JP7502975B2 - Processing device, processing method, and program - Google Patents

Description

The present invention relates to a processing device, a processing method, and a program, and is particularly suitable for use in deriving weighting coefficients to be set for objective functions in multi-objective optimization problems for creating production plans or logistics plans.

Production plans or distribution plans are formulated by solving mathematical programming problems. A mathematical programming problem is a problem of finding decision variables when the value of an objective function is minimized or maximized within a range that satisfies a constraint equation. When formulating a production plan or distribution plan, the decision variables are variables that need to be determined in order to determine the production plan or distribution plan. The constraint equation is a mathematical formula that represents the constraint conditions imposed when carrying out production or distribution in accordance with the production plan or distribution plan. The objective function is an evaluation index that evaluates the quality of the production plan or distribution plan, and includes one or more evaluation indexes whose values are determined based on the decision variables.

In production planning and logistics planning, multiple objectives must be achieved simultaneously. Moreover, the multiple objectives are often in a trade-off relationship with each other, and it is important to balance the evaluations between the evaluation indexes corresponding to each objective. A trade-off relationship is a relationship in which if the value of one evaluation index is changed to improve the evaluation of the production plan or logistics plan, the value of the other evaluation index is changed to worsen the evaluation of the production plan or logistics plan. For example, when formulating a production plan, various objectives such as cost, quality, productivity, and delivery date must be achieved simultaneously. In this case, for example, lowering cost improves the evaluation of the production plan or logistics plan, and raising quality improves the evaluation of the production plan or logistics plan. Generally, lowering cost reduces quality. Therefore, if the evaluation of the production plan or logistics plan is changed to improve in terms of cost, the evaluation of the production plan or logistics plan is changed to worsen in terms of quality, so there is a trade-off relationship between cost and quality.

A mathematical programming problem with multiple evaluation indices is called a multi-objective optimization problem. When solving a multi-objective optimization problem, there is a method of finding a Pareto optimal solution (a set of optimal solutions that exist on the boundary of the feasible region), but here we assume a method of solving a single-objective optimization problem by assigning a weighting coefficient to each of the objectives of the multi-objectives to make it a single objective (as one objective function). The weighting coefficient represents the balance of evaluation between each evaluation index, and the value of the weighting coefficient is determined by how much importance is given to the evaluation index for that weighting coefficient relative to other evaluation indices. Note that the objective function and weighting coefficient are sometimes called cost functions, cost coefficients, etc., respectively. In addition, each evaluation index may be called an objective function, but in this specification, each objective function is called an evaluation index, and the sum of evaluation indexes to which weighting coefficients are set is called the objective function, and these are distinguished. In addition, there are also cases where a reference weighting coefficient for a certain evaluation index is fixed to 1, and weighting coefficients for other evaluation indexes are set.

When solving a multi-objective optimization problem as a single objective, it is necessary to compare the magnitudes of the values of multiple evaluation indexes, each of which represents different objectives with completely different units (dimensions), on an equal footing. For this reason, it is not easy to adjust the weighting coefficients for each evaluation index. Also, weighting coefficients are not something that do not need to be changed once they have been determined; there are cases in which changes are necessary. In production plans and logistics plans, for example, the importance of multiple evaluation indexes may change depending on the external environment, production targets/logistics targets, operating conditions, etc. In such cases, if the weighting coefficients are not changed, there is a risk that appropriate production plans and logistics plans cannot be formulated.

One technique for determining the weighting coefficient value is described in Patent Document 1. Patent Document 1 describes how the final quality is expressed as a linear combination of each quality value or manufacturing condition, and how each regression coefficient is calculated in advance by multiple regression analysis.

Patent No. 6351880

However, in the technology described in Patent Document 1, regression coefficients are derived as weighting coefficients by multiple regression analysis, so in order to create training data, it is necessary to determine not only each quality value but also the correct value of the final quality corresponding to each quality value. For this reason, the final quality needs to be, for example, a measurable value. Therefore, if the correct value of the objective function (objective variable) is not determined, there is a risk that the weighting coefficients cannot be derived accurately.

The present invention was made in consideration of the above problems, and aims to make it possible to derive weighting coefficients to be set for objective functions in multi-objective problems for creating production plans or logistics plans, without determining the correct solution value of the objective function.

The processing device of the present invention is a processing device that executes a process of deriving a weighting coefficient in a planning objective function that is an objective function that reduces a multi-objective optimization problem for planning a production plan or a logistics plan to a single objective, the planning objective function having a plurality of planning evaluation indexes and a weighting coefficient to be multiplied by the planning evaluation indexes, and includes an acquisition means for acquiring values of the plurality of planning evaluation indexes based on a plurality of adopted plans that have been adopted as the production plan or the logistics plan, and values of the plurality of planning evaluation indexes based on a plurality of non-adopted plans that have not been adopted as the production plan or the logistics plan, and a processing means for indicating the difference between an adopted objective function that is the planning objective function based on the adopted plans and a non-adopted objective function that is the planning objective function based on the non-adopted plans. and a weighting coefficient derivation means for deriving decision variables including the objective function value difference and the weighting coefficient by solving an optimization problem, wherein the coefficient determination constraint equation, which is a constraint equation in the optimization problem, includes an adopted/non-adopted objective function value difference constraint equation indicating that the difference between the adopted objective function in a state in which the value of the planning evaluation index based on the adopted plan is substituted and the weighting coefficient is unknown, and the non-adopted objective function in a state in which the value of the planning evaluation index based on the non-adopted plan is substituted and the weighting coefficient is unknown, is limited by a limit value based on the objective function value difference, and the coefficient determination objective function, which is an objective function in the optimization problem, includes the objective function value difference as a coefficient determination evaluation index.

The processing method of the present invention is a processing method for executing a process of deriving a weighting coefficient in a planning objective function that is an objective function that reduces a multi-objective optimization problem for planning a production plan or a logistics plan to a single objective, the planning objective function having a plurality of planning evaluation indexes and a weighting coefficient to be multiplied by the planning evaluation indexes, the processing method including an acquisition process for acquiring values of the plurality of planning evaluation indexes based on a plurality of adopted plans that have been adopted as the production plan or the logistics plan, and values of the plurality of planning evaluation indexes based on a plurality of non-adopted plans that have not been adopted as the production plan or the logistics plan, and a process for indicating the difference between an adopted objective function, which is the planning objective function based on the adopted plans, and a non-adopted objective function, which is the planning objective function based on the non-adopted plans. and a weighting coefficient derivation process for deriving decision variables including the objective function value difference and the weighting coefficient by solving an optimization problem, wherein the coefficient determination constraint equation, which is a constraint equation in the optimization problem, includes an adopted/non-adopted objective function value difference constraint equation indicating that the difference between the adopted objective function in a state in which the value of the planning evaluation index based on the adopted plan is substituted and the weighting coefficient is unknown, and the non-adopted objective function in a state in which the value of the planning evaluation index based on the non-adopted plan is substituted and the weighting coefficient is unknown, is limited by a limit value based on the objective function value difference, and the coefficient determination objective function, which is an objective function in the optimization problem, includes the objective function value difference as a coefficient determination evaluation index.

The program of the present invention is intended to cause a computer to function as each of the means of the processing device.

According to the present invention, it is possible to derive a weighting coefficient to be set for an objective function in a multi-objective problem for creating a production plan or a logistics plan, without determining the correct solution value of the objective function.

FIG. 2 illustrates an example of a functional configuration of a processing device. 1 is a flowchart illustrating a first example of a processing method. 11 is a flowchart illustrating a second example of a processing method. FIG. 11 is a diagram showing first input data. FIG. 11 is a diagram showing second input data. FIG. 13 is a diagram showing third input data. FIG. 4 is a diagram showing fourth input data. FIG. 5 is a diagram showing fifth input data. FIG. 11 is a diagram showing an example of the number of production plans (adopted plans and non-adopted plans) formulated based on first to fifth input data. FIG. 13 is a diagram showing the number of occurrences of delivery delays, early production, and lot changes obtained from a production plan drawn up based on the first to fifth input data. 11 is a diagram showing an example of the number of times of delivery delays, early production, and lot changes obtained from an adoption plan drawn up based on first input data. FIG. FIG. 11 is a diagram showing an example of the number of times of delivery delays, early production, and lot changes obtained from a non-adopted plan drawn up based on first input data.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
First Embodiment
First, the first embodiment will be described.
Fig. 1 is a diagram showing an example of the functional configuration of the processing device 100. The hardware of the processing device 100 is realized by using, for example, an information processing device including a CPU, a ROM, a RAM, a HDD, and various interfaces, or dedicated hardware. Fig. 2 is a flowchart explaining an example of a processing method using the processing device 100 of this embodiment.

<Planning objective function Jr, planning evaluation index x _k >
The processing device 100 executes a process of deriving a weighting coefficient in a planning objective function (objective function of one equation) that is a multi-objective optimization problem for making a production plan or a logistics plan, the planning objective function having a plurality of planning evaluation indexes and a weighting coefficient to be multiplied by the plurality of planning evaluation indexes. In this embodiment, a case is illustrated in which a plurality of planning evaluation indexes x _k when the value of the planning objective function Jr shown in the following formula (1) is minimized is derived as an optimal solution by performing an optimization calculation by mathematical programming, and a production plan or a logistics plan is determined based on the derived optimal solution. In formula (1), k is a variable that identifies the planning evaluation index x _k , and the total number of planning evaluation indexes x _k is K (k ∈ K). min. indicates that the minimum value of the objective function (planning objective function Jr in formula (1)) is obtained. In this embodiment, since the mathematical programming problem is a multi-objective optimization problem having a plurality of planning evaluation indexes x _k , K is an integer of 2 or more. w[k] is a weighting coefficient by which the planning evaluation index x _k is multiplied.

The planning evaluation index x _k is an evaluation index for evaluating the quality of a production plan or a logistics plan, and is determined according to the purpose of planning the production plan or the logistics plan. In a multi-objective optimization problem, at least two of _{the multiple planning evaluation indexes x k are usually in a trade-off relationship. The trade-off relationship refers to a relationship in which, when the value of one planning evaluation index x k is changed} so as to improve the evaluation of the production plan or the logistics plan, the value of the other planning evaluation index x _k is changed so as to worsen the evaluation of the production plan or the logistics plan. Since the formula (1) illustrates a minimization problem that minimizes the value of the planning objective function Jr, improving the evaluation of the production plan or the logistics plan corresponds to reducing the value of the planning evaluation index x _k .

In general, when solving mathematical programming problems such as multi-objective optimization problems, the optimal value of the objective function is derived within the range that satisfies the constraint equation. Therefore, when creating a production plan or a logistics plan using the planning objective function Jr shown in equation (1), the minimum value of the planning objective function Jr shown in equation (1) is derived within the range that satisfies the constraint equation, which is a mathematical expression that represents the constraint conditions imposed when executing production or logistics according to the production plan or logistics plan. The constraint equation itself is not directly related to the gist of this embodiment, so a detailed description of it is omitted.

The planning evaluation index x _k is, for example, the number of times of delivery delay, early production, and lot changes.
The delivery delay indicates how late a product will be shipped relative to its delivery date, and is, for example, the value obtained by subtracting the delivery date from the scheduled shipping date of the product (if the scheduled shipping date of the product is earlier than the delivery date (i.e., if the value obtained by subtracting the delivery date from the scheduled shipping date of the product is a negative value), the delivery delay will be 0 (zero). When creating a production plan or logistics plan with the objective of suppressing products that will be late, the delivery delay is included in the planning evaluation index _xk .

Early delivery indicates how far ahead a product can be shipped relative to its delivery date, and is, for example, the value obtained by subtracting the scheduled shipping date from the product's delivery date (if the product's delivery date is earlier than the scheduled shipping date (i.e., if the value obtained by subtracting the scheduled shipping date from the product's delivery date is a negative value), early delivery is 0 (zero). When a product is able to be shipped before its delivery date, the product becomes inventory, and storage space for that product must be secured. When creating a production plan or logistics plan with the objective of reducing the need to secure such excess storage space, early delivery is included in the planning evaluation index _xk .

Next, we will explain the number of lot changes. In production and logistics processes that are processed through multiple steps, for example, multiple products are grouped into lots in order to simplify and streamline operating conditions, manufacturing work, sorting work, etc. A lot is a processing unit (e.g., production unit, transportation unit) that groups together multiple products that can be processed using operations with the same conditions (e.g., manufacturing work, sorting work, transportation work), and groups together multiple products that are processed in each process. Products that belong to the same lot are assigned the same lot number as information to identify the lot.

In each process in production or logistics, it is preferable to process as many products as possible in one lot. This is because when processing changes to a different lot, a changeover (preparation for work associated with the change of lot) is usually required. For this reason, for example, when a production plan or logistics plan is made with the objective of improving processing efficiency, the fewer the number of lot changes, the better so that the number of changeovers is reduced. When making a production plan or logistics plan with such an objective, the number of lot changes is included in the planning evaluation index x _k . Note that the number of lot changes refers to the sum of the number of lot changes counted for each process.

When many products are grouped together in the same lot in order to reduce the number of lot changes, the delivery dates of multiple products in the same lot are likely to vary. For example, products that have ample time before their delivery date may be processed (e.g., produced or transported) first, resulting in the processing of products that should have been processed first being postponed. In this case, there is a risk that the delivery date of the products that are postponed will be delayed.

In addition, the conditions for combining lots generally differ for each process. In other words, the processing order of the products in the later process does not necessarily follow the processing order of the products in the earlier process. In such cases, reducing the number of lot changes increases the possibility of delays in delivery or early production.
As described above, there is a trade-off between the number of lot changes and delivery time (delivery delays and early delivery).
Also, if you try to prevent late delivery, it becomes easier to make the delivery earlier. Therefore, there is a trade-off between late delivery and early delivery.

The planning evaluation index x _k is not limited to, for example, delays in delivery, early production, and the number of lot changes, but may be an evaluation index for evaluating the quality of a production plan or a logistics plan, and may be determined according to the purpose of formulating the production plan or the logistics plan. For example, an evaluation index related to the quality or cost of a product may be used as the planning evaluation index x _k .

The only difference between creating a production plan and creating a logistics plan is the specific content of the planning evaluation index x _k in equation (1), and the processing device 100 that derives the weighting coefficient w[k] can be applied to either a production plan or a logistics plan. However, in the following, for simplicity, the production plan or the logistics plan will be referred to as a production plan as necessary.

As shown in FIG. 1, the processing device 100 has an acquisition unit 101, a weighting coefficient derivation unit 102, and an output unit 103.

<Acquisition unit 101>
The acquisition unit 101 acquires values (actual values) of a plurality of planning evaluation indexes x _k based on a plurality of adopted plans adopted as production plans, and values (actual values) of a plurality of planning evaluation indexes x _k based on a plurality of non-adopted plans not adopted as production plans. The adopted plans are production plans that are actually used in the production of products, for example, a production plan prepared by a planner (e.g., an expert) or a production plan prepared using a known production simulator. The non-adopted plans are production plans that are prepared as production plans but are not used in the production of products, for example, a production plan prepared by a planner (e.g., an unskilled person) or a production plan prepared using a known production simulator.

In this embodiment, the acquisition unit 101 acquires information that identifies the contents of multiple adoption plans and information that identifies the contents of multiple non-adoption plans. Examples of the form of acquisition of this information include at least one of input operations to a user interface of the processing device 100, receiving information transmitted from an external device, and reading information stored in a portable storage medium.

The acquisition unit 101 executes, for each of the multiple adoption plans identified by the information acquired in this manner, pairing one adoption plan with one non-adoption plan. Two or more mutually different non-adoption plans may be paired with the same adoption plan. That is, there may be a pair of a certain adoption plan with a certain non-adoption plan, and a pair of the adoption plan with a non-adoption plan different from the non-adoption plan.

The paired adopted and non-adopted plans are production plans that have the same preconditions for planning (information that is set in advance for planning). When the preconditions for planning are the same, the values used as constants (fixed values) for calculating the value of the planning objective function Jr are the same. For example, the IDs of the products included in the paired adopted and non-adopted plans are the same. Furthermore, when late delivery and early delivery are used as the planning evaluation index x _k , the delivery dates of the products included in the paired adopted and non-adopted plans are the same. Furthermore, when the number of lot changes is used as the planning evaluation index x _k , the lot numbers of the products included in the paired adopted and non-adopted plans are the same.

The acquisition unit 101 creates a pair of one adopted plan and one non-adopted plan that have all the same information (product ID, delivery date, lot number). Alternatively, for example, if each of the adopted plan and non-adopted plan is assigned identification information of the prerequisites at the time of planning, the acquisition unit 101 may create a pair of one adopted plan and one non-adopted plan that have the same identification information.

The acquisition unit 101 acquires the value of the planning evaluation index x _k from the adopted plan, and acquires the value of the planning evaluation index x _k from the non-adopted plans that belong to the same pair as the adopted plan, for each pair.
For example, when the planning evaluation index x _k includes late delivery and early delivery, the adopted plan and the non-adopted plan include, for example, the scheduled shipping date when the production of the product is completed and ready to be shipped, and the delivery date of the product. When the value obtained by subtracting the scheduled shipping date from the delivery date of the product is 0 (zero) or a positive value, the value is identified as an early delivery, and 0 (zero) is identified as a late delivery. Also, when the value obtained by subtracting the delivery date from the scheduled shipping date of the product is 0 (zero) or a positive value, the value is identified as a late delivery, and 0 (zero) is identified as an early delivery.

Furthermore, when the planning evaluation index x _k includes the number of lot changes, the adopted plan and the non-adopted plan include, for example, the production order for each process of each product to which a lot number is set. The number of changes in the lot number when the lot numbers are arranged in the production order of the products is counted for each process, and the value obtained by adding up the number of changes in the lot number for each process is identified as the number of lot changes.

In each formula described in this embodiment, the variable that identifies the pairs acquired by the acquisition unit 101 in the above manner is i∈I (I is a set of pairs). In addition, an adopted plan and a non-adopted plan are denoted as OK and NG, respectively. As described above, two or more mutually different non-adopted plans may be paired with the same adopted plan, and these pairs are identified by different variables i.

<Weighting coefficient derivation unit 102>
The weighting coefficient derivation unit 102 derives decision variables including an objective function value difference ε[i] indicating the difference between an adopted objective function, which is a planning objective function Jr based on an adopted plan, and a non-adopted objective function, which is a planning objective function Jr based on a non-adopted plan, and a weighting coefficient w[k]. In this embodiment, a minimization problem for finding the minimum value of the planning objective function Jr is illustrated (i.e., a smaller value of the planning objective function Jr is a better plan), so the value of the non-adopted objective function is equal to or greater than the value of the adopted objective function. Therefore, in this embodiment, a case is illustrated in which the difference between the adopted objective function and the non-adopted objective function is expressed by a value obtained by subtracting the former (adopted objective function) from the latter (non-adopted objective function).

Here, in the following formulas, [k] in w[k] indicates a value for the planning evaluation index x _k . Also, [i] in ε[i] indicates a value for pair i. Also, the subscript k_i_OK in x _{k_i_OK} indicates that it is multiplied by the weight coefficient w[k], belongs to pair i (pair identified by variable i), and is based on the adoption plan. Similarly, the subscript k_i_NG in x _{k_i_NG} indicates that it is multiplied by the weight coefficient w[k], belongs to pair i (pair identified by variable i), and is based on the non-adoption plan.

In the example shown in formula (1), the value of the adopted objective function is Σ _k∈K w[k] x _{k_i_OK} . As described above, the value of the evaluation index for planning based on the adopted plan x _{k_i_OK} is identified from the adopted plan, so the unknown value of the adopted objective function is the weighting coefficient w[k]. Similarly, the value of the non-adopted objective function is Σ _k∈K w[k] x _{k_i_NG} . The value of the evaluation index for planning based on the non-adopted plan x _{k_i_NG} is identified from the non-adopted plan, so the unknown value of the adopted objective function is the weighting coefficient w[k].

In this embodiment, the coefficient determination constraint equation, which is a constraint equation for determining the weight coefficient w[k], includes an adopted/unadopted objective function value difference constraint equation, an objective function value difference constraint equation, and an upper and lower coefficient limit value constraint equation. In addition, in this embodiment, the coefficient determination objective function Jc, which is an objective function for determining the weight coefficient w[k], includes the objective function value difference ε[i] as a coefficient determination evaluation index.

The adopted/non-adopted objective function value difference constraint equation is a constraint equation indicating that the difference between the adopted objective function (Σ _k∈K w[k]· _{xk_i_OK} ) which is the planning objective function Jr in a state where the value of the planning evaluation index xk_i_OK based on the adopted plan is substituted and the weight coefficient w[k] is unknown, and the non-adopted objective function (Σ _k∈K w[k]· _{xk_i_NG} ) which is the planning objective function Jr in a state where the value of the planning evaluation index _{xk_i_NG} based on the non-adopted plan is _substituted and the weight coefficient w[k] is unknown, is limited by a limit value based on the objective function value difference ε[i]. The adopted/non-adopted objective function value difference constraint equation is expressed, for example, by the following equation (2).

The objective function value difference constraint equation is a constraint equation indicating that the magnitude relationship between the value of the adopted objective function and the value of the unadopted objective function is not reversed, and is expressed, for example, by the following equation (3).
The coefficient upper and lower limit value constraint equation is a constraint equation indicating that the weight coefficient w[k] is within a range of upper and lower limit values set in advance, and is expressed, for example, by the following equation (4).

In formula (2), the difference between the adopted objective function and the non-adopted objective function is _Σk∈Kw [k] _{.xk_i_NG} - _Σk∈Kw [k] _{.xk_i_OK} . Also, in formula (2), the limit value based on the objective function value difference ε[i] is the objective function value difference ε[i] itself, and indicates the lower limit of the difference between the adopted objective function and the non-adopted objective function. As shown in formula (2), in this embodiment, the adopted/non-adopted objective function value difference constraint formula indicates that the difference between the adopted objective function and the non-adopted objective function ( _Σk∈Kw [k] _{.xk_i_NG} - _Σk∈Kw [k] _{.xk_i_OK} ) is realized for each pair i to be equal to or greater than the objective function value difference ε[i].

By determining the objective function value difference ε[i] as shown in equation (2), the objective function value difference ε[i] is set to 0 or more as shown in equation (3), so that the value of the unadopted objective function is equal to or greater than the value of the adopted objective function.

In the formula (4), the lower limit _wLB and the upper limit _wUB of the weighting coefficient w[k] are preset based on the possible range of the weighting coefficient w[k]. The formula (4) is a constraint formula mainly for preventing the equation from becoming unsolvable.

In this embodiment, the objective function for determining coefficients Jc is expressed by the following equation (5).

In the example shown in formula (5), the value of the coefficient determination objective function Jc is the sum of the objective function value difference ε[i] for all pairs i. max. indicates that the maximum value of the objective function (coefficient determination objective function Jc in formula (5)) is obtained. Since the objective function value difference ε[i] is determined as shown in formulas (2) and (3), maximizing the sum of the objective function value difference ε[i] for all pairs i corresponds to maximizing the sum of the value (Σ _k∈K w[k]·x _{k_i_NG} -Σ _k∈K w[k]·x _{k_i_OK} ) obtained by subtracting the value of the adopted objective function from the value of the non-adopted objective function for each pair i. Therefore, the weight coefficient w[k] is derived when the value of the adopted objective function and the value of the non-adopted objective function are as largely separated as possible. As shown in equations (2) to (5), in this embodiment, the difference between the adopted objective function and the unadopted objective function can be evaluated directly without going through another function such as a discriminant function (separating hyperplane) in an SVM (Support Vector Machine).

The weighting coefficient derivation unit 102 derives the weighting coefficient w[k] and the objective function value difference ε[i] when the value of the coefficient determination objective function Jc shown in equation (5) is maximized within the range that satisfies equations (2) to (4) by performing an optimization calculation using mathematical programming. The optimization calculation using mathematical programming is realized, for example, by using a known solver for solving linear programming problems, so a detailed description thereof is omitted here. Note that, here, an example is shown in which the weighting coefficient derivation unit 102 derives the weighting coefficient w[k] and the objective function value difference ε[i] by performing an optimization calculation using mathematical programming, but it is not necessary to perform the optimization calculation using mathematical programming as long as the optimization problem is solved. For example, a genetic algorithm may be used.

<Output Unit 103>
The output unit 103 outputs information indicating the weighting coefficient w[k] derived by the weighting coefficient derivation unit 102. Examples of the form of information output include at least one of display on a computer display, storage in a storage medium inside or outside the processing device 100, and transmission to an external device.

<Flowchart>
Next, an example of a processing method using the processing apparatus 100 will be described with reference to the flow chart of FIG.
First, in step S201, the acquisition unit 101 acquires information specifying the contents of a plurality of adopted plans and information specifying the contents of a plurality of non-adopted plans.
Next, in step S202, the acquisition unit 101 performs the process of pairing one adoption plan and one non-adoption plan, which are formulated under the same preconditions, with each of the multiple adoption plans as one pair i.

Next, in step S203, the acquisition unit 101 acquires, for each pair i, the value of the planning evaluation index x _{k_i_OK} from the adopted plan, and acquires the value of the planning evaluation index x _{k_i_NG} from the non-adopted plan that belongs to the same pair i as the adopted plan.

Next, in step S204, the weighting coefficient derivation unit 102 uses the planning evaluation indexes _{xk_i_OK} , _{xk_i_NG} acquired for each pair i in step S203 and the lower limit _wLB and upper limit _wUB of the weighting coefficient w[k] that have been set in advance to perform optimization calculations using mathematical programming to derive the weighting coefficient w[k] and objective function value difference ε[i] when the value of the coefficient determination objective function Jc shown in equation (5) is maximized within the range that satisfies equations (2) to (4).
Finally, in step S205, the output unit 103 outputs information indicating the weighting coefficient w[k] derived in step S204.

<Summary>
As described above, in this embodiment, the processing device 100 obtains the values of a plurality of planning evaluation indexes x _{k_i_OK} based on a plurality of adopted plans and the values of a plurality of planning evaluation indexes x _{k_i_NG} based on a plurality of non-adopted plans. The processing device 100 derives decision variables including the objective function value difference ε[i] indicating the difference between the adopted objective function, which is the planning objective function Jr based on the adopted plan, and the non-adopted objective function, which is the planning objective function Jr based on the non-adopted plan, and the weighting coefficient w[k], by solving the optimization problem. At this time, the processing device 100 uses the coefficient determination objective function Jc shown in formula (5). In addition, the processing device 100 uses the adopted/non-adopted objective function value difference constraint formula shown in formula (2). Therefore, the weighting coefficient w[k] in the multi-objective optimization problem can be derived using the adopted plan and the non-adopted plan, which are actual plans. Therefore, the weighting coefficient w[k], which is an adjustment parameter when creating a production plan or a logistics plan by solving an optimization problem, can be automatically derived without determining the correct value of the objective function (objective variable). This reduces the adjustment period and human burden of the planner, which is caused by trial and error.

In this embodiment, the processing device 100 performs, for each of a plurality of adopted plans, pairing one adopted plan and one non-adopted plan, which have the same information set in advance when making a production plan, based on a plurality of adopted plans and a plurality of non-adopted plans. Then, the processing device 100 performs, for each pair i, acquiring the value of the planning evaluation index x _{k_i_OK} from the adopted plan, and acquiring the value of the planning evaluation index x _{k_i_NG} from the non-adopted plan that belongs to the same pair i as the adopted plan. Then, the processing device 100 derives decision variables including the objective function value difference ε[i] that defines the difference between the adopted objective function and the non-adopted objective function for each pair i, and the weight coefficient w[k], using the adopted/non-adopted objective function value difference constraint equation as shown in equation (2) as the constraint equation for each pair i. Therefore, the decision variables and constraint equations for deriving the weight coefficient w[k] can be reduced.

In addition, in this embodiment, the processing device 100 uses the upper and lower coefficient limit constraint equations shown in equation (4) as the coefficient determination constraint equations. Therefore, it is possible to more reliably prevent the weight coefficient w[k] from becoming unsolvable.

<Modification>
In this embodiment, a minimization problem for minimizing the value of the planning objective function Jr as shown in formula (1) has been exemplified. However, in this embodiment, a maximization problem for maximizing the value of the planning objective function Jr may be used. In this case, for example, formula (1) is replaced by the following formula (6), formula (2) by the following formula (7), formula (3) by the following formula (8), and formula (5) by the following formula (9).

The objective function Jc for coefficient determination is not limited to that shown in formula (5). The objective function Jc for coefficient determination may further include, for example, a coefficient that is multiplied by each of the evaluation indexes for coefficient determination and has a different value depending on the adoption plan from which the evaluation indexes for coefficient determination are derived. The objective function Jc for coefficient determination may be, for example, one expressed by the following formula (10).

Here, ρ is a forgetting coefficient, and a value close to 1 in the range of more than 0 and less than 1 is preset. In addition, when the objective function for coefficient determination Jc is expressed by formula (10), i is the order in which the pairs are arranged in order from the pair to which the newest recruitment plan belongs (i for the first pair is 1 (i = 1), i for the second pair from the top is 2 (i = 2), and i for the last pair is I (i = I). By using formula (10), the pair i to which the newest recruitment plan belongs has a greater influence on the value of the objective function for coefficient determination Jc, and the pair i to which the older recruitment plan belongs has a smaller influence on the value of the objective function for coefficient determination Jc. Therefore, for example, even if the importance of each evaluation index changes due to changes in the external environment, production targets, logistics targets, operating conditions, etc., it is possible to present an appropriate balance of weights according to the changes.

Alternatively, one of the weighting coefficients w[k] may be fixed to 1, and the remaining weighting coefficients w[k] may be derived as described in this embodiment.

Second Embodiment
Next, the second embodiment will be described. In the first embodiment, the case where the correspondence between the adopted plan and the non-adopted plan is clear (i.e., the preconditions at the time of planning (information set in advance at the time of planning)) are the same is exemplified. However, there are cases where the correspondence between the adopted plan and the non-adopted plan is not clearly left. In this embodiment, in order to be able to derive the weight coefficient w[k] even in such a case, the weight coefficient w[k] is derived without creating a pair of the adopted plan and the non-adopted plan based on the preconditions at the time of planning. Thus, the present embodiment differs from the first embodiment mainly in the configuration and processing by not creating a pair of the adopted plan and the non-adopted plan based on the preconditions at the time of planning. Therefore, in the description of this embodiment, the same parts as those in the first embodiment are given the same reference numerals as those in FIG. 1 and FIG. 2, and detailed description thereof will be omitted.

As shown in FIG. 1, the processing device 100 of this embodiment also has an acquisition unit 101, a weighting coefficient derivation unit 102, and an output unit 103. In this embodiment, as in the first embodiment, the processing device 100 can be applied to either a production plan or a logistics plan, but in the following description, the production plan or logistics plan will be referred to as a production plan as necessary.

<Acquisition unit 101>
As described in the first embodiment, the acquisition unit 101 acquires values (actual values) of a plurality of evaluation indexes x _k for planning based on a plurality of adopted plans that have been adopted as production plans, and values (actual values) of a plurality of evaluation indexes x _k for planning based on a plurality of unadopted plans that have not been adopted as production plans.

In this embodiment, the acquisition unit 101 acquires information for identifying the contents of a plurality of adopted plans and information for identifying the contents of a plurality of non-adopted plans. The acquisition unit 101 then acquires values of a plurality of planning evaluation indexes x _k based on the plurality of adopted plans and values of a plurality of planning evaluation indexes x _k based on the plurality of non-adopted plans. As described in the first embodiment, the value of the planning evaluation index x _k can be acquired (identified) from the adopted plans and non-adopted plans.

In the first embodiment, the acquisition unit 101 performs pairing i by forming one adopted plan and one non-adopted plan for each of the multiple adopted plans, and acquires the value of the planning evaluation index x _{k_i_OK} from the adopted plan and acquires the value of the planning evaluation index x _{k_i_NG} from the non-adopted plan that belongs to the same pair i as the adopted plan for each pair i. However, in this embodiment, such pair i is not created and the planning evaluation indexes x _{k_i_OK} and x _{k_i_NG} are not acquired for each pair i from the adopted plan and non-adopted plan. In this embodiment, the acquisition unit 101 acquires the values of multiple planning evaluation indexes x _k from each of the multiple adopted plans and acquires the values of multiple planning evaluation indexes x _k from each of the multiple non-adopted plans.

In the following equations, the variable for identifying the adopted plan is u∈U (U is a set of adopted plans), the variable for identifying the non-adopted plans is v∈V (V is a set of non-adopted plans), multiple planning evaluation indexes _xk based on the adopted plans are denoted as _{xk_U} , and multiple planning evaluation indexes _xk based on the non-adopted plans are denoted as _{xk_v} . In this way, in the following equations, the variables u and v identify whether the plan is adopted or not.

<Weighting coefficient derivation unit 102>
As described in the first embodiment, the weighting coefficient derivation unit 102 derives decision variables including an objective function value difference ε[u][v] indicating the difference between an adopted objective function, which is the objective function Jr for planning based on the adopted plan, and a non-adopted objective function, which is the objective function Jr for planning based on the non-adopted plan, and a weighting coefficient w[k].

However, in the first embodiment, the objective function value difference ε[i] is the difference between the adopted objective function and the non-adopted objective function determined for each pair i. In contrast, in the present embodiment, the objective function value difference ε[u][v] is the difference between the adopted objective function and the non-adopted objective function determined for each adopted plan and each non-adopted plan.

In this embodiment, a pair counting variable δ[u][v] is further included as a decision variable. The pair counting variable δ[u][v] is a variable for counting the number of pairs of adopted plans and non-adopted plans in which the value of the non-adopted objective function indicates a lower evaluation of the production plan than the value of the adopted objective function. In this embodiment, as in the first embodiment, the case where the objective function for planning Jr is equation (1) (i.e., a minimization problem) is illustrated. In this case, indicating that the value of the non-adopted objective function indicates a lower evaluation of the production plan than the value of the adopted objective function indicates that the value of the adopted objective function is not greater than the value of the non-adopted objective function. Specifically, the pair counting variable δ[u][v] is a 0-1 variable that is "1" when the value of the adopted objective function based on the adopted plan identified by the variable u is equal to or less than the value of the non-adopted objective function based on the non-adopted plan identified by the variable v (the value of the adopted objective function≦the value of the non-adopted objective function), and is "0" otherwise. Therefore, the sum of the pair count variables δ[u][v] is the total number of pairs of adopted and unadopted plans for which the value of the adopted objective function is less than or equal to the value of the unadopted objective function.

In this embodiment, as in the first embodiment, the case where the planning objective function Jr is equation (1) is exemplified. In this case, the value of the adopted objective function is Σ _k∈K w[k] x _{k_u} . As described above, the value of the planning evaluation index x _{k_u} based on the adopted plan is identified from the adopted plan, so the unknown value of the adopted objective function is the weight coefficient w[k]. Similarly, the value of the non-adopted objective function is Σ _k∈K w[k] x _{k_v} . The value of the planning evaluation index x _{k_v} based on the non-adopted plan is identified from the non-adopted plan, so the unknown value of the adopted objective function is the weight coefficient w[k].

In this embodiment, as in the first embodiment, the coefficient determination constraint equation, which is a constraint equation for determining the weight coefficient w[k], includes an adopted/unadopted objective function value difference constraint equation, an objective function value difference constraint equation, and an upper and lower coefficient limit value constraint equation. In addition, in this embodiment, the coefficient determination objective function Jc, which is an objective function for determining the weight coefficient w[k], includes the objective function value difference ε[i] and the pair count variable δ[u][v] as coefficient determination evaluation indexes.

However, in the first embodiment, the adopted/unadopted objective function value difference constraint equation, the objective function value difference constraint equation, and the coefficient upper and lower limit value constraint equation are expressed by the following equations (2), (3), and (4). In contrast, in the present embodiment, the adopted/unadopted objective function value difference constraint equation, the objective function value difference constraint equation, and the coefficient upper and lower limit value constraint equation are expressed by the following equations (11), (12), and (13). In addition, in the first embodiment, the coefficient determination objective function Jc is expressed by the equation (5). In contrast, in the present embodiment, the coefficient determination objective function Jc is expressed by the following equation (14). Note that although equation (13) is the same as equation (4), it is recited for ease of notation and explanation.

In equation (11), the adopted/non-adopted objective function value difference constraint equation is a constraint equation indicating that the difference between the non-adopted objective function (Σ k∈K _{xk_v} ·w[k]), which is the planning objective function Jr in a state in which the value of the planning evaluation index _{xk_v} based on the non-adopted plan is substituted and the weighting coefficient w[k] is unknown, and the adopted objective function (Σ _{k∈K xk_u} ·w[ _k ]), which is the planning objective function Jr in a state in which the value of the planning evaluation index _{xk_u} based on the adopted plan is substituted and the weighting coefficient w[k] is unknown, is limited by a limit value based on the objective function value difference ε[u][v].

In equation (12), M _big is a positive constant that assumes the upper limit of the absolute value that can be taken on the right side of equation (12), and is set in advance.
Therefore, when the pair counting variable δ[u][v] is 0 (zero), the formula (12) becomes a self-evident formula, and the objective function value difference ε[u][v] is allowed to be negative. Accordingly, the adopted/non-adopted objective function value difference constraint formula of the formula (11) allows the value of the non-adopted objective function to be smaller (better) than the value of the adopted objective function in the adopted objective function based on the adopted plan identified by the variable u and the non-adopted objective function based on the non-adopted plan identified by the variable v. This is because, in this embodiment, the preconditions at the time of planning of the adopted plan identified by the variable u and the non-adopted plan identified by the variable v may not be the same, and in such a case, the comparison is made between plans with different preconditions at the time of planning, so that the value of the adopted objective function is not always smaller (better) than the value of the non-adopted objective function.

On the other hand, if the pair counting variable δ[u][v] is 1, then the objective function value difference ε[u][v] is constrained to be greater than or equal to 0 (i.e., the objective function value difference ε[u][v] is not allowed to be negative). Accordingly, it is not permitted for the value of the non-adopted objective function based on the adopted plan identified by the variable u to be smaller (better) than the value of the adopted objective function, and the difference between the non-adopted objective function (Σk∈K xk_v·w[k]), which is the planning objective function Jr in a state where the value of the planning evaluation index _{xk_v} based on the non-adopted plan is substituted and the weighting coefficient w[k] is unknown, and the adopted objective function ( _{Σk∈K xk_u} ·w[k]), which is _the planning objective function Jr in a state where the value of the planning evaluation index _{xk_u} based on the adopted plan is substituted and the weighting coefficient w[k] is unknown, is limited by a limit value based on _the objective function value difference ε[u][v].

As shown in formula (11), in this embodiment, the adopted/unadopted objective function value difference constraint formula indicates that the difference between the unadopted objective function and the adopted objective function (Σ _k∈K x _{k_v}・w[k]-Σ _k∈K x _{k_u}・w[k]) is equal to or greater than the objective function value difference ε[u][v], for each adopted plan and each unadopted plan. By determining the objective function value difference ε[u][v] as shown in formula (11), the objective function value difference ε[u][v] can also take a negative value as shown in formula (12). By doing so, even in the undesirable case where ε[u][v], which is the lower limit of the difference between the unadopted objective function and the adopted objective function (Σ _k∈K x _{k_v}・w[k]-Σ _k∈K x _{k_u}・w[k]), becomes negative, the influence can be minimized by the second term on the right side of the objective function formula (14).

In this embodiment, the value of the coefficient determination objective function Jc is, as shown in formula (14), a weighted linear sum of the sum of the pair counting variables δ[u][v] for all possible pairs of the adopted plan u and the non-adopted plan v, and the sum of the objective function value difference ε[u][v] for all possible pairs of the adopted plan u and the non-adopted plan v. _p1 is a weighting coefficient multiplied by the pair counting variable δ[u][v], and _p2 is a weighting coefficient multiplied by the objective function value difference ε[u][v], both of which have positive values.

Since the objective function value difference ε[u][v] is determined as shown in formulas (11) and (12), increasing the sum of the objective function value difference ε[u][v] for all possible pairs of adopted plan u and non-adopted plan v corresponds to increasing the sum of the value (Σ _k∈K x k_v·w[k] - Σ _k∈K x _{k_u} ·w[k]) obtained by subtracting the value of the adopted objective function from the value of the non-adopted objective function for each pair of adopted plan _u and non-adopted plan v. Therefore, the weighting coefficient w[k] is calculated when the value of the non-adopted objective function and the value of the adopted objective function largely deviate from each other.

However, if there are too few pairs of adopted and non-adopted plans where the value of the non-adopted objective function indicates a lower evaluation of the production plan than the value of the adopted objective function (i.e., pairs of u, v where δ[u][v] = 1), there is a risk that an appropriate weighting coefficient w[k] will not be derived. Therefore, it is recommended to increase the number of pairs of adopted and non-adopted plans where the value of the non-adopted objective function indicates a lower evaluation of the production plan than the value of the adopted objective function (i.e., pairs of u, v where δ[u][v] = 1).

As described above, equation (14) shows that in order to realize both a large deviation between the values of the non-adopted objective function and the adopted objective function and an increase in the number of pairs of adopted and non-adopted plans in which the value of the non-adopted objective function indicates a lower evaluation of the production plan than the value of the adopted objective function, the weighting coefficients _p1 and _p2 are used to adjust which evaluation is given more importance.

The weighting coefficients p ₁ and p ₂ , like the weighting coefficient w[k], are intended to balance the evaluation of the pair counting variable δ[u][v] and the objective function value difference ε[u][v]. However, the weighting coefficients p ₁ and p ₂ are set in advance when deriving the weighting coefficient w[k], the objective function value difference ε[u][v], and the pair counting variable δ[u] based on the formulas (11) to (14). The pair counting variable δ[u][v] and the objective function value difference ε[u][v] are both evaluation indexes that evaluate the relationship between the magnitude of the adopted objective function value and the non-adopted objective function value, and have the same purpose. When setting the weighting coefficients p ₁ and p ₂ , for example, p ₂ = 1, and p ₁ is set large until δ[u][v] = 1 for about 60 to 70% or more of all pairs of (u, v).

The weighting coefficient derivation unit 102 derives the weighting coefficient w[k], the objective function value difference ε[u][v], and the pair counting variable δ[u][v] when the value of the coefficient determination objective function Jc shown in equation (14) is maximized within the range satisfying equations (11) to (13) by performing optimization calculations using mathematical programming. The optimization calculations using mathematical programming are realized, for example, by using a known solver for solving linear programming problems (mixed integer programming problems), so a detailed description thereof is omitted here. As described in the first embodiment, it is not necessarily necessary to perform optimization calculations using mathematical programming when deriving the weighting coefficient w[k], the objective function value difference ε[u][v], and the pair counting variable δ[u][v].

<Flowchart>
Next, an example of a processing method using the processing apparatus 100 of this embodiment will be described with reference to the flowchart of FIG.
First, in step S301, the acquisition unit 101 acquires information specifying the contents of a plurality of adopted plans and information specifying the contents of a plurality of non-adopted plans.
Next, in step S302, the acquisition unit 101 acquires the value of the planning evaluation index x _{k_u} from the adopted plan, and acquires the value of the planning evaluation index x _{k_v} from the non-adopted plans.

Next, in step S303, the weighting coefficient derivation unit 102 uses the planning evaluation indexes _{xk_u} , _{xk_v} acquired in step S302 and the lower limit _wLB and upper limit _wUB of the weighting coefficient w[k] that are set in advance to perform optimization calculations using mathematical programming to derive the weighting coefficient w[k], objective function value difference ε[u][v], and pair count variable δ[u][v] when the value of the coefficient determination objective function Jc shown in equation (14) is maximized within the range that satisfies equations (11) to (13).
Finally, in step S304, the output unit 103 outputs information indicating the weighting coefficient w[k] derived in step S303.

<Summary>
As described above, in this embodiment, the objective function value difference ε[u][v] is determined for each pair of an arbitrary adopted plan and an arbitrary non-adopted plan. In addition to the weighting coefficient w[k] and the objective function value difference ε[u][v], the pair counting variable δ[u][v] is included in the decision variables. The processing device 100 derives these decision variables by solving an optimization problem. At this time, the processing device 100 uses the coefficient determination objective function Jc shown in equation (14). In addition, the processing device 100 uses the adopted/non-adopted objective function value difference constraint equation shown in equation (11). Therefore, in addition to the effects described in the first embodiment, the effect of being able to derive the weighting coefficient w[k] can be obtained even when the correspondence between the adopted plan and the non-adopted plan is not clearly left.

<Modification>
In this embodiment as well, the various modified examples described in the first embodiment can be adopted.
For example, in this embodiment, as in the first embodiment, a minimization problem for minimizing the value of the planning objective function Jr as shown in formula (1) is exemplified. However, as described in the modified example of the first embodiment, this embodiment may also be a maximization problem for maximizing the value of the planning objective function Jr. In this case, for example, formula (1) is rewritten as formula (6). Furthermore, formula (11) is replaced by the following formula (15). Note that even in the case of a maximization problem, formulas (12) to (14) are used in the same way as in the minimization problem.

As explained in the modified example of the first embodiment, in this embodiment, the objective function Jc for determining the coefficients is not limited to that shown in equation (14). The objective function Jc for determining the coefficients may be, for example, that expressed by the following equation (16).

Formula (16) corresponds to formula (9) described in the modified example of the first embodiment, and ρ is a forgetting coefficient, which is set in advance to a value close to 1 in the range of more than 0 and less than 1. In addition, when the objective function for coefficient determination Jc is expressed by formula (16), u and v are, for example, the order in which the recruitment plans are arranged in order of the most recent creation date and time (the first recruitment plan u(v) is set to 1 (u(v) = 1), the second recruitment plan u(v) is set to 2 (u(v) = 2), and the last recruitment plan u(v) is set to |U| + |V| (u(v) = |U| + |V|)). Alternatively, u and v may be considered to be quantities that represent the time when the data was collected by going back in time, starting from the current time as 0 (zero). By using formula (16), the newer the recruitment plan, the greater the influence on the value of the objective function for coefficient determination Jc, and the older the recruitment plan, the smaller the influence on the value of the objective function for coefficient determination Jc.

(Calculation example)
Next, a calculation example will be described. In this calculation example, the weight coefficients w[1], w[2], and w[3] in the planning objective function Jr for planning the processing completion times in two processes as a production plan for producing 10 products in two processes will be derived using the method described in the first embodiment. Note that this calculation example is a hypothetical case.

In this calculation example, the planning objective function Jr has three planning evaluation indexes _xk , namely, delivery tardiness _x1 , delivery early _x2 , and the number of lot changes _x3 , and is expressed by the following equation (17).

In addition, in this calculation example, the production plans (adopted plans and non-adopted plans) drawn up for each of the five preconditions (information that is set in advance when drawing up a plan) were used as training data when drawing up a plan. Here, the preconditions when drawing up a plan (information that is set in advance when drawing up a plan) are referred to as input data.

Figures 4A, 4B, 4C, 4D, and 4E are diagrams showing the first input data 401, the second input data 402, the third input data 403, the fourth input data 404, and the fifth input data 405, respectively.

The first to fifth input data 401 to 405 include a product ID, a process 1 lot number, a process 2 lot number, and a delivery date. The product ID, the process 1 lot number, the process 2 lot number, and the delivery date are prerequisites for deriving the delivery date delay x ₁ , the delivery date early production x ₂ , and the number of lot changes x ₃ , and are used as constants (fixed values).

Figure 5 is a diagram showing in table form the number of production plans (adopted plans and non-adopted plans) created based on the first to fifth input data 401 to 405. In Figure 5, input data numbers 1, 2, 3, 4, and 5 indicate the first input data 401, the second input data 402, the third input data 403, the fourth input data 404, and the fifth input data 405, respectively. Figure 5 shows that one adopted plan and two non-adopted plans have been created based on the first input data 401, the second input data 402, and the fourth input data 404. It also shows that one adopted plan and three non-adopted plans have been created based on the third input data 403. It also shows that one adopted plan and one non-adopted plan have been created based on the fifth input data 405.

In this calculation example, the hiring plan is formulated with the weighting factors w[1], w[2], and w[3] set to 3, 1, and 10, respectively (w[1] = 3, w[2] = 1, and w[3] = 10). Therefore, in this calculation example, these values (w[1] = 3, w[2] = 1, and w[3] = 10) are the correct values for the weighting factors w[1], w[2], and w[3]. On the other hand, the non-hiring plan is formulated with at least one of the weighting factors w[1], w[2], and w[3] different from the correct value. In this calculation example, a hypothetical case is shown to investigate whether the weighting factor w[k] (w[1] = 3, w[2] = 1, and w[3] = 10) used in creating the hiring plan can be reproduced by the method of the first embodiment. In this way, the correct values of the weighting coefficients w[1], w[2], and w[3] are compared with the result of deriving the weighting coefficient w[k] using the method of the first embodiment, and are not used when deriving the weighting coefficient w[k] using the method of the first embodiment.

6 is a diagram showing the delivery delay x ₁ , delivery early production x ₂ , and the number of lot changes x ₃ obtained from the production plans (adopted plan and non-adopted plan) drawn up based on the first to fifth input data 401 to 405. In FIG. 6 , "adopted" indicates a value based on the adopted plan, and "non-adopted" indicates a value based on the non-adopted plan.

Here, the process of deriving the delivery delay x ₁ , delivery early production x ₂ , and the number of lot changes x ₃ will be explained using an adopted plan and a non-adopted plan drawn up based on the first input data 401 with input data number 1 in FIG. 6 as examples.
FIG. 7 is a diagram showing the delivery delay x ₁ , delivery early production x ₂ , and the number of lot changes x ₃ acquired from the adoption plan drawn up based on the first input data 401 .

As mentioned above, in this calculation example, the processing times of two processes are planned as a production plan. In FIG. 7(a), the processing time (process 2 processing time) of the lower process (downstream process) process 2 cannot be earlier than the processing time (process 1 processing time) of the upper process (upstream process) process 1 (i.e., process 2 cannot be executed earlier than process 1). Therefore, for example, if the product whose processing order is the first in process 2 is kth in process 1, the processing time (process 2 processing time) of process 2 is k, and the processing times of products whose processing order is second or later in process 2 are also (k+1) or more. In other words, the processing time (process 2 processing time) of process 2 is a time that takes into account the time delay between processes. The due date is also set with the same concept as the process 2 processing time. Note that FIG. 7(a) shows the first input data 401 (product ID, process 1 lot number, process 2 lot number, and due date) together with the production plan (process 1 processing time, process 2 processing time). Also, for ease of explanation, in Figures 7(a) to 7(c), the delivery date, process 1 processing time, and process 2 processing time are represented not as actual times, but as integers greater than or equal to 0, with smaller values corresponding to earlier times.

In FIG. 7A, if the value obtained by subtracting the delivery date from the process 2 processing time is a positive value, the value is the value of late delivery. If the value obtained by subtracting the delivery date from the process 2 processing time is a value equal to or less than 0 (zero), the value of late delivery is 0 (zero). On the other hand, if the value obtained by subtracting the process 2 processing time from the delivery date is a positive value, the value is the value of early delivery. If the value obtained by subtracting the process 2 processing time from the delivery date is a value equal to or less than 0 (zero), the value of early delivery is 0 (zero). By performing such calculations for the products of each product ID, the late delivery and early delivery of the products of each product ID are derived. The sum of the values shown in the late delivery column in FIG. 7A (the numerical value (=3) shown in the margin below the late delivery column) becomes the value (=3) in the late delivery x ₁ column in the adoption plan with input data number "1" in FIG. 6. Similarly, the sum of the values shown in the Early Delivery column in FIG. 7(a) (the numerical value (=3) shown in the margin below the Early Delivery column) becomes the value (=3) in the Early Delivery x ₂ column in the adoption plan with input data number "1" in FIG. 6.

In Figure 7(b), the products shown in Figure 7(a) are rearranged so that the products with the earlier process times in step 1 are ranked higher. In Figure 7(b), the lot number in step 1 has been changed four times: when the process target was changed from product ID 6 to product ID 3, when the process target was changed from product ID 3 to product ID 1, when the process target was changed from product ID 10 to product ID 2, and when the process target was changed from product ID 5 to product ID 9 (see the value (=4) shown in the margin below the lot change column).

Fig. 7(c) shows the products rearranged so that the earlier the process time in process 2 shown in Fig. 7(a) is, the higher the record. In Fig. 7(c), the process 2 lot number has been changed three times: when the process target was changed from product with product ID 7 to product with product ID 8, when the process target was changed from product with product ID 1 to product with product ID 10, and when the process target was changed from product with product ID 9 to product with product ID 6 (see the value (=3) shown in the margin below the lot change column).
The sum (=7) of the number of changes in the lot number in process 1 (=4) and the number of changes in the lot number in process 2 (=3) becomes the value (=7) in the column for the number of lot changes _x3 in the adopted plan whose input data number is “1” in FIG. 6.

8 is a diagram showing delivery delay x ₁ , early delivery x ₂ , and the number of lot changes x ₃ obtained from the non-adopted plan drawn up based on the first input data 401. Fig. 8 illustrates delivery delay x ₁ , early delivery x ₂ , and the number of lot changes x ₃ obtained from the non-adopted plan in the first row with the input data number "1" in Fig. 6 .

8(a), 8(b), and 8(c) correspond to FIG. 7(a), 7(b), and 7(c), respectively. In the same manner as described with reference to FIG. 7, the sum of the values shown in the column of late delivery date in FIG. 8(a) (the numerical value (=12) shown in the margin under the column of late delivery date) is derived, and the value (=12) of the column of late delivery date x ₁ in the non-adopted plan in the first row of FIG. 6 with the input data number "1" is obtained. Similarly, the sum of the values shown in the column of early delivery date in FIG. 8(a) (the numerical value (=2) shown in the margin under the column of early delivery date) becomes the value (=2) of the column of early delivery date x ₂ in the non-adopted plan in the first row of FIG. 6 with the input data number "1". Also, the sum (=5) of the number of changes of the lot number in process 1 (=3) and the number of changes of the lot number in process 2 (=2) becomes the value (=5) of the column of number of lot changes x ₃ in the non-adopted plan in the first row of FIG. 6 with the input data number "1".

Although detailed values are omitted, the delivery tardiness x ₁ , delivery advancement x ₂ , and number of lot changes x ₃ are derived for the other production plans (adopted plans and non-adopted plans), and the results are shown in FIG.

In FIG. 6, one adoption and one non-adoption in the same input data number form one pair i. For example, a non-adoption and an adoption in the first row with input data number "1" form one pair i, and a non-adoption and an adoption in the second row with input data number "1" form one pair i. In this way, two pairs i are created from the first input data 401 with input data number "1" (see step S202 in FIG. 2). Similarly, two, three, two and one pairs i are created from the second, third, fourth and fifth input data 402, 403, 404 and 405 with input data numbers "2", "3", "4" and "5", respectively (see step S202 in FIG. 2).

6, late delivery date _x1 , early delivery date _x2 , and number of lot changes _x3 in the adopted column correspond to the evaluation indexes _{xk_i_OK} for planning based on the adopted plan. Also, late delivery date _x1 , early delivery date _x2 , and number of lot changes _x3 in the non-adopted column correspond to the evaluation indexes _{xk_i_NG} for planning based on the non-adopted plan. The values of the evaluation indexes _{xk_i_OK} for planning based on the adopted plan and the evaluation indexes _{xk_i_NG} for planning based on the non-adopted plan are obtained for each pair i created as described above (see step S203 in FIG. 2).

Then, using the planning evaluation indexes _{xk_i_OK} and _{xk_i_NG} for each pair i, the weighting coefficient w[k] and the objective function value difference ε[i] when the value of the coefficient determination objective function Jc shown in equation (5) is maximized within the range satisfying equations (2) to (4) were derived by performing optimization calculations using mathematical programming (see step S204 in Figure 2).

As a result, the weighting factors w[1], w[2], and w[3] were derived as 4, 1, and 10 (w[1] = 4, w[2] = 1, w[3] = 10), respectively. Only the weighting factor w[1] was different from the correct value (w[1] = 3, w[2] = 1, w[3] = 10), but despite the small amount of input data (5), a result close to the correct value was obtained.

Other Embodiments
The above-described embodiment of the present invention can be realized by a computer executing a program. A computer-readable recording medium on which the program is recorded and a computer program product such as the program can also be applied as an embodiment of the present invention. Examples of the recording medium that can be used include a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a non-volatile memory card, and a ROM. The embodiment of the present invention may be realized by a PLC (Programmable Logic Controller) or dedicated hardware such as an ASIC (Application Specific Integrated Circuit).
Furthermore, the above-described embodiments of the present invention are merely examples of the implementation of the present invention, and the technical scope of the present invention should not be interpreted as being limited by these. In other words, the present invention can be implemented in various forms without departing from its technical concept or main features.

100 Processing device 101 Acquisition unit 102 Weighting coefficient derivation unit 103 Output unit

Claims (7)

A processing device that executes a process of deriving a weighting coefficient in a planning objective function that is an objective function that reduces a multi-objective optimization problem for planning a production plan or a logistics plan to a single objective, the planning objective function having a plurality of planning evaluation indexes and a weighting coefficient to be multiplied to the planning evaluation indexes,
an acquisition means for acquiring values of the plurality of evaluation indexes for planning based on a plurality of adopted plans adopted as the production plan or the logistics plan, and values of the plurality of evaluation indexes for planning based on a plurality of non-adopted plans not adopted as the production plan or the logistics plan;
a weighting coefficient derivation means for deriving decision variables including an objective function value difference indicating a difference between an adopted objective function, which is the planning objective function based on the adopted plan, and a non-adopted objective function, which is the planning objective function based on the non-adopted plan, and the weighting coefficient by solving an optimization problem;
The coefficient determination constraint equation, which is a constraint equation in the optimization problem, includes an adopted/non-adopted objective function value difference constraint equation indicating that a difference between the adopted objective function in a state in which a value of the planning evaluation index based on the adopted plan is substituted and the weighting coefficient is unknown, and the non-adopted objective function in a state in which a value of the planning evaluation index based on the non-adopted plan is substituted and the weighting coefficient is unknown, is limited by a limit value based on the objective function value difference,
2. The processing device according to claim 1, wherein a coefficient determination objective function, which is an objective function in the optimization problem, includes the objective function value difference as a coefficient determination evaluation index. Among the plurality of adopted plans and the plurality of non-adopted plans, one adopted plan and one non-adopted plan having the same information set in advance when the production plan or the logistics plan is formulated are regarded as one pair,
the adopted/unadopted objective function value difference constraint equation indicates that a difference between the adopted objective function and the unadopted objective function is limited by a limit value based on the objective function value difference for each pair;
2. The processing device according to claim 1, wherein the objective function value difference is a difference between the adopted objective function and the unadopted objective function, the difference being determined for each pair. The decision variables further include a pair count variable for counting the number of pairs of the adopted plan and the non-adopted plan for which a value of the non-adopted objective function indicates a lower evaluation of the production plan or the logistics plan than a value of the adopted objective function;
The objective function value difference for a pair of the adopted plan and the non-adopted plan, where the value of the non-adopted objective function indicates a lower evaluation of the production plan or logistics plan than the value of the adopted objective function, is not permitted to take a value indicating that the value of the non-adopted objective function is a higher evaluation of the production plan or logistics plan than the value of the adopted objective function, and the objective function value difference for a pair of the adopted plan and the non-adopted plan, where the value of the non-adopted objective function does not indicate a lower evaluation of the production plan or logistics plan than the value of the adopted objective function, is permitted to take a value indicating that the value of the non-adopted objective function is a higher evaluation of the production plan or logistics plan than the value of the adopted objective function,
2. The processing device according to claim 1, wherein the coefficient determination objective function includes the objective function value difference and the pair count variable as coefficient determination evaluation indexes. The processing device according to any one of claims 1 to 3, characterized in that the coefficient determination constraint equation further includes an upper and lower coefficient limit value constraint equation indicating that the weight coefficient is within a range of upper and lower limit values. The processing device according to any one of claims 1 to 4, characterized in that the objective function for coefficient determination further includes a coefficient that is multiplied by each of the evaluation indexes for coefficient determination and has a different value depending on the adoption plan from which the evaluation indexes for coefficient determination are derived. A processing method for executing a process of deriving a weighting coefficient in a planning objective function which is an objective function that turns a multi-objective optimization problem for planning a production plan or a logistics plan into a single objective, the planning objective function having a plurality of planning evaluation indexes and a weighting coefficient by which the planning evaluation indexes are multiplied, comprising:
an acquisition step of acquiring values of the plurality of evaluation indexes for planning based on a plurality of adopted plans adopted as the production plan or the logistics plan, and values of the plurality of evaluation indexes for planning based on a plurality of non-adopted plans not adopted as the production plan or the logistics plan;
a weighting coefficient derivation step of deriving decision variables including an objective function value difference indicating a difference between an adopted objective function, which is the planning objective function based on the adopted plan, and a non-adopted objective function, which is the planning objective function based on the non-adopted plan, and the weighting coefficient by solving an optimization problem;
The coefficient determination constraint equation, which is a constraint equation in the optimization problem, includes an adopted/non-adopted objective function value difference constraint equation indicating that a difference between the adopted objective function in a state in which a value of the planning evaluation index based on the adopted plan is substituted and the weighting coefficient is unknown, and the non-adopted objective function in a state in which a value of the planning evaluation index based on the non-adopted plan is substituted and the weighting coefficient is unknown, is limited by a limit value based on the objective function value difference,
A processing method, characterized in that a coefficient determination objective function, which is an objective function in the optimization problem, includes the objective function value difference as a coefficient determination evaluation index. A program for causing a computer to function as each of the means of the processing device according to any one of claims 1 to 5.

Images