JP2022083200A - Processing device, processing method, and program - Google Patents

Abstract

To make it possible to derive a weighting factor to be set to an objective function without determining a correct answer value of the objective function in a multipurpose problem for planning a production plan or a distribution plan.SOLUTION: A processing device 100 derives a decision variable containing an objective function value difference and a weighting factor by executing an optimization calculation. In this case, the processing device 100 uses an objective function used for determining factors including the objective function value difference. Further, the processing device 100 uses an adoption/rejection objective function value difference constraint equation into which a value of an evaluation index for planning based on an adoption plan and a rejection plan is substituted, and which indicates that a difference between an adoption objective function value and a rejection objective function value in a state that the weighting factor is unknown is constrained by a constraining value based on the objective function value difference.SELECTED DRAWING: Figure 1

Description

The present invention relates to processing equipment, processing methods, and programs, and is particularly suitable for use in deriving a weighting coefficient set for an objective function in a multi-objective optimization problem for planning a production plan or a distribution plan. It is a thing.

Production planning or distribution planning is made by solving mathematical planning problems. The mathematical programming problem is a problem of finding the decision variable when the value of the objective function becomes the minimum or the maximum within the range that satisfies the constraint expression. When formulating a production plan or a distribution plan, a decision variable is a variable that needs to be determined in order to establish a production plan or a distribution plan. The constraint formula is a formula that expresses the constraint conditions imposed when the production or the distribution is executed according to the production plan or the distribution plan. The objective function is an evaluation index for evaluating the degree of quality of a production plan or a distribution plan, and includes one or more evaluation indexes whose values are determined based on determinants.

In production planning and distribution planning, it is required to achieve multiple objectives at the same time, and multiple objectives are often in a trade-off relationship with each other, and among the evaluation indicators corresponding to each objective. It is important to balance the evaluation. The trade-off relationship is that when the value of one evaluation index is changed so that the evaluation of the production plan or distribution plan is good, the value of the other evaluation index is badly evaluated for the production plan or distribution plan. A relationship that is changed. For example, when formulating a production plan, it is required to simultaneously achieve various objectives such as cost, quality, productivity, and delivery date. In this case, for example, lowering the cost improves the evaluation of the production plan or the distribution plan, and increasing the quality improves the evaluation of the production plan or the distribution plan. Also, in general, lowering costs lowers quality. Therefore, if the evaluation of the production plan or the distribution plan in terms of cost is changed to be better, the evaluation of the production plan or distribution plan in terms of quality is changed to be worse, so the trade between cost and quality is made. It is in an off relationship.

Such a mathematical planning problem having a plurality of evaluation indexes is called a multipurpose optimization problem. When solving a multi-objective optimization problem, there is also a method of finding a Pareto optimal solution (a set of optimal solutions existing at the boundary of the feasible region), but here, a weighting coefficient is given to each multi-objective purpose to make it one-purpose. We assume a method to solve a single-objective optimization problem (as one objective function). The weighting coefficient represents the balance of evaluation among each evaluation index, and the value of the weighting coefficient is determined by how much the evaluation index for the weighting coefficient is emphasized with respect to other evaluation indexes. The objective function and the weighting coefficient may be referred to as a cost function, a cost coefficient, or the like, respectively. In addition, individual evaluation indexes may be referred to as objective functions, but in the present specification, individual objective functions are referred to as evaluation indexes, and the sum of evaluation indexes with weighting coefficients is referred to as objective functions to distinguish them. I decided to. Further, the weighting coefficient as a reference may be fixed to 1 for a certain evaluation index, and the weighting coefficient for other evaluation indexes may be set.

When solving a multi-objective optimization problem with one purpose, it is necessary to compare the magnitude of the values of multiple evaluation indexes representing different purposes in completely different units (dimensions) on the same ground. Therefore, it is not easy to adjust the weighting factor for each evaluation index. In addition, the weighting factor does not need to be changed once it is set, and it may be necessary to change it. In a production plan or a distribution plan, the importance of a plurality of evaluation indexes may be changed depending on, for example, the external environment, the production target / distribution target, the operating condition, and the like. In such a case, if the weighting coefficient is not changed, it may not be possible to formulate an appropriate production plan / distribution plan.

As a technique for determining the value of the weighting coefficient, there is a technique described in Patent Document 1. Patent Document 1 describes that the final quality is expressed by a linear combination of each quality value or manufacturing conditions, and each regression coefficient is obtained in advance by multiple regression analysis.

Japanese Patent No. 6351880

However, in the technique described in Patent Document 1, since the regression coefficient is derived as a weighting coefficient by multiple regression analysis, the correct answer value of the final quality corresponding to each quality value as well as each quality value is used to create the teacher data. Also need to be determined. Therefore, 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, the weighting coefficient may not be derived accurately.

The present invention has been made in view of the above problems, and is set for the objective function without determining the correct value of the objective function in the multi-objective problem for formulating a production plan or a distribution plan. The purpose is to be able to derive the weighting coefficient.

The processing apparatus of the present invention is an objective function for one purpose of a multi-objective optimization problem for drafting a production plan or a distribution plan, and is multiplied by a plurality of evaluation indexes for planning and the evaluation index for planning. A processing device that executes a process of deriving the weighting coefficient in a planning objective function having a weighting coefficient, and the plurality of plans based on the plurality of hiring plans adopted as the production plan or the distribution plan. Based on the acquisition means for acquiring the value of the evaluation index for planning and the value of the evaluation index for planning based on the plurality of non-adoption plans that were not adopted as the production plan or the distribution plan, and the adoption plan. Determinant variable including the objective function value difference indicating the difference between the adopted objective function which is the objective function for planning and the non-adopted objective function which is the objective function for planning based on the non-adopted plan, and the weighting coefficient. The weight coefficient deriving means for deriving by solving the optimization problem, and the constraint expression for determining the coefficient, which is the constraint expression in the optimization problem, is the evaluation index for planning based on the adoption plan. A state in which the value is assigned and the weighting coefficient is unknown, the adoption objective function and the value of the planning evaluation index based on the non-adoption plan are substituted, and the weighting coefficient is unknown. It is an objective function in the optimization problem, including an adopted / non-adopted objective function value difference constraint expression indicating that the difference between the non-adopted objective function and the non-adopted objective function is limited by a limit value based on the objective function value difference. The objective function for determining the coefficient is characterized in that the difference between the objective function values is included as an evaluation index for determining the coefficient.

The processing method of the present invention is an objective function for one purpose of a multi-objective optimization problem for drafting a production plan or a distribution plan, and is multiplied by a plurality of evaluation indexes for planning and the evaluation index for planning. A processing method for executing a process of deriving the weighting coefficient in a planning objective function having the weighting coefficient to be performed, and the plurality of plans based on the plurality of adoption plans adopted as the production plan or the distribution plan. Based on the acquisition process to acquire the value of the evaluation index for planning and the value of the evaluation index for planning based on the plurality of non-adoption plans that were not adopted as the production plan or the distribution plan, and the adoption plan. Determinant variable including the objective function value difference indicating the difference between the adopted objective function which is the objective function for planning and the non-adopted objective function which is the objective function for planning based on the non-adopted plan, and the weighting coefficient. The weight coefficient derivation process is derived by solving the optimization problem, and the constraint expression for determining the coefficient, which is the constraint expression in the optimization problem, is the evaluation index for planning based on the adoption plan. A state in which the value is assigned and the weighting coefficient is unknown, the adoption objective function and the value of the planning evaluation index based on the non-adoption plan are substituted, and the weighting coefficient is unknown. It is an objective function in the optimization problem, including an adopted / non-adopted objective function value difference constraint expression indicating that the difference between the non-adopted objective function and the non-adopted objective function is limited by a limit value based on the objective function value difference. The objective function for determining the coefficient is characterized in that the difference between the objective function values is included as an evaluation index for determining the coefficient.

The program of the present invention is for making a computer function as each means of the processing apparatus.

According to the present invention, it is possible to derive the weighting coefficient set for the objective function without determining the correct answer value of the objective function in the multi-objective problem for formulating a production plan or a distribution plan.

It is a figure which shows an example of the functional structure of a processing apparatus. It is a flowchart explaining the 1st example of the processing method. It is a flowchart explaining the 2nd example of the processing method. It is a figure which shows the 1st input data. It is a figure which shows the 2nd input data. It is a figure which shows the 3rd input data. It is a figure which shows the 4th input data. It is a figure which shows the 5th input data. It is a figure which shows an example of the number of production plans (adoption plan and non-adoption plan) drafted based on the 1st to 5th input data. It is a figure which shows the number of times of delivery delay, delivery early making, and lot change acquired from the production plan drafted based on the 1st to 5th input data. It is a figure which shows an example of the number of times of late delivery, early delivery, and lot change acquired from the recruitment plan drafted based on the first input data. It is a figure which shows an example of the number of times of late delivery, early delivery, and lot change acquired from the non-adoption plan drafted based on the first input data.

Hereinafter, embodiments 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 a functional configuration of the processing device 100. The hardware of the processing device 100 is realized by using, for example, an information processing device having a CPU, ROM, RAM, HDD, and various interfaces, or dedicated hardware. FIG. 2 is a flowchart illustrating an example of a processing method using the processing apparatus 100 of the present embodiment.

<Planning objective function Jr, planning evaluation index x _k >
The processing device 100 is an objective function (objective function of one equation) that aims at a multi-objective optimization problem for formulating a production plan or a distribution plan, and has a plurality of evaluation indexes for planning and the plurality of evaluation indexes for planning. The process of deriving the weighting coefficient in the objective function for planning having the weighting coefficient multiplied by the evaluation index for planning is executed. In the present embodiment, a plurality of planning evaluation indexes x _k when the value of the planning objective function Jr shown in the following equation (1) is minimized are optimized by the actuarial programming method. An example is an example in which a production plan or a distribution plan is determined based on the derived optimum solution derived as the optimum solution. In equation (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 (in the equation (1), the objective function Jr for planning) is obtained. In this embodiment, _K is an integer of 2 or more because the mathematical planning problem is a multi-objective optimization problem having a plurality of evaluation indexes xx for planning. w [ _k ] is a weighting coefficient multiplied by the evaluation index xk for planning.

The evaluation index _xk for planning is an evaluation index for evaluating the degree of quality of the production plan or the distribution plan, and is determined according to the purpose of formulating the production plan or the distribution plan. In a multi-objective optimization problem, at least two planning evaluation indexes x _k are usually in a trade-off relationship among a plurality of planning evaluation indexes x _k . The trade-off relationship is that when the value of one planning evaluation index x _k is changed so that the evaluation of the production plan or distribution plan is improved, the value of the other planning evaluation index x _k is the production plan. Or, it refers to a relationship that is changed so that the evaluation of the distribution plan becomes worse. Equation (1) exemplifies the minimization problem that minimizes the value of the planning objective function Jr. Therefore, improving the evaluation of the production plan or distribution plan reduces the value of the planning evaluation index x _k . Corresponds to that.

In general, when solving a mathematical programming problem such as a multi-objective optimization problem, the optimum value of the objective function is derived within the range that satisfies the constraint expression. Therefore, when formulating a production plan or a distribution plan using the planning objective function Jr shown in Eq. (1), a mathematical formula representing the constraints imposed when executing production or distribution according to the production plan or distribution plan. As long as the constraint equation is satisfied, the minimum value of the planning objective function Jr shown in equation (1) is derived. Since the constraint equation itself is not directly related to the gist of the present embodiment, its detailed description will be omitted.

The evaluation index _xk for planning is, for example, late delivery, early delivery, and the number of lot changes.
The late delivery date indicates how much the product will be shipped later than the delivery date. For example, it is a value obtained by subtracting the delivery date from the estimated shipping date of the product (the estimated shipping date of the product is from the delivery date). If it is early (that is, if the estimated shipping date of the product minus the delivery date is a negative value), the delivery delay will be 0 (zero)). When a production plan or a distribution plan having a purpose of suppressing a product that is delayed in delivery is formulated, the delay in delivery is included in the evaluation index _xk for planning.

Early delivery indicates how quickly a product can be shipped with respect to the delivery date. For example, it is a value obtained by subtracting the estimated shipping date from the delivery date of the product (the delivery date of the product is earlier than the scheduled shipping date). In the case (that is, the value obtained by subtracting the estimated shipping date from the delivery date of the product is a negative value), the early delivery date is 0 (zero)). If a product can be shipped before the delivery date, the product will be in stock and a place for the product must be secured. When planning a production plan or a distribution plan having the purpose of suppressing the securing of such extra storage space, early delivery is included in the evaluation index _xk for planning.

Next, the number of lot changes will be described. In the production process / logistics process that is processed through a plurality of processes, for example, in order to simplify and improve the efficiency of operating conditions, manufacturing work, sorting work, etc., a plurality of products are put together in a lot. A lot is a processing unit (for example, production unit, transportation unit) in which a plurality of products that can be processed under the same operation (for example, manufacturing work, sorting work, transportation work) are grouped together, and is processed in each process. It is a collection of multiple products into one group. Products belonging to the same lot are given the same lot number as information for identifying the lot.

In each process in production or distribution, it is preferable to process as many products as possible in one lot. This is because when the processing is changed to a different lot, it is usually necessary to change the setup (work preparation for changing the lot). Therefore, for example, when planning a production plan or a distribution plan for the purpose of improving processing efficiency, it is preferable that the number of lot changes is small so that the setup change work is reduced. When planning a production plan or a distribution plan having such a purpose, the number of lot changes is included in the evaluation index _xk for planning. The number of lot changes is the sum of the number of lot changes counted for each process.

If many products are combined into the same lot in order to reduce the number of lot changes, it is highly possible that the delivery dates of multiple products contained in the same lot will vary. For example, a product that has time to deliver may be processed first (for example, production, transportation), and as a result, the processing of a product that should be processed first may be postponed. In this case, the product whose processing has been postponed may be delayed in delivery.

In general, the conditions for collecting lots differ from process to process. That is, the processing order of the subsequent process does not always follow the processing order of the product in the earlier process. In such cases, reducing the number of lot changes is more likely to result in late delivery and early delivery.
As described above, there is a trade-off relationship between the number of lot changes and the delivery date (delayed delivery and early delivery).
In addition, if the delivery date is not delayed, it is easy for the delivery date to be made early. Therefore, there is a trade-off between late delivery and early delivery.

The evaluation index _xk for planning is not limited to, for example, the number of late delivery, early delivery, and lot change, and is an evaluation index for evaluating the degree of quality of the production plan or distribution plan, and is a production plan or It may be determined according to the purpose of making a distribution plan. For example, an evaluation index related to product quality or cost may be used as a planning evaluation index _xk .

The specific content of the evaluation index xk for planning in equation (1) is different between the case of making a production plan and the case of making a distribution plan, and the processing device for deriving the weight coefficient w [ _k ]. Reference numeral 100 can be applied to both a production plan and a distribution plan, but in the following, for the sake of simplicity, the production plan or the distribution plan will be referred to as a production plan as necessary. ..

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

<Acquisition unit 101>
The acquisition unit 101 has a value (actual value) of a plurality of evaluation indexes _xk for planning based on a plurality of hiring plans adopted as a production plan, and a plurality of non-hiring plans based on a plurality of non-hiring plans not adopted as a production plan. The value (actual value) of the evaluation index _xk for planning is acquired. The adoption plan is a production plan actually used for the production of the product, for example, a production plan made by a planner (for example, a skilled person) or a production plan made by using a known production simulator. A non-adoption plan is a production plan that is drafted as a production plan but is not used for product production. For example, a production plan drafted by a planner (for example, an unskilled person) or a known production simulator is used. It is a production plan that was devised.

In the present embodiment, the acquisition unit 101 acquires information for specifying the contents of the plurality of hiring plans and information for specifying the contents of the plurality of non-hiring plans. Examples of the acquisition form of these information include at least one of an input operation to the user interface of the processing device 100, reception of information transmitted from an external device, and reading of information stored in a portable storage medium. ..

The acquisition unit 101 makes one pair of one hiring plan and one non-hiring plan among the plurality of hiring plans and the plurality of non-hiring plans specified by the information acquired in this way. , Implement for each of multiple hiring plans. Two or more non-hiring plans that are different from each other may be paired for the same hiring plan. That is, there may be a pair of a certain hiring plan and a certain non-hiring plan, and a pair of the hiring plan and a non-hiring plan different from the non-hiring plan.

The paired hiring plan and non-hiring plan are production plans with the same preconditions (information set in advance at the time of planning) at the time of planning. If the preconditions for planning are the same, the values used as constants (fixed values) when calculating the value of the objective function Jr for planning are the same. For example, the IDs of the products included in the paired hiring plan and the non-hiring plan are the same. In addition, when late delivery and early delivery are used as the evaluation index _xk for planning, the delivery dates of the products included in the paired adoption plan and non-adoption plan are the same. Further, when the number of lot changes is used as the evaluation index _xk for planning, the lot numbers of the products included in the paired adoption plan and the non-adoption plan are the same.

The acquisition unit 101 creates one hiring plan and one non-hiring plan with all the same information (product ID, delivery date, lot number) as one pair. Further, instead of doing so, for example, when the identification information of the preconditions for planning is given to each of the hiring plan and the non-hiring plan, the acquisition unit 101 has the same identification information. One hiring plan and one non-hiring plan may be created as one pair.

The acquisition unit 101 acquires the value of the evaluation index x _k for planning from the hiring plan and acquires the value of the evaluation index x _k for planning from the non-hiring plan belonging to the same pair as the hiring plan. Execute for each pair.
For example, if the planning evaluation index _xk includes late delivery and early delivery, the hiring and non-hiring plans include, for example, the expected shipping date when the product is ready for production and ready to be shipped. , Product delivery date and included. If the value obtained by subtracting the estimated shipping date from the delivery date of the product is 0 (zero) or a positive value, the value is specified as early delivery and 0 (zero) is specified as late delivery. Further, when the value obtained by subtracting the delivery date from the scheduled shipment date of the product is 0 (zero) or a positive value, the value is specified as the late delivery date, and 0 (zero) is specified as the early delivery date.

Further, when the evaluation index _xk for planning includes the number of lot changes, the adoption plan and the non-adoption plan include, for example, the production order of each product for which a lot number is set for each process. Counting the number of lot number changes when the lot numbers are arranged in the order of product production is executed for each process, and the value obtained by adding the number of lot number changes for each process is specified as the number of lot changes.

In each of the equations described in this embodiment, the variable that identifies the pair acquired by the acquisition unit 101 as described above is defined as i ∈ I (I is a set of pairs). In addition, the hiring plan and the non-hiring plan are described as OK and NG, respectively. As described above, two or more non-recruitment plans that are different from each other may be paired with respect to the same recruitment plan, but these pairs are identified by different variables i.

<Weighting coefficient derivation unit 102>
The weight coefficient derivation unit 102 is an objective function value difference ε showing the difference between the adoption objective function Jr. A decision variable including [i] and a weight coefficient w [k] is derived. In this embodiment, the minimization problem for finding the minimum value of the planning objective function Jr is illustrated (that is, the smaller the value of the planning objective function Jr is, the better the plan is). The value of the function is greater than or equal to the value of the target function to be adopted. Therefore, in the present embodiment, the case where the difference between the adopted objective function and the non-adopted objective function is represented by a value obtained by subtracting the former (adopted objective function) from the latter (non-adopted objective function) is illustrated.

Here, in each of the following equations, it is assumed that [k] of w [k] is a value with respect to the evaluation index x _k for planning. Further, it is assumed that [i] of ε [i] is a value for pair i. Further, the subscript k_i_OK of x _{k_i_OK} indicates that it is multiplied by the weighting coefficient w [k], belongs to the pair i (the pair identified by the variable i), and is based on the recruitment plan. do. Similarly, the subscript k_i_NG of x _{k_i_NG} indicates that it is multiplied by the weighting factor w [k], belongs to pair i (the pair identified by the variable i), and is based on the non-adoption plan. It shall be.

In the example shown in _{Eq. (1), the value of the adopted objective function is Σ k ∈ K w [k] · x k_i_OK .} As described above, since the value of the evaluation index x _{k_i_OK} for planning based on the recruitment plan is specified from the recruitment plan, the unknown value in the recruitment 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 .} Since the value of the evaluation index x _{k_i_NG} for planning based on the non-adoption plan is specified from the non-adoption plan, the unknown value in the adoption objective function is the weighting coefficient w [k].

In the present embodiment, the constraint equations for determining the coefficients, which are the constraint equations for determining the weighting coefficient w [k], include the adopted / non-adopted objective function value difference constraint equation, the objective function value difference constraint equation, and the coefficients. The lower limit constraint expression and is included. Further, in the present embodiment, the coefficient determination objective function Jc, which is an objective function for determining the weighting coefficient w [k], includes the objective function value difference ε [i] as the coefficient determination evaluation index.

The adoption / non-adoption objective function value difference constraint formula is an objective function Jr for planning in a state where the value of the evaluation index x _{k_i_OK} for planning based on the adoption plan is substituted and the weighting coefficient w [k] is unknown. A state in which a certain adoption objective function (Σ k ∈ K w [k] · x _{k_i_OK} ) and the _value of the evaluation index x _{k_i_NG} for planning based on the non-adoption plan are substituted, and the weight coefficient w [k] is unknown. The difference _{between the non-adopted objective function (Σ k ∈ K w [k] · x k_i_NG )} , which is the objective function Jr for planning, is limited by the limit value based on the objective function value difference ε [i]. It is a constraint expression shown. The adopted / non-adopted objective function value difference constraint equation is expressed by the following equation (2), for example.

The objective function value difference constraint equation is a constraint equation showing that the magnitude relationship between the value of the adopted objective function and the value of the non-adopted objective function is not reversed, and is expressed by the following equation (3), for example.
The coefficient upper / lower limit value constraint equation is a constraint equation indicating that the weighting coefficient w [k] is within the range of the preset upper / lower limit values, and is represented by, for example, the following equation (4).

In the equation (2), the difference between the adopted objective function and the non-adopted objective function is Σ _{k ∈ K} w [k] · x _{k_i_NG} −Σ _{k ∈ K} w [k] · x _{k_i_OK} . Further, in the equation (2), the limit value based on the objective function value difference ε [i] is the objective function value difference ε [i] itself, and the lower limit value of the difference between the adopted objective function and the non-adopted objective function. Is shown. As shown in the equation (2), in the present embodiment, the adopted / non-adopted objective function value difference constraint equation is the difference between the adopted objective function and the non-adopted objective function (Σ k ∈ K w [k] · x _{k_i_NG} − _. It is shown that Σ k ∈ K w [k] · x _{k_i_OK} ) is greater than or _equal to the objective function value difference ε [i] so that it can be realized for each pair i.

As the objective function value difference ε [i] is determined as shown in the equation (2), the objective function value difference ε [i] is set to 0 or more as shown in the equation (3), and the value of the non-adopted objective function is set. Is greater than or equal to the value of the adoption objective function.

In the equation (4), the lower limit value w _LB and the upper limit value w _UB of the weighting coefficient w [k] are preset based on the range that can be taken as the weighting coefficient w [k]. The equation (4) is mainly a constraint equation for preventing the solution from becoming unsolvable.

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

In the example shown in the equation (5), the value of the objective function Jc for determining the coefficient is the sum of all the pairs i of the objective function value difference ε [i]. max. Indicates that the maximum value of the objective function (objective function Jc for determining the coefficient in the equation (5)) is obtained. Since the objective function value difference ε [i] is determined as shown in Eqs. (2) and (3), maximizing the sum of all pairs i of the objective function value difference ε [i] is not possible. Maximize the sum of the values obtained by subtracting the value of the adopted objective function from the value of the non-adopted objective function for each pair i (Σ _{k ∈ K} w [k] ・ x _{k_i_NG} －Σ _{k ∈ K} w [k] ・ x _{k_i_OK} ) Corresponds to what you do. Therefore, the weighting coefficient w [k] when the value of the adopted objective function and the value of the non-adopted objective function deviate as much as possible is derived. As shown in equations (2) to (5), in the present embodiment, the difference between the adopted objective function and the non-adopted objective function is like a discrimination function (separation hyperplane) in SVM (Support Vector Machine). It can be evaluated directly without going through other functions.

The weighting coefficient deriving unit 102 has a weighting coefficient w [k] and a purpose when the value of the coefficient determining objective function Jc shown in the equation (5) becomes maximum within the range satisfying the equations (2) to (4). The function value difference ε [i] is derived by executing the optimization calculation by the mathematical programming method. Since the optimization calculation by the mathematical programming method is realized by using, for example, a known solver for solving a linear programming problem, a detailed description thereof will be omitted here. Here, the weight coefficient derivation unit 102 exemplifies the case where the weight coefficient w [k] and the objective function value difference ε [i] are derived by executing the optimization calculation by the mathematical programming method, but it is not always the case. If the optimization problem is solved, it is not necessary to execute the optimization calculation by the mathematical programming method. 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 deriving unit 102. As the output form of the information, for example, at least one of display on a computer display, storage in an internal or external storage medium of the processing device 100, and transmission to an external device can be mentioned.

<Flow chart>
Next, an example of a processing method using the processing apparatus 100 will be described with reference to the flowchart of FIG.
First, in step S201, the acquisition unit 101 acquires information for specifying the contents of the plurality of hiring plans and information for specifying the contents of the plurality of non-hiring plans.
Next, in step S202, the acquisition unit 101 sets one pair i of one hiring plan and one non-hiring plan drafted under the same preconditions for each of the plurality of hiring plans. Run.

Next, in step S203, the acquisition unit 101 acquires the value of the planning evaluation index x _{k_i_OK} from the hiring plan, and also acquires the planning evaluation index x _{k_i_NG} from the non-hiring plan belonging to the same pair i as the hiring plan. Is executed for each pair i to acquire the value of.

Next, in step S204, the weighting coefficient derivation unit 102 has the evaluation indexes for planning x _{k_i_OK} and x _{k_i_NG} acquired for each pair i in step S203, and the lower limit of the preset weighting coefficient w [k]. Using the value w _LB and the upper limit value w _UB , the weight when the value of the coefficient determination objective function Jc shown in equation (5) becomes maximum within the range satisfying equations (2) to (4). The coefficient w [k] and the objective function value difference ε [i] are derived by executing the optimization calculation by the mathematical programming method.
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 the present embodiment, the processing apparatus 100 has a plurality of planning evaluation indexes x _{k_i_OK} values based on a plurality of hiring plans and a plurality of planning evaluation indexes x _{k_i_NG} based on a plurality of non-adopting plans. Get the value and. The processing device 100 has an objective function value difference ε [i] indicating the difference between the adopted objective function Jr. ] And the weighting coefficient w [k] are derived by solving the optimization problem. At this time, the processing apparatus 100 uses the coefficient determination objective function Jc shown in the equation (5). Further, the processing apparatus 100 uses the adopted / non-adopted objective function value difference constraint equation shown in the equation (2). Therefore, the weighting coefficient w [k] in the multi-objective optimization problem can be derived by using the adoption plan and the non-adoption plan which are actual plans. Therefore, the weighting coefficient w [k], which is an adjustment parameter when planning a production plan or a distribution plan by solving an optimization problem, is automatically set even if the correct value of the objective function (objective variable) is not determined. Can be derived from. Therefore, it is possible to reduce the adjustment period and the human load due to trial and error of the planner.

Further, in the present embodiment, the processing apparatus 100 has one adoption plan and one non-adoption plan in which the information set in advance at the time of drafting the production plan is the same based on the plurality of adoption plans and the plurality of non-adoption plans. Making one pair i with the hiring plan is executed for each of the plurality of hiring plans. Then, the processing apparatus 100 acquires the value of the planning evaluation index x _{k_i_OK} from the hiring plan and the value of the planning evaluation index x _{k_i_NG} from the non-adopting plan belonging to the same pair i as the hiring plan. Do this for each pair i. Then, as shown in the equation (2), the processing apparatus 100 uses the adopted / non-adopted objective function value difference constraint expression as the constraint expression for each pair i, and the difference between the adopted objective function and the non-adopted objective function for each pair i. A determinant including the defined objective function value difference ε [i] and the weighting coefficient w [k] is derived. Therefore, the coefficient of determination and the constraint equation for deriving the weighting coefficient w [k] can be reduced.

Further, in the present embodiment, the processing apparatus 100 uses the coefficient upper / lower limit value constraint equation shown in the equation (4) as the coefficient determination constraint equation. Therefore, it is possible to more reliably prevent the weighting coefficient w [k] from becoming unsolvable.

<Modification example>
In this embodiment, as shown in Eq. (1), the minimization problem that minimizes the value of the objective function Jr for planning is illustrated. However, in the present embodiment, it may be a maximization problem that maximizes the value of the objective function Jr for planning. In this case, for example, the formula (1) is changed to the following formula (6), the formula (2) is changed to the following formula (7), the formula (3) is changed to the following formula (8), and the formula (5) is used. The equation is replaced with the following equation (9), respectively.

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

Here, ρ is a forgetting coefficient, and a value close to 1 is preset in the range of more than 0 and less than 1. Further, when the objective function Jc for determining the coefficient is expressed by the equation (10), i is the order in which each pair is arranged in order from the pair to which the hiring plan with the new creation date belongs (i for the first pair). Is 1 (i = 1), i for the second pair from the beginning is 2 (i = 2), and i for the last pair is I (i = I). For example, the pair i to which the new recruitment plan belongs has a greater influence on the value of the coefficient determination objective function Jc, and the pair i to which the old recruitment plan belongs has an influence on the value of the coefficient determination objective function Jc. Therefore, even if the importance of each evaluation index changes due to changes in the external environment, production target / distribution target, operating conditions, etc., an appropriate weight balance according to the change. Can be presented.

Further, one of the weighting factors w [k] may be fixed to 1, and the remaining weighting factors w [k] may be derived as described in the present embodiment.

(Second embodiment)
Next, a second embodiment will be described. In the first embodiment, the case where the correspondence between the hiring plan and the non-hiring plan is clear (that is, the preconditions for planning (information set in advance at the time of planning)) is the same. The case was illustrated. However, there are cases where the correspondence between hiring plans and non-hiring plans is not clearly left. In the present embodiment, the weighting coefficient w [k] can be derived even in such a case, without creating a pair of a hiring plan and a non-hiring plan based on the preconditions at the time of planning. , The weighting coefficient w [k] is derived. As described above, the present embodiment is mainly different from the first embodiment in the configuration and processing by not creating a pair of a hiring plan and a non-hiring plan based on the preconditions at the time of planning. Therefore, in the description of the present embodiment, the same parts as those of the first embodiment are designated by the same reference numerals as those given in FIGS. 1 and 2, and detailed description thereof will be omitted.

As shown in FIG. 1, the processing apparatus 100 of the present embodiment also has an acquisition unit 101, a weighting coefficient derivation unit 102, and an output unit 103. In the present embodiment as well, as in the first embodiment, the processing apparatus 100 can be applied to both the production plan and the distribution plan, but in the following, the production plan or the distribution plan is applied as needed. I will explain it as a production plan.

<Acquisition unit 101>
As described in the first embodiment, the acquisition unit 101 is adopted as a production plan and a value (actual value) of a plurality of evaluation indexes _xx for planning based on the plurality of hiring plans adopted as the production plan. Obtain the values (actual values) of a plurality of evaluation indexes _xk for planning based on a plurality of non-adopted plans that did not exist.

In the present embodiment, the acquisition unit 101 acquires information for specifying the contents of the plurality of hiring plans and information for specifying the contents of the plurality of non-hiring plans. Then, the acquisition unit 101 acquires the values of the plurality of planning evaluation indexes x _k based on the plurality of hiring plans and the values of the plurality of planning evaluation indexes x _k based on the plurality of non-adopting plans. The fact that the value of the evaluation index _xk for planning can be acquired (specified) from the hiring plan / non-hiring plan is as described in the first embodiment.

In the first embodiment, the acquisition unit 101 executes one pair i of one hiring plan and one non-hiring plan for each of the plurality of hiring plans, and evaluates the hiring plan for planning. The value of the index x _{k_i_OK} is acquired, and the value of the evaluation index x _{k_i_NG} for planning is acquired from the non-adoption plan belonging to the same pair i as the recruitment plan for each pair i. However, in the present embodiment, such creation of the pair i and acquisition of each pair i of the evaluation index x _{k_i_OK} / x _{k_i_NG} for planning from the adoption plan / non-adoption plan are not performed. In the present embodiment, the acquisition unit 101 acquires the values of a plurality of planning evaluation indexes _xk from each of the plurality of hiring plans, and also obtains a plurality of planning evaluation indexes from each of the plurality of non-adopting plans. Get the value of x _k .

Here, in each of the following equations, the variable that identifies the hiring plan is u ∈ U (U is a set of hiring plans), and the variable that identifies the non-hiring plan is v ∈ V (V is a set of non-hiring plans). , A plurality of evaluation indexes for planning based on the recruitment plan x _k are expressed as x _{k_U} , and a plurality of evaluation indexes for planning based on the non-adoption plan x _k are expressed as x _{k_v} . In this way, in each of the following equations, the variables u and v distinguish between the adoption plan and the non-adoption plan.

<Weighting coefficient derivation unit 102>
As described in the first embodiment, the weighting coefficient derivation unit 102 has an adoption objective function Jr, which is a planning objective function Jr based on the adoption plan, and a non-adoption objective function Jr, which is a planning objective function Jr based on the non-adoption plan. A decision variable including the objective function value difference ε [u] [v] indicating the difference from the function and the weighting coefficient w [k] is derived.

However, in the first embodiment, the objective function value difference ε [i] defines the difference between the adopted objective function and the non-adopted objective function for each pair i. On the other hand, in the present embodiment, the objective function value difference ε [u] [v] defines the difference between the adopted objective function and the non-adopted objective function for each adopted plan and each non-adopted plan.

Further, in the present embodiment, the pair counting variable δ [u] [v] is further included as a decision variable. The pair counting variable δ [u] [v] is for counting the number of pairs of the hiring plan and the non-hiring plan indicating that the value of the non-adopting objective function has a lower evaluation for the production plan than the value of the hiring objective function. It is a variable. Similar to the first embodiment, this embodiment also exemplifies the case where the objective function Jr for planning is the equation (1) (that is, the minimization problem). In this case, indicating that the value of the non-adopted objective function has a lower evaluation for the production plan than the value of the adopted objective function means that the value of the adopted objective function is not larger than the value of the non-adopted objective function. Specifically, in the pair counting variable δ [u] [v], the value of the adoption objective function based on the adoption plan identified by the variable u is the value of the non-adoption objective function based on the non-adoption plan identified by the variable v. It is a 0-1 variable that becomes "1" when the following (value of the adopted objective function ≤ value of the non-adopted objective function), and becomes "0" otherwise. Therefore, the sum of the pair counting variables δ [u] [v] is the total number of pairs of the adoption plan and the non-adoption plan in which the value of the adoption objective function is equal to or less than the value of the non-adoption objective function.

Similar to the first embodiment, this embodiment also illustrates the case where the objective function Jr for planning is the equation (1). Then, the value of the adopted objective function is Σ k ∈ _{K w [k] · x k_u .} As described above, since the value of the evaluation index x _{k_u} for planning based on the recruitment plan is specified from the recruitment plan, the unknown value in the recruitment 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_v .} Since the value of the evaluation index x _{k_v} for planning based on the non-adoption plan is specified from the non-adoption plan, the unknown value in the adoption objective function is the weighting coefficient w [k].

In this embodiment as well as in the first embodiment, the constraint equations for determining the coefficients, which are the constraint equations for determining the weighting coefficient w [k], include the adopted / non-adopted objective function value difference constraint equation and the objective function. A value difference constraint expression and a coefficient upper / lower limit value constraint expression are included. Further, in the present embodiment, the coefficient determination objective function Jc, which is the objective function for determining the weight coefficient w [k], includes the objective function value difference ε [i] and the pair counting variable δ [u] [v]. Is included as an evaluation index for determining the coefficient.

However, in the first embodiment, the adopted / non-adopted objective function value difference constraint equation, the objective function value difference constraint equation, and the coefficient upper / lower limit value constraint equation are the equations (2), (3), and (4), respectively. It is expressed by an expression. On the other hand, in the present embodiment, the adopted / non-adopted objective function value difference constraint equation, objective function value difference constraint equation, and coefficient upper / lower limit value constraint equation are the following equations (11), (12), and (12), respectively. It is expressed by equation 13). Further, in the first embodiment, the objective function Jc for determining the coefficient is expressed by the equation (5). On the other hand, in the present embodiment, the objective function Jc for determining the coefficient is expressed by the following equation (14). Equation (13) is the same as equation (4), but is reprinted for ease of notation and explanation.

In the equation (11), in the adoption / non-adoption objective function value difference constraint equation, the value of the evaluation index x _{k_v} for planning based on the non-adoption plan is substituted, and the weight coefficient w [k] is unknown. The non-adopted objective function (Σ k _{∈ K x k_v ·} w [k]), which is the objective function Jr for planning, and the value of the evaluation index x _{k_u} for planning based on the recruitment plan are substituted, and the weight coefficient w [ The difference between the adopted objective function (Σ k ∈ K x _{k_u} · w [k]), which is the objective function Jr for planning in a state where k] is unknown, _becomes the objective function value difference ε [u] [v]. It is a constraint expression indicating that it is limited by the limit value based on it.

In the equation (12), M _big is a constant of a positive value assuming an upper limit of a value that can be taken as an absolute value on the right side of the equation (12), and is set in advance.
Therefore, when the pair counting variable δ [u] [v] is 0 (zero), the equation (12) becomes a trivial equation, and it is permissible that the objective function value difference ε [u] [v] becomes negative. Will be done. Along with this, the adoption / non-adoption objective function according to Eq. (11) The adoption objective function based on the adoption plan identified by the variable u and the non-adoption objective function based on the non-adoption plan identified by the variable v by the value difference constraint equation. It is permissible that the value of the non-adopted objective function becomes smaller (better) than the value of the adopted objective function. This is because, in the present embodiment, the preconditions for planning the hiring plan identified by the variable u and the non-adopting plan identified by the variable v may not be the same. In such a case, It is considered that the value of the adopted objective function is not always smaller (better) than the value of the non-adopted objective function because it is a comparison between plans whose preconditions for planning are not the same.

On the other hand, when the pair count variable δ [u] [v] is 1, the objective function value difference ε [u] [v] is subject to a constraint of 0 (zero) or more (that is, the objective function). It is not permissible for the value difference ε [u] [v] to be negative). Along with this, the value of the non-adopted objective function is smaller 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. In the planning objective function Jr in a state where it is not allowed to become (improve), the value of the planning evaluation index x _{k_v} based on the non-adoption plan is substituted, and the weighting coefficient w [k] is unknown. A state in which a certain non-adoption objective function (Σ k _{∈ K x k_v ·} w [k]) and the value of the evaluation index x _{k_u} for planning based on the adoption plan are substituted, and the weight coefficient w [k] is unknown. The difference _{between the adopted objective function (Σ k ∈ K x k_u ·} w [k]), which is the objective function Jr for planning, is limited by the limit value based on the objective function value difference ε [u] [v]. ..

As shown in the equation (11), in the present embodiment, the adopted / non-adopted objective function value difference constraint equation is the difference between the non-adopted objective function and the adopted objective function (Σ k _{∈ K x k_v ·} w [k] −. It is shown that the fact that Σ k ∈ K x _{k_u} · w [k]) is _equal to or greater than the objective function value difference ε [u] [v] is realized for each arbitrary adoption plan / arbitrary non-adoption plan. As the objective function value difference ε [u] [v] is determined as shown in the equation (11), the objective function value difference ε [u] [v] is a negative value as shown in the equation (12). It is also possible. By _doing so, _{ε [ u} ] [ Even when v] is negative, the influence can be minimized by the second term on the right side of the objective function (14).

In the present embodiment, the values of the objective function Jc for determining the coefficient are all possible as a pair of the adoption plan u and the non-adoption plan v of the pair counting variables δ [u] [v] as shown in the equation (14). It is a weighted linear sum of the sum of the pairs and the sum of all the pairs of the objective function value difference ε [u] [v] that can be taken as a pair of the adoption plan u and the non-adoption plan v. p ₁ is a weighting coefficient multiplied by the pair counting variable δ [u] [v], and p ₂ is a weighting coefficient multiplied by the objective function value difference ε [u] [v], both of which are positive. Has a value of.

Since the objective function value difference ε [u] [v] is determined as shown in the equations (11) and (12), the adoption plan u and the non-adoption plan v of the objective function value difference ε [u] [v]. To increase the sum of all possible _pairs of It corresponds to increasing the sum of x _{k_v} · w [k] −Σ _k∈K x _{k_u} · w [k]). Therefore, the weighting coefficient w [k] when the value of the non-adopted objective function and the value of the adopted objective function deviate greatly is calculated.

However, a pair of a hiring plan and a non-hiring plan (that is, δ [u] [v] = 1 indicating that the value of the non-adopting objective function has a lower evaluation for the production plan than the value of the hiring objective function, u, v. If the number of pairs) is too small, an appropriate weighting coefficient w [k] may not be derived. Therefore, a pair of a recruitment plan and a non-adoption plan (that is, δ [u] [v] = 1) indicating that the value of the non-adoption objective function has a lower evaluation for the production plan than the value of the adoption objective function u, The number of pairs of v) is increased.

As described above, in Eq. (14), the value of the non-adopted objective function and the value of the adopted objective function deviate greatly, and the value of the non-adopted objective function has a lower evaluation for the production plan than the value of the adopted objective function. It is shown that the weighting factors p1 and p2 _are used to adjust which evaluation is important in realizing both the hiring plan and the non _- hiring plan that show that the number of pairs increases.

_The weighting coefficients p1 and p2 are used to balance the evaluation of the _pair counting variable δ [u] [v] and the objective function value difference ε [u] [v], similarly to the weighting coefficient w [k]. It is a thing. However, the weighting coefficients p1 and p2 _are the weighting coefficients w [ _k ], the objective function value difference ε [u] [v], and the pair counting variable δ [u] based on the equations (11) to (14). Is set in advance when deriving. 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 value of the adopted objective function and the value of the non-adopted objective function. And the purpose is the same. When setting the weighting coefficients p ₁ and p ₂ , for example, p ₂ = 1, and about 60 to 70% or more of p ₁ is δ [u] [v] = 1 for all pairs of (u, v). Set large until.

The weighting coefficient deriving unit 102 has a weighting coefficient w [k] when the value of the objective function Jc for determining the coefficient shown in the equation (14) becomes maximum within the range satisfying the equations (11) to (13). The function value difference ε [u] [v] and the pair count variable δ [u] [v] are derived by executing the optimization calculation by the mathematical programming method. Since the optimization calculation by the mathematical programming method is realized by using, for example, a known solver for solving a linear programming problem (mixed integer programming problem), detailed description thereof will be omitted here. As described in the first embodiment, when deriving the weighting coefficient w [k], the objective function value difference ε [u] [v], and the pair counting variable δ [u] [v], it is not always mathematical. There is no need to perform planning optimization calculations.

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

Next, in step S303, the weighting coefficient derivation unit 102 includes the evaluation indexes for planning x _{k_u} and x _{k_v} acquired in step S302, and the lower limit value w _LB of the preset weighting coefficient w [k]. Using the upper limit value w _UB , the weighting coefficient w [k] when the value of the coefficient determination objective function Jc shown in the equation (14) becomes maximum within the range satisfying the equations (11) to (13). ], Objective function value difference ε [u] [v], and pair counting variable δ [u] [v] are derived by executing optimization calculation by mathematical programming.
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 the present embodiment, the objective function value difference ε [u] [v] is defined for each pair of an arbitrary adoption plan and an arbitrary non-adoption plan. Further, in addition to the weight coefficient w [k] and the objective function value difference ε [u] [v], the pair counting variable δ [u] [v] is included in the determination variable. The processing device 100 derives these decision variables by solving an optimization problem. At this time, the processing apparatus 100 uses the coefficient determination objective function Jc shown in the equation (14). Further, the processing apparatus 100 uses the adopted / non-adopted objective function value difference constraint equation shown in the equation (11). Therefore, in addition to the effect described in the first embodiment, there is an effect that the weighting coefficient w [k] can be derived even when the correspondence between the hiring plan and the non-hiring plan is not clearly left. can get.

<Modification example>
Also in this embodiment, various modifications described in the first embodiment can be adopted.
For example, in this embodiment as well as in the first embodiment, the minimization problem of minimizing the value of the objective function Jr for planning is exemplified as shown in the equation (1). However, as described in the modified example of the first embodiment, the present embodiment may also be a maximization problem that maximizes the value of the objective function Jr for planning. In this case, for example, the equation (1) is rewritten into the equation (6). Further, the equation (11) is replaced with the following equation (15). Even when the maximization problem is used, the equations (12) to (14) are used in the same manner as the minimization problem.

Further, as described in the modified example of the first embodiment, the objective function Jc for determining the coefficient is not limited to the one shown in the equation (14) in this embodiment as well. The objective function Jc for determining the coefficient may be expressed by the following equation (16), for example.

Equation (16) corresponds to equation (9) described in the modified example of the first embodiment, ρ is a forgetting coefficient, and a value close to 1 is preset in the range of more than 0 and less than 1. Will be done. Further, when the objective function Jc for determining the coefficient is expressed by the equation (16), u and v are, for example, the order in which the hiring plans are arranged in order from the one with the newest creation date and time (the first hiring plan). u (v) is 1 (u (v) = 1), the second hiring plan u (v) from the beginning is 2 (u (v) = 2), and the last hiring plan u (v) is | U | + | V | (u (v) = | U | + | V |)). Alternatively, u and v may be considered as quantities representing the time when the data is collected by going back to the past with the current time as the starting point 0 (zero). According to the equation (16), the newer the adoption plan, the greater the influence on the value of the coefficient determination objective function Jc, and the older the adoption plan, the greater the influence on the value of the coefficient determination objective function Jc. Can be made smaller.

(Calculation example)
Next, a calculation example will be described. In this calculation example, the weight coefficients w [1] and w [in the planning objective function Jr for planning the processing completion time in the two processes as the production plan when 10 products are produced in the two processes. A case where 2] and w [3] are derived by using the method described in the first embodiment will be described. This calculation example is a virtual example.

In this calculation example, the planning objective function Jr has three planning evaluation indexes x _k : late delivery x ₁ , early delivery x ₂ , and number of lot changes x ₃ . It shall be expressed by an expression.

Further, in this calculation example, the production plan (adoption plan and non-adoption plan) formulated in each of the five preconditions as the preconditions (information set in advance at the time of planning) at the time of planning is used as teacher data. Using. Here, the preconditions (information set in advance at the time of planning) at the time of planning are referred to as input data.

4A, 4B, 4C, 4D, and 4E show the first input data 401, the second input data 402, the third input data 403, the fourth input data 404, and the fifth input, respectively. It is a figure which shows the data 405.

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, process 1 lot number, process 2 lot number, and delivery date are prerequisites for deriving delivery delay x ₁ , early delivery x ₂ , and number of lot changes x ₃ , and are constants (fixed values). It is used.

FIG. 5 is a diagram showing the number of production plans (adoption plan and non-adoption plan) drafted based on the first to fifth input data 401 to 405 in a table format. In FIG. 5, the input data numbers 1, 2, 3, 4, and 5 are the first input data 401, the second input data 402, the third input data 403, the fourth input data 404, and the fifth, respectively. The input data 405 of the above is shown. FIG. 5 shows that one recruitment plan and two non-adoption plans were drafted based on the first input data 401, the second input data 402, and the fourth input data 404. It also indicates that one hiring plan and three non-hiring plans have been drafted based on the third input data 403. It also indicates that one hiring plan and one non-hiring plan have been drafted based on the fifth input data 405.

In this calculation example, in the adoption plan, the weighting coefficients w [1], w [2], and w [3] are set to 3, 1, and 10, respectively (w [1] = 3, w [2] = 1, It was planned (as w [3] = 10). Therefore, in this calculation example, these values (w [1] = 3, w [2] = 1, w [3] = 10) are weighting coefficients w [1], w [2], w [3]. It becomes the correct answer value of. On the other hand, the non-adoption plan is designed by making at least one of the weighting coefficients w [1], w [2], and w [3] different from the correct answer value. As described above, in this calculation example, the weighting coefficient w [k] (w [1] = 3, w [2] = 1, w [3] = 10) used when creating the recruitment plan is set to the first. A virtual example for investigating whether it can be reproduced by the method of the embodiment is shown. As described above, the correct answer values of the weighting coefficients w [1], w [2], and w [3] are compared with the derivation result of the weighting coefficient w [k] by the method of the first embodiment. It is not used when deriving the weighting coefficient w [k] by the method of the first embodiment.

FIG. 6 shows delivery delay x ₁ , early delivery x ₂ , and lot change acquired from the production plans (adoption plan and non-adoption plan) formulated based on the first to fifth input data 401 to 405. It is a figure which shows the number of times x ₃ of. In FIG. 6, recruitment indicates that the value is based on the recruitment plan, and non-adoption indicates that the value is based on the non-adoption plan.

Here, the adoption plan and the adoption process formulated based on the first input data 401 with the input data number 1 in FIG. 6 for the derivation process of the late delivery x ₁ , the early delivery x ₂ , and the number of lot changes x ₃ . Let's take a non-recruitment plan as an example.
FIG. 7 is a diagram showing delivery delay x ₁ , early delivery x ₂ , and number of lot changes x ₃ acquired from the recruitment plan drafted based on the first input data 401.

As described above, in this calculation example, the processing times of the two processes are planned as the production plan. In FIG. 7A, the processing time (process 2 processing time) in the lower process (downstream process) step 2 is the processing time in the upper process (upstream side process) step 1 (process 1 processing). It is assumed that the time cannot be earlier than the time) (that is, the process 2 cannot be executed earlier than the process 1). ”. Therefore, for example, when the processing order in the process 2 is the first product and the processing order in the process 1 is the kth, the processing time in the process 2 (process 2 processing time) is set to k, and the processing in the process 2 is performed. It is assumed that the processing time of the second and subsequent products is also (k + 1) or more. That is, the processing time in the process 2 (process 2 processing time) is assumed to be a time in which the time delay accompanying the process is taken into consideration. It is assumed that the delivery date is set in the same way as the process 2 processing time. Note that FIG. 7A shows the first input data 401 (product ID, process 1 lot number, process 2 lot number, and delivery date) together with the production plan (process 1 processing time, process 2 processing time). .. Further, in FIGS. 7 (a) to 7 (c), for convenience of explanation, the delivery date, the process 1 processing time, and the process 2 processing time are not the actual times, but the smaller the value, the earlier the time corresponds to 0. It shall be represented by the above integers.

In FIG. 7A, when the value obtained by subtracting the delivery date from the process 2 processing time is a positive value, the value is the value of the delivery delay. Step 2 When the value obtained by subtracting the delivery date from the processing time is 0 (zero) or less, the value of the delivery delay is 0 (zero). On the other hand, when the value obtained by subtracting the process 2 processing time from the delivery date is a positive value, the value is the value for early delivery. When the value obtained by subtracting the process 2 processing time from the delivery date is 0 (zero) or less, the value for early delivery is 0 (zero). By executing such a calculation for the product of each product ID, the late delivery date and the early delivery date of the product of each product ID are derived. The added value of the value shown in the delivery delay column of FIG. 7 (a) (the numerical value (= 3) shown in the margin below the delivery delay column) is the delivery date in the adoption plan in which the input data number of FIG. 6 is "1". It becomes the value (= 3) in the column of delay x ₁ . Similarly, the added value of the value shown in the column for early delivery in FIG. 7 (a) (the numerical value (= 3) shown in the margin below the column for early delivery) is that the input data number in FIG. 6 is "1". It becomes the value (= 3) in the column of early delivery x ₂ in the recruitment plan of.

7 (b) shows that each product is rearranged so that the earlier the process 1 processing time shown in FIG. 7 (a) is, the higher the record is. In FIG. 7B, the process 1 lot number is changed when the processing target is changed from the product with the product ID 6 to the product with the product ID 3 and from the product with the product ID 3 to the product. When the processing target is changed to the product with ID 1, when the processing target is changed from the product with product ID 10 to the product with product ID 2, and when the product ID is 5 to the product ID is 9. When the processing target is changed to the product and 4 times (see the numerical value (= 4) shown in the margin below the lot change column).

FIG. 7 (c) shows that each product is rearranged so that the earlier the process 2 processing time shown in FIG. 7 (a) is, the higher the record is. In FIG. 7 (c), the process 2 lot number is changed when the processing target is changed from the product with the product ID 7 to the product with the product ID 8 and from the product with the product ID 1 to the product. The processing target is changed to the product with ID 10 and the processing target is changed from the product with product ID 9 to the product with product ID 6 (under the lot change column). Refer to the numerical value (= 3) shown in the margin of.
The addition value (= 7) of the number of changes in the process 1 lot number (= 4) and the number of changes in the process 2 lot number (= 3) is the number of lot changes in the adoption plan in which the input data number in FIG. 6 is "1". It becomes the value (= 7) in the column of _x3 .

FIG. 8 is a diagram showing delivery delay x ₁ , early delivery x ₂ , and number of lot changes x ₃ acquired from the non-adoption plan drafted based on the first input data 401. FIG. 8 exemplifies delivery delay x ₁ , early delivery x ₂ , and number of lot changes x ₃ obtained from the non-adoption plan in the first line where the input data number of FIG. 6 is “1”.

8 (a), 8 (b), and 8 (c) correspond to FIGS. 7 (a), 7 (b), and 7 (c), respectively. By the same method as described with reference to FIG. 7, the added value of the value shown in the delivery delay column of FIG. 8A (the numerical value (= 12) shown in the margin below the delivery delay column) is derived. Then, the value (= 12) in the column of delivery delay x ₁ in the non-adoption plan in the first line where the input data number in FIG. 6 is "1" is obtained. Similarly, the added value of the value shown in the column for early delivery (the numerical value (= 2) shown in the margin below the column for early delivery) in FIG. 8A is the input data number of FIG. 6 is “1”. It is the value (= 2) in the column of early delivery x ₂ in the non-adoption plan in the first line of. Further, the added value (= 5) of the number of changes in the process 1 lot number (= 3) and the number of changes in the process 2 lot number (= 2) is not the first line in which the input data number in FIG. 6 is "1". The value (= 5) in the column of the number of lot changes x ₃ in the recruitment plan.

Although detailed values are omitted, for other production plans (adoption plan and non-adoption plan), delivery delay x ₁ , early delivery x ₂ , and number of lot changes x ₃ are derived, and the results are obtained. Is shown in FIG.

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

Further, in FIG. 6, the late delivery date x ₁ , the early delivery date x ₂ , and the number of lot changes x ₃ in the recruitment column correspond to the evaluation index x _{k_i_OK} for planning based on the recruitment plan. In addition, the late delivery date x ₁ , the early delivery date x ₂ , and the number of lot changes x ₃ in the non-adopted column correspond to the evaluation index x _{k_i_NG} for planning based on the non-adopted plan. The value of the planning evaluation index x _{k_i_OK} based on such a recruitment plan and the value of the planning evaluation index x _{k_i_NG} based on the non-employment plan are acquired for each pair i created as described above (FIG. 2). (See step S203).

Then, using the evaluation indexes x _{k_i_OK} and x _{k_i_NG} for planning for each pair i, the value of the coefficient determination objective function Jc shown in the equation (5) is set within the range satisfying the equations (2) to (4). The weighting factor w [k] and the objective function value difference ε [i] at the maximum were derived by executing the optimization calculation by the mathematical programming method (see step S204 in FIG. 2).

As a result, the weighting coefficients w [1], w [2], and w [3] are 4, 1, and 10 (w [1] = 4, w [2] = 1, w [3] = 10), respectively. Was derived. Only the weighting coefficient w [1] is different from the correct answer value (w [1] = 3, w [2] = 1, w [3] = 10), but it is a small number (5) of input data. Despite this, results close to the correct answer were obtained.

(Other embodiments)
The embodiment of the present invention described above can be realized by executing a program by a computer. Further, a computer-readable recording medium on which the program is recorded and a computer program product such as the program can also be applied as an embodiment of the present invention. As the recording medium, for example, a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a non-volatile memory card, a ROM, or the like can be used. Further, the embodiment of the present invention may be realized by a PLC (Programmable Logic Controller) or by dedicated hardware such as an ASIC (Application Specific Integrated Circuit).
In addition, the embodiments of the present invention described above are merely examples of embodiment of the present invention, and the technical scope of the present invention should not be construed in a limited manner by these. It is a thing. That is, the present invention can be implemented in various forms without departing from the technical idea or its main features.

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

Claims (7)

It is an objective function that aims at a multi-objective optimization problem for planning a production plan or a distribution plan, and has a plurality of evaluation indexes for planning and a weighting coefficient multiplied by the evaluation index for planning. It is a processing device that executes the process of deriving the weighting coefficient in the objective function for planning.
The values of the plurality of planning evaluation indexes based on the plurality of recruitment plans adopted as the production plan or the distribution plan, and the plurality of plans based on the plurality of non-adoption plans not adopted as the production plan or the distribution plan. The value of the evaluation index for planning, the acquisition method to acquire, and
The objective function value difference indicating the difference between the adoption objective function, which is the objective function for planning based on the adoption plan, and the non-adopted objective function, which is the objective function for planning based on the non-adoption plan, and the weight coefficient. It has a weighting coefficient deriving means for deriving a decision variable including, by solving an optimization problem.
The constraint formula for determining the coefficient, which is the constraint formula in the optimization problem, includes the adoption objective function in a state where the value of the evaluation index for planning based on the adoption plan is substituted and the weighting coefficient is unknown. The difference between the non-adopted objective function in which the value of the evaluation index for planning based on the non-adopted plan is substituted and the weighting coefficient is unknown is due to the limit value based on the objective function value difference. Adopted / non-adopted objective function that indicates that it is restricted, including the difference constraint expression
The coefficient determination objective function, which is an objective function in the optimization problem, is a processing device including the objective function value difference as a coefficient determination evaluation index. Among the plurality of hiring plans and the plurality of non-hiring plans, one hiring plan and one non-hiring plan having the same information preset in the planning of the production plan or the distribution plan. As one pair
In the adopted / non-adopted objective function value difference constraint formula, it is realized for each pair that the difference between the adopted objective function and the non-adopted objective function is limited by a limit value based on the objective function value difference. Show that
The processing device according to claim 1, wherein the objective function value difference is a difference between the adopted objective function and the non-adopted objective function defined for each pair. The decision variable is for counting the number of pairs of the adoption plan and the non-adoption plan indicating that the value of the non-adoption objective function has a lower evaluation for the production plan or distribution plan than the value of the adoption objective function. Including the pair count variable of
The objective function value difference for the adoption plan and the non-adoption plan pair indicating that the value of the non-adoption objective function has a lower evaluation for the production plan or the distribution plan than the value of the adoption objective function is the non-adoption. It is not permissible for the value of the objective function to take a value indicating that the evaluation of the production plan or distribution plan is higher than the value of the adopted objective function, and the value of the non-adopted objective function is higher than the value of the adopted objective function. Also does not indicate that the evaluation of the production plan or the distribution plan is low. It is permissible to take a value that indicates a high evaluation of the production plan or distribution plan,
The processing apparatus according to claim 1, wherein the coefficient determination objective function includes the objective function value difference and the pair counting variable as an evaluation index for coefficient determination. 13. Processing equipment. The coefficient determination objective function is a coefficient that is multiplied by each of the coefficient determination evaluation indexes, and has a coefficient having a different value depending on the adoption plan that is the derivation source of the coefficient determination evaluation index. The processing apparatus according to any one of claims 1 to 4, further comprising. It is an objective function that aims at a multi-objective optimization problem for planning a production plan or a distribution plan, and has a plurality of evaluation indexes for planning and a weighting coefficient multiplied by the evaluation index for planning. It is a processing method for executing the processing for deriving the weighting coefficient in the objective function for planning.
The values of the plurality of planning evaluation indexes based on the plurality of recruitment plans adopted as the production plan or the distribution plan, and the plurality of plans based on the plurality of non-adoption plans not adopted as the production plan or the distribution plan. The value of the evaluation index for planning, the acquisition process to acquire, and
The objective function value difference indicating the difference between the adoption objective function, which is the objective function for planning based on the adoption plan, and the non-adopted objective function, which is the objective function for planning based on the non-adoption plan, and the weight coefficient. It has a weighting coefficient derivation step of deriving a decision variable including, by solving an optimization problem.
The constraint formula for determining the coefficient, which is the constraint formula in the optimization problem, includes the adoption objective function in a state where the value of the evaluation index for planning based on the adoption plan is substituted and the weighting coefficient is unknown. The difference between the non-adopted objective function in which the value of the evaluation index for planning based on the non-adopted plan is substituted and the weighting coefficient is unknown is due to the limit value based on the objective function value difference. Adopted / non-adopted objective function that indicates that it is restricted, including the difference constraint expression
The coefficient determination objective function, which is an objective function in the optimization problem, is a processing method including the objective function value difference as a coefficient determination evaluation index. A program for operating a computer as each means of the processing apparatus according to any one of claims 1 to 5.

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