JPH09300180A - Method and system of combining - Google Patents

Abstract

PROBLEM TO BE SOLVED: To reduce calculation time for solving optimum combination problem by dividing problem of optimum combination into multiple partial problems, and each partial problem is solved applying Heulistic Method. SOLUTION: When the production volume is defined as variable I referring to the Heulistic Method from the blocks belonged to the first group lot, by selecting the lot which supplies the necessary value, the solution AI for the partial problem Q1 is derived. (Step 4). From tone lot belonging to the remaining partial problem Q0 , applying mathematical program, the lots are selected, and find the solution A0 for the partial problem of deciding the production volume. (Step 8). Combining all the solutions, the original problem namely the combined blocks for production can be outputted. (Step 9).

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention divides each of a plurality of materials of a certain size (for example, steel plates) into a plurality of products smaller than the materials (for example, strips cut from the steel plate). Occasionally, when the above products are combined so that one material can be divided and applied, and when this combination is applied with only enough material to produce the product, the use of the material The present invention relates to a combination method for obtaining a combination with a reduced amount and a combination device used for implementing the combination method.

[0002]

2. Description of the Related Art When there are elements to be combined, the problem of finding the combination of elements that gives the best evaluation is called the combination optimization problem. For example, when a plurality of plate-shaped products having different sizes are divided and applied with a plurality of plate-shaped materials of a certain size, a piece of a size that cannot be applied to the product is generated. Since this scrap is useless, the larger the size, the worse the yield. The size of the scrap depends on the method of dividing the plate material, that is, the method of combining the plate products.

Therefore, a method for obtaining a combination with good yield of the plate-shaped products is described in the following document "An LP-based appr".
oach to cutting stock problems with multiple objec
tives, ”G.WASCHER, European Journal of Operational
Proposed in Research, Vol.44-2, Jan.1990. The method of the above-mentioned document is to prepare a combination of plate-like products which can be applied with plate-like materials as much as possible, satisfy the production target amount of plate-like products, and reduce the waste of plate-like materials in lots. The combination is obtained using linear programming, which is one of mathematical programming methods.

The planing plan problem which is a typical solution target of the mathematical programming will be described below. The planing plan problem is a problem of dividing a plate-shaped material having a predetermined width and applying it to a plurality of plate-shaped products to be produced, a combination of the plate-shaped products, and a production amount of this combination. Is. As a specific example, a roll-shaped steel plate having a width of 500 (mm) is cut into a length of 400 (mm) and used as a material, and a plurality of the above-mentioned materials are unified into a longitudinal dimension of 400 (mm). An explanation will be given in accordance with a planing plan problem in which strips of a size are combined so as to reduce the waste of materials and planed. The length of the strip is aligned with the length of the rolled steel sheet, and the strip is cut from the material. The allowable width of the material is 500 (mm) and the allowable range of the width is 50 (mm).

Table 1 is a table showing the size and quantity of strips to be produced. Taking the No. 1 strip as an example, it indicates that the size to be produced is 60 (mm) wide and 400 (mm) long, and the quantity to be produced is 5 (sheets).

[0006]

[Table 1]

Table 2 is a table showing an example of a combination in which the difference between the total width of the combined strips and the material width of 500 (mm) is within the surplus allowable range of 50 (mm). A combination of strips that can be used by dividing one material is called a lot. Taking the No. 1 lot as an example, the No. 1 strip is 8
(Sheet) It is possible to make a board, and as a result, there is a surplus of 20 (mm).

[0008]

[Table 2]

FIG. 7 is an explanatory view showing an example of the rolled steel plate in the above-mentioned planing plan problem, the strip of Table 1 above, and the lot of Table 2 above in which the strips are combined. In the figure, the width of the rolled steel plate is 500 (mm) and the long side of the strip is 400
(mm), the allowable range of the remainder remaining after the strips are cut from the material obtained by cutting the rolled steel plate into the length of 400 (mm) is set to 50 (mm). In addition, lot 1 and lot 2 in Table 2 above
Is shown.

Lot 1 is 60 (mm) from a material with a width of 500 (mm)
Strip 8 strips of width. Lot 2 is 500 (mm)
Cut 7 (62) strips 62 (mm) wide and 1 (64) strips 64 (mm) wide from the material of width. The shaded areas existing in all lots represent cut edges remaining after the strips are cut. Mathematical programming is a solution that finds a solution that minimizes (or maximizes) an objective function under given constraints. Equation 1 shows a general equation of mathematical programming. [Equation 1] Objective function f (x) → minimum (or maximum) constraint condition xεS, where S⊆X where X is a basic space, and S is its region. A solution x that satisfies xεS is called a feasible solution. The constraints defining the region S are given by some inequalities or equations.

The objective function quantitatively evaluates the quality of the solution. When f (x) ≤ f (y) (in the case of minimization) holds for one possible solution x with respect to any other possible solution y,
This x is called an optimal solution. Also, there exists a solution set H containing possible solutions x, and f (x) ≤
When f (y) holds, this x is called a local optimum solution (or simply a local solution). The optimal solution (essentially a local optimal solution) is a solution to be obtained.

[0012]

When the above-described planing plan problem is determined by using the mathematical programming method, lots, which are combinations of plate-like products, are prepared as much as possible. Then, all types of lots are appropriately combined so as to satisfy the constraint condition, the combination of the lots is evaluated by the objective function, and the combination of the lots with the best evaluation is obtained. This lot type increases exponentially with the increase in the number of plate-like products associated with the lot. That is,
As the number of types of plate-like products increases, the calculation time until the combination of lots is obtained exponentially increases, which is not suitable for practical use.

Such a problem applies to all combinatorial optimization problems represented by a planing plan. Therefore,
When using mathematical programming to solve combinatorial optimization problems, some kind of ingenuity is needed to reduce the calculation time. The present invention has been made to solve such a problem, and a combination method and a combination for reducing the calculation time by simplifying the calculation target by devising a combination procedure of product types The purpose is to provide a device.

[0014]

The combination method according to the first aspect of the present invention divides one material to obtain one or a plurality of types of products, and uses a plurality of the materials to obtain the required products of each type. In producing a quantity, in a combination method of combining the types of the products so that the usage amount of the material is reduced as much as possible, a plurality of types of products to be produced by a heuristic method based on the respective required quantities. Multiple groups created by dividing each group into groups, combining the types of products belonging to each group to satisfy the required quantity of the products, and creating a combination that uses as little material as possible The combination of is a combination of the types of products to be produced.

In the combination method according to the second invention, one material is divided to obtain one or a plurality of kinds of products, and a plurality of the materials are used to produce a required quantity of each kind of product, In a combination method of combining the types of the products so that the amount of the material used is as small as possible, the required quantity from a set of the types of the products to be produced matches a predetermined quantity or a multiple of the predetermined quantity. Create a first group of product types and a second group of other product types, combine the product types belonging to the first group to satisfy the required quantity of the product, and A small first combination is created by a heuristic method, the types of products belonging to the second group are combined to satisfy the required quantity of the product, and the second combination with a small amount of material used is calculated by the mathematical programming method. Create, first set alignment and a second
It is characterized in that the combination is a combination of types of products to be produced.

In the combination method according to the third invention, one material is divided to obtain one or a plurality of kinds of products, and a plurality of the materials are used to produce a required quantity of each kind of product, In a combination method of combining the types of the products so that the amount of the material used is as small as possible, the required quantity from a set of the types of the products to be produced matches a predetermined quantity or a multiple of the predetermined quantity. A first group of product types is created, and the types of products belonging to the first group are combined to satisfy the required quantity of the product, and a first combination that uses less material is created by a heuristic method. , A plurality of first combinations are iteratively created by changing the predetermined quantity from the set that reduces the kinds of products that satisfy the required quantity by the first combination already created from the set of product types to be produced. Then, satisfying the required quantity of the product by combining the types of products belonging to the set obtained by subtracting the type of products that satisfy the required quantity by the first combination already created from the set of types of products to be produced, Moreover, the second combination that uses less material is created by mathematical programming,
It is characterized in that the first combination and the second combination are combinations of types of products to be produced.

The combination device according to the fourth aspect of the invention divides one material to obtain one or a plurality of types of products, and uses a plurality of the materials to produce a required quantity of each type of product, In a combination device that combines the types of products so that the usage of the material is reduced as much as possible, the required quantity from a set of types of products to be produced is equal to a predetermined quantity or a multiple of the predetermined quantity. Means for creating the first group of product types and the second group of other product types are combined with the types of products belonging to the first group to satisfy the required quantity of the product, A means for creating a small first combination by a heuristic and a kind of products belonging to the second group are combined to satisfy the required quantity of the product, and a second combination with a small amount of material used is mathematically Characterized in that it comprises a means for creating the image method.

The combination apparatus according to the fifth aspect of the invention divides one material to obtain one or a plurality of types of products, and uses a plurality of the materials to produce a required quantity of each type of product, In a combination device that combines the types of products so that the usage of the material is reduced as much as possible, the required quantity from a set of types of products to be produced is equal to a predetermined quantity or a multiple of the predetermined quantity. The means for creating the first group of product types and the types of products belonging to the first group are combined to satisfy the required quantity of the product, and the first combination with a small amount of material used is made by the heuristic method. A means for creating and a set of products to be produced by the first combination already created from the set of products to be produced are subtracted from the set of products that satisfy the required quantity, and a predetermined quantity is changed to repeatedly create a plurality of products. The combination of the means for creating one combination and the types of products belonging to the set obtained by subtracting the types of products satisfying the required quantity by the already created first combination from the set of types of products to be produced And a means for creating a second combination by mathematical programming that satisfies the required quantity and the amount of material used is small.

Equations 2, 3, 4, and 5 shown below are formulations of the above-described planing plan problem based on mathematical programming.

[0020]

[Equation 1]

Equation 2 is an objective function. In Expression 2, P _j
Represents the quantity that actually produces lot j. D _i represents the required quantity for producing the strip i. V _i represents the width of the strip i. X
_ij represents the number of strips i included in the lot j by the elements of the two-dimensional matrix. W _max represents the width of the material, that is, the upper limit of the width of each lot. B ₁ and B ₂ respectively represent weighting factors. The first term having the weighting factor B ₁ represents the total amount of waste material that is discarded without being allocated to the strips when all the lots obtained by combining the strips are produced. _Second with weighting factor B 2
The term represents the total amount that exceeds the required amount of each strip when all the lots are produced, that is, the total excess production amount. Therefore, the expression 2 represents that the amount of the product not used as a product when the product is produced based on a plurality of lots which is the created plan is to be minimized, that is, to be minimized.

Expressions 3, 4, and 5 are all restrictions when obtaining a lot based on Expression 2 described above. In Equation 3, X _ij · P _j represents the amount of strip i produced by lot j. Therefore, Equation 3 shows that the production amount of each strip i when all the above lots are produced should satisfy the required amount. X in formula 4
_ij · V _i represents the width of the strip i in the lot j. W _min
Represents the required width that the width of the lot must satisfy, that is, the lower limit of the total width that is applied as a strip when one material is divided according to the combination indicated by the lot. Therefore, the equation 4 indicates that the width of the lot j occupying the material should fall within a predetermined range from W _min to W _max . In Expression 5, P _min represents the required amount for producing a lot, which is determined by the operating unit of the production line. Equation 5 therefore represents that each of the lots should be produced for at least P _min .

Elements to be combined when solving the above-mentioned planing plan problem using mathematical programming (strip)
As the number of types increases, the number of combinations (combinations of lots) to be evaluated increases, and since this increasing tendency is exponential, the calculation time until the combination is calculated extremely increases. When this calculation time exceeds the practicable limit, it is desired to shorten the calculation time even if the goodness of evaluation of the combination to be obtained, that is, the waste of material is sacrificed to some extent.

This reduction in calculation time is achieved by reducing the number of combinations to be evaluated. Specifically, it is possible to divide the elements to be combined into groups of appropriate size and combine elements belonging to the same group to create a combination that is a candidate for a combination to be obtained. According to this method, the combination that combines elements belonging to different groups is not created, so the number of combinations is significantly reduced, but the goodness of the evaluation of the combination obtained by the method of dividing into groups is Will be done. Therefore, some kind of guideline for group division is required so that the goodness of combination evaluation is not sacrificed. Therefore, the present invention attempts to shorten the calculation time of mathematical programming by obtaining the guideline of this group division by a heuristic method.

Now, an outline of the heuristic method adopted in the present invention will be described. The heuristic method is a solution method that uses empirical knowledge as a guideline for problem solving. Here, empirical knowledge does not mean knowledge that always holds like mathematical theorems and laws of physics, but means knowledge that is empirically effective in problem solving. Specific examples of this knowledge include the following. In the above-mentioned problem of creating a planing plan, what kind of combination and how much is to be produced are required, but depending on the type of strip, it is possible to allocate one material to multiple strips of the same type. is there.

For example, two or more strips whose width is less than half the width of the material can be cut into one material. Therefore, when selecting lots to meet the required amount of this strip,
Not only lots that combine only one sheet, but lots that combine multiple sheets are listed as selection candidates. From these lots, the required amount of this strip and the excess production of other strips produced at the same time as this strip are determined. However, a complicated calculation is required to find out which lot, that is, how many combinations of strips will be produced.

It is assumed that the required number of strips is eight. Then, when considering to select a lot so as to satisfy the required amount of this strip only from a lot in which one strip is combined, eight lots will be produced and satisfied, but at this time, they are different from each other. Eight types of lots may be produced and satisfied one by one, or only one type of lot may be produced and satisfied. Therefore, how many lots should be selected to meet the required amount of this strip,
At the same time, it is necessary to calculate how much each selected lot will be produced. Furthermore, when two or more strips of this strip can be cut into one material, not only lots in which one strip is combined but also lots in which two or more strips are combined are candidates for selection, and more complicated calculations are required. become.

Therefore, when two or more strips of this strip can be cut into one material, paying attention to this fact, considering that only lots in which two strips are combined are candidates for selection, the production amount of the lot. Can be defined as 4 by dividing the required amount of 8 sheets by 2. That is, four lots will be produced to satisfy the required amount of this strip, but at this time, four different lots may be produced one by one, and only one lot may be produced. You may produce four to satisfy. Therefore, when the production amount is set to 4, if only one kind of lot that does not excessively produce other strips produced at the same time is selected, the calculation time required for obtaining the production amount of the lot can be reduced. .

Further, depending on the constraint conditions, it is allowed to produce the strips in excess of the required amount to some extent. Specifically, the required amount is 7, and by combining 2 strips of one material that can be cut into 2 strips into one lot, and producing 4 of these lots, let's meet the required amount. , The production volume is 8 for the required 7 strips.
The quantity of excess production is one piece. If this excess production falls within the allowable range due to the constraint conditions, this lot satisfies the requirement to be selected as a solution. However, it is desirable that the excess production be as small as possible.

Therefore, when the production amount is set to a predetermined amount (4 in the above example) and a lot is selected, there is a possibility that the strip may be produced in excess of the required amount (the required amount is Excessive production can be eliminated by removing (7 strips) from the group. That is, in order to prevent the production amount of the strips from exceeding the required amount when a predetermined number of lots of strips are combined, it is necessary to create a group of strip types in which the required amount is equal to the predetermined amount or a multiple thereof. Good.

Therefore, a group of strip types whose required quantity is equal to or equal to a predetermined quantity or a multiple thereof is created, and the production quantity is set to a predetermined quantity from a lot in which the types of strips belonging to this group are combined. If a lot that satisfies the required amount of strips combined with it is selected, the calculation time required to obtain the production volume of the lot can be reduced and at the same time the strips are not overproduced, that is, the solution evaluation. It can be expected to secure the goodness of.

In addition, when there is a large difference in the required amount of each strip in the group, a large number of types of lots having a small production amount are combined to satisfy the required amount of strips that are required in lot selection. A situation arises, which is a factor in increasing the calculation time. Therefore, creating a group of strips of a large number or a small number depending on the required amount leads to a reduction in lot types.

Further, when selecting a lot having a good evaluation by the objective function from lot candidates satisfying the constraint condition, other lots combining strips satisfying the selected lot are unnecessary and are deleted from the lot candidate. Therefore, if the evaluation of the objective function is about the same when selecting lots, selecting lots that combine more types of strips significantly reduces lot candidates, that is, shortens the calculation time. Is effective for. Also, a wide strip,
That is, when combining the lots in order from a strip having a larger constraint than others, it is possible to omit a wasteful calculation time required to calculate a combination that does not satisfy the constraint condition.

The above empirical knowledge is called heuristics. The present invention divides a plurality of products to be combined into groups in which the sacrifice of the goodness of the combination is less sacrificed based on the heuristic method as described above, so that the combination of products in which the amount of materials used is as small as possible Reduce the calculation time when creating. Further, in order to obtain the combination for each group described above, the calculation time is shortened when the combination of products using the least amount of materials is created by using mathematical programming or heuristics.

[0035]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described in detail below based on the above-described planing plan making apparatus for preparing a planing plan. FIG. 2 is a block diagram showing a configuration of a planing planner used for implementing the present invention. In the figure, reference numeral 102 denotes an arithmetic unit for performing all arithmetic processing according to the present invention. The arithmetic unit 102 is connected to the input unit 101 which uses a keyboard for inputting a required width and quantity. Further, the arithmetic unit 102 is connected to an output unit 103 using a monitor or printer for outputting the prepared planing plan.

The arithmetic unit 102 generates a plurality of types of lots in which the widths of a plurality of strips input by the input unit 101 are combined. Of the combinations of this lot, the combination with the highest yield is the planing plan that should be sought. The planing plan created by the arithmetic unit 102 is input to the output unit 103. The input device 101 and the output device 103 may be replaced with information processing devices that input and output data.

FIG. 1 is a flow chart showing the processing procedure of the planing plan creation processing in the arithmetic unit 102. First, the operator inputs the width V _i (uniform length) and the required amount D _{i of} the strip to be produced, the width W _{max of} the material, the required amount P _min and the required width W _{min of the} lot, and the upper limit value of the variable I. Is accepted and the variable I is reset (S1). This variable I defines a group for dividing into groups by the heuristic method, specifically, the group of a kind of strip whose required amount matches a predetermined number or its multiples, that is, the predetermined number for creating the first group. Holds the value. Then, the value of the variable I is changed to the upper limit value of the variable I to create a plurality of the first groups. The upper limit of this variable I is appropriately set by the operator based on the nature of the solution target and empirical knowledge.

The required amount P of the lot is set as an initial value in the variable I.
Substitute _min (S2). From all groups of strip types (original problems) to be produced, a strip type group (first group) whose required amount matches the value of the variable I and its multiples based on heuristics is created as described below. Letting the solution of the group be the subproblem Q _I (S
3). The multiplier that defines the multiple at this time is set to 2 based on heuristics. That is, the group of strips whose required amount is equal to the value of the variable I and twice the value is the first group.

Next, when the production amount is set to the value of the variable I based on heuristics from a lot in which strips belonging to the above group are combined, the lot satisfying the required amount of strips combined with this is set. Is selected as the solution A _I of the partial problem Q _I. (S4). The amount satisfied by producing a lot of solution A _I is reduced from the original problem, and the rest is newly set as the original problem (S5). To create the next first group, 1 is added to the variable I (S6), it is determined whether this value is less than the upper limit value of the variable I (S7), and if it is less than the upper limit value, the process is performed in S3. Return and repeat the subsequent processing procedure.

When a plurality of sub-problems Q _I are created from the original problem by repeating the processing procedure from S3 to S7 until the value of the variable I reaches the required value P _{min of the} lot from the upper limit value of the variable I,
Each time, a subproblem Q _I is created from the original problem at that time based on the value of the variable I, the production amount is set to I from the lot that combines the strips belonging to this subproblem Q _I , and the lot is selected. If the required quantity is not satisfied by the selected lot, it will be returned to the original question. Then, the original problem at the time when the value of the variable I becomes equal to its upper limit value is set as the partial problem Q ₀ to be solved using mathematical programming. That is, the strips belonging to the subproblem Q ₀ to be solved by the mathematical programming method are reduced as much as possible by repeating the processing procedure from S3 to S7.

This partial problem Q₀Strips belonging to (second group
Group) using a well-known mathematical programming method.
Partial problem Q in which a lot is selected and the production amount is determined₀of
Solution A ₀(S8). Find all solutions found
As a solution to the original problem, that is, a combination of strips to be produced
Output (S9).

FIG. 3 shows the partial problem Q in S3._IGenerate
It is a flow chart which shows a processing procedure. First, the value of variable I
Is the lot requirement P_minIs determined whether or not (S31)
 , If they are equal, that is, it is determined that it is the first group division
If you do, the required amount D_iIs the value of variable I, that is, lot
Required amount P_minCreate a group of the following strips i
To find the solution of the group_IAnd (S3
2). Furthermore, the required amount D _iIs approximately twice the specified quantity, that is,
If the value of the variable I is approximately twice the value of 2I-2 or more and 2I or less,
Create a group of strips i and
In addition to the group created in
A new sub-question Q_I(S34). S32
The value of the variable I is the required quantity P of the lot in_minIs equal to
If it is not, that is, it is determined that it is the second or subsequent group division
If the required amount D_iIs a predetermined quantity, that is, the value of variable I
The value is approximately equal to or greater than I-1 and less than or equal to I
Create a group and solve for this group
The partial problem Q_I(S33). After that, the processing is moved to S34,
The required amount D as in the above_iStands for a predetermined quantity
A group of strips that doubles, or approximately doubles the value of variable I
And create the group you created in the previous step.
In addition to the group
Partial problem Q_IAnd

The group after the second time in S33
The value of the variable I in one phase of the division is equal to the value of the variable I in the next phase.
Since it is equal to the value of, minus 1, the value of variable I
Required amount D_iStrip i that matches
You will have two opportunities. This is a partial problem Q_I
The strip i adopted in_ISolution A_INo lock
Is not included in the elements of the solution, ie, solution A_INot produced by
If the next sub-problem Q _{I + 1}Adopted as the element of the lot
This is because the probability of being selected is high. In this case, the solution
Production of this strip i when selected as an element of a lot of
Is the required amount D_iOne more, but this excess is an acceptable range.
Consider it as a fence. That is, a predetermined number for creating the first group
The quantity is not limited to one. Also in S34
It is the same as where it was.

For example, when the required amount P _{min of the} lot is 8, the value of the variable I is 8 in the first group division, and the required amount D _i is 8 or less from the original problem, or
A sub-problem Q ₈ consisting of a strip i of 14 or more and 16 or less is generated. Then, the solution A ₈ of the sub-problem Q ₈ is solved by S4 described above, and the strip i satisfied by the solution A ₈ is subtracted from the original problem by S5 to make the rest a new original problem. That is, the strip i, which has been adopted for the subproblem Q ₈ but is not satisfied by the solution A ₈ , is returned to the original problem. If the value of the variable I is incremented by 1 in S6 and it is determined in S7 that the value of the variable I is less than the upper limit value, the second group division is performed. At the time of this second group division, the value of the variable I is 9 and the necessary amount D _i is 8 or more and 9 or less or 16 or more and 18 or less from the original problem, and the subproblem Q _{9 is} composed of strips i. Is generated.

FIG. 4 shows the subproblem Q in S4._ISolve for
7 is a flowchart showing a processing procedure according to the present invention. First a partial problem
Q_IThe strips i are combined, and the total value of the width is
Required width W _minAnd the width W of the material_maxTo meet
Number of different lots that can be combined and generated
Make it a candidate (S41). At this time, the generated lot is identified
Number them.

Next, when the production quantity of the lot is assumed to be the value of the variable I, the lot that cannot meet the required quantity of the strip i is deleted from the lot candidates (S42). In the above example, among the elements of the sub-problem Q ₈ , the required amount D _i is 14 or more.
For strips i of 16 or less, 2 in 1 lot when the production volume is 8
The required amount cannot be met without removing the plank. Therefore, in S42, the lot in which only one strip i having the required amount D _i of 14 or more and 16 or less is cut is deleted from the lot candidates.

After the lot candidates are sorted in the order of the number of types of strips (S43), the lot candidates are narrowed down to one and adopted (S44). After deleting a lot that has a strip that is an element of the adopted lot as its element from the lot candidates
(S45) If lot candidates remain (S46), the process returns to S44, and the subsequent processing procedure is repeated. If no lot candidate remains, the production amount of all lots adopted so far is set as the value of the variable I, and this is set as the solution A _I (S47).

FIG. 5 is a flow chart showing a processing procedure for narrowing down lots in S44. First, the lot with the most types of strips is selected from the lot candidates (S441), and it is determined whether or not the number of selected lots is one (S442). When there are a plurality of selected lots, the lot having the widest strip is selected (S443), and it is determined whether or not there is one selected lot (S444). When there are a plurality of selected lots, the lot with the highest yield is selected (S445), and it is determined whether or not there is one selected lot (S446). When there are a plurality of selected lots, the lot with the smallest identification number is adopted (S447). If one lot is selected in S442, S444 and S446, that lot is adopted.

FIG. 6 is a flowchart showing a processing procedure for solving the remaining original problem Q ₀ in S8. First, by combining the remaining strips i of the original problem Q ₀ , the total value of the widths satisfies the required width W _{min of the} lot, and the width W of the material
A number of lots that satisfy _max can be combined and generated, and the lot candidates are used (S81). Then, the production amount of each lot candidate is determined using a known mathematical programming method (S82).
. Solution A ₀ of the lot and the production amount obtained the original problem Q ₀
(S83). Although the above-described embodiment has explained the planing planner for creating the planing plan, it goes without saying that the same can be carried out in a system for finding a solution to another combination optimization problem. Nor.

[0050]

As described above, according to the present invention, when a combination optimization problem is solved, a heuristic method is used to divide the combination optimization problem into a plurality of subproblems and solve the problems individually. , It is possible to reduce the calculation time required to solve the combinatorial optimization problem to be obtained. Further, by solving the partial problem using a heuristic method, it is possible to reduce the calculation time required to solve the combination optimization problem.

[Brief description of drawings]

FIG. 1 is a flowchart showing a processing procedure of a planing plan.

FIG. 2 is a block diagram of a planing planner.

FIG. 3 is a flowchart showing a processing procedure for generating a partial problem.

FIG. 4 is a flowchart showing a processing procedure for solving a partial problem.

FIG. 5 is a flowchart showing a processing procedure for narrowing down lots.

FIG. 6 is a flowchart showing a processing procedure for solving a remaining original problem.

FIG. 7 is an explanatory diagram showing an example of a planing plan.

[Explanation of symbols]

 101 Input device 102 Arithmetic device 103 Output device

Claims (5)

[Claims] 1. When one material is divided to obtain one or a plurality of types of products, and a plurality of the materials are used to produce a required quantity of each type of product, the amount of the material used is as large as possible. In the combination method of combining the product types so that the number of products is reduced, the type of the product to be produced is divided into a plurality of groups by the heuristic method based on the required quantity of each product,
For each group, combine the types of products that belong to the group to satisfy the required quantity of the product, and create a combination that uses as little material as possible to produce multiple created combinations. A combination method characterized in that it is a combination of the types of products to be manufactured. 2. When one material is divided to obtain one or a plurality of types of products and a plurality of the materials are used to produce a required quantity of each type of product, the amount of the materials used is as large as possible. In the combination method of combining the product types so that the number of product types is reduced, a first group of product types whose required quantity is equal to a predetermined quantity or a multiple of the predetermined quantity from a set of product types to be produced, and Create a second group of other product types, combine the product types that belong to the first group to satisfy the required quantity of the product, and use the heuristic method of the first combination that uses less material. Create a second combination that combines the types of products that belong to the second group and satisfies the required quantity of the product, and that uses less material, and then creates the first combination and the second combination. Combination method characterized by the combination of the type of product to be produced a combination. 3. When one material is divided to obtain one or a plurality of types of products and a plurality of the materials are used to produce a required quantity of each type of product, the amount of the materials used can be as large as possible. In the combination method of combining the product types so that the number of product types decreases, a first group of product types whose required quantity is equal to a predetermined quantity or a multiple of the predetermined quantity is selected from a set of product types to be produced. Create a first combination that combines the types of products that belong to the first group and satisfies the required quantity of the products, and that uses less material, and use the heuristic method to determine the type of products to be produced. The first combination already created from the set is subtracted from the types of products that satisfy the required quantity, and while changing the predetermined quantity from the set, a plurality of first combinations are repeatedly created to determine the types of products to be produced. The first combination that has already been created from the combination satisfies the required quantity by satisfying the required quantity by combining the types of products that belong to the set in which the types of products that satisfy the required quantity are reduced. A combination method characterized in that a combination is created by mathematical programming, and the first combination and the second combination are combinations of types of products to be produced. 4. When one material is divided to obtain one or a plurality of types of products and a plurality of the materials are used to produce a required quantity of each type of product, the amount of the material used is as large as possible. In the combination device for combining the product types so that the number of product types is reduced, a first group of product types whose required quantity is equal to a predetermined quantity or a multiple of the predetermined quantity from a set of product types to be produced, and The heuristic method is to combine the means for creating the second group of other product types with the product types belonging to the first group to satisfy the required quantity of the product and to use the first combination with a small amount of the material used. And a means for combining the types of products belonging to the second group to satisfy the required quantity of the products and creating a second combination using a small amount of materials by mathematical programming. A combination device characterized by comprising. 5. When one material is divided to obtain one or a plurality of types of products and a plurality of the materials are used to produce a required quantity of each type of product, the amount of the material used can be as large as possible. In the combination device for combining the product types so that the number of product types is reduced, a first group of product types whose required quantity is equal to a predetermined quantity or a multiple of the predetermined quantity is selected from a set of product types to be produced. First means that the required quantity of the product is satisfied by combining the means for creating and the type of the product belonging to the first group, and the amount of the material used is small.
A method of creating a combination by a heuristic method, and iterating while changing a predetermined quantity from a set obtained by subtracting the kinds of products that satisfy the required quantity by the already created first combination from the set of kinds of products to be produced. Multiple first
The means for creating a combination is combined with the product types belonging to the set obtained by subtracting the product types satisfying the required quantity by the already created first combination from the set of product types to be produced. And a means for creating a second combination that satisfies the required quantity and uses a small amount of material by mathematical programming.