals. The repair time is also assumed to follow an exponential distribution, with random time. Therefore, in numerical experiments with failures, a list of failure start times and repair times are used, created using the sequence of failure intervals and repair times derived from the distribution functions described above. The reliability parameter Rs used to calculate the number of machines required for each product type in each equipment group is the average value within the period, assuming that production begins with 100% reliability according to equation (2.1) and continues without failures until the deadline of the job with the latest due date. The minimum value within the period can also be used as parameter Rs. However, in this case, the minimum reliability within the period is always used. For greater accuracy, reliability, which changes with t, can be used directly instead of basic statistics such as the average or minimum. In this case, however, the value must be revised at each evaluation point t.

[0061] The following describes the job data. First, SMT2020 is used for data on the number of varieties and the production process of each variety (including QTC). Next, as mentioned above, jobs are assumed to arrive according to a Poisson distribution. Using the average (estimated) number of arriving jobs per unit time in SMT2020, λ = 0.04, random numbers are generated for each variety so that a total of just over 100 jobs arrive.

[0062] Next, the delivery date j is set for each job j using equation (2.4).

number

[0063] Setup time A S1(k,l) is determined for each product type k, l processed in process s by equation (2.5).

number

[0064] [Experiment overview] In the next section, [Performance Evaluation of the Proposed Method], we will consider the performance evaluation results of the proposed method. In particular, in [Effectiveness Verification of Optimizing Capacity and Flow], we first verify the effect of optimizing capacity and flow. Next, in [Performance Verification of Objective Function], we verify the effect of adding inter-factory transportation to the objective function. Next, in [Effectiveness Verification of Transportation Optimization Mechanism], we verify the effect of the transportation optimization mechanism. After that, in [Performance Comparison with Other Methods (No Breakdowns)], we compare the performance of the proposed method with other methods. Note that in [Effectiveness Verification of Optimizing Capacity and Flow] - [Performance Comparison with Other Methods (No Breakdowns)], experiments were conducted under conditions without breakdowns in order to confirm the basic performance of the proposed method. Finally, in [Performance Comparison with Other Methods (With Breakdowns)], we compare the performance of the proposed method with other methods under conditions with breakdowns. Here, we restate the following from equation (1.5):

number

[0065] The evaluation metrics used are makespan, QTC compliance rate, on-time delivery rate, on-time delivery rate (effective), total setup times, setup time ratio (per unit cycle time), total calculation time, and terms E, T, C, and H related to the objective function. In this experiment, considering that jobs are transported between factories, a single makespan across multiple factories is used, which is the time required to process all jobs to be scheduled at all factories that use them. The QTC compliance rate is calculated by dividing the number of jobs that met all QTCs for jobs with QTCs set at any process by the total number of jobs with QTCs, and multiplying the result by 100. The on-time delivery rate is calculated by dividing the number of jobs that met the deadline by the total number of jobs, and multiplying the result by 100. In a real-world scenario, jobs that do not meet QTC are typically discarded or restarted from a previous process. However, in this experiment, jobs that did not meet QTC were processed to completion along with other jobs. Therefore, the on-time delivery rate calculated here may differ from the rate calculated when appropriate measures are taken for jobs that did not meet QTC. Therefore, as a more stringent evaluation of the delivery deadline compliance rate, the delivery deadline compliance rate (real) obtained by dividing the number of jobs that comply with both the QTC and the delivery deadline by the total number of jobs and multiplying the result by 100 is also used as an evaluation index.

[0066] The total number of setups is the number of setups required for all jobs subject to scheduling to complete all processing in the target section. The setup time ratio is the proportion of setup time in the total time required for production, and is the value obtained by dividing the total setup time by C and multiplying by 100. The reason why this is defined differently from the general setup rate is that it is possible to express the results across multiple factories with a single index.

[0067] [Performance evaluation of the proposed method] [Verifying the effectiveness of optimizing usage capacity and flow] First, we compare the production planning method in which a limit is placed on the number of machines in each product type's starting equipment group, with one in which no limit is placed on the number of machines, to verify the effects of optimizing usage capacity and flow. However, in order to confirm basic performance, we assume that no machine failures will occur. We conduct numerical experiments using the equipment group DE-FE-51 in SMT2020 as the starting equipment group, and scheduling the first five processes that use DE-FE-51 for each product type. We create a common hybrid flow for all product types, taking into consideration the order in which each product type's equipment group is used, and the rewritten flow is shown in Table 2. Table 3 also shows the QTC settings used in this experiment. [Table 2] [Table 3] The number of factories is F = 3, and the parameter a determines the length of delivery time for product k. k are as shown in Table 4 below. Parameter b, which expresses the variability in delivery times, follows a uniform distribution of [0.8, 1.2], and parameter c, which determines the length of setup time, follows a uniform distribution of [0.2, 0.5], and was given randomly for each product k and l processed before and after process s. [Table 4]

[0068] Additionally, the transport time from equipment group m to equipment group m' within the same factory is set to Trm(m,m') = 10 (min), the transport time from equipment group m to the stock of factory f where that equipment group is located is set to Tr(m,f) = 10 (min), and the transport time from the stock of factory f to the stock of factory f' is set to Trf(f,f') = 60 (min). The feasibility of scheduling is verified using data assuming a scale of 100 or more total jobs by generating each product type according to a Poisson distribution with λ = 0.04 (lot / min) over the job arrival period T1 = 360 (min). Finally, the weight parameters that can be set by the user are set to u' f =0.1,v' f =1,z' f = 2 (= number of factories - 1). Table 5 shows the results for each index depending on whether or not there are restrictions on equipment use. [Table 5] First, Table 5 shows that with equipment constraints, E, T, C, and H are approximately 5.55%, 21.5%, 6.98%, and 50.0% better than without them. Therefore, while E and T, E and C, etc., are inherently in a trade-off relationship, imposing equipment constraints appears to have improved the overall solution performance of the scheduling method. Furthermore, imposing equipment constraints reduced the number of machines considered for use in processing each job during simulation, resulting in a reduction of total computation time by approximately 3.24%. Next, with equipment constraints, the total number of setups was reduced by approximately 11.4% and the setup time ratio by approximately 17.3% compared to without them. By limiting the range of equipment use, the number of product types handled by each machine was reduced, thereby eliminating unnecessary setups. Furthermore, the reduction in setups also had a positive impact on the aforementioned C (total cycle time) and makespan. With equipment constraints, C improved by approximately 6.98% and makespan improved by approximately 9.50%, suggesting that reducing setups also improved overall production efficiency. Furthermore, when we look at H (total inter-building transport time) and QTC compliance, with equipment constraints, H was 50.0% better and QTC compliance was approximately 10.7% better. It is believed that overall production efficiency improved through capacity allocation, resulting in a reduction in unnecessary transport and an improved QTC compliance. Finally, while the standard delivery date compliance was approximately 0.87% better without equipment constraints, the actual delivery date compliance was 4.76% better with equipment constraints due to the higher QTC compliance. These excellent results in overall production system process efficiency (C, etc.), QTC and delivery date criteria (QTC compliance rate, actual delivery date compliance rate, etc.), flow time criteria (C, makespan), and computational efficiency suggest that scheduling with equipment constraints generally performed well, confirming the desired effects of optimizing utilization capacity and flow. The performance of the objective function FC, expanded with H, is described in more detail below.

[0069] [Objective function performance verification] Next, we evaluate the performance of the objective function. Here, as in [Verifying the effect of optimizing usage capacity and flow], we conduct experiments assuming that no breakdowns occur in order to compare basic performance. We compare the results when using the multi-objective function FC, which includes the aforementioned H, as the objective function for the production planning method, with the multi-objective function FB (equation (2.6)), which removes the term H from FC.

number

[0070] The same problem setting and data used will be used as in [Verifying the effectiveness of optimizing usage ability and flow]. Table 6 shows a comparison of each indicator in the numerical verification results. [Table 6] First, we describe the effect of adding H to the objective function, comparing FC and FB. Table 6 shows that FC performed approximately 42.9% better than FB for H. This indicates that the objective function FC with H appropriately suppresses inter-factory transport. Additionally, the QTC compliance rate was approximately 3.07% better for FC than for FB. Because the transport optimization mechanism targets jobs expected to exceed QTC, the objective function FC suppresses inter-factory transport, resulting in job allocation that maximizes QTC compliance at the factories where the jobs reside. Regarding other indicators, FC performed approximately 0.0048% worse than FB for E, 36.0% worse for T, and approximately 1.41% worse for makespan, but approximately 1.00% better for C. Furthermore, with the same total number of setups, FC performed approximately 1.60% better for setup time ratio and approximately 0.79% shorter for FB. Here, objective function FB does not have H, making it easier to improve T, and considering that the difference in delivery date compliance rate (actual) is 0.92% (FC is worse), the differences in each indicator other than H, QTC compliance rate, and T are small, at 1.5% or less. Taking these results together, it can be said that objective function FC has significantly reduced inter-factory transportation and improved QTC compliance rate, while maintaining performance equivalent to FB in terms of production efficiency and delivery date compliance.

[0071] [Verification of the effectiveness of the transport optimization mechanism] Here, we verify the effectiveness of the transport optimization mechanism by comparing the performance of the following four patterns.

[0072] (1) When using only a simple transport mechanism and transporting only jobs for which the current factory does not have equipment capable of processing the next process.

[0073] (2) When using only a simple transport mechanism to transport jobs for which the current factory does not have equipment capable of processing the next process, and jobs for which QTC is expected to be exceeded if processed in the current factory.

[0074] (3) When using the simplified transport mechanism to transport only jobs for which the current factory does not have equipment capable of processing the next process, and then using the transport optimization mechanism.

[0075] (4) When using the simplified transport mechanism to transport jobs for which the current factory does not have equipment capable of processing the next process and jobs for which QTC is expected to be exceeded if processed in the current factory, the transport optimization mechanism is used. The problem settings and data used are the same as those used in [Verifying the effectiveness of optimizing usage capabilities and flow]. Table 7 shows a comparison of the indicators from the numerical verification results, and Figure 8 shows a comparison of H and QTC compliance rates. [Table 7] Figure 8 shows that H is larger and QTC adherence rate is higher for (1), (2), (3), and (4) in that order. The more opportunities for transportation consideration, the more transportation is used (H is approximately 90.9% larger for (4) than for (1)). It can be said that the two types of transportation mechanisms introduced in this experiment improved QTC adherence rate as intended ((4) has a QTC adherence rate 12.6% higher than (1)). Table 7 shows that (1) showed the best on-time delivery rate, approximately 5.26% better than (4). However, due to the improved QTC adherence rate, (4) showed the best on-time delivery rate (actual), approximately 2.80% better than (1), which had a poor on-time delivery rate. The total calculation time also increased in the order of (1), (2), (3), and (4), with (4) taking approximately 59.1% longer than (1). This can be attributed to the increased number of transport decisions due to the increase in the number of transport mechanisms and target jobs.However, the calculation time of approximately 14.6 hours for (4) is still at a practical level, and above all, the result of the improvement in QTC compliance rate obtained by introducing the transport mechanism is more important.Taking into account the fact that no significant differences were observed in other indicators, it can be concluded that (4) showed the best performance.

[0076] [Performance comparison with other methods (no failures)] Here, we compare the proposed method with a conventional method of determining the next job each machine will process based on the descending order of the Critical Ratio (the value obtained by dividing the remaining processing time by the time remaining until the delivery date) (hereafter referred to as CR descending order), which is similar to the production planning method proposed here. Note that in CR descending order, each job is transported to the factory that can start processing it the earliest for each process. The problem setting and usage data are the same as those used in [Verifying the effectiveness of utilization capacity and flow optimization]. Table 8 shows a comparison of each indicator from the numerical verification results. [Table 8] Table 8 shows that the proposed method achieved approximately 73.4% better results in terms of H. This suggests that compared to the CR descending method, which determines transportation for each job and process, the proposed method, which determines transportation based on each factory's load and transportation needs and uses a multi-objective function including H, can significantly reduce unnecessary transportation between factories. Furthermore, the proposed method also achieved approximately 57.7% better results in terms of QTC compliance rate, confirming the high performance of the proposed method in terms of QTC compliance. The CR descending method achieved a 100% delivery on-time rate, approximately 22.8% better than the proposed method, but due to the difference in performance in QTC compliance rate, the proposed method achieved approximately 29.4% better delivery on-time rate (actual).

[0077] Next, in terms of total setup times and setup time ratio, the proposed method performed approximately 10.7% and 6.04% better than CR descending order, respectively. This can be said to be a result that reaffirms the effectiveness of optimizing capacity usage and flow, as confirmed in [Effectiveness Verification of Optimizing Capacity Usage and Flow]. Furthermore, as a result of reducing unnecessary inter-factory transportation and setup time, the proposed method performed approximately 14.3% better than CR descending order in C.

[0078] In terms of makespan, the proposed method showed results that were approximately 7.56% worse than CR descending order. When production is carried out according to the solution of the proposed method, each job can only start processing when it is at the head of the determined sequence and the equipment is free, whereas arriving jobs are queued to wait for processing, and if the equipment is free when they enter the queue, they can start processing immediately, which is thought to have resulted in a tighter schedule and a smaller makespan.

[0079] Overall, it is more important that the proposed method showed good performance in terms of QTC compliance rate, delivery date compliance rate (actual), setup time, and inter-factory transportation, so it can be concluded that the proposed method has better performance than CR descending order.

[0080] [Performance comparison with other methods (with failure)] Here, we compare the proposed method with CR descending order under conditions where a failure occurs. A failure is generated with a failure rate of Λ = 1000, and the other problem settings and usage data are the same as those used in [Verifying the effectiveness of optimizing usage capacity and flow]. Table 9 shows the verification results for each indicator. [Table 9] Table 9 shows that, even with a fault, the proposed method performed approximately 80.7% better in H and approximately 148.8% better in QTC compliance, just as it did without a fault. Furthermore, with respect to on-time delivery, which CR descending order outperformed without a fault, the proposed method performed approximately 86.2% better with a fault, resulting in a 440.0% better actual on-time delivery rate. Furthermore, due to the reduction in unnecessary inter-factory transportation and setup, the proposed method also performed approximately 38.6% better in C. Furthermore, with regard to the metrics mentioned above, the difference between the two methods was more pronounced than without a fault, demonstrating the superiority and stability of the proposed method in terms of responding to situations where a fault occurs (vulnerability of the comparative method). While CR descending order performed better in makespan, overall, it can be concluded that the proposed method has superior scheduling performance, even with a fault.

[0081] [Embodiment 2] Another embodiment of the present invention will be described below. For ease of explanation, components having the same functions as those described in the above embodiment will be denoted by the same reference numerals, and their description will not be repeated. FIG. 9 is a functional block diagram showing an example of a production resource allocation device 20 that realizes a production resource allocation method according to this embodiment. As shown in FIG. 9, the production resource allocation device 20 includes a second solution-finding unit 21 and a second model 22. The production resource allocation method described below is realized by the second solution-finding unit 21 and the second model 22.

[0082] [Dealing with the trade-off between production efficiency and risk diversification, and the P3D-QAP method] First, we explain how to deal with the trade-off between production efficiency and risk diversification, which is the premise of the production resource allocation method, and the P3D-QAP (Pseudo-Periodical Priority Dispatching with Quadric-assignment Problem) method.

[0083] As shown in the following <Method for determining the upper limit on the number of factories responsible for product type k>, it has been confirmed that, in order to deal with unplanned equipment shutdowns, it is possible to adjust the balance between risk diversification and efficiency improvement across multiple factories by introducing a reliability parameter r that represents the risk of factory shutdown when setting the upper limit on the number of factories responsible for each product type.However, the following discussion is limited to the shutdown of an entire factory.

[0084] <Method for determining the upper limit of the number of factories responsible for product type k> (1) The number of jobs of product k that can be processed in one factory per unit time, i.e., the service rate μ k Calculate.

number

number

number

[0085] On the other hand, the conventional P3D-QAP method did not take into account the availability rate of equipment, the reliability of equipment groups, waiting time constraints, or transportation between multiple factories and buildings.The P3D-QAP method is executed in the following three steps.

[0086] Step 1: Determine the number of units dedicated to single-item processing and the production load.

number

[0087] Step 2: Determine the priority of the shared machine utilization for the production loads that were not allocated in Step 1. <Evaluation Formula I: When only the lower limit of work in progress is considered>

number

number

number

[0088] [Production resource allocation method] Here, we propose a production resource allocation method (P3D-QAP2MF) that extends the P3D-QAP method, a method for determining the number of factories responsible for the aforementioned trade-off between production efficiency and risk distribution, to multi-factory scheduling. Furthermore, in this extension, we newly consider the QTC exceedance risk (QTC violation risk) and delivery deadline exceedance risk, which are fundamental factors behind inter-factory transport. By optimizing the allocation of equipment to product-process pairs in each equipment group, we aim to reduce setup time and improve QTC and delivery deadline adherence rates. Furthermore, by centrally managing similar equipment across the entire factory, we reduce inter-factory transport. To achieve this, we define two exceedance risk indicators to prevent QTC and process delivery deadline exceedances and use them in a manner that takes inter-factory transport into account. Our production resource allocation method determines the equipment allocation for each product-process pair in each equipment group, and periodically reviews the equipment allocation itself to respond to changes in work-in-process quantities and production demand / supply capacity. Below, we explain the optimization method for equipment allocation at the start time t of the review cycle.

[0089] [Determining the number of allocatable devices] The allocation of equipment for each product type and process of equipment group M at evaluation time t is determined. First, regarding equipment failures, a repair system is assumed in which equipment failures occur over time and are maintained. The failure rate of equipment m at time t is expressed as the following formula (3.1.1) under the assumption that equipment m has been operating without failure up to time t.

number

[0090] The following formula (3.1.2) represents the failure rate of equipment m considered during the planning period [t, t+T2], and is evaluated as the average failure rate of equipment m at the start and end points of the planning period.

number

[0091] The following formula (3.1.3) is the probability that one or more devices in the equipment group M are in operation during the planning period [t, t+T2], simplified as r m It is expressed using (t,T2). M Let (t, T2) be the reliability of the equipment group M in the planning period considered at the evaluation time t, and r' M (t) (Equation (3.1.4)).

number

[0092] The number of pieces of equipment required for each product type and process is calculated using formula (3.1.5). This method extends the above-mentioned method for dealing with the trade-off between production efficiency and risk distribution to the equipment unit.

number

[0093] Next, the ratio of the number of equipment required by each process to the number of actual equipment is calculated, and the number of actual equipment is allocated proportionally to each product type-process (equation (3.1.6)). Even in situations where the number of required equipment exceeds the number of actual equipment, it is possible to allocate a relatively appropriate number of equipment to each product type-process. This is generally called the proportional allocation method, and is particularly widely used for capacity allocation when demand exceeds capacity. Even in situations where the number of required equipment exceeds the number of actual equipment, it is possible to allocate a relatively appropriate number of equipment to each product type-process. In this method, it is assumed that all parallel equipment is technically capable of processing all of the target product types-processes, and equation (3.1.7) is held true for all product types i and processes s.

number

[0094] [Determining the processing type for shared equipment using the P3D method] Based on the number of allocatable devices NA(i,s,t) calculated above, determine the product type-process that uses the dedicated device. The processing capacity of the device is set to 1, and the number of allocatable dedicated devices N d(i, s, t) is calculated using formula (3.1.8). Similarly, the maximum number of allocatable devices N u (i, s, t) is calculated using equation (3.1.9). Furthermore, the priority of using the shared equipment at time t is calculated using equation (3.1.10) following steps 1 and 2 of the P3D-QAP method described above. From equation (3.1.11), the number of shared equipment N s (t) items are calculated. The processing priority (formula (3.1.10)) of the shared device is calculated as N items from the top. s (t) product types and processes are to be processed by the shared equipment. N lim For (i, s, t), this method uses the upper limit of work in progress corresponding to the minimum of QTC and inter-process due date. It is an extension of the P3D method that takes QTC into account.

number

[0095] [Equipment allocation for product types and processes, addressing the trade-off between production efficiency and risk] Determine which specific equipment to allocate to each product type and process based on the total number of allocable equipment calculated above. When allocating equipment, first calculate the QTC excess risk (formula (3.1.16)) and delivery deadline excess risk (formula (3.1.17)).

number

number

number

number

number

[0096] It can be said that in the production resource allocation method, the objective function includes a term representing the constraint violation risk, which represents the QTC violation risk including the transportation time that occurs when a factory equipped with a device that allocates the current process according to the solution is different from a factory equipped with a device that allocates the previous process according to the solution.

number

[0097] It can be said that in the production resource allocation method, the objective function includes a term representing the risk of violating the constraint, which term represents the risk of violating the delivery date constraint, including the transportation time that occurs when a factory equipped with a device that allocates the current process according to the solution is different from a factory equipped with a device that allocates the previous process according to the solution.

[0098] δ(i,s,j,M f The first and second terms of ε(i,s,j,M in equation (3.1.13) represent the remaining time from evaluation time t to the time when QTC is exceeded. On the other hand, the third, fourth, and fifth terms represent the time required from evaluation time t to the start of processing in the next process. Similarly, ε(i,s,j,M in equation (3.1.13) f The first and second terms of δ(i,s,j,M f ,t) is similar to that of QTC. In addition, to consider the difference in the yield rate when QTC is met and exceeded, the parameter α(δ(i,s,j,M f ,t)) (Equation (3.1.14)) is set as parameter β(ε(i,s,j,M f ,t)) (Equation (3.1.15)) is introduced. Both parameters take negative values ​​and are assumed to be inflected at the constraint exceedance point. Overall, the larger the QTC exceedance risk and delivery deadline exceedance risk, the higher the exceedance risk. For example, if QTC is exceeded, δ(i,s,j,M f ,t) takes a negative value, and α(δ(i,s,j,M f,t)) takes a large negative value in absolute value. Their multiplication takes a large positive value. Conversely, if QTC is not exceeded, δ(i,s,j,M f ,t) takes a positive value, and α(δ(i,s,j,M f ,t)) has a small negative absolute value, and the multiplication is a small negative value. It indicates that there is room for error and contributes to optimizing the objective function value.

[0099] Next, the multi-objective function shown in equation (3.1.18) is used to determine the equipment allocation for each product type and process. While the P3D-QAP method described above has a single objective of optimizing setup time, this method adds the risk of QTC violation, risk of missing due dates, and defective product throughput to the objective function terms. Weight parameters q, u, v, and w are introduced for weighted sums to each term. The improvement of production efficiency, expressed in total setup time, the risk of QTC violation, risk of missing due dates, and defective product throughput are simultaneously solved as a multi-objective optimization problem, and the aim is to achieve overall optimization across equipment groups in multiple factories. The multi-objective function shown in equation (3.1.18) corresponds to the second objective function in the second model 22.

number

number

[0100] By the above equipment allocation, first, one equipment is allocated to one product type-process. Now, for a product type-process that has both shared and dedicated equipment allocated, it is necessary to decide which equipment will be used as a shared equipment. In this method, equipment m that satisfies equation (3.1.19) is allocated to f is a shared device.

number

[0101] As described above, the production resource allocation method according to this embodiment is a method for allocating each of a plurality of processes for producing each of a plurality of product types to each of one or more pieces of equipment installed in one or more factories, and includes a solution process for solving an optimization problem, the solution of which is at least one of whether or not to allocate each process to each piece of equipment and the amount of time available for allocation, using an objective function that represents the cost or benefit of the solution. The objective function includes a term that represents a constraint violation risk that takes into account the transportation time that occurs when the factory in which the equipment to which the current process is allocated according to the solution is installed is different from the factory in which the equipment to which the previous process is allocated according to the solution is installed. This makes it possible to realize multi-objective optimization of equipment allocation for each product type and process, taking into consideration setup time, QTC, delivery time constraints, and machine differences in yield rates. Furthermore, in addition to inter-building transportation, it is possible to periodically consider factors such as the reliability of equipment groups, which changes from moment to moment, and fluctuations in demand, and appropriately restrict or relax the equipment that each product type and process can use.

[0102] Furthermore, in the production resource allocation method, the objective function includes, in addition to a term representing the constraint violation risk, a term representing the setup time that occurs when each process is allocated to one of the multiple factories in accordance with the solution.

[0103] Furthermore, it can be said that the objective function includes, in addition to the term representing the constraint violation risk, a term representing the defective product throughput that occurs when each process is assigned to one of the plurality of processes according to the solution.

[0104] [Additional product types and processes are assigned to shared equipment] For shared equipment, the production load of the product type / process assigned to the shared equipment above is taken into consideration, and additional product types / processes are assigned to equipment with spare capacity. The objective function of equation (3.1.20) is used for the assignment. The decimal value of the number of allocatable equipment NA(i,s,t) (i.e., NA(i,s,t)-N d Let (i, s, t) be the production load for product i and process s on a shared device. The processing capacity of the device is set to 1, and the aim is to maximize the throughput of non-defective products while allocating products and processes so that they are below this processing capacity.

number

[0105] [Example of Embodiment 2] Next, the results of numerical verification of the above-described production resource allocation method will be explained.

[0106] [Numerical experiment setup] Here, we will explain the transport settings for multiple factories that will be used in the numerical experiments of this method. When a certain lot is to be processed by equipment in a factory other than the factory where the lot is currently located, the lot must be transported to the relevant equipment. Figure 10 shows the transport routes between and within factories as an example of two factories. In Figure 10, the production factory consists of two factories, Factory A and Factory B.

[0107] Equipment group A1 (equipment group 1 belonging to factory A) and equipment group B1 (equipment group 1 belonging to factory B) are equipment groups with the same processing functions, but for convenience, they are named differently depending on the factory to which they belong. In Figure 10, there are n (f) pieces of equipment in each factory f. Each equipment and each factory has a stock that stores lots waiting to be processed or transported. Stocks include stock (I) that stores lots waiting to be processed by the equipment and stock (O) that stores lots waiting to be transported. In Figure 10, arrows indicate the movement of lots between stocks. Solid arrows indicate intra-factory transport, and dashed arrows indicate inter-factory transport. For example, assume that lot 1 is stored in stock (O) of equipment in equipment group A0-1, which is the upstream process of equipment group A1 in factory A. Equipment that can process lot 1 belongs to either equipment group A1 or equipment group B1. For example, if lot 1 is processed by equipment A1-1 belonging to equipment group A1, lot 1 is transported from the stock (O) of equipment group A0-1 in factory A to the stock (I) of equipment A1-1. On the other hand, if lot 1 is processed by equipment B1-1 belonging to equipment group B1, lot 1 is transported between stocks in the following order: Factory A-stock (O) for factory exit, Factory B-stock (I) for factory entry, and then the stock (I) of intra-factory transport equipment B1-1. In this way, when inter-factory transport occurs, first, transport to the stock for factory exit (from the stock (O) of equipment group A1 to Factory A-stock (O)), second, transport between factories (e.g., from Factory A-stock (O) to Factory B-stock (I)), and third, transport within the destination factory (e.g., from Factory B-stock (I) to the stock (I) of equipment B1-1). While the third transport is usually not much different from the intra-factory transport, the first and second transport times are significantly longer.

[0108] In the numerical experiments of this method, we use SMT2020, a testbed model data set that simulates an actual semiconductor manufacturing factory, which has been newly expanded to a multi-factory model using this method. The original SMT2020 is a single-factory model data set consisting of 105 types of equipment, over 1,000 pieces of equipment, and up to 10 product varieties. The production process for each product variety ranges from as few as 350 steps to as many as over 600 steps, giving it a certain level of scale and reasonable complexity. Each variety has a Regular Lot with a normal delivery time and a Hot Lot (express product) with a short delivery time, and some varieties have a Super Hot Lot (ultra-express product) with an even shorter delivery time. In addition, planned equipment maintenance and irregular equipment failures are incorporated.

[0109] In this method, basic verification is performed by extracting only the dry etch equipment group DE_FE_51 and the equipment group related to subsequent processes from dataset 2 of SMT2020, which simulates high-mix, low-volume production. DE_FE_51 is a device that processes on a lot-by-lot basis. Table 9 shows the processing time and delivery time coefficient. [Table 10] QTC is set to 180 minutes. The mean time between failures (MTBF) is 10080 minutes, and the mean time to repair (MTTR) is 231.84 minutes. Equation (4.1.1) expresses the failure rate k of equipment m as m The average uptime (=MTBF / (MTBF+MTTR)) is approximately 0.9775.

number

number

[0110] The original SMT2020 is model data simulating a single factory. In this method, a multi-factory model is generated by replicating this single factory, and verification is performed. In the numerical experiments, the number of factories is set to three. The arrival intervals between lots across all three factories are 86.15 minutes for regular lots and 10,080 minutes for hot lots. The transport time within the factory, i.e., the transport time between (factory stock) and (equipment stock), indicated by the solid arrows in Figure 10, is set to 10 minutes. Furthermore, the transport time between factories, i.e., the transport time between (factory stock) and (factory stock), indicated by the dashed arrows in Figure 10, is set to 60 minutes.

[0111] In this method, a lot of a certain product type-process pair searches for a dedicated processing device for that product type-process pair, or a shared device, and enters its queue. As mentioned above, the P3D criteria are used to prioritize the allocation of equipment for product types and processes. In addition, within the queue, that is, for multiple jobs of the same product type-process, lots are arranged according to the FIFO (First in First Out) or CR (Critical Ratio) rules rather than randomly. The equipment selects a lot from the top of the queue and begins processing it. In other words, the actual job priority is determined using a two-stage criteria such as P3D-FIFO or P3D-CR.

[0112] [Comparative method] As a comparison method, the conventional method of selecting the machine that can start processing the earliest is used. The method of selecting the machine that can start processing the earliest is used to select the processing equipment for each lot, among the equipment that can start processing that is scattered in the same building and other buildings. There are also no restrictions on the equipment that can process, and lots can be processed by all parallel equipment processing. Each lot is selected as the processing equipment that can start processing the earliest. Priority in the queue follows FIFO, i.e., it is the P3D-FIFO standard.

[0113] [Verification results and discussion] First, to determine the planning period length T2 and the weighting parameters q, u, v, and w for the weighted sum in equation (3.1.18), each parameter is varied to verify performance. The overall simulation period was fixed at 5,760 minutes (4 days). The results are shown in Table 11. In particular, we focused on the QTC compliance rate (Qtime compliance rate in Table 11), which is the main focus of this method, and the number of conforming products, and used parameters No. 3, which provided the best results for these indicators: T2=180, number of reviews 32, q=1, u=3, v=5, w=300. [Table 11] The comparison results between the proposed method and the comparative method are shown in Table 12. The explanation of each parameter is also given below. [Table 12] Table 12 shows that the proposed production resource allocation method increased the number of non-defective products by 19, or approximately 3.0%, compared to the method for selecting the fastest machine capable of starting processing. The Q-time compliance rate improved by approximately 3.0%, and the actual delivery compliance rate, which represents the percentage of lots that comply with both QTC and process due date constraints, improved by approximately 2.3%. The setup time ratio decreased by approximately 10.73%. Maintaining QTC typically requires frequent product changeovers to maintain production volume, and QTC compliance and setup time reduction are in a trade-off relationship. However, the effectiveness of the multi-objective function appears to have achieved both improved Q-time compliance and reduced setup time. Numerical verification of the proposed method found no significant difference in transport time between the two methods, with only a slight reduction of 3 minutes in total transport time. Further improvement through parameter adjustments is desirable. While issues remain, the targeted effectiveness of the multi-objective function is evident in the improvements in both Q-time compliance and setup rate. The reason why no improvement in the delivery date compliance rate (including QTC excess lots) was observed is thought to be that the adoption of FIFO under the P3D standard resulted in the same processing priority being given to lots with normal delivery dates and hot lots with short delivery dates, and both methods were unable to meet the delivery dates of hot lots. It is thought that the lower-level rules of P3D need to be changed to at least rules that take delivery dates into consideration, such as EDD or C / R. Accordingly, it is desirable to expand the dispatching rules of the comparison method.

[0114] Table 13 shows the results using the P3D-CR standard. In this case, noteworthy performance results were achieved: setup time was reduced by approximately 84.1% and total transport time was reduced by approximately 55.6% while maintaining a Qtime compliance rate of 100%. This result is compared with the conventional method used by a real company (using the Earliest Available Machine Selection method, which selects the factory and equipment that can begin processing earliest as the upper level, and the CR standard as the lower level). In addition to the performance results shown in Table 13, the equipment with the highest utilization rate improved by approximately 6.9% and the equipment with the lowest utilization rate decreased by approximately 15.3%, achieving more balanced equipment utilization and creating spare time for processing during equipment maintenance, etc. Furthermore, more jobs were completed while reducing the average utilization rate of the entire equipment by 1.4% (see the row for good product throughput (= number of good products) in Table 13). [Table 13]

[0115] [Conclusion] This method addresses multi-factory scheduling, which has seen growing demand in recent years as a means of ensuring stable product supply and rapid response to customer demand. In particular, it addresses dynamic and stochastic influences, such as equipment downtime risk, which have been under-discussed in previous studies, and the resulting impacts on quality assurance time (Qtime), process delivery deadline overruns, and inter-factory transportation. This method extends the P3D-QAP method to handle multi-factories (MFs) and proposes a production resource allocation method that newly defines and introduces QTC overrun risk and delivery deadline overrun risk, which are factors that cause inter-factory transportation. A series of procedures for allocating product types and process loads to appropriate equipment based on multi-objective optimization was developed, aiming simultaneously to optimize total setup time, QTC and delivery deadline overrun risks, and maximize good product throughput for all parallel equipment scattered across multiple factories.

[0116] In the numerical experiments, the comparison method for MF was the "fastest processing start machine selection method," which selects the machine that can start processing earliest for each lot from among the processing equipment in multiple factories. The results of the numerical experiments showed improvements in the non-defective product rate, the on-time delivery rate (effective), which represents the percentage of lots that comply with both QTC and process due date constraints, and the setup time ratio. Specifically, compared to the fastest processing start machine selection method, the production resource allocation method increased the number of non-defective products by approximately 3.0%, improved the QTime on-time rate by approximately 3.0%, improved the on-time delivery rate (effective), and reduced the setup time ratio by approximately 10.73%. The above results demonstrate the performance improvement effect of using the multi-objective algorithm proposed in this method.

[0117] [Embodiment 3] Another embodiment of the present invention will be described below. For ease of explanation, components having the same functions as those described in the above embodiment will be denoted by the same reference numerals, and their description will not be repeated. FIG. 11 is a functional block diagram showing an example of a production planning device 10A that realizes a production planning method according to this embodiment. As shown in FIG. 11, the production planning device 10A includes a production resource allocation device 20.

[0118] More specifically, in the production planning method according to this embodiment, the production resource allocation method described in embodiment 2 is executed as a preprocessing. By using the production resource allocation method described in embodiment 2 instead of the proportional allocation method used in the production planning method described in embodiment 1, further effects such as a significant reduction in setup time and a reduction in processing time associated with transportation can be achieved.

[0119] As described above, the production planning method according to this embodiment further includes an allocation step of determining, for each process, the number of machines to be used in each machine group to process that process, and a calculation step of calculating, for each process, the number of machines for each product type to be used in each machine group to process that process and their usage conditions, based on the service rate for that process for that product type, the arrival rate for that process for that product type, and the reliability of that machine group. In the solution-finding step, an optimization problem having as its solution the factories to which each job is allocated and the processing order of the jobs allocated to each factory is solved using the smaller of the number of machines determined in the allocation step and the number of machines for each product type calculated in the calculation step as a constraint. In the allocation step, another optimization problem having as its solution at least one of whether to allocate each process to each machine and the amount of time available for allocation is solved using another objective function representing the cost or benefit of the solution. The other objective function includes a term that represents the risk of constraint violation, taking into account the transportation time that occurs when the factory in which the equipment that allocates the current process according to the solution is installed is different from the factory in which the equipment that allocates the previous process according to the solution is installed.

[0120] (Physical configuration of the production planning device 10, 10A, and the production resource allocation device 20) 12, the production planning device 10, 10A, and the production resource allocation device 20 can be configured by a computer 910 equipped with a bus 911, a processor 912, a memory 913, and an input / output interface 914. The processor 912, the memory 913, and the input / output interface 914 are connected to one another via the bus 911. In this example, the processor 912 is an example of a hardware element that realizes the first solution finding unit 11 and the second solution finding unit 21. The memory 913 is an example of a hardware element that realizes a storage unit that stores the first model 12 and the second model 22.

[0121] Furthermore, an input device 920 through which a user inputs various information to the computer 910 and an output device 930 through which the computer 910 outputs various information to the user may be connected to the input / output interface 914. The input device 920 and the output device 930 may be built into the computer 910 or may be externally attached to the computer 910.

[0122] [Embodiment 4] The optimization methods mentioned above (P3D-QAP2MF, DABC-TRANS) use variables to introduce estimated / predicted values ​​into the optimization method. P3D-QAP2MF uses the job arrival rate λ(i,s) for product i and process s estimated / predicted at the latest at planning time t (i.e., the sum of the output volume per unit time (throughput) of the preceding processes of the product / process that uses the relevant equipment group = the inflow volume to the relevant equipment group, which is the next process). DABC-TRANS uses the same arrival rate λ as well as the job arrival sequence J (a sequence of jobs with identifiers and arrival (scheduled) times associated with λ; used to generate an initial solution).

[0123] Furthermore, not only for production demand (arrival rate λ, etc.), but also for production capacity (service rate), the effective service rate (processing capacity per unit time (output rate)) of the equipment group is calculated as Nμ / r(t), and by introducing reliability r(t) which changes with time t, the system is able to explicitly reflect the level of reliability (1 or less). This allows for optimization in line with dynamically changing actual conditions.

[0124] Furthermore, the target processing resources are not limited to a single base / factory / building, but multiple bases / factories / buildings or bases. To do this, loss factors (such as transportation between factories) when processing across multiple factories are taken into consideration. The total transportation time or a risk index that integrates transportation loss and constraints is introduced into the objective function (the difference between grace time, etc. and production time loss such as transportation time and setup time) to optimize transportation losses.

[0125] Now, for the equipment groups to be planned, the section from the originating equipment group that satisfies the condition of a specified number of processes or cumulative processing time or less is obtained from the process master information. Next, the inflow of jobs to all equipment groups included in the target section is predicted. For the prediction, it is assumed that a method that can incorporate the influence of points and times distant from the target equipment group, such as node2vec, is used. For all equipment groups included in the target section, predicted values ​​are obtained as target nodes.

[0126] Modeling and performance evaluation of production systems has primarily relied on discrete event simulation and queuing theory, which model a series of directly connected processes and evaluate their performance as a whole. In particular, for complex production systems, such as semiconductor manufacturing, which contain tens to hundreds of repetitive processes (re-entrant flow), it has been thought that the only way to model and evaluate the performance of the entire system is to perform a comprehensive analysis. Meanwhile, traditional forecasting methods, such as time-series analysis, ignore the interconnected structure of the flow (the causes of fluctuations and changes). For these reasons, it has been difficult to accurately model and evaluate / predict the performance of production systems with a certain level of volume and complexity.

[0127] As a practical matter, the limitations of modeling and maintaining increasingly large-scale and complex production systems are becoming apparent amid the trend toward specialized, monopolized, and megafab manufacturing, which leverage economies of scale. In fact, the number of successful applications of major discrete event simulators in the semiconductor manufacturing field (planned-actual accuracy of ±5% or less) is extremely low, at just 1% over the past 20 years, with planning accuracy generally remaining at 15-25%. The underlying factors behind this are the number of cutting-edge manufacturing equipment that must be managed, ranging from thousands to tens of thousands of units at a single site. Furthermore, the equipment is subject to dynamic changes and uncertainty due to frequent failures in advanced processes, and multiple products require hundreds to thousands of production processes to produce a single product. Furthermore, the large-scale and complex conditions, including the aforementioned repetitive processing flows, make modeling even more difficult.

[0128] In this embodiment, the dynamic (performance-wise) connection structure, i.e., the influence and strength of other resources that affect the performance of a resource (resource group) of interest, is extracted in a data-driven manner, the influence of distant locations and points in time is identified, and these are used in the prediction model. By using data on the entire production process or multiple factories, static connections (production processes, etc.) are also implicitly reflected, making it possible to identify the influencing factors of the target of modeling and evaluation.

[0129] Unlike conventional modeling techniques that involve building a static model as a whole and then building and modifying it by adding dynamic conditions to each part, this technology does not rely on refinement, but instead uses data-driven automatic calculations using mass-production transaction data, etc. to derive the influencing factors and predicted values ​​for the performance of the target node that you want to know. This makes it possible to create modeling that can quickly respond to scales and complexity above a certain level, as well as changes and fluctuations in those factors.

[0130] The foundation of this data-driven automatic modeling is a data modeling method that can cross time and space and the features it uses. Specifically, it involves (1) the extraction of important equipment groups that affect target equipment groups based on static and dynamic data from the entire production process (incorporating static and dynamic conditions by using data from a certain period of time covering the production process or the entire factory), and (2) a model (e.g., BPNN) that predicts in-process and throughput using factors (features: average in-process processing lot, start rate, coefficient of variation of service time, number of equipment, service rate, utilization rate %) of the extracted important equipment groups.

[0131] In particular, to extract important equipment groups that affect the target equipment group, a suitable method is to use node2vec, for example, which represents equipment groups as nodes and process connections as edges, and then considers the process connections to extract nearby nodes that have a strong influence on the target node (equipment group).By using data from an appropriate period, dynamic characteristics (time-series fluctuations and correlations) can be taken into account.

[0132] Next, any prediction model can be used, and a robust method with excellent accuracy and stability is preferable. In the embodiment, if the important influencing factors can be well identified, even a very simple prediction model (BPNN with one hidden layer) can easily achieve a highly accurate model (less than 10% in MAPE index), and it is fast and has very high computational efficiency, which shows that it is generally superior to conventional techniques. The key feature is that the arrival rate, service rate, coefficient of variation of service rate, and availability rate of resource groups are used as important indices used in the queueing model.

[0133] VAR-LinGAM, a single method spanning time and space (factors and time points) and covering everything from factor identification to forecasting, is also applicable. However, numerical verification of this study has shown that when dealing with real-world problems with a huge number of candidate factors, the depth of the time axis becomes shallow. Therefore, to obtain meaningful results, it is desirable to perform screening and variable selection as preprocessing of VAR-LinGAM. In addition to general screening and variable selection methods, various safe screening and safe pruning methods, factorization machines (FMs) and their derivatives, sparse FMs with feature selection, and pliable lasso, which directly introduces constraint structures, are considered suitable for screening high-dimensional data (retaining only meaningful interactions between the time and space axes).

[0134] In summary, the production planning method may use the results of an analysis of "prediction or causation" of the impact of "distant points and times" on at least one of "work in progress or throughput" as input to the solution-finding process or pre-processing of the solution-finding process, as at least one of information on job arrival rates, job sequences, and inventory.

[0135] Furthermore, the production resource allocation method may use the results of an analysis of "prediction or causation" of the impact of "distant points and times" on at least one of "work in progress or throughput" as input to the solution-finding process or pre-processing of the solution-finding process, as at least one of information on job arrival rates, job sequences, and inventory.

[0136] [Embodiment 5] In addition to production resources (e.g., manufacturing equipment) in manufacturing systems, systems requiring processing resources that are the target of optimization for planning and process allocation also include communication and computer systems, middleware such as operating systems (OSs), and parallel computing systems such as cloud computing. Table 14 shows some specific examples. The rows in Table 14 represent applications, and the columns represent issues. In fact, the original P3D standard's approach to quasi-periodic plan review was inspired by the Round-Robin algorithm in time-sharing systems used in OS scheduling (see Japanese Patent Publication No. 2003-022119). While the challenges (i.e., the requirements for meeting the columns in Table 14) vary slightly depending on the application, they share a commonality in terms of resource sharing and the management of parallel shared resources (see columns 2, 6, and 7 in Table 14). Therefore, it can be applied to applications other than manufacturing systems. [Table 14]

[0137] Table 15 shows major parallel distributed systems other than production systems. The processing unit (processing building) is derived as a superordinate concept of the structural units in Table 15. Furthermore, each system is similar in that it has parallel distribution costs that cannot be ignored. While embodiments 1 to 4 have been described in detail with respect to production systems, similar processes and algorithms can also be used for parallel distributed systems other than No. 1 in Table 15. [Table 15]

[0138] [Software implementation example] The functions of the production planning device 10, 10A, and the production resource allocation device 20 (hereinafter referred to as the "device") can be realized by a program for causing a computer to function as the device, and a program for causing a computer to function as each control block (first solution-finding unit 11, second solution-finding unit 21) of the device.

[0139] In this case, the device includes a computer having at least one control device (e.g., a processor) and at least one storage device (e.g., a memory) as hardware for executing the program. The control device and storage device execute the program, thereby realizing the functions described in each of the above embodiments.

[0140] The program may be non-transitory and may be recorded on one or more computer-readable recording media. The recording media may or may not be included in the device. In the latter case, the program may be supplied to the device via any wired or wireless transmission medium.

[0141] Furthermore, some or all of the functions of the control blocks can be realized by logic circuits. For example, an integrated circuit in which a logic circuit that functions as each of the control blocks is formed is also included in the scope of the present invention. In addition, the functions of the control blocks can also be realized by, for example, a quantum computer.

[0142] Furthermore, each process described in each of the above embodiments may be executed by AI (Artificial Intelligence). In this case, the AI ​​may run on the control device or on another device (for example, an edge computer or a cloud server).

[0143] The present invention is not limited to the above-described embodiments, and various modifications are possible within the scope of the claims. Embodiments obtained by appropriately combining the technical means disclosed in different embodiments are also included in the technical scope of the present invention.

[0144] 〔summary〕 A processing plan formulation method according to aspect 1 of the present invention is a processing plan formulation method for formulating a processing plan for processing a plurality of jobs at a plurality of constituent units, and includes a solution process for solving an optimization problem whose solution is the constituent units to which each job is allocated and the processing order of the jobs allocated to each constituent unit, using an objective function that represents the cost or benefit of the processing plan derived from the solution, wherein the processing plan includes interactions between constituent units for processing the steps that make up a job at constituent units other than the constituent units to which the job is allocated, and the objective function includes a term that represents the cost of interactions between the constituent units.

[0145] In the processing plan formulation method according to aspect 2 of the present invention, the constituent units are factories, the processing plan is a production plan in the factories, and the exchange between the constituent units is inter-factory transport between the plurality of factories.

[0146] In the process planning method according to aspect 3 of the present invention, in the solution-finding step of aspect 2, when deriving the production plan in the solution-finding step, a factory is determined for each process in each job so as to optimize the risk of violating the Qtime constraint, and then the processing start time and processing end time of each job are determined.

[0147] In the process plan formulation method according to aspect 4 of the present invention, in the case of aspect 2 or 3, when deriving the production plan in the solution-finding step, for each process, (1) jobs for which there is no equipment in the allocated factory that can process that process, and jobs for which the process would violate the Qtime constraint if processed in the allocated factory, are selected as jobs for which that process will be processed in a factory other than the factory to which that job is allocated, and if all jobs still do not satisfy the Qtime constraint, (2) a factory for processing that process for each job is determined so as to optimize the degree to which all jobs violate the Qtime constraint overall, and then the processing start time and processing end time for that job are determined.

[0148] In the processing plan formulation method according to a fifth aspect of the present invention, in any one of the second to fourth aspects, the term representing the cost of inter-factory transportation is calculated by dividing the transportation time H taken to complete the processing of each job j by the total transportation time H j Sum of Σ j H j Includes a term multiplied by a coefficient.

[0149] In the processing plan formulation method according to a sixth aspect of the present invention, in the fifth aspect, the objective function includes a deadline of each job j, d j (1) The cycle time C of each job j j Sum of Σ j C j (2) The term obtained by multiplying the coefficient of each job j by E j =max{0,d j -C j} sum Σ j E j (3) The delayed due date of each job j, T j =max{0,C j -d j} sum Σ j T j It further includes a term multiplied by a coefficient.

[0150] A processing plan development method according to aspect 7 of the present invention is, in any of aspects 2 to 6, wherein the coefficient of each term included in the objective function is the product of a first coefficient set by the user and a second coefficient optimized in the solution-finding process.

[0151] A processing plan development method according to an eighth aspect of the present invention is any of the second to seventh aspects, and further includes an allocation step of determining, for each process, the number of devices to be used in each device group to process that process using a proportional allocation method, and a calculation step of calculating, for each process, the number of devices for each product type to be used in each device group to process that process based on the service rate for that product type, the arrival rate for that product type, and the reliability of that device group, and in the solution step, an optimization problem whose solution is the factory to which each job is allocated and the processing order of the jobs allocated to each factory is solved using the smaller number of devices between the number of devices determined in the allocation step and the number of devices for each product type calculated in the calculation step as a constraint.

[0152] A processing plan development method according to a ninth aspect of the present invention is the method according to any one of the second to eighth aspects, further comprising: an allocation step of determining, for each process, the number of devices to be used in each device group to process that process; and a calculation step of calculating, for each process, the number of devices for each product type to be used in each device group to process that process based on the service rate of that product type for that process, the arrival rate of that product type for that process, and the reliability of that device group; and in the solution-finding step, an optimization problem to be solved by determining the factories to which each job is allocated and the processing order of the jobs allocated to each factory is solved by the allocation step. a solution is obtained using the smaller number of devices out of the number of devices determined in the step (a) and the number of devices for each product type calculated in the calculation step, as a constraint condition; and in the allocation step, another optimization problem, the solution of which is at least one of whether to allocate each process to each device and the amount of time that can be allocated, is solved using another objective function that represents the cost or benefit of the solution, and the other objective function includes a term that represents a constraint violation risk that takes into account transportation time that occurs when a factory equipped with a device that allocates a current process according to the solution is different from a factory equipped with a device that allocates a preceding process according to the solution.

[0153] A processing resource allocation method according to aspect 10 of the present invention is a processing resource allocation method for allocating each of a plurality of processes for producing each of a plurality of product types to each of one or more pieces of equipment installed in one or more factories, and includes a solution process for solving an optimization problem whose solution is at least one of whether or not to allocate each process to each piece of equipment and the amount of time that can be allocated, using an objective function that represents the cost or benefit of the solution, and the objective function includes a term that represents the constraint violation risk that takes into account the transportation time that occurs when the factory in which the equipment that allocates the current process according to the solution is installed is different from the factory in which the equipment that allocates the previous process according to the solution is installed.

[0154] In a processing resource allocation method according to an eleventh aspect of the present invention, in the tenth aspect, the objective function includes, as a term representing the constraint violation risk, a term representing the Qtime constraint violation risk, including transport time, which occurs when a factory in which a device that allocates a current process according to the solution is installed is different from a factory in which a device that allocates a previous process according to the solution is installed; or, as a term representing the constraint violation risk, a term representing the delivery date constraint violation risk, including transport time, which occurs when a factory in which a device that allocates a current process according to the solution is installed is different from a factory in which a device that allocates a previous process according to the solution is installed; or, in addition to the term representing the constraint violation risk, a term representing the setup time that occurs when each process is assigned to one of the multiple factories according to the solution is included; or, in addition to the term representing the constraint violation risk, a term representing the defective product throughput that occurs when each process is assigned to one of the multiple processes according to the solution is included.

[0155] A processing plan formulation method according to aspect 12 of the present invention, in any of aspects 2 to 9, uses the results of a prediction or causal analysis of the impact on at least one of work-in-progress or throughput at a remote location and time as input to the solution-finding process or pre-processing of the solution-finding process, as information on at least one of job arrival rate, job sequence, and inventory.

[0156] A processing resource allocation method according to aspect 13 of the present invention uses, as input to the solution-finding process or pre-processing for the solution-finding process, the results of a prediction or causal analysis of the impact on work-in-progress or throughput at at least one of a remote location and time as information on at least one of job arrival rate, job sequence, and inventory.

[0157] A processing plan formulation device according to aspect 14 of the present invention is a processing plan formulation device that formulates a processing plan for processing multiple jobs using multiple constituent units, and includes a first solution unit that solves an optimization problem whose solution is the constituent units to which each job is allocated and the processing order of the jobs allocated to each constituent unit, using an objective function that represents the cost or benefit of the processing plan derived from the solution, and the processing plan includes interactions between constituent units for processing steps that make up a job using constituent units other than the constituent units to which the job is allocated, and the objective function includes a term that represents the cost of interactions between the constituent units.

[0158] A processing resource allocation device according to aspect 15 of the present invention is a processing resource allocation device that allocates each of a plurality of processes for producing each of a plurality of varieties to each of one or more pieces of equipment installed in each of one or more factories, and is equipped with a second solution-finding unit that solves an optimization problem whose solution is at least one of whether or not to allocate each process to each piece of equipment and the amount of time that can be allocated, using an objective function that represents the cost or benefit of the solution, and the objective function includes a term that represents the risk of constraint violation that takes into account the transportation time that occurs when the factory in which the equipment that allocates the current process according to the solution is installed is different from the factory in which the equipment that allocates the previous process according to the solution is installed.

[0159] A control program according to a sixteenth aspect of the present invention is a control program that causes a computer to execute the processing planning method, and executes the solution-finding step.

[0160] A control program according to a seventeenth aspect of the present invention is a control program that causes a computer to execute the processing resource allocation method, and executes the solution-finding step. [Explanation of symbols]

[0161] 10, 10A Production planning device (processing planning device) 11 1st solution part 12 First Model 20 Production resource allocation device 21 Second solution part 22 Second Model

Claims

1. A processing plan formulation method for formulating a processing plan for processing a plurality of jobs in a plurality of units, comprising: a solving step of solving an optimization problem, the solution of which is the constituent units to which each job is allocated and the processing order of the jobs allocated to each constituent unit, using an objective function that represents the cost or benefit of a processing plan derived from the solution; The processing plan includes communication between constituent units for processing the steps constituting the job in a constituent unit different from the constituent unit to which the job is allocated, The objective function includes a term representing the cost of interaction between the constituent units. How to develop a treatment plan.

2. 2. The processing plan development method according to claim 1, wherein the constituent units are factories, the processing plan is a production plan in the factories, and the exchange between the constituent units is inter-factory transport between the plurality of factories.

3. When deriving the production plan in the solution-finding step, for each process, a factory that processes each job is determined so as to optimize the risk of violating the Qtime constraint, and then a processing start time and a processing end time for each job are determined. The treatment planning method of claim 2 .

4. When deriving the production plan in the solution-finding process, for each process, (1) a job for which there is no device in the allocated factory that can process that process, and a job for which the process would violate the Qtime constraint if processed in the allocated factory, are selected as jobs to process that process in a factory other than the factory to which the job is allocated, and if all jobs still do not satisfy the Qtime constraint, (2) a factory that processes that process for each job is determined so as to optimize the degree to which all jobs violate the Qtime constraint overall, and then the processing start time and processing end time for each job are determined. The method for formulating a treatment plan according to claim 2 or 3.

5. The term representing the cost of transportation between factories is the transportation time H taken to complete the processing of each job j. ｊ Sum of Σ ｊ H ｊ 4. The method for formulating a treatment plan according to claim 2 or 3, further comprising a term obtained by multiplying by a coefficient.

6. The objective function is to set the due date of each job j as d ｊ (1) The cycle time C of each job j ｊ Sum of Σ ｊ C ｊ (2) The term obtained by multiplying the coefficient of each job j by the ｊ = max {0, d ｊ -C ｊ } sum Σ ｊ E ｊ (3) the delayed due date T of each job j ｊ =max{0, C ｊ -d ｊ } sum Σ ｊ T ｊ It further includes a term multiplied by a coefficient, The treatment planning method according to claim 5 .

7. a coefficient of each term included in the objective function is a product of a first coefficient that can be set by a user and a second coefficient that is optimized in the solution-finding step; The method for formulating a treatment plan according to claim 2 or 3.

8. an allocation step of determining, for each process, the number of devices to be used in each device group for processing that process using a proportional allocation method; further comprising a calculation step of calculating, for each process, the number of devices for each product type to be used to process that process in each device group based on the service rate of that process for that product type, the arrival rate of that process for that product type, and the reliability of that device group; In the solution-finding step, an optimization problem, the solution of which is a factory to allocate each job and the processing order of the jobs allocated to each factory, is solved using the smaller number of equipment between the number of equipment determined in the allocation step and the number of equipment for each product type calculated in the calculation step as a constraint. The method for formulating a treatment plan according to claim 2 or 3.

9. an allocation step of determining, for each process, the number of devices to be used in each device group for processing that process; further comprising a calculation step of calculating, for each process, the number of devices for each product type to be used to process that process in each device group based on the service rate of that process for that product type, the arrival rate of that process for that product type, and the reliability of that device group; In the solution-finding step, an optimization problem is solved, the solution being a factory to which each job is allocated and a processing order of the jobs allocated to each factory, with the smaller number of devices being the number of devices determined in the allocation step and the number of devices for each product type calculated in the calculation step as a constraint; In the allocation step, another optimization problem is solved, the solution being at least one of whether to allocate each process to each device and the amount of time that can be allocated, using another objective function that represents the cost or benefit of the solution; The other objective function includes a term representing a constraint violation risk that takes into account a transportation time that occurs when a factory in which a device that allocates a current process according to the solution is installed is different from a factory in which a device that allocates a preceding process according to the solution is installed. The method for formulating a treatment plan according to claim 2 or 3.

10. 1. A processing resource allocation method for allocating each of a plurality of processes for producing each of a plurality of product types to each of one or more devices provided in each of one or more factories, the method comprising: a solution step of solving an optimization problem, the solution of which is at least one of whether to allocate each process to each device and the amount of time that can be allocated, using an objective function that represents the cost or benefit of the solution; The objective function includes a term that represents a constraint violation risk that takes into account a transportation time that occurs when a factory in which a device that allocates a current process according to the solution is installed is different from a factory in which a device that allocates a preceding process according to the solution is installed. Processing resource allocation method.

11. The objective function includes: The term representing the constraint violation risk includes a term representing a Qtime constraint violation risk including a transport time that occurs when a factory in which a device that allocates a current process according to the solution is installed is different from a factory in which a device that allocates a previous process according to the solution is installed, or The term representing the constraint violation risk includes a term representing a delivery time constraint violation risk including a transportation time that occurs when a factory in which a device that allocates a current process according to the solution is installed is different from a factory in which a device that allocates a previous process according to the solution is installed, or In addition to the term representing the constraint violation risk, a term representing the setup time that occurs when each process is assigned to one of the multiple factories according to the solution is included; or In addition to the term representing the constraint violation risk, a term representing the defective throughput that occurs when each process is assigned to one of the plurality of processes according to the solution is included.

11. The method of claim 10.

12. 4. The process planning method according to claim 2, wherein as an input to the solution-finding step or pre-processing for the solution-finding step, a result of a prediction or causal analysis of the impact on work-in-progress or throughput at at least one of a remote location and time is used as information on at least one of job arrival rate, job sequence, and inventory.

13. 12. The processing resource allocation method according to claim 10, wherein as an input to the solution-finding step or pre-processing for the solution-finding step, a result of a prediction or causal analysis of the impact on work-in-progress or throughput at at least one of a remote location and time is used as information on at least one of job arrival rate, job sequence, and inventory.

14. A processing plan formulation device that formulates a processing plan for processing a plurality of jobs in a plurality of component units, a first solution-finding unit that solves an optimization problem, the solution of which is the constituent units to which jobs are allocated and the processing order of the jobs allocated to each constituent unit, by using an objective function that represents a cost or benefit of a processing plan derived from the solution; The processing plan includes communication between constituent units for processing the steps constituting the job in a constituent unit different from the constituent unit to which the job is allocated, The objective function includes a term representing the cost of interaction between the constituent units. Treatment planning device.

15. A processing resource allocation device that allocates each of a plurality of processes for producing each of a plurality of product types to each of one or more devices provided in each of one or more factories, a second solution-finding unit that solves an optimization problem, the solution of which is at least one of whether to allocate each process to each device and the amount of time that can be allocated, by using an objective function that represents a cost or a benefit of the solution; The objective function includes a term that represents a constraint violation risk that takes into account a transportation time that occurs when a factory in which a device that allocates a current process according to the solution is installed is different from a factory in which a device that allocates a preceding process according to the solution is installed. Processing resource allocation device.

16. A processing plan development program that causes a computer to execute the processing plan development method according to claim 1, A process planning program that executes the solution-finding step.

17. A processing resource allocation program that causes a computer to execute the processing resource allocation method according to claim 10, a processing resource allocation program that executes the solution-finding step;

Images