JP2005092726A - Push-pull mixed optimal complex production planning method, push-pull mixed optimal complex production planning device, and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a push-pull mixed optimal complex production planning method capable of forming an optimal production plan integrally in a complex production system. <P>SOLUTION: This push-pull mixed optimal complex production planning device is provided with a main control part 11, a pretreatment part 12, and a multi-item multi-process lot size scheduling part 13. The main control part 11 is provided with an input/output control part 111, a production planning control part 112, and a scheduling control part 113. The pretreatment part 12 performs pretreatment for the production plan in every production planning (phase 1 cycle) and performs pretreatment for scheduling in every scheduling (phase 2 cycle). The multi-item multi-process lot size scheduling part 13 forms an optimal production plan in every production planning (phase 1 cycle) by using an optimization scheduling algorithm and forms an optimal production schedule in every scheduling (phase 2 cycle) by using an optimization scheduling algorithm. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a push-pull mixed type optimal mixed production planning method and a push-pull mixed type optimal combined production for creating an optimal production plan in a combined production method capable of combined production of an ordered product and a prospective product in the same process. The present invention relates to a planning device and a program.

  In general, in a production system composed of multiple processes and multiple machines, various orders are generally classified into a plurality of items for switching production. In this type of production system, that is, a multi-item multi-step production system, setup is involved each time the item to be processed is switched in any process and any mechanical equipment. This setup requires setup time and setup costs. Both the setup time and setup cost depend on the item to be processed. On the other hand, the inventory of items incurs storage costs in proportion to the period, which depends on the item.

  Therefore, a lot size scheduling method for a multi-item multi-step production system that determines the overall system schedule (optimum schedule) so that the total cost over the target period can be minimized as long as the item does not run out or is delayed. A multi-item multi-process lot size scheduling method) has been proposed (see, for example, Patent Document 1 or Non-Patent Document 1). In this multi-item multi-process lot size scheduling method, for each item and each machine, and for each time slot in which the planning target period is divided at a constant time interval, the time slot is used for the production of the item. By using a decision variable (primitive object) indicating whether or not it is used according to the above, the overall optimization problem is decomposed into partial optimization problems, thereby reducing the calculation time. In the multi-item multi-process lot size scheduling method, the partial optimization problem is combined to form the whole as one problem. Is set to be non-negative). A Lagrangian decomposition / adjustment method is applied to optimize the objective function and satisfy the interrelationship constraints. This multi-item multi-process lot size scheduling method enumerates various aspects of various heterogeneous determinations, such as lot size, lot order, and placement, which are included in the multi-item multi-process scheduling problem. It is possible to generate an economical and reasonable feasible schedule by solving the various aspects from the viewpoint of overall optimization, without needing to be aware of this, and without requiring artificial constraints.

  The scheduling described in the above document uses an algorithm called O2O (Object oriented Optimization) -technology. O2O-technology is a technology that pursues real-time performance, high resolution, and overall optimization by fusing object-oriented technology and optimization technology, and has the following characteristics.

  1. Using multiple 0-1 variables with subscripts as primitive objects, the time optimization problem is accurately formulated into a mixed integer programming with high resolution without placing artificial constraints.

  2. Primitive objects themselves have no meaning by themselves, but multiple together represent the state of the plan and the aspect of the decision.

  3. Focusing on the possibility of adding and separating problems, the overall optimization problem is decomposed into partial optimization problems, the mathematical dimension of the partial optimization problem is dropped, and the calculation time is greatly reduced.

  4). In order to combine the partial optimization problems and configure the whole as one problem, various interrelation constraints are placed.

5). Lagrangian decomposition / adjustment method is used to satisfy the relational constraints simultaneously with the optimization of the objective function.
JP 2002-328977 A (0011 paragraph) Aditya Warman, Kenji Muramatsu, “Multi-item multi-step dynamic lot size scheduling with setup time: Lagrange decomposition adjustment method”, Journal of Japan Society for Management Engineering, 2002, Vol.53, No.5, p. 385-396

  Recently, the trend of customer demand, product diversification, life cycle shortening, etc. is accelerating. As a result, in a multi-item multi-process production system, an order item and a prospective item (that is, an item that is expected to be ordered or forecasted because it is not in time to arrange it after the order is confirmed, such as a key with a long production lead time, for example. It is becoming difficult to distinguish them from devices. In such a multi-item multi-step production system, two or more items including two types of order items and prospective items are commonly produced using the same process. Also, in this type of multi-item multi-step production system, items that are commonly used for ordered products and prospective products (for example, common parts and semi-finished products before coloring) may be produced in the previous process. Such a production system is called a complex production system. In this complex production system, without distinguishing between ordered items and prospective items, an optimal processing plan (production plan) is formulated together for the ordered items and prospective items and their necessary items. A method of planning a production plan with global optimization is desired.

  On the other hand, the multi-item multi-process lot size scheduling method described in the above-mentioned document (Patent Document 1 or Non-Patent Document 1) determines various aspects of determination of various kinds of heterogeneity such as lot size, lot order, arrangement, etc. It is known that it can be optimized simultaneously.

Therefore, the above-mentioned multi-item multi-process lot size scheduling method (algorithm for realizing) can be applied to formulate an optimal processing plan collectively for ordered items and prospective items and necessary items. Conceivable. In order to effectively produce two or more items, including two types of order items and prospective items, by using the same process in common by formulating an optimal processing plan, The initial stock level and the end-of-period stock level for each item in the above must be appropriately determined in advance. For example, if an item with a long production lead time is out of stock, the product will also be lost in sales or will be delayed in delivery, so it is inevitable to have an in-process product or product inventory at an appropriate level. Therefore, it is desirable that each item has an appropriate inventory level at each time point.

  However, the conventional multi-item multi-process lot size scheduling method described above does not consider application to a complex production system that mixes and produces each item, including ordered items and prospective items, in the same process. The determination of the initial stock level and the end-of-period stock level of each item in the above from the viewpoint of overall optimization is not considered. In particular, the pull-type production method that produces products according to orders (shipment requests) is generally applied to the production of ordered items, while the production of prospective products is produced based on a shipment plan. The push type production method is generally applied, and scheduling that allows push-pull mixed type production is not considered.

  The present invention has been made in consideration of the above circumstances, and its purpose is a push that enables an optimal production plan to be created collectively in a complex production system that produces items including ordered items and prospective items using the same process. -To provide a mixed-pull optimal mixed production planning method and a mixed push-pull mixed production management system.

  One aspect of the present invention is that a two-stage production planning method (push-pull mixed type optimum combined production planning method) for creating an optimum production plan for a combined production method of an ordered product and a prospective product in the same process. Proposed). In the first stage, a plan with a long plan period is created using an O2O-technology algorithm, and the stock level by item at the end of the plan period of the second stage plan is determined from the result. Similarly, optimal scheduling is performed using the algorithm of the O2O-technology for the shipping request over the planning period and the target in-process inventory level at the end of the period.

  Without distinguishing between ordered and prospective products in a complex production system, the optimal processing plan (production plan) is created collectively for the ordered and prospective products and their necessary items. A production plan can be made in an oriented manner.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
FIG. 1 is a block diagram showing a configuration of a push-pull mixed type combined production management system (hereinafter referred to as a combined production management system) according to an embodiment of the present invention. This complex production management system applies a two-stage production planning method (hereinafter referred to as a push-pull mixed type optimum complex production planning method) for creating an optimum production plan in the complex production system. The complex production system is a system that consists of multiple processes and multiple machines, and uses a single process to produce a plurality of items including two types of ordered items and prospective items. The push-pull mixed type optimal combined production planning method is composed of a phase 1 (first stage) plan (hereinafter referred to as a production plan) and a phase 2 (second stage) plan (hereinafter referred to as scheduling). Is done. In production planning, a production inventory plan over a long planning target period is created using an O2O-technology algorithm. In the scheduling, a relatively short planning target period (scheduling target period) is set using an algorithm of O 2 O-technology compared to the production plan. A multi-item multi-process lot size scheduling algorithm that realizes the multi-item multi-process lot size scheduling method described in Patent Document 1 or Non-Patent Document 1 is applied to both production planning and scheduling. In the present embodiment, the scheduling is repeated for one production plan until the end condition of the scheduling cycle is satisfied. Further, the production plan is repeated until the end condition of the production plan cycle is satisfied. As the inventory level at the beginning of each item used in the production plan (initial inventory level), the inventory level of the time slot in the latest production schedule corresponding to the beginning of the planning target period of the production plan is used. On the other hand, the inventory level at the end of each product used in scheduling (the target inventory level at the end of the target period) uses the inventory level of the time slot in the latest production plan corresponding to the end of the planning target period of the scheduling. In addition, the inventory level of the time slot in the preceding scheduling corresponding to the beginning of the planning target period of the scheduling is used as the inventory level at the beginning of each item used in scheduling (initial inventory level). In scheduling, a multi-item multi-process lot size scheduling algorithm (hereinafter referred to as “optimization”) is used for both the requested shipping amount (firm shipment data) in the planning period and the target inventory level determined at the end of the period determined from the corresponding production plan. Optimal scheduling using a scheduling algorithm is performed.

  The complex production management system of FIG. 1 is realized by a computer such as a personal computer having the block configuration shown in FIG. The computer of FIG. 2 includes a CPU 21, a main memory 22, a magnetic disk device (hereinafter referred to as HDD) 23, a CD-ROM device 24, a keyboard 25, and a display 26. These CPU 21, main memory 22, HDD 23, CD-ROM device 24, keyboard 25 and display 26 are interconnected by a system bus 27. The CPU 21 is a main controller of the computer. The main memory 22 stores various programs executed by the CPU 21, data, and the like. The HDD 23 is an external storage device for the computer. The CD-ROM device 24 has a function of reading information stored in advance in a CD-ROM 242 as a recording medium into the computer. The CD-ROM 242 stores in advance a push-pull mixed optimum combined production planning program 241 for realizing an optimum production plan by the push-pull mixed optimum combined production planning method. It is assumed that the program 241 is read from the CD-ROM 242 into the computer by the CD-ROM device 24 and stored (installed) in the HDD 23. The program 241 can be downloaded to the HDD 23 via a communication line (not shown). The keyboard 25 is an input device for inputting production data and the like necessary for generating an optimal schedule, and the display 26 is an output device for display. In the present embodiment, the functional configuration of the mixed production management system of FIG. 1 is that the CPU 21 reads the push / pull mixed optimal combined production planning program 241 installed in the HDD 23 onto the main memory 22 and executes the program 241. It is realized by.

  FIG. 3 shows an example of a mixed production system (push / pull mixed type combined production system) that permits push-pull mixed type production to be managed by the combined production management system of FIG. In FIG. 3, a circled number represents an item. Item 0 indicates the market (outside the system). Of items 11 to 23, items 16, 17, and 18 are final items of the ordered items. The items 22 and 23 are the final items of the prospective products. Note that the items 16, 17, and 18 may be fictitious items for collectively processing orders or incorporating them into a plan. 3 is a multi-item multi-step production system in which items 1 to 23 are processed by machines 1 to 12, and is an order assembly process 301 that is a pull-type process (process) and a push-type process. A prospective product assembly process 302, a key device production process 303 that is a push-type process, and a general parts procurement process 304 that is a pull-type process. A key device is a product that has the characteristics of a company that can only be produced by that company, a key product of the business, and it is produced systematically. General parts can be made in time even after they are ordered. Item 2 is produced by both machine 1 and machine 2, item 14 is produced by both machine 7 and machine 8, and item 20 is produced by both machine 10 and machine 11. However, it is not produced by both machines at the same time, but only by one machine at a time.

The optimization scheduling algorithm is described in Patent Document 1 or Non-Patent Document 1. However, this algorithm is an important algorithm that is used to realize an optimum production plan by the push-pull mixed optimum mixed production planning method. Therefore, the optimization scheduling algorithm will be described below.
(Symbol used)
First, symbols used in the optimization scheduling algorithm (symbols described in Patent Document 1 or Non-Patent Document 1) are summarized below.
(1) Subscripts and their sets First, subscripts and their sets applied in this embodiment are defined as follows.
i: Item or its processing number, i∈I (1, 2,..., n _i )
Where i = 0 represents a market (outside the system) k: machine number, kεK (1, 2,..., N _k ) t: time slot number, tεT (1, 2,..., N _t ) A: Set of work-in-progress items S (i): Set of subsequent direct connection points of item i K (i): Set of machines that can be used to process item i M (i): Set of items that machine k can process Set P (i): Set of preceding direct connection points of item i (2) Input data Next, preset input data (production data and requested shipping quantity data) applied in the present embodiment are as follows. Defined in
p _i ^k : processing amount of item i per time slot in machine k s _imax ^k : setup time for item i of machine k s _i0 ^k : remaining time of setup in time slot t = 0 of machine k and item i, That is, initial value x _i0 : actual inventory quantity of item i at time slot t = 0, 0 for problems that do not have inventory δ _i0 ^k : processing of item i at machine k at time slot t = 0 State, that is, initial value r _i0t : Shipment request amount data indicating the external demand of the item i in the time slot t, which is drawn out of the system as, for example, a repair part (for the sake of simplification of explanation in this embodiment) , R _i0t = 0 for items i other than the final item (product))
ρ _ij : the required amount of the item i to be incorporated into the item j per unit of the item j c _i ^k : the setup cost of the item i in the machine k h _i : time for the value newly added by the processing of the item i Inventory storage cost per slot (Echelon inventory storage cost)
r _ijt : requirement of item i used to produce item j in time slot t r _{i · t} : requirement of item i in time slot t τ _ij : lead of item i until it is incorporated into item j Time (3) Decision variable and state variable Next, the decision variable and the state variable are defined as follows.
δ _it ^k : a decision variable (primitive object) indicating the processing (“processing or not”) of the item i of the machine k in the time slot t. A decision variable (primitive object) is a plurality of subscripted 0 or 1 variables (0-1 variables), which are not meaningful by themselves. Represent. For example, if a consecutive time slot for an item and machinery takes the value 1, it represents the size of the lot.
δ _it ^k is 1 when item i is processed by machine k in time slot t, 0 otherwise
Where δ _it is a vector having δ _it ^l , l∈K (i) as elements,
δ _i = (δ _i1 ,…, δ _it ,… δ _int )
δ = (δ ₁ ,…, δ _i ,… δ _ni )
s _it ^k : remaining time for setup of machine k in time slot t of item i
0 ≦ s _it ^k ≦ s _imax ^k
here,
s _it is a vector whose elements are s _ti ^l and l∈K (i)
s _i = (s _i1 , ..., s _it , ... s _int )
s = (s ₁ , ..., s _i , ... s _ni )
x _it : Apparent stock quantity of the item i at the end of the time slot t. The definition formula is expressed as follows.

Note that x _i0 is a value at the time slot t = 0 of the apparent stock quantity x _it , that is, an initial value for the work in progress iεA. However, in equation (1), x _i0 represents the actual initial inventory.

<Restrictions>
Next, constraint conditions used in the above optimization scheduling algorithm will be described. As described in the above documents (Patent Document 1 or Non-Patent Document 1), various interrelation constraints are prepared in order to combine the partial optimization problems and configure the whole as one problem.
(1) Relationship between various requirements The requirement of item j is expanded to item i in consideration of the lead time τ _ij of item i until item i is incorporated into item j. Here, item i is a work in progress. Therefore, r _ijt is expressed by the following equation (2) using ρ _ij and r _{j · (t−τij)} reflecting the lead time τ _ij . Further, r j _{· t} is expressed by the following equation using the r _ijt and _r i0t (3).

In the above equation (3), r _{j · t} is expressed by the sum of the cumulative amount indicated by the first term on the right side and the amount drawn outside the system in the time slot t indicated by the second term on the right side. Yes. The first term on the right side is the sum of the required amount r _ijt of the item i used to produce the item j in the time slot t for all items j included in S (i), that is, the subsequent process (following direct connection point) ) Represents the amount incorporated into item j.

(2) State transition Transition equation of the remaining time of the machine setup time (remaining setup time):
As described above, s _it ^k represents the remaining setup time (remaining setup time) of each item i in the time slot t. s _it ^k is s _it ^k = 0 when the machine (production line) is idle, and is changed when the item is switched, that is, when the processing state is changed from δ _{it -1} ^k = 0 to δ _it ^k = 1. _imax ^k . Thereafter, s _it ^k decreases by 1 every time when one time slot elapses until it becomes 0, and thereafter, the state is maintained until switching occurs again. Therefore, s _it ^k follows:

Inventory transition equation:
Actual processing of each item i in the time slot t is limited to a state ^where δ _it ^k = 1 and s _it ^k = 0. Therefore, the inventory transition follows the following formula.

In the above equation (5), x _it is a required amount based on the sum of the apparent inventory amount (first item on the right side) of the item i at the end of the time slot t-1 and the processing amount (second item on the right side) in the time slot t. It is expressed as r _{i · t} (right side third term) minus. r _{i · t} is the required amount of time slot t obtained by developing external demand. Thus, x _it for work in process I∈A, it represents the amount of stock apparent in the time slot t end. However, x _it represents the actual stock for t = 0. The x also represents the actual stock on the final product.

Restrictions on mechanical interference:
In any time slot t, machine k can process at most one item. During the setup or processing of one item, it is not possible to set up another item. This restriction is called a restriction on mechanical interference, and the following equation must be satisfied.

Conditions for preventing out of stock (restrictions on out of stock restrictions):
Out of stock is not allowed for any item i in any time slot t. This is called the non-negative condition of inventory. For the final item, the apparent inventory simultaneously represents the actual inventory. For this reason, the non-negative condition of inventory is handled explicitly in the partial optimization problem. However, for work-in-progress, the actual work-in-progress must be formulated and a non-negative condition for this must be set.

The work-in-process inventory amount of the item i in the time slot t is an amount obtained by subtracting the accumulated payout amount from the sum of the initial inventory amount x _i0 and the accumulated production amount. However, the quantity r _i0t shipped directly to the outside must be deducted in advance. Therefore, the non-negative condition of the work-in-process inventory quantity of the item i in the time slot t is expressed by the following equation.

  The second term on the left side of the above equation (7) is the cumulative amount up to the end of the time slot t of the processing amount obtained by subtracting the amount shipped directly from the processing amount of the item i in each time slot, that is, the cumulative production amount. Represent. The third term on the left side represents the cumulative payout amount up to the end of time slot t.

However, when the item is a final product, only the parts of the first term and the second term on the left side of Equation (7) are provided. By substituting the apparent inventory quantity definition formula (1) into the constraint formula of the above formula (7), the following formula is obtained.

Here, the second term on the left side disappears as a value 0 from the equations (2) and (3) when the lead time τ _ij = 0.

Restrictions on the number of machines that can be used:
The number of machines that can be used simultaneously is limited to at most c. Therefore, the following formula must be satisfied.

<cost>
There are two types of costs associated with scheduling problems. One is the setup cost c _i ^k that is incurred when machine k switches to item i. Another is the echelon inventory holding cost h _i generated in proportion to the amount of inventory x _it apparent to each end of each time slot t. These are represented by c _i ^k (1−δ _it−1 ^k ) δ _it ^k and h _i x _it , respectively. Therefore, if the cost of the item i in the time slot t is represented by f _i (δ _i , s _i , x _i ), the cost f _i (δ _i , s _i , x _i ), that is, the cost function for the item i is It is represented by (10).

Here, the cost in the time slot t also depends on the decision variable δ _it−1 ^k in the time slot t−1.

<problem>
As a result, the optimization problem to be dealt with in the end is that the value of the function representing the sum of all items of the cost f _i (δ _i , s _i , x _i ) of Equation (10), that is, the value of the objective function is constant. Is to be minimized under the constraints of. Therefore, the optimization problem is formulated as

  It should be noted that st (4), (5), (6), (8), (9) in equation (11) is a problem to be handled in equations (4), (5), (6), (8). , (9).

《Solution based on Lagrangian decomposition adjustment method》
<Handling of constraints>
This problem is related to equations (2), (3), (4), (5), (6), (8), and (9) as constraints. In the solution proposed here, these constraints are handled in two ways. The first is taken into the subproblem and handled explicitly when solving each problem. The second is related to a plurality of subproblems as a mutual relation constraint.

  Expressions (2) and (3) represent the relationship between input data and do not include a decision variable, and therefore do not fall into any of the above. Equations (4) and (5) are transition equations and are specific to the item. Therefore, equations (4) and (5) are indispensable when solving the item-specific subproblem by dynamic programming. They therefore belong to the first type. The machine constraint equation (9) that can be used simultaneously (once) is also unique to the item. Therefore, equation (9) also belongs to the first type, and is also handled in the partial problem.

  However, the equation (6) relating to the mechanical interference relates to a plurality of items. For this reason, Expression (6) belongs to the mutual relationship constraint that is the second type. Next, attention should be paid to the constraint equation (8) for avoiding out of stock. That is, when the item is the final item, since the third term on the left side is not related in Expression (7), the processing is independent from the beginning. In this case, inventory non-negative constraints can be handled explicitly in the subproblem. On the other hand, if the item is a work-in-progress, the above item 3 is related and the independence of processing is violated. In this case, inventory non-negative constraints cannot be handled in the subproblem. Therefore, in the present embodiment, the expression (8) is treated as a mutual relationship constraint that is the second type in order to guarantee processing consistency.

<Lagrange function>
The Lagrangian function shown in the following equation is derived by relaxing the interrelationship constraint, that is, the mechanical interference constraint (6) and the non-negative constraint (8) on the work-in-process inventory.

Here, μ _t ^k and λ _it are Lagrange multipliers representing penalty costs (line usage fees) for the machine interference constraint condition (6) and the non-negative condition (8) of the work-in-process inventory, respectively. Here, μ _t is a vector whose elements are μ _t ^l and lεK (i), and μ = (μ ₁ , μ _t ,..., Μ _nt ). Similarly, λ _{i is} also a vector, and λ _i = (λ _i1 ,..., Λ _it ,..., Λ _int ), λ = (λ ₁ ,..., Λ _i ,..., Λ _nt ).

<Lagrange issue>
After all, the problem of the above equation (11) in which the equations (2), (3), (4), (5), (6), (8), (9) are related as constraints is as follows: It is equivalent to the Lagrangian problem shown in 13). This equation (13) is expressed by the equation (4) in the constraint equations (2), (3), (4), (5), (6), (8), (9) related to the equation (11). ), (5), (9) are constraints.

Here, in order to resolve the problem by item, Equation (12) is first arranged for item i, and the following Lagrangian function is derived.

Here, if a (i) is expressed as 1 when the item i has a subsequent direct connection point (that is, it can be a work-in-progress), and 0 otherwise, the above equation (14) is expressed as the following equation: be able to.

<Partial optimization problem>
From the above equation (15), the problem represented by equation (11) can be decomposed into the following subproblem (partial optimization problem) for a given μ and λ. In other words, the global optimization problem can be decomposed into a partial optimization problem by paying attention to the possibility of adding and separating problems. As a result, it is possible to reduce the mathematical dimension of the partial optimization problem and shorten the calculation time.

  The partial optimization problem shown in equation (16) for item i can be solved independently for others for a given μ, λ. This solution will be described later.

<Adjustment of Lagrange multiplier>
In the present embodiment, as Lagrange multiplier, two and mu _t ^k and lambda _it is used. For this reason, the update of the Lagrange multiplier at the νth iteration of the iterative calculation requires two rules: an update rule for the Lagrange multiplier used for machine interference and an update rule for the Lagrange multiplier used for inventory fulfillment of work in progress.

Update rules for Lagrange multipliers used for machine interference:
First, a Lagrange multiplier update rule used for mechanical interference is as shown in the following equation.

Update rules for Lagrange multipliers used to fulfill work in process inventory:
Next, the update rule of the Lagrange multiplier used for stock fulfillment of work in progress is as shown in the following equation.

  In the above equation (18), α and β are scalar step sizes. The values of α and β are determined by trial and error by numerical calculation. Here, α and β can be made to depend on k (machine) and i (item), respectively.

《Dynamic programming of partial optimization problem》
Next, a method for resolving the partial optimization problem represented by Expression (16) by re-formulation into dynamic programming will be described.

<Available conditions>
The decision δ _it ^k that can be taken in time slot t is not only dependent on the inventory status x in the preceding time slot t−1. That is, the decision δ _it ^k also depends on the state of all available machines in the preceding time slot t−1 and the remaining setup time s _it−1 ^k in the same time slot t. The state that (δ _it ^k , s _it ^k ) is (0, 0) (first state) can be taken in the next time slot is the same first state or state (1, s _imax ^k ) ( 2nd state). The first state indicates that machine k is idle. The second state indicates when the item is switched, that is, when the setup is started. The second state, that is, the state (1, s _imax ^k ) that can be taken in the next time slot is only the (1, s _imax ^k −1) state (third state). The third state indicates that one time slot has elapsed since the start of setup and the remaining setup time is s _imax ^k −1. Hereinafter, similarly, each time the time passes one time slot, at [delta] _it ^k is left 1 state of the ^{_{(δ it k, s it k}} ), only s _it ^k decreases by 1 . Eventually, (δ _it ^k , s _it ^k ) transitions to the (1,1) state (fourth state). The fourth state is that the remaining setup time is 1 (for one time slot), indicating that the state is just before the end of setup. A period from the second state to the fourth state is a period during setup (during production). The state that the fourth state, ie, the state (1, 1) can take in the next time slot is only the state (5, 0). The state that the fifth state, ie, the (1, 0) state can take in the next time slot is either the same fifth state or the (0, 0) state (first state).

<Optimum cost function and its calculation>
Next, the optimal cost function and its calculation will be described. In this embodiment, for a given Lagrangian multiplier μ, λ _i , the optimal cost function is V _t (δ _it , s _it , x _it , μ, λ _i ).
Represented by This optimal cost function V _t is defined as the sum of the costs that accompany the optimal decision taken in each time slot from time slot 0 to time slot t. However, in the time slot t, _it is assumed that the decision variable (the machine setting state), the remaining setup time, and the inventory state (the inventory amount at the end of the time slot) of the item i are δ _it , s _it , and x _it , respectively. .

What is important here is that, in addition to the vector s _it and the variable x _it , the vector δ _{it of the} decision variable is included in the optimal cost function as the vector of the state variable. That is, the decision variables [delta] _it is that it also plays the role of the state variable. This is due to the fact that the setup cost generated in time slot t also depends on the determination of time slot t-1. In other words, the information in the preceding time slot t-1 is necessary to calculate the cost occurring in the time slot t. In this case, the optimal cost function can be expressed by the following recursive relational expression by dynamic programming.

Here, when x _it-1 is not within the allowable range, V _t (δ _it , s _it , x _it , μ, λ _i ) is always given for any δ _it-1 ^k , s _it-1 ^k . + ∞. At this time, _it is assumed that δ _it-1 ^* (δ _it , s _it , x _it , μ, λ _i ) represents the optimum determination of the above equation (20).

If s _it ^l = 0 (lεK (i)), then the decision δ selected as given δ _it ^l , s _it ^l (lεK (i)), x _it , μ, λ _{i If it is} determined that s _it-1 ^k and x _it-1 from the equations (4) and (5) for _it-1 ^l (l∈K (i)), the optimal cost function in the time slot t-1 The value is determined. However, s _it ^l = 0, the state of the s _it s in time slot t-1 transitioning to the state of the ^l = 0 _it-1 ^l is, s _it-1 ^l = 0 and s _it-1 ^l = It cannot be specified which of 1 is taken. Therefore, in order to deal with this, the minimum value (min) represented by the above equation (20) is determined for s _{it-1 in} addition to δ _it-1 . On the other hand, all costs incurred in time slot t are fixed. Therefore, the above equation (20) can be calculated.

<Determination of optimal solution>
Now, for the item i, the optimal cost function value V _t (δ _it , s _it , x _it , μ, λ _i ) of the above equation (20) and the optimal determination, that is, δ _it-1 ^* (δ _it , s _it , _Assume that x _it , μ, λ _i ) are all obtained for each time slot t (t = 1,..., n _t ). Also, V _t (δ _it , s _it , x _it , μ, λ _i ) and δ _it-1 ^* (δ _it , s _it , x _it , μ, λ _i ) for each time slot of item i are For example, it is assumed that it is stored in a memory (here, cost storage area 223) in the form of a table. Further, for s _it ^l = 0 (lεK (i)), the optimum remaining setup time s _it-1 ^* (δ _it , s _it , x _it , μ, λ _i ) is also stored in the memory. Are stored in the same manner. The procedure for determining the optimal solution for the item, that is, the schedule and the state transition at this time is shown in FIG.

  The optimization scheduling algorithm applied in the present embodiment has been described above.

  Next, the configuration of the system of FIG. 1 will be described. The complex production management system of FIG. 1 applies a main control unit 11, a pre-processing unit 12, and the like in order to execute the optimum production plan by the push-pull mixed optimum complex production planning method by applying the above optimization scheduling algorithm. And a multi-item multi-process lot size scheduling unit 13. Each of these units 11 to 13 is a functional element realized by the CPU 21 in the computer of FIG. 2 executing the push-pull mixed type optimal combined production planning program 241.

  The main control unit 11 includes an input / output control unit 111, a production plan control unit 112, and a scheduling control unit 113. The input / output control unit 111 inputs various system parameters necessary for optimum production planning, various data necessary for production planning (phase 1 planning), and various data necessary for scheduling (phase 2 planning) by user operation. To control. The production plan control unit 112 sets a production plan mode for drafting a production plan (phase 1 plan), and generates an optimum production plan using the preprocessing unit 12 and the multi-item multi-process lot size scheduling unit 13. To control. The scheduling control unit 113 sets a scheduling mode for creating a scheduling (phase 2 plan), and generates an optimum production schedule using the preprocessing unit 12 and the multi-item multi-process lot size scheduling unit 13. Take control. The preprocessing unit 12 performs preprocessing for the production plan for each production plan (phase 1 cycle). The preprocessing unit 12 performs preprocessing for the scheduling every scheduling (phase 2 cycle). The multi-item multi-process lot size scheduling unit 13 generates an optimal production plan for each production plan (phase 1 cycle) using an optimization scheduling algorithm. Similarly, the multi-item multi-process lot size scheduling unit 13 generates an optimal production schedule using an optimization scheduling algorithm for each scheduling (phase 2 cycle).

  The multi-item multi-process lot size scheduling unit 13 includes an optimization unit 131, an inventory amount extraction unit 132, a remaining setup time extraction unit 133, a machine interference determination unit 134, a machine interference control unit 135, and an optimal production plan. / Schedule generation unit 136, satisfaction determination unit 137, and inventory control unit 138. The optimization unit 131 solves the partial optimization problem of Expression (16) for each item i independently of other items, and executes an operation for obtaining the solution. At this time, the optimization unit 131 solves the partial optimization problem using the optimal cost function of Expression (20) under the constraints of inventory transition and remaining setup time transition. The inventory quantity extraction unit 132 extracts an inventory quantity necessary for the operation of the optimization unit 131. The remaining setup time extraction unit 133 extracts the remaining setup time necessary for the operation in the optimization unit 131.

The machine interference determination unit 134 determines whether the machine interference can be considered to be eliminated from the solution for each item i obtained by the optimization unit 131. The machine interference control unit 135 controls the optimization unit 131 so that the machine interference is reduced when the machine interference is not eliminated. Specifically, the Lagrange multiplier (μ _t ^k ) necessary for the control (adjustment) of the machine interference in the optimal cost function used by the optimization unit 131 is updated.

The sufficiency determination unit 137 determines whether the work-in-process inventory is satisfied from the solution for each item i obtained by the optimization unit 131. The inventory control unit 138 controls the optimization unit 131 so that the work-in-process inventory is satisfied when the work-in-process inventory is not satisfied, that is, when the work-in-process inventory is out of stock. Specifically, the Lagrangian multiplier (λ _it ) necessary for the control (adjustment) of the work in progress in the optimal cost function used by the optimization unit 131 is updated. When it is determined that the machine interference and the out-of-stock inventory of the work-in-process inventory have been eliminated, the optimum production plan / schedule generation unit 136 generates a production plan or a production schedule using the solution obtained at that time.

In the main memory 22, a system parameter storage area 220, a production data storage area 221, a scheduling data storage area 222, and a cost storage area 223 are secured. The area 220 is used to store various system parameters described later. Area 221 is used to store production technology data. This production technology data includes data of p _i ^k , s _imax ^k , c _i ^k (second production technology data) for each item i and machine k, and s _i0 ^k , δ _i0 for each item i and machine k. ^k , c _i ^k data, x _i0 , ρ _ij (first production technology data) by item i, h _i , τ _ij data by item i, and item i R _ijt , r _{i ·} t in each time slot t. The area 222 is used to store data (inventory storage cost data, beginning inventory data, target period end inventory data, demand forecast data, and firm order data) necessary for the production plan (phase 1 plan). The area 223 includes a cost sum V _t (δ _it , s _it , x _it , μ, λ _i ) calculated by the optimization unit 131 and the sum V _t (δ _it , s _it , x _It is used to store δ _it ^* , s _it ^* , x _it ^* corresponding to _it , μ, λ _i ) in tabular form. Here, _it is also possible to secure a separate area for storing δ _it ^* , s _it ^* , and x _it ^* .

  The main memory 22 further includes an intermediate result storage area 224, a final result storage area 225, and a production plan / schedule storage area 226. The area 225 is used to store an intermediate result of the solution obtained by solving the optimum subproblem by the optimization unit 131. The area 226 is used to store the final result of the solution obtained by solving the optimum subproblem by the optimization unit 131. The area 227 is used to store a production plan or production schedule generated by the optimum production plan / schedule generation unit 136.

  Next, in the mixed production management system shown in FIG. 1, the optimum production plan and optimum applied to the mixed production system as shown in FIG. 3 by the push-pull mixed type optimum mixed production planning method (two-stage production planning method). An outline of the operation when planning a production schedule will be described. This will be described with reference to FIG.

  First, in the production plan 401 that is the first-stage plan (phase 1 plan), an optimal production plan is generated by the multi-item multi-process lot size scheduling unit 13. The production plan 401 is repeated until the end condition of the production plan 401 is satisfied. The target period (plan target period) 402 of the production plan 401 is set to a relatively long period (for example, one year). A period from the planning point (planning point) 403 of the production plan 401 to the start point (start) of the planning target period 402 of the production plan 401 is referred to as a planned lead time 404. In the repetition of the production plan 401, a period from the planning time 403 of a certain production plan 401 to the planning time 403 of the next production plan 401 is referred to as a plan cycle time 405.

  On the other hand, in the scheduling 411 that is the second-stage plan (phase 2 plan), an optimal production schedule is generated by the multi-item multi-process lot size scheduling unit 13. The scheduling 411 is repeated each time the production plan 401 is executed until the end condition of the scheduling 411 is satisfied. The target period (plan target period) 412 of the scheduling 411 is set to a shorter period (for example, two weeks) than the plan target period 402 of the production plan 401. A period from the planning time point (planning time point) 413 of the scheduling 411 to the start time point (start) of the planning target period 412 of the scheduling 411 is referred to as a planned lead time 414. In the repetition of the scheduling 411, a period from the planning time 413 of a certain scheduling 411 to the planning time 413 of the next scheduling 411 is referred to as a planning cycle time 415.

  Of the inventory level change data for each time slot obtained by the execution of the production plan 401, the stock level data 406 for each time slot corresponding to the end of the plan target period 412 (the end of the plan target period) in the scheduling 411 Gives the target inventory level at the end of the period in the scheduling 411 (target period end inventory level). The inventory level by item at the beginning of the planning target period 402 of the production plan 401 is the time corresponding to the beginning of the planning target period 402 among the transition data of the inventory level by item for each time slot obtained by executing the latest scheduling 411. It is given by the stock level data 416 of each slot item.

  In the scheduling 411, the multi-item multi-process lot size scheduling unit 13 is used for both the shipping request amount (final shipping data) in the scheduling target period 412 and the item-specific target period end stock level given by the data 406. Optimal scheduling is performed. Here, the inventory level by item at the beginning of the planning target period 412 of the scheduling 411 (initial inventory level by item) is the transition data of the inventory level by item for each time slot obtained by executing the preceding scheduling 411, It is given by the stock level data 417 of the item of the time slot corresponding to the beginning of the planning target period 412.

  The compound production method is a method of producing two or more items including two types of order items and prospective products using the same process in common. Suppose that there are time fluctuations such as fluctuations, switching between new and old products.

  The complex production method is a configuration with items that are produced in the previous process and used in common for the ordered and prospective products (for example, common parts and semi-finished products before coloring), and demand for at least one item. Suppose that there is time variation such as seasonal variation.

  The compound production method is a method of producing two or more items including two types of order items and prospective products using the same process in common. There is a configuration with items that are produced in the previous process and used in common for both types of prospective items and order items (for example, common parts and semi-finished products before coloring), and demand for at least one item Suppose that there is time variation such as seasonal variation.

  The characteristics of the above-described push-pull mixed type optimal combined production planning method (two-stage production planning method) are summarized below. First, in the optimum composite production planning method, the multi-item multi-process lot size scheduling unit 13 is used not only for scheduling but also for production planning. According to this planning method, (1) the resolution of the production plan itself can be increased to the same level as scheduling. (2) Despite increasing the resolution, the calculation time is set to a reasonable time (scheduling calculation). Time x production planning plan period / scheduling plan period) (3) The resolution is improved and the problem is solved by formulating it with few artificial constraints in advance. The effect of being able to optimize a different aspect of determination using a multi-item multi-process lot size scheduling algorithm can be expected. As a result, it is possible to obtain a special effect that the simulation function and the optimization function can be simultaneously incorporated into the production plan. For example, in an existing production inventory plan, a fixed standard lead time and a fixed lot size registered in advance based on a time bucket, and these items are used to guarantee the feasibility of the plan in advance. The fixed standard lead time is set longer. Therefore, there is a defect in which the accumulated lead time of each item, which should be able to be shortened depending on the method of processing, is already set longer than actual at the stage of developing the required amount. In addition, the name of the plan is a production inventory plan, but the limit to the adjustment of the load level is the limit, and it has not succeeded in handling the situation of processing between processes. On the other hand, in this embodiment, there is no concept of a time bucket, and a plan can be made without registering a fixed lead time and a fixed lot size in advance. Therefore, both the item lead time and the item lot size are determined to be time variant depending on the situation for the first time when the problem is solved by the optimization scheduling algorithm. This plan is different from the actual one in that demand data is not fixed but forecast data. In this sense, it can be said that the proposed method has a simulation function and an optimization function.

  In addition, it is possible to level up seasonal fluctuations by accumulating work-in-progress, inventories and product inventories by moving ahead of the production peak toward the busy season. Of the two-stage plans, the target period for the second stage in the first-stage scheduling (phase 2 plan) is longer than the second-stage production plan (phase 1 plan). By optimizing the inventory, a more optimal and robust production management system can be realized. By obtaining the boundary conditions for obtaining the optimal production scheduling of the second stage optimally in the production plan of the first stage, it is possible to further ensure the overall optimization.

  Next, system parameters applied in the complex production management system of FIG. 1 will be described. System parameters are roughly classified into production planning (phase 1 planning) parameters and scheduling (phase 2 planning) parameters. The production plan parameters include a production plan time slot and a plan target period 402, a plan lead time 404 and a plan cycle time 405 shown in FIG. The scheduling parameters include a scheduling time slot, and a planning target period 412, a planning lead time 414, and a planning cycle time 415 shown in FIG. Here, in order to facilitate management, the time widths of the time slot of the production plan and the time slot of the scheduling are set to the same value.

  Next, the procedure of the push-pull mixed type optimal combined production planning method will be described with reference to the flowchart of FIG. First, in order to make an optimum production plan and an optimum production schedule by the complex production management system of FIG. 1, it is necessary for the user to determine various system parameters. The input / output control unit 111 in the main control unit 11 determines (defines) a predetermined type of system parameter for each of the production plan and scheduling for the user (production manager) of the complex production management system of FIG. ) Is displayed on the display 26, for example, and the corresponding system parameter is determined (defined) through the screen (step S1). Here, system parameters are input by the user operating the keyboard 25, but a system parameter file may be input via a storage medium, a network, or the like.

  In step S1, the planning target period, the planning lead time, the planning cycle time, and the time slot of the production plan are defined as system parameters specific to the production plan, and the scheduling target period, the planning lead are set as system parameters specific to scheduling. Time, planned cycle time and time slot are defined. Here, one year is defined as the planning target period of the production plan. However, to simplify the explanation, it is assumed that one month is four weeks and one year is 48 weeks. Also, two weeks are defined as the scheduling target period. That is, the scheduling target period of scheduling is 1/24 of the planning target period of the production plan. As the time width of the time slot of the production plan and scheduling, the plan target period of production plan / 2640 = the schedule target period of scheduling / 110 is defined. That is, 2640 and 110 are defined as the number of time slots in the planning target period of each of the production plan and scheduling. Each system parameter is stored in the system parameter storage area 220 of the main memory 22 by the input / output control unit 111.

  When step S1 is executed, the production plan control unit 112 in the main control unit 11 sets the system shown in FIG. 1 to the production plan mode (phase 1). The input / output control unit 111 in the main control unit 11 prepares data for production planning in the production planning mode (step S2). Here, as the data for the production plan, there are first and second production technology data, inventory storage cost data, opening inventory data, target period end inventory data, demand forecast data, and firm order data. Be prepared.

The first production technology data is data indicating the required amount ρ _ij per unit of the item j of the item i to be incorporated in each item j, and is prepared, for example, in a table format shown in FIG. The second production technology data includes data indicating the processing amount p _i ^k of the item i per time slot in each machine k, data indicating the setup time s _imax ^k for the item i of the machine k, and items of the machine k. i includes data indicating the setup cost c _i ^k of, are provided in tabular form as shown in FIG. 7, for example.

The inventory storage cost data is data indicating the inventory storage cost h _i of each item i, and the beginning inventory data is the inventory amount (inventory level) at the time slot t = 0 of the production plan of each item i (the beginning of the target period of the production plan). ) Data indicating x _i0 . Stock goal period end inventory data to target in the time slot t = n _t of production plans for each item i (end of the time horizon of the production plan) data indicating the (target period end stock) z _int, forecast data is a forecast value D _i ^m monthly considering seasonal variation of the end item i. The inventory storage cost data, the beginning inventory data, the target period end inventory data, and the demand forecast data are prepared, for example, in a table format shown in FIG.

  In the first production plan, the tabular data in FIGS. 6 to 8 is input by the input / output control unit 111 when the user operates the keyboard 25, for example. 6 and 7 are stored in the production data storage area 221, and the table data in FIG. 8 are stored in the scheduling data storage area 222, respectively. The data in the table format shown in FIGS. 6 to 8 may be managed as a file, and the file may be input via a storage medium or a network. In the case of the second and subsequent production plans, the inventory level data by item (data 417 in FIG. 4) of the corresponding time slot t in the latest production schedule is used as the initial inventory data.

The demand forecast data includes, for example, monthly demand forecast values (monthly demand forecast values) used over the year for each final item (product) i shown in FIG. It is created by multiplying the product by the seasonal index of the product (that is, the seasonal index by product). Even if the demand forecast data is prepared by the user's operation, the monthly demand forecast value prepared in the table format shown in FIG. 9 and the seasonal index for each product prepared in the table format shown in FIG. In addition, it may be configured to be generated by the preprocessing unit 12. The confirmed order data indicates the order quantity given for each time slot for the confirmed order item i. For example, it is prepared in a table format shown in FIG. Here, the confirmed order data indicates the order quantity given for each time slot with respect to the confirmed ordered items (here, items 16, 17, and 18). In addition to the firm order data, the tabular data in FIG. 11 is data indicating the initial inventory level for each item in scheduling, that is, in the scheduling time slot t = 0 of each item i (the beginning of the scheduling target period). Includes data (initial inventory data) indicating the inventory quantity x _i0 . Tabular data further in FIG. 11, the target in-item target period end data indicating the inventory levels, i.e. scheduling of each item i time slot t = n _t (end of the time horizon of the production plan) in the scheduling Stock It includes data (target period end inventory data) indicating quantity (target period end inventory) z _int .

  When step S2 is executed, the production plan control unit 112 in the main control unit 11 sets the system in FIG. 1 to the production plan mode (phase 1). Then, the production plan control unit 112 activates the preprocessing unit 12. In the production planning mode, the preprocessing unit 12 performs preprocessing for production planning as follows (step S3). First, the preprocessing unit 12 disassembles the demand forecast data included in the tabular data shown in FIG. 8, that is, the demand forecast value for each item and for each month (step S3a). Next, the pre-processing unit 12 determines the confirmed order data included in the tabular data shown in FIG. 11, that is, the order quantity given for each confirmed time order item for each time slot. Add to the predicted value (step S3b). Next, the preprocessing unit 12 generates the demand forecast data in which the confirmed order data is reflected, that is, the demand forecast value for each item and the time slot in which the order quantity is reflected in the first production in the table format shown in FIG. The parts are developed based on the technical data (step S3c). Parts expansion of demand forecast data means converting demand forecast values for each item and time slot into data in the form of a table that shows demand forecast values for each item including parts and for each time slot. is there. FIG. 12 shows an example of demand forecast data broken down by time slot after the parts development. The demand forecast data disassembled for each time slot after the parts development is stored in the scheduling data storage area 222 of the main memory 22.

  As described above, the preprocessing for the production planning by the preprocessing unit 12 is performed, and the demand forecast data decomposed for each time slot after the parts development is stored in the scheduling data storage area 222 of the main memory 22 And Then, the production plan control unit 112 includes the first and second production technology data shown in FIGS. 6 and 7 stored in the production data storage area 221 of the main memory 22 and the scheduling data storage area of the main memory 22. The multi-item multi-process lot size scheduling unit 13 generates an optimum production plan using the demand prediction data disassembled for each time slot after the parts expansion shown in FIG. 12 stored in 222 (step S4).

  Hereinafter, operations of the production plan control unit 112 and the multi-item multi-process lot size scheduling unit 13 will be described with reference to the flowchart of FIG. The flowchart of FIG. 13 corresponds to the flowchart of FIG.

First, the production plan control unit 112 sets the repetition number (repetition number) ν to an initial value 0 (step S11). In addition, the production plan control unit 112 determines the time slot t (tεT (1,2,..., N _t ) for each item i (i∈I (1,2,..., N _i )) on the intermediate result storage area 224. )) another and machine k (k∈K (1,2, ..., n k) ) of another, and setting the respective decision variable _{^δit kν} and s _it ^kν to an initial value 0 (step S12). Also, the production plan control unit 112 performs Lagrange multipliers μ for each time slot t (tεT (1, 2,..., N _t )) and for each machine k (kεK (1, 2,..., N _k )). _t ^{kν is} set ^to an initial value 0 (step S13). In this step S13, the Lagrange multiplier λ _t ^{ν for each} time slot t (tεT (1, 2,..., N _t )) is also set to the initial value 0.

The production plan control unit 112 activates the optimization unit 131 when executing steps S11 to S13. The optimization unit 131 first initializes the item i to 1 (step S14). Next, the optimization unit 131 solves the partial optimization problem shown in the equation (16) of the item i under the constraints of the remaining setup time transition equation (4) and the inventory transition equation (5) (step S15). . Here, the optimal cost function of Expression (20) is used to solve the partial optimization problem. Further, as a result of solving the partial optimization problem, for the item i, for each machine k available for processing the item i, the solution for each time slot δ _it ^kν (∀t∈T, k∈K (i) ) Is required.

FIG. 14 shows the detailed procedure of step S15. Here, in order to solve the partial optimization problem of the item i, the optimization unit 131 uses the optimum cost function value V _t (δ _it , s _it , x _it , μ, λ _i ) and the optimum determination δ _{it− described below.} Find ₁ ^* (δ _it , s _it , x _it ). Therefore, the optimization unit 131 first sets the time slot t to 1 (step S31). The optimization unit 131 then selects the optimal cost function value V _t (δ _it , s _it , x _it ) for all possible combinations (δ _it , s _it , x _it ) for the item i. , Μ, λ _i ) are calculated (step S32). The calculation of the optimum cost function value is executed by using the optimum cost function of the equation (20) in the range of the machine k that can be used for the processing (production) of the item i (kεK (i)). In the step S32, the calculated optimal cost function value V _t (δ _it , s _it , x _it , μ, λ _i ) is determined as the optimum determination δ _it-1 ^* (δ _it , s _it , x _It ) is stored in the cost storage area 223 in tabular form.

Next, the optimization unit 131 increments t by 1 (step S33). If t after the increment is not greater than n _t (step S34), the optimization unit 131 performs the processes of steps S32 and S33 on the t after the increment. The process of step S32, S33 is repeated until t = n _t (step S34).

Then, when t the incremented is greater than n _t, the optimization unit 131 sets t to n _t (step S35). The optimization unit 131, the optimal cost V _t of cost storage area _{223 (δ it, x it,} s it) follows a reversed from t = n _t. That optimization unit 131, as described above, first, t = n _t all [delta] _it may take against time slots, s _it, a combination of _{x it (δ it, s it} , x it) V _t from the _{(δ it, s it, x} it, μ, λ i) looking for a minimum value of (optimal cost), the time of δ _it, s _it, x _it the optimal solution δ _it ^*, s _it ^* , X _it ^* (step S36).

The optimization unit 131 then _{^{may, δ it *, s it *}} , x it * optimal decision to _{^{δ it-1 * (δ it}} *, s it *, x it *) for specifying the (step S37). The optimization unit 131 uses the δ _it ^* , s _it ^* , and x _it ^* to obtain s _it-1 ^* and x _it-1 ^* at the time slot t−1 immediately before the optimal cost V t is reached. (Step S38). Here, s _it-1 ^* and x _it-1 ^* are obtained by substituting δ _it ^* , s _it ^* , and x _it ^* into the equations (4) and (5). However, as described above, δ _it-1 ^* (δ _it , s _it , x _it , μ, λ _i ) for each time slot of the item i stored in the cost storage area 223 in a table format. It is also possible to obtain s _it-1 ^* and x _it-1 ^{* based} on. The optimization unit 131 repeats steps S36 to S38 until t = 1 while decrementing t by 1 (step S39) (step S40).

As described above, δ _it ^kν (t = 1,..., N _t , kεK (i)) giving the optimum cost for the item i is obtained by the optimization unit 131 (step S15). Then, the optimization unit 131 ^updates δ _it ^kν on the intermediate result storage area 224 to the latest obtained δit ^kν (step S16).

Next, the optimization unit 131 increments i by 1 (step S17). If i after this increment is not greater than n _i (step S18), the optimization unit 131 determines that there is an unprocessed item. In this case, the optimization unit 131 executes steps S15 to S17 for the item i indicated by i after the increment.

Eventually, when i after increment becomes larger than n _i , the optimization unit 131 solves all items of i = 1,..., N _i δ _it ^kν (∀i∈I, t∈T, k∈K ( i)) is determined to have been requested. In this case, the optimization unit 131 activates the mechanical interference determination unit 134 and the satisfaction determination unit 137.

For each machine k, the machine interference determination unit 134 ^calculates δ _it ^k = between each item i from solutions δ _it ^{kν of} all items i ( ^iεM (i)) processed (produced) by the machine k. The number of machine interferences representing the number of times one time slot overlaps is calculated. Here, the average number of mechanical interferences is calculated. The average number of machine interferences is the sum of the number of machine interferences over all items and all periods (all planning target periods) in the number of repetitions ν for all machines, n _t × n _k (total number of time slots × total number of machines) It is calculated by dividing by. The determination unit 14 determines whether the mechanical interference can be considered to be eliminated based on whether the calculated mechanical interference number (average mechanical interference number) is smaller than a predetermined threshold (step S19).

On the other hand, the satisfaction determination unit 137 calculates the total number of time slots in which the work-in-process inventory quantity is negative (that is, the non-negative condition is not satisfied) for all items i (i∈I (1, 2,..., N _i )). Ask. In step S19, the determination unit 18 determines whether the work-in-process inventory is satisfied from the total number of time slots obtained. Specifically, for all items, the total number of time slots in which the work-in-process inventory amount is negative is obtained. By dividing the total number of time slots by ni × nt (the total number of items × the total number of time slots), the average shortage of work-in-process inventory is obtained. Therefore, it is determined whether the work-in-process inventory is satisfied depending on whether this ratio is smaller than a predetermined threshold. Here, each work-in-process inventory quantity is calculated according to the above equation (8) using x _it that forms a pair with the corresponding solution δ _it ^kν obtained in step S15.

  If at least one of the condition that the machine interference is eliminated and the condition that the work-in-process inventory quantity is satisfied is not satisfied, the number of repetitions (the number of repetitions) v is incremented by 1 (step S20). ). Then, at least one of the machine interference control unit 135 and the inventory control unit 138 is activated. Here, the machine interference control unit 135 is activated when the machine interference is not eliminated, and the satisfaction determination unit 137 is activated when the work-in-process inventory amount is not satisfied. When both the above conditions are not satisfied, both the mechanical interference control unit 135 and the satisfaction determination unit 137 are activated.

When the machine interference control unit 135 is activated, the machine interference control unit 135 updates (adjusts) the Lagrange multiplier μ _t ^kν used for the machine interference according to the equation (17), and notifies the optimization unit 131 (step S21). On the other hand, when the satisfaction determination unit 137 is activated, the optimization unit 131 updates (adjusts) the Lagrange multiplier λ _t ^ν used for inventory satisfaction of the work in progress according to the equation (18) in step S21. Notify

Then, the optimization unit 131 repeatedly executes steps S15 to S17 for the number of items using the updated Lagrange multipliers μ _t ^kν and / or λ _t ^ν (step S18). As a result, a solution δ _it ^kν for each item and each machine is obtained for each time slot. Eventually, in step S19, it is assumed that the mechanical interference determination unit 134 determines that mechanical interference has been eliminated. In step S19, the satisfaction determination unit 137 determines that the work-in-process inventory amount is satisfied. Then, the item-specific and machine-specific solutions δ _it ^{kν at} that time are stored in the final result storage area 225, and the optimum production plan / schedule generating unit 136 is activated (step S22).

The optimum production plan / schedule generation unit 136 generates an optimum production plan based on the item-specific and machine-specific solutions δ _it ^kν stored in the final result storage area 225 and stores the optimum production plan in the production plan / schedule storage area 226. Store (step S23). As described above, the solution δ _it ^kν for each item and each machine is represented by a 0-1 variable. Therefore, in the production plan, the solution δ _it ^kν is obtained by processing (setting up or producing) the item i by the machine k in the slot for each item i and machine k for each time slot t engraved on the time axis. 1; otherwise, 0. Therefore, the optimum production plan / schedule generation unit 136 may generate a production plan that represents the lot size and the time position of each lot for each item and machine, based on the sequence of 1 in the solution δ _it ^kν and its time position. it can. The time position of the lot provides information for determining the lot order in a viable production plan. In other words, in this embodiment, when the solution δ _it ^kν that can be regarded as eliminating the machine interference of the solution (production plan) between items and that the work-in-process inventory amount is satisfied is obtained. , Lot size and lot order can be generated at the same time. Here, data indicating a Gantt chart for each item over the production plan target period is generated using the solution δ _it ^kν for each item for each time slot t and for each machine. In addition, the actual inventory y _{it for} each time slot of each item i is obtained as in the following equation according to the equation (8), and data indicating the inventory transition for each item over the production plan target period is generated.

  The data representing the production plan stored in the production plan / schedule storage area 226, that is, the data indicating the inventory transition for each item over the production plan target period and the data indicating the Gantt chart for each item over the production plan target period are: 2 is displayed on the display 26 in FIG. 2 by the input / output control unit 111, and is printed out from a printer device (not shown) in response to a print instruction input from the keyboard 25 or automatically (step S5). ). FIG. 15 shows an example of data indicating inventory transition by item.

  When step S5 ends, the production plan control unit 112 passes control to the scheduling control unit 113. Then, the scheduling control unit 113 sets the system of FIG. 1 to the scheduling mode (phase 2). In the scheduling mode, the input / output control unit 111 prepares data for scheduling in the same manner as in the previous production plan mode (step S6). Here, in addition to the first and second production technology data shown in FIGS. 6 and 7 and the confirmed order data shown in FIG. 11, the inventory storage cost shown in FIG. Data, beginning inventory data, and target period end inventory data are prepared. The initial inventory data is data indicating the initial inventory level for each item (or each process). In the case of the second and subsequent scheduling, the initial inventory data includes data (data 318 in FIG. 4) indicating the inventory level of the latest production schedule generated in the previous scheduling corresponding to the start time of the scheduling. Used. The target period end inventory data is data indicating the inventory level for each item (or for each process) at the end of the scheduling target period. For the target period end inventory data, data (data 407 in FIG. 4) indicating the inventory level by item (or by process) at the corresponding time point of the latest production plan is used. The beginning inventory data and the target period end inventory data are given in the form of a table shown in FIG. 11 together with, for example, confirmed order data.

  Data for scheduling prepared by the user (that is, first and second production technology data, inventory storage cost data, opening inventory data, target period end inventory data, and firm order data) are input / output controlled. In the production data storage area 221 and the scheduling data storage area 222 of the main memory 22 by the unit 111 (the first and second production technology data among the data for the production plan prepared by the user are stored in the production data of the main memory 22. In the area 221, the beginning inventory data, the target period end inventory data, and the confirmed order data are respectively stored in the scheduling data storage area 222 of the main memory 22.

  Then, the scheduling control unit 113 activates the preprocessing unit 12. In the scheduling mode, the preprocessing unit 12 performs preprocessing for production schedule planning as follows (step S7). That is, the pre-processing unit 12 develops the confirmed order data shown in FIG. 11 (that is, the order quantity given for each confirmed time order by time slot) based on the first production technology data in the table format shown in FIG. To do. Part expansion of firm order data is to convert the order quantity for each item and each time slot into data showing the order quantity for each item including the part and each time slot. Data). FIG. 16 shows an example of the order data after the parts development. The order data after parts development is stored in the intermediate result storage area 224 of the main memory 22.

As described above, it is assumed that the preprocessing for planning the production schedule by the preprocessing unit 12 is performed, and the received order data after the parts development is stored in the intermediate result storage area 224 of the main memory 22. Then, the scheduling control unit 113 stores the first and second production technology data shown in FIGS. 6 and 7 stored in the production data storage area 221 of the main memory 22 and the intermediate result storage area 224 of the main memory 22. The multi-item multi-process lot size scheduling unit as in the case of creating an optimum production plan by the control of the previous production plan control unit 112 using the order data after parts expansion shown in FIG. 13 generates an optimum production schedule according to the flowchart of FIG. 13 (step S8). Here, the solution δ _it ^kν for each item and machine is obtained for each time slot, and the solution for each item and machine when _it is determined that the machine interference has been resolved and the work-in-process inventory is sufficient. δ _it ^kν is stored in the final result storage area 225. Based on the item-by-item and machine-by-machine solutions δ _it ^kν stored in the final result storage area 225, the production schedule is set by the optimum production plan / schedule generation unit 136 in the multi-item multi-process lot size scheduling unit 13. Generated. This production schedule is stored in the production plan / schedule storage area 226 of the main memory 22.

  Data representing a production schedule stored in the production plan / schedule storage area 226, that is, data indicating inventory transition (FIG. 17) by item (or by family) over the scheduling target period, and by item over the scheduling target period (FIG. 17) Alternatively, the data indicating the Gantt chart (FIG. 18) for each family is displayed on the display 26 by the input / output control unit 111, and in response to a print instruction input from the keyboard 25 or automatically. It is printed out from (not shown) (step S9).

  In step S10, it is determined whether or not a phase 2 cycle end condition is satisfied. Phase 2 is repeatedly executed until the end of the scheduling period comes after the beginning of the next production plan.

  In step S11, it is determined whether or not a phase 1 cycle end condition is satisfied. The phase 1 cycle end condition is determined by whether or not it has exceeded (for example) one year at the time of the current planning, and is continuously executed until it exceeds one year.

  As can be seen from FIG. 5, in this embodiment, every time the scheduling process is executed a certain number of times, a loop for executing the production planning process once is repeated. This can be said to be a method of sequentially optimizing not only the end-of-period stock level of each item but also the initial stock level. However, it is also possible to abort the calculation in the middle depending on the reduction situation of the number of violations of constraints.

  According to the present embodiment, the O2O-technology algorithm is used not only for scheduling but also for production planning for planning. As a result, firstly, the resolution of the production plan itself can be improved as well as the scheduling. Second, although the resolution is improved, the calculation time can be suppressed to a reasonable time (scheduling calculation time × ratio of both planning target periods). Third, the resolution is improved and the problem is solved by formulating it with few artificial constraints in advance, so that various heterogeneous determination aspects can be optimized by the algorithm.

  As a result, the simulation function and the optimization function can be simultaneously incorporated into the production plan. For example, in an existing production inventory plan, a fixed standard lead time and a fixed lot size registered in advance based on a time bucket, and these items are used to guarantee the feasibility of the plan in advance. The fixed standard lead time is set longer. Therefore, there is a defect in which the accumulated lead time of each item, which should be able to be shortened depending on the method of processing, is already set longer than actual at the stage of developing the required amount. In addition, the name of the plan is a production inventory plan, but the limit to the adjustment of the load level is the limit, and it has not succeeded in handling the situation of processing across processes. On the other hand, in the proposed method of the present invention, there is no concept of a time bucket, and a plan can be made without registering a fixed lead time and a fixed lot size in advance. Therefore, both the item lead time and the item lot size are determined to be time variant depending on the situation for the first time when the problem is solved by the optimization algorithm of O2O-technology. This plan is different from the actual one in that demand data is not fixed but forecast data. In this sense, it can be said that the proposed method has a simulation function and an optimization function.

  It is also possible to level up seasonal fluctuations by accumulating work-in-progress, inventory and product inventory toward the busy season.

  By optimizing the planned end-of-period inventory, which is a requirement in the second stage in the first stage plan, which is longer than the second stage, a more optimal and robust production management system can be obtained.

  By obtaining the boundary condition for obtaining the optimal plan for the second stage optimally in the first stage, it is possible to further ensure the overall optimization.

  Note that the present invention is not limited to the above-described embodiment as it is, and can be embodied by modifying the constituent elements without departing from the scope of the invention in the implementation stage. Further, various inventions can be formed by appropriately combining a plurality of constituent elements disclosed in the embodiment. For example, some components may be deleted from all the components shown in the embodiment. Furthermore, you may combine suitably the component covering different embodiment.

  The present invention also provides a computer-readable recording medium on which a program for causing a computer to execute predetermined means, causing a computer to function as predetermined means, or causing a computer to realize predetermined functions is recorded. Can also be implemented.

The block diagram which shows the structure of the push-pull mixed type complex production management system which concerns on one Embodiment of this invention. The figure which shows the implementation example of the complex production management system shown in FIG. The figure which shows an example of the complex production system (push / pull mixed type complex production system) which permits the production of the push / pull mixed type which becomes the management object by the complex production management system of FIG. The figure which shows the outline | summary of operation | movement in the case of planning the optimal production plan applied to the complex production system shown in FIG. 3, and an optimal production schedule. The flowchart which shows the procedure of the push-pull mixed type optimal complex production planning method. The figure which shows 1st production technology data. The figure which shows 2nd production technology data. The figure which shows stock storage cost data, beginning stock data, target period end stock data, and demand forecast data. The figure which shows the monthly demand forecast value of a product. The figure which shows the seasonal index according to a product. The figure which shows firm order data. The figure which shows the demand forecast data decomposed | disassembled for every time slot. The flowchart which shows operation | movement of a production plan control part and a multi-item multi-process lot size scheduling part. FIG. 14 is a detailed flowchart of a solution step of the partial optimization problem in FIG. 13. The figure which shows an example of the data which show the inventory transition according to item. The figure which shows an example of the order data after components expansion | deployment. The figure which shows an example of the data which show the inventory transition according to the item (or according to family) over the scheduling object period. The figure which shows an example of the data which show the Gantt chart according to item (or according to family) over a scheduling object period.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 11 ... Main control part, 12 ... Pre-processing part, 13 ... Multi-item multi-process lot size scheduling part, 22 ... Main memory, 111 ... Input / output control part, 112 ... Production plan control part, 113 ... Scheduling control part, 131 ... Optimizing unit, 135 ... mechanical interference control unit, 138 ... inventory control unit, 220 ... system parameter storage area, 221 ... production data storage area, 222 ... scheduling data storage area, 241 ... push-pull mixed type optimal combined production planning program .

Claims (7)

It is a push-pull mixed type optimal combined production planning method for creating an optimal production plan in a combined production method that allows combined production of ordered products and prospective products in the same process,
A first step of creating a production plan for the first planning period and outputting transition data of the in-process inventory level at each time point;
Second scheduling for scheduling a second planned period shorter than the first planned period based on the transition data of the in-process inventory level output from the first step and determining a target in-process inventory level by process at the end of the planned period Comprising the steps of:
From the production plan data in the latest production plan, take the inventory level data of the time slot corresponding to the end of the schedule target period of the schedule, and use this as the end-of-period inventory level data of the schedule to be established,
Take out the inventory level data of the time slot corresponding to the beginning of the production plan from the transition data of the inventory level by item in the latest schedule, and use this as the initial inventory level data of the production plan.
A push-pull mixed type optimal mixed production planning method that extracts the inventory level data of the time slot corresponding to the beginning of the next scheduling from the change data of the inventory level by item in the latest schedule, and uses this as the beginning inventory level data of the next scheduling. The first step includes
Sub-steps to determine the target period, planned lead time, planned cycle time, time slot,
Sub-steps for entering production technology data, inventory storage cost data, opening stock data, target end-of-life stock data, demand forecast data, firm order data,
Sub-step for decomposing the demand forecast data by time slot, reflecting the confirmed order data in the demand forecast data after disassembly, deploying the reflection result based on the production technology data, and obtaining the demand forecast data after parts deployment;
2. The push-pull mixed type optimal combined production planning method according to claim 1, further comprising a sub-step of making a production plan based on demand forecast data after parts development and production technology data. The second step includes
Sub-steps for entering production technology data, inventory storage cost data, opening inventory data, target period end inventory data, firm order data,
Sub-step to obtain final order data by disassembling firm order data by item and time slot,
The push-pull mixed type optimal combined production planning method according to claim 1, further comprising a substep of performing scheduling based on the production technology data and the order data. 4. The second step is repeatedly executed until the end of the scheduling period is after the beginning of the next production plan, and the first step is repeatedly performed until a predetermined period elapses. The push-pull mixed type optimal combined production planning method described in any one of the items. A program for realizing a push-pull mixed type optimal combined production planning method for creating an optimal production plan in a combined production method capable of combined production of ordered products and prospective products in the same process,
On the computer,
A first step of creating a production plan for the first planning period and outputting transition data of the in-process inventory level at each time point;
Second scheduling for scheduling a second planned period shorter than the first planned period based on the transition data of the in-process inventory level output in the first step and determining a target in-process inventory level for each process at the end of the planned period And execute the steps
The inventory level data at the end of the schedule of the schedule newly established by the inventory level data of the time slot corresponding to the end of the planning target period of the schedule in the production plan data in the latest production plan,
The inventory level data of the time slot corresponding to the beginning of the production plan in the transition data of the inventory level by item in the latest schedule is the initial inventory level data of the production plan,
A program in which the inventory level data of the time slot corresponding to the beginning of the next scheduling in the transition data of the inventory level by item in the latest schedule is the initial inventory level data of the next scheduling. 6. The program according to claim 5, wherein the second step is repeatedly executed until the end of the scheduling period is after the beginning of the next production plan, and the first step is repeatedly executed until a predetermined period elapses. A push-pull mixed type optimal combined production planning device for creating an optimal production plan in a combined production method that enables combined production of ordered products and prospective products in the same process,
A first means for creating a production plan for the first planning period and outputting transition data of the in-process inventory level at each time point;
Second scheduling for scheduling a second planned period shorter than the first planned period based on the transition data of the in-process inventory level output from the first means and determining a target in-process inventory level by process at the end of the planned period Comprising the following means:
The inventory level data at the end of the schedule of the schedule newly established by the inventory level data of the time slot corresponding to the end of the planning target period of the schedule in the production plan data in the latest production plan,
The inventory level data of the time slot corresponding to the beginning of the production plan in the transition data of the inventory level by item in the latest schedule is the initial inventory level data of the production plan,
A push-pull mixed type optimal mixed production planning device in which the inventory level data of the time slot corresponding to the beginning of the next scheduling in the transition data of the inventory level by item in the latest schedule is the beginning inventory level data of the next scheduling.

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