JP4909869B2 - Material assignment system - Google Patents

Description

  The present invention relates to a member assignment system, a member assignment program, a recording medium, a member assignment method, and a member processing apparatus.

For pre-cutting of house structural materials, raw materials of several lengths (mainly 3m to 6m) are prepared for each specification such as cross-sectional shape, tree type, grade and layer. A member (product) of a predetermined length is cut out from there. In general-sized houses, there are about 20 types of structural materials called horizontal members such as beams, girders, and foundations. From the raw materials of several lengths prepared for each product specification, about 200 products are cut out when the average of these structural materials is 10 for each building. Depending on the product specifications, the product size, and the combination of raw materials to be cut out, the amount of parts that are cut off from the raw materials and wasted differs. Then, the technique which improves a member allocation method was developed (refer patent document 1).
Japanese Patent No. 3565262

    The purpose of the calculation of the member allocation method as described above is to cut out the required product with a few raw materials (highest yield) from a raw material group of several lengths prepared for each product specification. Various other technologies have been developed, but it is said that the allocation method at the pre-cut factory using these technologies is approximately 90%. In the case of a building designed and produced according to a certain standard, the yield can be further improved by determining the size of the structural material suitable for the size of the raw material. However, when a structural material is cut out from a raw material based on a variety of designs by order production, development of a calculation method for further improving the yield is required. In fact, a large amount of waste can be reduced simply by improving the yield by 1%. The present invention uses a calculation result of an existing member allocation method, a member allocation system and a member allocation program for optimizing a combination for cutting out a required product from a raw material group of several lengths prepared for each product specification, It is an object to provide a recording medium, a member allocation method, and a member processing apparatus.

The following configurations are means for solving the above-described problems.
<Configuration 1>
The number of each type of raw material required when each of m products of a predetermined length is cut out from k types of raw materials of a predetermined length, and the combination of products assigned to each raw material is optimized. There,
Accepting the input of product length data of m required products, and generating an m-th order product length vector Lp having the product length as an element and a product request quantity vector b having the product request quantity as an element Product length setting means for storing in the storage device;
A raw material length setting means that receives input of raw material length data of k types of prepared lengths, generates a k-th order raw material length vector Lm having the raw material length as an element, and stores it in a storage device;
The raw material and product which can economically allocate one or a plurality of products by comparing the product length data of the required m products with the raw material length data of the k kinds of raw materials prepared An allocation pattern vector generation means for enumerating m-th order allocation pattern vectors,
An allocation pattern matrix generation unit that generates an allocation pattern matrix A in which the allocation pattern vectors generated by the allocation pattern vector generation unit are arranged and stores the allocation pattern matrix A in a storage device;
An element for selecting a corresponding raw material by selecting from n allocation patterns included in the allocation pattern matrix defines a use number vector x of x i, and an m-th order cost coefficient vector corresponding to the raw material length vector Lm; An objective function generating means for generating an objective function indicating a sum of products of the used number vectors x and storing the objective function in a storage device;
The number of products cut out by n allocation patterns selected from the allocation pattern matrix A has been relaxed as a first constraint condition Ax ≧ b, which must be equal to or greater than the quantity of each required product . A constraint condition generation means for generating a third constraint condition expression 0 ≦ xi ≦ 1 and storing it in the storage device;
Initial setting means for receiving an input of an initial executable solution obtained by an arbitrary method and storing it in a storage device;
Simplex operation means for receiving input of the initial executable solution, the objective function, and the constraint condition expression, and executing simplex operation processing;
If the simplex operation process results in a solution where the value of xi is either 0 or 1 and does not include any other value , the member assignment data is output with the solution as the optimal solution, otherwise Is a combination of the number of raw materials used that takes the objective function value of the initial feasible solution as a maximum value, the objective function value obtained as a result of the simplex operation processing as a minimum value, and takes the objective function value in that range. Are selected from among them, and the number of raw materials of which length is selected and used for allocation is selected for the constraint condition generation means. A request is made to generate a second constraint condition expression Cx = d, where the product of the use matrix C and the raw material use number vector x is equal to the raw material use scheduled quantity vector d, and the first constraint condition expression and the second constraint condition expression are requested. And the third Under the constraint condition of the constraint condition expression, the simplex operation means is requested to perform the arithmetic processing, and the simplex arithmetic processing obtained thereafter results in a solution where the value of xi is either 0 or 1 and does not include any other In this case, the member allocation data is output with the solution as an optimal solution, and in other cases, the next candidate whose objective function is close to the minimum value is selected from the listed combinations of the number of raw materials used. Select and request the constraint condition generation means to generate a new second constraint condition expression Cx = d, and repeat the operation of requesting the simplex operation means to perform arithmetic processing under this new constraint condition. A member allocation system comprising search control means for controlling the member.

Since the initial executable solution obtained in advance by an arbitrary method is included in the assigned pattern vector and simplex operation processing is performed, the optimum solution search range of the operation processing with many combinations can be narrowed from the beginning. In addition, first, since the simplex calculation process is performed using the relaxed third constraint condition expression 0 ≦ xi ≦ 1, the minimum value of the objective function value can be easily searched. In other words, the objective function value of the initial feasible solution is set to the maximum value, the objective function value obtained as a result of the simplex operation processing is set to the minimum value, and combinations of the number of raw materials used that take the objective function value in the range are listed. Then, the second constraint condition expression Cx = d and the relaxed third constraint condition expression 0 ≦ xi ≦ 1 can be generated, and the simplex operation process can be executed again. Thereby, the calculation process for obtaining the optimum value can be executed in a shorter time. In addition to the reduction of the total raw material length, the raw material length includes components such as processing costs according to the type of raw material. Thereby, even if calculation is performed only about the raw material length, the allocation can be optimized in consideration of the price of the raw material.

  <Configuration 2>
  The member allocation system according to Configuration 1, wherein the search control means sets an upper limit value for the number of repetitions of the second and subsequent simplex operations.

  This prevents long-term computation processing from being continued when the list of combination lists is large.

<Configuration 3>
Means for optimizing the combination of products assigned to each raw material by obtaining the number of each type of raw material required when each of m products having a predetermined length is cut out from k kinds of raw materials each having a predetermined length; A pre-cut device that accepts optimized member allocation data and cuts the m products from the k kinds of raw materials that are sequentially supplied;
Accepting the input of product length data of m required products, and generating an m-th order product length vector Lp having the product length as an element and a product request quantity vector b having the product request quantity as an element Product length setting means for storing in the storage device;
A raw material length setting means that receives input of raw material length data of k types of prepared lengths, generates a k-th order raw material length vector Lm having the raw material length as an element, and stores it in a storage device;
The raw material and product which can economically allocate one or a plurality of products by comparing the product length data of the required m products with the raw material length data of the k kinds of raw materials prepared An allocation pattern vector generation means for enumerating m-th order allocation pattern vectors,
An allocation pattern matrix generation unit that generates an allocation pattern matrix A in which the allocation pattern vectors generated by the allocation pattern vector generation unit are arranged and stores the allocation pattern matrix A in a storage device;
An element for selecting a corresponding raw material by selecting from n allocation patterns included in the allocation pattern matrix defines a use number vector x of x i, and an m-th order cost coefficient vector corresponding to the raw material length vector Lm; An objective function generating means for generating an objective function indicating a sum of products of the used number vectors x and storing the objective function in a storage device;
The number of products cut out by n allocation patterns selected from the allocation pattern matrix A has been relaxed as a first constraint condition Ax ≧ b, which must be equal to or greater than the quantity of each required product . A constraint condition generation means for generating a third constraint condition expression 0 ≦ xi ≦ 1 and storing it in the storage device;
Initial setting means for receiving an input of an initial executable solution obtained by an arbitrary method and storing it in a storage device;
Simplex operation means for receiving input of the initial executable solution, the objective function, and the constraint condition expression, and executing simplex operation processing;
If the simplex operation process results in a solution where the value of xi is either 0 or 1 and does not include any other value , the member assignment data is output with the solution as the optimal solution, otherwise Is a combination of the number of raw materials used that takes the objective function value of the initial feasible solution as a maximum value, the objective function value obtained as a result of the simplex operation processing as a minimum value, and takes the objective function value in that range. Are selected from among them, and the number of raw materials of which length is selected and used for allocation is selected for the constraint condition generation means. A request is made to generate a second constraint condition expression Cx = d, where the product of the use matrix C and the raw material use number vector x is equal to the raw material use scheduled quantity vector d, and the first constraint condition expression and the second constraint condition expression are requested. And the third Under the constraint condition of the constraint condition expression, the simplex operation means is requested to perform the arithmetic processing, and the simplex arithmetic processing obtained thereafter results in a solution where the value of xi is either 0 or 1 and does not include any other In this case, the member allocation data is output with the solution as an optimal solution, and in other cases, the next candidate whose objective function is close to the minimum value is selected from the listed combinations of the number of raw materials used. Select and request the constraint condition generation means to generate a new second constraint condition expression Cx = d, and repeat the operation of requesting the simplex operation means to perform arithmetic processing under this new constraint condition. A member processing apparatus comprising a search control means for controlling the apparatus.

  The member processing apparatus incorporating the arithmetic processing function of the configuration 1 automatically cuts out the products by the optimum assignment when the corresponding product length or material length is designated.

  <Configuration 4>
  The member processing apparatus according to Configuration 2, wherein the search control means sets an upper limit value for the number of repetitions of the second and subsequent simplex operation processes.

  <Configuration 5>
  A member assignment program that causes a computer to function as each means described in Configuration 1.
  <Configuration 6>
  A computer-readable recording medium having recorded thereon a member assignment program that causes the computer to function as each means described in Configuration 1.

<Configuration 7>
A method that optimizes the combination of products assigned to each raw material by obtaining the number of each type of raw material required when cutting out m products each having a predetermined length from k kinds of raw materials each having a predetermined length. There,
The product length setting means accepts the input of the product length data of m required products, and the m-th order product length vector Lp with the product length as an element and the product request quantity vector with the product request quantity as an element generating b and storing it in a storage device;
A step in which raw material length setting means receives input of raw material length data of k types of prepared lengths, generates a k-th raw material length vector Lm having the raw material length as an element, and stores it in a storage device;
The allocation pattern vector generation means compares the required product length data of the m products and the prepared raw material length data of the k kinds of raw materials, and economically determines one or more products. Enumerating m-th order allocation pattern vectors indicating the relationship between raw materials and products that can be allocated;
An allocation pattern matrix generation unit that generates an allocation pattern matrix A in which the allocation pattern vectors generated by the allocation pattern vector generation unit are arranged and stores the allocation pattern matrix A in a storage device;
The objective function generation means selects n allocation patterns included in the allocation pattern matrix and selects a corresponding raw material, defines an used number vector x of xi, and corresponds to the raw material length vector Lm. generating an objective function indicating a sum of products of m-th order cost coefficient vectors and the used number vectors x and storing the objective function in a storage device;
The first constraint condition expression Ax that the number of products cut out by the constraint condition generation means with the n number of allocation patterns selected from the allocation pattern matrix A must be equal to or greater than the quantity of each product that is determined. Generating a third constraint condition 0 ≦ xi ≦ 1 relaxed as ≧ b and storing it in the storage device;
An initial setting means for receiving an input of an initial executable solution obtained by an arbitrary method and storing it in a storage device;
A simplex computing means for receiving input of the initial executable solution, the objective function, and the constraint expression, and executing a simplex computing process;
The search control means outputs a member allocation data with the solution as the optimal solution when the value of xi is either 0 or 1 and does not include any other by the simplex operation processing, In other cases, the raw material which takes the value of the objective function in the range with the value of the objective function of the initial feasible solution as the maximum value and the value of the objective function obtained as a result of the simplex operation processing as the minimum value. Enumerating the combinations of the number of used and selecting the one whose objective function is close to the minimum value from among the combinations,
The search control means determines how many raw materials of which length to select and use for allocation to the constraint generation means. The product of the raw material use matrix C and the raw material use number vector x is the raw material use. Requesting generation of a second constraint condition expression Cx = d that is equal to the planned quantity vector d ;
The search control means requesting a simplex computing means to perform arithmetic processing under the constraint conditions of the first constraint condition expression, the second constraint condition expression, and the third constraint condition expression ;
When the search control means obtains a simplex operation process , and the solution is a solution that does not include any other value when the value of xi is 0 or 1, member assignment data is determined with that solution as the optimum solution. Otherwise, select the next candidate whose objective function is close to the minimum value from the listed combinations of the number of used raw materials , and A member assignment comprising: a step of requesting the generation of a new second constraint condition expression Cx = d, and a control to repeat the operation of requesting a calculation process to the simplex operation means under the new constraint condition Method.

  In the present invention, based on a practical solution obtained by an existing arbitrary method, it is evaluated by a simplex method to obtain a further improved solution. The simplex method is known as a method for searching for an optimal solution of a linear programming problem. However, if there are several tens of types of product lengths and raw materials required, the number of combinations may exceed several hundred thousand. The optimal value can be obtained by creating a parameter for arithmetic processing as it is based on the condition that any one of m types of products is assigned to n raw materials arbitrarily selected from k types of raw materials. There is a possibility that the simplex operation processing for the search takes too much time. Therefore, in the present invention, a constraint condition for the arithmetic processing by the simplex method is added to efficiently calculate while narrowing down the comparison target range. Hereinafter, embodiments of the present invention will be described in detail for each example.

FIG. 1 is a block diagram of a member allocation system 10 according to the first embodiment.
The member assignment system 10 shown in the drawing is operated by a computer program installed in the computer 12. This system is used, for example, by a terminal device 16 connected to the computer 12 via the network 14. The terminal device 16 is provided, for example, in a precut factory that precuts building structural materials. The member assignment system 10 receives the condition data for precut from the terminal device 16, executes the calculation process, and returns the result. The terminal device 16 controls the precut device 17 using the returned member allocation data. As the pre-cut device 17, for example, a device as described in Patent Document 1 can be used.

The computer 12 is provided with an arithmetic processing device 20 and a storage device 40. As shown in the figure, the arithmetic processing unit 20 includes a product length setting means 21, a raw material length setting means 22, an initial setting means 23, an allocation pattern vector generation means 24, an allocation pattern matrix generation means 25, a constraint condition generation means 26, a cost. Computer programs such as a coefficient vector generation unit 27, an objective function generation unit 28, a simplex operation processing unit 29, and a search control unit 30 are installed. These computer programs cooperate to execute arithmetic processing.

  The storage device 40 includes a product length vector Lp41, a product request quantity vector b42, a raw material length vector Lm43 (or a cost coefficient vector), an initial executable solution 44, a raw material use scheduled quantity vector d45, an allocation pattern matrix 46, as shown in the figure. The raw material use matrix C47, the first constraint condition formula 48, the second constraint condition formula 49, the third constraint condition formula 50, the objective function 51, the combination list 52, the member allocation data 53, and the like are stored. All of these data are generated by the operation of the computer program and stored in the storage device 40. Subsequently, the computer program and the data stored in the storage device 40 will be specifically described.

FIG. 2 is a hardware block diagram of a computer constituting the member assignment system 10.
Before describing specific functions of the member assignment system 10, the hardware of the member assignment system 10 will be described. As shown in the figure, an internal bus 110 housed in the main body case 3 of the computer 12 includes a CPU (Central Processing Unit) 111, a ROM (Read Only Memory) 112, a RAM (Random Access Memory) 113, and an HDD. A (hard disk) 114, an input / output interface 115, and a network interface 116 are connected. A display 3, a keyboard 4, and a mouse 5 are connected to the input / output interface 115. A terminal device 16 is connected to the network interface 116 via the network 14 . The above hardware is the same as that provided in a generally well-known personal computer. The terminal device 16 supplies the member allocation data 53 to the member selection supply device 120 of the precut device 17. As a result, the specified raw material is supplied to the member cutting device 121 and cut with the specified allocation pattern. The cut product is conveyed and discharged by the product conveying device 122.

  The storage device 40 illustrated in FIG. 1 includes a ROM 112, a RAM 113, and an HDD 114. The arithmetic processing unit 20 illustrated in FIG. 1 includes a CPU 111, a ROM 112, a RAM 113, and the like. Various types of information are mainly stored and saved in the HDD 114. A computer program executed by the CPU 111 is stored in the ROM 112 or loaded into the RAM 113 as appropriate. The terminal device may have the same configuration. The network can be the Internet or an intranet.

FIG. 3 is an explanatory diagram for explaining parameters of the arithmetic processing.
With reference to this figure, the definition of parameters used for arithmetic processing and the function of each computer program will be described.
[Product length vector Lp]
Let m be the quantity of products to be produced. In the illustrated example, m = 7.
The product length is expressed as Lp1, Lp2, ..., Lpm. The unit is, for example, m (meter).
The m-th order product length vector Lp is defined as follows.
Lp = (Lp1, Lp2,…, Lpm)
However, (Lp1 ≧ Lp2 ≧… ≧ Lpm)
In the illustrated example, Lp = (Lp1, Lp2, Lp3, Lp4, Lp5, Lp6, Lp7).

[Product request quantity vector b]
When the production of a product of quantity m is requested, a product demand quantity vector b is defined as follows. In this embodiment, explanation will be made assuming that bi = 1. bi may be any positive integer.
b = (b1, b2,..., bm) ^T
(The superscript T represents transposition. B is a column vector. The same applies to the following.)
In the illustrated example, b = (1,1,1,1,1,1,1) ^T.
The product length setting means 21 accepts the input of the product length data of m required products, and the m-th order product length vector Lp41 having the product length as an element and the product request quantity having the product request quantity as an element. The vector b42 is generated and stored in the storage device 40 that is stored in the storage device.

[Raw material data]
The raw materials include k kinds of lengths. In the illustrated example, k = 3.
The raw material length is expressed as Lm1, Lm2, ..., Lmk. The unit is, for example, m (meter).
The kth-order raw material length vector Lm is defined as follows.
Lm = (Lm1, Lm2, ..., Lmk)
However, (Lm1>Lm2>...> Lmk)
In the illustrated example, Lm = (Lm1, Lm2, Lm3).
The raw material length setting means 22 receives input of raw material length data of k types of prepared lengths, generates a k-th raw material length vector Lm43 having the raw material length as an element, and stores it in the storage device 40.

[Raw material use planned quantity vector d]
The raw material use scheduled quantity vector d45 indicates how many materials each having k types of lengths are used for a feasible solution. This is defined as follows.
d = (d1, d2,..., dk) ^T
In the illustrated example, d = (d1, d2, d3) ^T = (1, 2, 1) ^T. The raw material use scheduled quantity vector d45 is used in a third constraint condition expression described later.

[Number of used vectors x]
Any one of m types of products is allocated to n raw materials arbitrarily selected from k types of raw materials. At this time, an nth-order used number vector x representing the number of used n raw materials used is defined as follows. When n raw materials are selected from k types of raw materials, the same raw material may be selected twice or more. In the following example, two raw materials having a raw material length Lm2 are selected in duplicate.
x = (x1, x2,..., xn) ^T
For example, in the above specific example, the required products are assigned to the four raw materials listed as Lm1, Lm2, Lm2, and Lm3. At this time, x1 is set for the first Lm1, x2 for the second Lm2, x3 for the third Lm2, and x4 for the fourth Lm3. In the illustrated example, x1 = x2 = x3 = x4 = 1. When the selected raw materials and the unselected raw materials are listed, the value of xi set to the unselected raw materials is zero. That is, each element xi of the nth-order used number vector x is 0 or 1. The used number vector x is used in the constraint condition expression. This handling will be described more specifically in Example 3.

[Assignment pattern vector aj]
Data allocated so as to cut out any of m products from any one raw material is represented by an mth-order allocation pattern vector aj. This is defined as follows.
aj = (a1, a2, ..., am) ^T
Below, the allocation pattern vector in the example of a figure is shown.
Allocate one Lp2 and one Lp6 to Lm1 (0,1,0,0,0,1,0) ^T
Allocate one Lp1 to Lm2 (1, 0, 0, 0, 0, 0, 0) ^T
Assign Lp3 and Lp5 to Lm2 (0, 0, 1, 0, 1, 0, 0) ^T
Assign Lp4 and Lp7 to Lm3 (0, 0, 0, 1, 0, 0, 1) ^T

The above allocation pattern vector aj is generated so as to satisfy the following expression.
Lp · aj≤L (j = 1, 2, ..., n)
The product (Lp · aj) on the left side of this equation is the sum of one product length or a plurality of product lengths assigned to the selected raw material. The raw material of the minimum length Lmi that can be assigned this length is selected. L indicates the length Lmi of the selected raw material. In actual machining, the cutting length and blade thickness for taking out the rectangle are considered, but are ignored here.

For example, in the example shown in the figure, when one Lp3 and one Lp5 are allocated to Lm2, either one of the raw materials Lm1 or Lm2 can be allocated. However, since Lm1> Lm2, the assignment target is Lm2. In this way, find a relationship that can be allocated economically.
The example in the figure enumerates a set of allocation pattern vectors corresponding to feasible solutions. However, as a preparation for obtaining an optimal solution by the simplex method, as many allocation pattern vectors as possible can be enumerated in advance.
The allocation pattern vector generation means 24 economically allocates one or a plurality of products by comparing the product length data of m required products with the raw material length data of k kinds of prepared raw materials. An m-th order allocation pattern vector 46 a indicating the relationship between the raw material and the product that can be generated is generated and stored in the storage device 40.

[Assignment pattern matrix]
When allocating any of m types of products to n raw materials arbitrarily selected from k types of raw materials, n allocation pattern vectors are arranged. An m × n-order allocation pattern matrix in which n aj are arranged is defined below.
A = (aij) (i = 1, 2,..., M, j = 1, 2,..., N)
The allocation pattern matrix generation unit 25 generates an m × n-order allocation pattern matrix in which n allocation pattern vectors 46 a generated by the allocation pattern vector generation unit 24 are arranged, and stores them in the storage device 40.

[First constraint]
The product of the allocation pattern matrix A and the used number vector x is the number of products cut out from the selected raw materials with the corresponding allocation pattern. Accordingly, the number of each product cut out from the raw material selected from the allocation pattern matrix A with the corresponding allocation pattern must be equal to or greater than the quantity of each required product. The required quantity of each product corresponds to the product request quantity vector b. Therefore, the required number of products cannot be obtained unless at least the following formula is satisfied.
Σaij · xj ≧ bi
When the inequality sign is established, it is overmade. For convenience of calculation, the above inequality is used as a constraint. This constraint condition expression is expressed as Ax ≧ b.
In the example of the figure, the number of products produced and the number of required products are 7, and the equal sign is established.
The constraint condition generating means 26 generates a first constraint condition expression that the number of each product cut out from the raw material selected from the allocation pattern matrix A with the corresponding allocation pattern is equal to or greater than the number of each required product. Then, it is stored in the storage device 40.

[Raw material use matrix C]
A k-th-order raw material usage vector cj indicating which raw material to be used out of k kinds of raw materials is defined as follows.
cj = (c1j, c2j,..., ckj) ^T
However, c1j, c2j,..., Ckj are all 0 or 1.
As described above, the raw material usage matrix C is used to represent n raw materials selected from k kinds of raw materials. This is defined by a k × n-order matrix in which n cj are arranged.
C = (cij) (i = 1, 2,..., K, j = 1, 2,..., N)
In the illustrated example, cij is as follows.
c1 = (1, 0, 0) ^T
c2 = (0,1,0) ^T
c3 = (0,1,0) ^T
c4 = (0,0,1) ^T
The allocation pattern matrix generation means 25 generates a k × n-order raw material usage matrix C that enumerates raw material usage vectors cj indicating which raw material of k types of raw materials is used in each allocation pattern, Store in a storage device.

[Second constraint]
Since cj is a vector that designates one of k kinds of raw materials, the following equation is satisfied.
Σcij = 1
Only one of the k numbers is 1 and all others are 0.
The length of each raw material is selected to be the minimum length that can be assigned.
ΣLmi · cij = L
This L is a value indicated by an allocation pattern vector generation condition Lp · aj ≦ L.

Further, as already defined, the used number vector x of n raw materials was x = (x1, x2,..., Xn). Further, the raw material use scheduled quantity vector d indicates the number of uses for each raw material length.
Therefore, the condition of the following formula must be satisfied.
.SIGMA.cij.xj = di (i = 1, 2,..., K)
This constraint condition expression is expressed as Cx = d.
This defines how many raw materials of which length are selected and used for actual allocation. The specific relationship between the constraints of Ax ≧ b and Cx = d will be described more clearly in the third embodiment.
The constraint condition generation unit 26 generates a second constraint condition expression that the product of the raw material use matrix C generated by the allocation pattern matrix generation unit 25 and the raw material use number vector x is equal to the raw material use scheduled quantity vector d. And store it in the storage device.

[Third constraint]
Each element xi of the used number vector x is 0 or 1. This is because it has a meaning to determine which one of the many allocation pattern vectors listed is to be selected. Therefore, a constraint condition expression such as the following expression is established.
xi∈ {0,1}
In this embodiment, this constraint condition is relaxed. That is, a constraint condition expression of 0 ≦ xi ≦ 1 is set.
The constraint condition generation means generates a third constraint condition expression indicating that each element xi of the used number vector x is 0 ≦ xi ≦ 1, and stores it in the storage device.

[Cost factor vector]
Not only the price but also the transportation cost, storage cost, processing fee, etc. differ for each raw material of different length. All cost elements to be included in the calculation are included in the nth-order cost coefficient vector f and defined as follows.
f = (f1, f2,..., fn)
Since the cost coefficient vector f is applied only to the selected n kinds of raw materials, it is an n-order vector. For convenience of calculation, f1, f2,..., Fn are converted into expenses, and the unit is a circle. Therefore, as the objective function value is smaller, a product can be obtained at a lower cost.

If the price of the raw material is proportional to the length, it is agreed that the yield is the highest and the total cost is the lowest. However, prices per unit length when different by raw materials length adjusts the cost factor.
The cost coefficient vector generating means 27 generates an nth-order cost coefficient vector f including a price component in each element of the raw material length vector Lm. The element fi of the cost coefficient vector f is data whose unit is a circle. If the cost coefficient coefficient vector generation means 27 replaces the raw material length vector Lm with the cost coefficient vector f, the following processing can be performed without considering the cost coefficient vector f.

[Objective function]
In this calculation, any one of m types of products is assigned to n raw materials arbitrarily selected from k types of raw materials. At this time, a product can be obtained at a lower cost as the objective function value is smaller. Therefore, an objective function indicating the total cost for the n selected raw materials is defined as follows.
Min Σfi ・ xi
The objective function generation means 28 generates an objective function that indicates the total cost for the n selected raw materials, and stores it in the storage device.

[Use integer programming as a continuous relaxation problem]
In order to execute arithmetic processing by the simplex method, an objective function and constraint conditions are defined as follows.
Min Σfi ・ xi
subject to. Ax ≧ b
Cx = d
0≤xi≤1
The first expression is an objective function generated by the objective function generation means.
The second expression is a first constraint condition expression generated by the constraint condition generation means.
The third expression is a second constraint condition expression generated by the constraint condition generation means.
The fourth expression is a third constraint condition expression generated by the constraint condition generation means.
The objective function indicates the total cost of the n selected raw materials.
The first constraint condition expression shows the relationship among the allocation pattern matrix A, the used number vector x, and the product request quantity vector b.
The second constraint condition expression shows the relationship among the raw material use matrix C, the raw material use number vector x, and the raw material use scheduled quantity vector d.
The third constraint condition expression indicates that xi is 0 or more and 1 or less.

The initial setting means 23 receives an arbitrary initial executable solution 44 acquired by an arbitrary method. Then, parameters for simplex operation processing are generated. Examples of the arbitrary method include a first fit method and a method described in Patent Document 1. The initial feasible solution can be represented by a used number vector x of raw materials that designates an allocation pattern vector selected from the above allocation pattern matrix A46. This will also be described more specifically in the third embodiment. The parameters input for the first simplex operation processing are data constituting the objective function Σfi · xi, the first constraint condition expression Ax ≧ b, and the third constraint condition expression 0 ≦ xi ≦ 1.

  The search control means 30 causes the simplex arithmetic processing means to input parameters excluding the constraint condition of Cx = d and execute the first arithmetic processing. The simplex operation processing means changes the basis variable of the simplex table so as to improve the value of the objective function and outputs a solution. The third constraint condition expression 0 ≦ xi ≦ 1 relaxes the constraint condition of xiε {0, 1}. Accordingly, the solution may include something other than an integer such as xi = 0.5. There may be a plurality of solutions having the same objective function value.

  The search control means 30 detects a solution in which the value of xi is either 0 or 1 and does not include anything other than the obtained solutions. When it is detected, the member assignment data 53 is generated with the solution as the optimum solution, and the process is terminated. In other cases, the search control means regenerates parameters for the next simplex operation process. First, the objective function value F0 of the feasible solution that has been initially set is set to the maximum value. This is because the goal is to improve the default solution. Further, the value F1 of the objective function of the solution obtained by the first simplex calculation process is set to the minimum value. Since the solution is obtained by relaxing the conditions, the objective function value at that time is determined as the limit value.

  Next, the search control means 30 enumerates combinations of the numbers of raw materials whose objective function values are F1 or more and F0 or less, and generates a combination list. This corresponds to the raw material scheduled use quantity vector d. From this combination list, the one with the smallest objective function value is selected as the next candidate. Although a specific example will be described in the third embodiment, the constraint condition generation unit 26 generates the second constraint condition expression Cx = d. If there is a change in the parameters such as the objective function and the allocation pattern vector, the first constraint condition expression Ax ≧ b is also generated. Thereafter, the search control means 30 inputs the generated parameters to the simplex arithmetic processing means 29 to execute arithmetic processing. The third constraint condition expression 0 ≦ xi ≦ 1 is not changed.

  As a result, the obtained solution is detected when the value of xi is 0 or 1 and does not include any other value. When detected, the solution is regarded as an optimal solution. In other cases, the next candidate having the second smallest objective function value in the list of combinations of the number of raw materials is selected. Then, in the same manner as the previous time, the second constraint condition expression Cx = d is generated, the parameters are changed, and the generated parameters are input to the simplex calculation processing means to execute calculation processing.

  In this way, the simplex operation process is repeated to search for the optimum solution. When a large number of combinations of raw material combinations are generated, an upper limit is set for the number of combinations of raw material combinations, and if an optimal solution is not found even after searching a certain number of times, an initial executable solution is obtained. As an optimal solution, the member allocation data 53 may be output. In the above arithmetic processing, since the constraint condition indicating the relationship between the allocation pattern matrix A, the used number vector x, and the product request quantity vector b is used, the product length is not included in the parameters of the simplex arithmetic processing, and the calculation is complicated. Don't be. In addition, since the parameter is set so that the used number vector x of the raw material in which each element takes a value of only 0 or 1 becomes a basis variable, and simplex operation processing is executed under a relaxed constraint condition of 0 ≦ xi ≦ 1, Even when the optimum solution cannot be obtained, the search function can be limited by obtaining the minimum value of the objective function.

FIG. 4 is a flowchart of the first simplex operation processing operation.
An embodiment of a computer program for controlling the above system will be described with reference to these drawings.
In step S11, the raw material length setting means 22 accepts raw material data. The terminal device 16 receives input of all raw material length data to be used, generates data corresponding to the raw material length vector Lm43, and stores it in the storage device 40. In step S12, the product length setting means 21 accepts input of the product length and quantity. The input of the requested product length data is received from the terminal device 16, data corresponding to the product length vector Lp 41 and the product request quantity vector b 42 is generated and stored in the storage device 40.

  In step S13, the initial setting means 23 receives an input of the initial executable solution 44. The result is stored in the storage device 40. In step S14, the allocation pattern vector generation means 24 compares the product length vector Lp41, the raw material length vector Lm43, etc., and generates an allocation pattern vector. The allocation pattern vector is stored in the storage device 40. Subsequently, in step S <b> 15, the allocation pattern matrix generation unit 25 generates the allocation pattern matrix 46 and stores it in the storage device 40. Next, in step S <b> 16, the constraint condition generation unit 26 generates a first constraint condition expression 48, a second constraint condition expression 49, and a third constraint condition expression 50 and stores them in the storage device 40.

  In step S17, the cost coefficient vector generation means 27 generates a cost coefficient vector, and in step S18, the objective function generation means 28 sets the objective function 51 using the cost coefficient vector. The result is stored in the storage device 40. Next, the search control means 30 inputs the first calculation parameter to the simplex calculation processing means 29 in step S19. In step S20, a simplex operation using this operation parameter is executed. When the solution is obtained, the search control means 30 determines whether or not it is an integer solution in step S21. If the result of this determination is yes, it is an optimal solution, so that member assignment data is output in step S23 and the process is terminated. If no, the process proceeds to step S22. In step S22, the search control means 30 controls the change of the constraint condition and the recalculation by the simplex method. This process will be described with reference to FIG.

FIG. 5 is a flowchart of the calculation process after the completion of the first simplex calculation.
The operation of this flowchart is controlled by the search control means 30 and executed by the simplex operation processing means 29. First, in step S31, the maximum value of the objective function is set from the initial executable solution. Next, in step S32, the minimum value of the objective function is set from the calculation processing result in step S20 of FIG. In step S33, a raw material combination list is generated within the set objective function range. The results are stored in the storage device 40 by arranging them in ascending order of the objective function. In step S34, the one with the smallest objective function value is selected from the combination list. In step S35, a request is made to the constraint condition generation means 26 to set a constraint condition of Cx = d.

In step S36, the objective function generation unit 28 is requested to set the objective function. In step S37, a simplex operation is executed. In step S38, the search control means 30 determines whether an integer solution has been obtained. If the result of this determination is yes, this process ends, and the process proceeds to step S23 in FIG. On the other hand, if no, the process proceeds to step S39. In step S39, it is determined whether or not the pivot calculation process in step S38 has been repeated W times set in advance. W times is an upper limit value. As a result, if a solution is not obtained even after a long search, the process is stopped. That is, in step S40, the initial executable solution is output as a calculation processing result. If the number of repetitions is less than W times, the process returns to step S34, the combination list having the next largest objective function value is selected, and the simplex operation process is executed again. Through the above processing, the computer program automatically searches for an optimal solution.

6 to 11 are explanatory diagrams of specific calculation examples.
With reference to these drawings, the operation of the above-described apparatus will be described more specifically by an actual calculation example.
(Raw material data)
For example, there are five kinds of prepared raw materials. The length is as follows. The unit of length is 0.1 mm (millimeter).
Lm1 = 60000
Lm2 = 49000
Lm3 = 4 5 000
Lm4 = 4 0 000
Lm5 = 30000
(Product length data)
Seven products are required, and the length is as follows. The unit of length is 0.1 mm (millimeter).
Lp1 = 53050
Lp2 = 44350
Lp3 = 30700
Lp4 = 26250
Lp5 = 21050
Lp6 = 17840
Lp7 = 17150

(Assignment pattern vector)
FIG. 6A is an explanatory diagram of an allocation pattern vector.
The above seven types of product lengths are listed in one vertical column from the top to the bottom on the left side of the figure. In addition, the raw material lengths are listed in one horizontal row from the left to the right at the top. A vertical line below each raw material length is an assigned pattern vector. For example, one having a product length of 44350 can be assigned to one having a raw material length of 45000. For example, one with a product length of 30700 and 17840 can be assigned to one with a raw material length of 49000. This table compares the product length data of seven products with the raw material length data of five types of raw materials in this way, and the raw materials and products that can economically allocate one or more products. 7th order allocation pattern vectors indicating the relationship with Here, x1 to x5 are allocation pattern vectors obtained from the initial executable solution, and x6 to x18 are additionally generated allocation pattern vectors.

  x1 to x18 are each element of the used number vector x of the raw material. Whether or not the raw material of the length displayed on the lower side is used in the corresponding allocation pattern is indicated by a numerical value of 0 or 1. When the value of x1 to x18 is 0, the raw material is not used, and when it is 1, it is used. Which of the listed allocation pattern vectors is to be selected is displayed based on the used number vector x of raw materials.

  An initial feasible solution has already been obtained by the method shown in Patent Document 1 and the like. For example, a solution that x1 = x2 = x3 = x4 = x5 = 1 is obtained by the First Fit method. The other values of X6 to x18 are 0 solutions. That is, when seven products are cut out from the five raw materials shown below x1 to x5 in a corresponding allocation pattern, the required product is obtained. Further improve and optimize the combination of raw materials and products.

  An allocation pattern matrix A is obtained by arranging 18 seventh-order allocation pattern vectors shown below x1 to x18. The product of the allocation pattern matrix A and the used number vector x is the number of products cut out from the selected raw material with the corresponding allocation pattern. The vertical column below the required number display at the top left of the figure shows the number of products sought. This corresponds to the product request quantity vector b. Therefore, the constraint condition of Ax ≧ b is established that the number of each product cut out from the raw material selected from the above allocation pattern matrix A with the corresponding allocation pattern must be equal to or greater than the quantity of each required product. To do.

(Objective function)
In order to simplify the explanation, each element of the cost coefficient vector f is matched with the raw material length. That is, the numerical value of length is read as a circle as it is.
The 18 numerical values on the right side of the raw material length in FIG. 6A are elements of the cost coefficient vector f. Therefore, the value of the objective function Σ (fi · xi) of the feasible solution input as the initial value is 233,000, which is the sum of the used raw material lengths x1 to x5. In the following calculation, a solution that improves this is obtained, so the upper limit value of the objective function is set to 233000.

(Raw material usage matrix C)
FIG. 6B shows raw material use vectors cj corresponding to the respective assigned pattern vectors in FIG. The raw material used when the allocation pattern vector of x1-x18 is selected is shown. Accordingly, the product of the raw material usage vector cj and the raw material usage number vector x indicates a breakdown of the number of raw materials used for each raw material length.

(Simplex method arithmetic processing)
Input the following objective function and constraints to the simplex algorithm module to solve the continuous relaxation problem. The constraint condition of Cx = d is excluded, and the arithmetic processing is performed under a relaxed condition of 0 ≦ xi ≦ 1.
min: Σ (fi × xi)
sub. to Ax ≧ b
Elements x1 to x18 of the used number vector x of raw materials must be 0 or 1. Therefore, first, simplex operation processing is executed under the condition that xi can take a range of 0 ≦ xi ≦ 1. Then, it is checked whether there is a solution that xi is 0 or 1.

7 and 8 are explanatory diagrams of solutions obtained by the simplex method arithmetic processing.
The raw material length group as shown in FIG. 6A is set as an objective function, and the allocation pattern matrix A is input as a constraint condition. In the simplex calculation process, the combinations of the allocation pattern vectors are changed so that the value of the objective function becomes smaller as the calculation proceeds. The solution of the continuous relaxation problem with the objective function value = 221000 was obtained by the simplex operation processing. A commercially available general-purpose program module can be used for this simplex operation processing.

  In the tables of FIG. 7 and FIG. 8, the display of the allocation pattern vector having a solution value of 0 is excluded. That is, FIG. 7 shows a solution that x4 = x1 = x16 = 1, x12 = x9 = x3 = 0.5, and the others are zero. FIG. 8 shows a solution that x4 = x1 = 1, x2 = x9 = x10 = x16 = x3 = 0.5, and the others are zero. For example, in the example of FIG. 7, when one raw material length is 60000, 45000, 49000 each and 0.5 raw material length is 40000, 49000, 45000 each, an objective function value is 221000. Results were obtained. Certainly, the objective function value is smaller than the initial value. However, since the constraint condition of xi ∈ {0, 1} was relaxed so that 0 ≦ xi ≦ 1, an infeasible solution of xi = 0.5 was obtained.

  In the present invention, the objective function value when the above solution is obtained is set to the lower limit value of the optimum value. That is, since the objective is to improve the initial feasible solution, the initial value of the objective function value is set to the maximum value 233000, and the objective function value 221000 obtained by the first simplex operation processing is set to the minimum value. Assuming that there is an optimum value in this range, the search is performed again. Here, the case where the objective function value becomes a value smaller than 221000 or more and 233000 by combining an arbitrary number of raw materials is listed. For example, calculation results to be aggregated while selecting combinations may be sorted in ascending order.

  It is not necessary to enumerate all the combinations. While enumerating in order from the sum of the raw material lengths, that is, from the smallest objective function value, the second and subsequent simplex operations are executed, and an executable solution, that is, an optimal solution is obtained. If it is obtained, the process may be terminated. Therefore, for example, no. 1-No. By enumerating combinations up to the 10th place and performing a simplex operation process with a sufficiently narrow search range, the operation processing time can be shortened.

  For example, no. 1 is a combination of three raw material lengths of 49000, 1 of 45000, and 1 of 30000. That is, in the second and subsequent simplex operation processes, the raw material use scheduled quantity vector d is determined, and a constraint condition Cx = d is added. Then, simplex operation processing is executed again. Similar to the first time, the solution is obtained by relaxing the constraint condition 0 ≦ xi ≦ 1. When a solution that all xi are 0 or 1 is obtained, precut data is generated based on the result. In other cases, the next candidate is selected from the listed combinations of raw materials, the raw material use scheduled quantity vector d is determined, and the raw material use matrix shown in FIG. 6B is rewritten.

FIG. 9 is an explanatory diagram of a solution obtained by the simplex method arithmetic processing.
No. In one example, since the maximum raw material length used is 49000, a product with a product length of 53050 is clearly not obtained. No. 2, the raw material length 49000 is 2 pieces, 45000 is 1 piece, and 40000 is 2 pieces. No. 3, the raw material length 49000 is one, 45000 is one, 40000 is one, and 30000 is three. No. 4, all the raw material lengths 60000 to 30000 are combined into one. By repeating the above arithmetic processing, the combination number of the raw material No. 4, an integer solution with all base variables of the simplex table being 1 was obtained. Select one each having a raw material length of 60.000.40000.45000.30000.49000, and assign a product to be cut out. Thereby, the sum total of raw material length becomes 224000. Since the sum of the raw material lengths of the initial feasible solution was 233,000, it was possible to find an allocation pattern that can save raw materials by 9000. Data indicating the listed combinations is output as member assignment data and transmitted to the terminal device.

FIG. 10 is a block diagram of the member processing apparatus for explaining the effect of the arithmetic processing in the third embodiment.
The member assignment data 53 was obtained by the above processing. This is supplied to the precut device 17 at the precut factory. The raw materials are selected in the order shown in FIG. 10 and cut according to the corresponding assignment pattern to obtain a product. In this example, the yield in the case of the initial feasible solution was 0.903, but became 0.939 after the improvement. In a pre-cut factory that allocates a large amount of product to a large amount of raw materials and cuts it, a cost reduction can be achieved by simply improving the yield by about 1%. In addition, if the amount of waste can be reduced by 1%, facilities and costs for waste disposal can be saved. In the above example, the types of raw materials and the types and quantities of products required are simplified. However, if a wide variety of raw materials and products are handled, it is expected that the yield will be significantly improved to a level that could not be achieved by the conventional method. be able to.

  Note that the computer program executed by the above-described arithmetic processing device may be modularized in units shown in functional blocks, or may be integrated by combining a plurality of functional blocks. Further, the above computer program may be used by being incorporated into an existing application program. The computer program for realizing the present invention can be recorded on a computer-readable recording medium such as a CD-ROM and installed in any information processing apparatus for use.

1 is a block diagram of a member allocation system 10 according to a first embodiment. 2 is a hardware block diagram of a computer constituting the member allocation system 10. FIG. It is explanatory drawing for demonstrating the parameter of a calculation process. It is a first simplex operation processing flowchart. It is a flowchart of the arithmetic processing after the completion of the first simplex operation. It is explanatory drawing of a specific calculation example, (a) is explanatory drawing of the allocation pattern vector, (b) is explanatory drawing of the raw material use vector cj. It is explanatory drawing of the solution obtained by the simplex method arithmetic processing. It is explanatory drawing of another solution obtained by the simplex method arithmetic processing. It is explanatory drawing of the solution obtained by the simplex method arithmetic processing. It is a block diagram of the member processing apparatus explaining the effect of the arithmetic processing in Example 3.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Member allocation system 12 Computer 14 Network 16 Terminal apparatus 20 Processing unit 21 Product length setting means 22 Raw material length setting means 23 Initial setting means 24 Allocation pattern vector generation means 25 Allocation pattern matrix generation means 26 Constraint condition generation means 27 Cost counting coefficient Vector generating means 28 Objective function generating means 29 Simplex arithmetic processing means 30 Search control means 40 Storage device 41 Product length vector Lp
42 Product requirement quantity vector b
43 Raw material length vector Lm
44 Initial feasible solution 45 Raw material use planned quantity vector d
46 Allocation pattern matrix 46a Allocation pattern vector 47 Raw material use matrix C
48 First constraint condition expression 49 Second constraint condition expression 50 Third constraint condition expression 51 Objective function 52 Combination list 53 Member allocation data

Claims (7)

The number of each type of raw material required when each of m products of a predetermined length is cut out from k types of raw materials of a predetermined length, and the combination of products assigned to each raw material is optimized. There,
Accepting the input of product length data of m required products, and generating an m-th order product length vector Lp having the product length as an element and a product request quantity vector b having the product request quantity as an element Product length setting means for storing in the storage device;
A raw material length setting means that receives input of raw material length data of k types of prepared lengths, generates a k-th order raw material length vector Lm having the raw material length as an element, and stores it in a storage device;
The raw material and product which can economically allocate one or a plurality of products by comparing the product length data of the required m products with the raw material length data of the k kinds of raw materials prepared An allocation pattern vector generation means for enumerating m-th order allocation pattern vectors,
An allocation pattern matrix generation unit that generates an allocation pattern matrix A in which the allocation pattern vectors generated by the allocation pattern vector generation unit are arranged and stores the allocation pattern matrix A in a storage device;
An element for selecting a corresponding raw material by selecting from n allocation patterns included in the allocation pattern matrix defines a use number vector x of x i, and an m-th order cost coefficient vector corresponding to the raw material length vector Lm; An objective function generating means for generating an objective function indicating a sum of products of the used number vectors x and storing the objective function in a storage device;
The number of products cut out by n allocation patterns selected from the allocation pattern matrix A has been relaxed as a first constraint condition Ax ≧ b, which must be equal to or greater than the quantity of each required product . A constraint condition generation means for generating a third constraint condition expression 0 ≦ xi ≦ 1 and storing it in the storage device;
Initial setting means for receiving an input of an initial executable solution obtained by an arbitrary method and storing it in a storage device;
Simplex operation means for receiving input of the initial executable solution, the objective function, and the constraint condition expression, and executing simplex operation processing;
If the simplex operation process results in a solution where the value of xi is either 0 or 1 and does not include any other value , the member assignment data is output with the solution as the optimal solution, otherwise Is a combination of the number of raw materials used that takes the objective function value of the initial feasible solution as a maximum value, the objective function value obtained as a result of the simplex operation processing as a minimum value, and takes the objective function value in that range. Are selected from among them, and the number of raw materials of which length is selected and used for allocation is selected for the constraint condition generation means. A request is made to generate a second constraint condition expression Cx = d, where the product of the use matrix C and the raw material use number vector x is equal to the raw material use scheduled quantity vector d, and the first constraint condition expression and the second constraint condition expression are requested. And the third Under the constraint condition of the constraint condition expression, the simplex operation means is requested to perform the arithmetic processing, and the simplex arithmetic processing obtained thereafter results in a solution where the value of xi is either 0 or 1 and does not include any other In this case, the member allocation data is output with the solution as an optimal solution, and in other cases, the next candidate whose objective function is close to the minimum value is selected from the listed combinations of the number of raw materials used. Select and request the constraint condition generation means to generate a new second constraint condition expression Cx = d, and repeat the operation of requesting the simplex operation means to perform arithmetic processing under this new constraint condition. A member allocation system comprising search control means for controlling the member. In the member allocation system according to claim 1 ,
The search control means provides an upper limit value for the number of repetitions of the second and subsequent simplex operation processes. Means for optimizing the combination of products assigned to each raw material by obtaining the number of each type of raw material required when each of m products having a predetermined length is cut out from k kinds of raw materials each having a predetermined length; A pre-cut device that accepts optimized member allocation data and cuts the m products from the k kinds of raw materials that are sequentially supplied;
Accepting the input of product length data of m required products, and generating an m-th order product length vector Lp having the product length as an element and a product request quantity vector b having the product request quantity as an element Product length setting means for storing in the storage device;
A raw material length setting means that receives input of raw material length data of k types of prepared lengths, generates a k-th order raw material length vector Lm having the raw material length as an element, and stores it in a storage device;
The raw material and product which can economically allocate one or a plurality of products by comparing the product length data of the required m products with the raw material length data of the k kinds of raw materials prepared An allocation pattern vector generation means for enumerating m-th order allocation pattern vectors,
An allocation pattern matrix generation unit that generates an allocation pattern matrix A in which the allocation pattern vectors generated by the allocation pattern vector generation unit are arranged and stores the allocation pattern matrix A in a storage device;
An element for selecting a corresponding raw material by selecting from n allocation patterns included in the allocation pattern matrix defines a use number vector x of x i, and an m-th order cost coefficient vector corresponding to the raw material length vector Lm; An objective function generating means for generating an objective function indicating a sum of products of the used number vectors x and storing the objective function in a storage device;
The number of products cut out by n allocation patterns selected from the allocation pattern matrix A has been relaxed as a first constraint condition Ax ≧ b, which must be equal to or greater than the quantity of each required product . A constraint condition generation means for generating a third constraint condition expression 0 ≦ xi ≦ 1 and storing it in the storage device;
Initial setting means for receiving an input of an initial executable solution obtained by an arbitrary method and storing it in a storage device;
Simplex operation means for receiving input of the initial executable solution, the objective function, and the constraint condition expression, and executing simplex operation processing;
If the simplex operation process results in a solution where the value of xi is either 0 or 1 and does not include any other value , the member assignment data is output with the solution as the optimal solution, otherwise Is a combination of the number of raw materials used that takes the objective function value of the initial feasible solution as a maximum value, the objective function value obtained as a result of the simplex operation processing as a minimum value, and takes the objective function value in that range. Are selected from among them, and the number of raw materials of which length is selected and used for allocation is selected for the constraint condition generation means. A request is made to generate a second constraint condition expression Cx = d, where the product of the use matrix C and the raw material use number vector x is equal to the raw material use scheduled quantity vector d, and the first constraint condition expression and the second constraint condition expression are requested. And the third Under the constraint condition of the constraint condition expression, the simplex operation means is requested to perform the arithmetic processing, and the simplex arithmetic processing obtained thereafter results in a solution where the value of xi is either 0 or 1 and does not include any other In this case, the member allocation data is output with the solution as an optimal solution, and in other cases, the next candidate whose objective function is close to the minimum value is selected from the listed combinations of the number of raw materials used. Select and request the constraint condition generation means to generate a new second constraint condition expression Cx = d, and repeat the operation of requesting the simplex operation means to perform arithmetic processing under this new constraint condition. A member processing apparatus comprising a search control means for controlling the apparatus.   The member processing apparatus according to claim 2,
  The search control means provides an upper limit value for the number of repetitions of the second and subsequent simplex operation processes.   The member allocation program which makes a computer function as each means of Claim 1.   A computer-readable recording medium having recorded thereon a member assignment program that causes the computer to function as each means according to claim 1. A method that optimizes the combination of products assigned to each raw material by obtaining the number of each type of raw material required when cutting out m products each having a predetermined length from k kinds of raw materials each having a predetermined length. There,
The product length setting means accepts the input of the product length data of m required products, and the m-th order product length vector Lp with the product length as an element and the product request quantity vector with the product request quantity as an element generating b and storing it in a storage device;
A step in which raw material length setting means receives input of raw material length data of k types of prepared lengths, generates a k-th raw material length vector Lm having the raw material length as an element, and stores it in a storage device;
The allocation pattern vector generation means compares the required product length data of the m products and the prepared raw material length data of the k kinds of raw materials, and economically determines one or more products. Enumerating m-th order allocation pattern vectors indicating the relationship between raw materials and products that can be allocated;
An allocation pattern matrix generation unit that generates an allocation pattern matrix A in which the allocation pattern vectors generated by the allocation pattern vector generation unit are arranged and stores the allocation pattern matrix A in a storage device;
The objective function generation means selects n allocation patterns included in the allocation pattern matrix and selects a corresponding raw material, defines an used number vector x of xi, and corresponds to the raw material length vector Lm. generating an objective function indicating a sum of products of m-th order cost coefficient vectors and the used number vectors x and storing the objective function in a storage device;
The first constraint condition expression Ax that the number of products cut out by the constraint condition generation means with the n number of allocation patterns selected from the allocation pattern matrix A must be equal to or greater than the quantity of each product that is determined. Generating a third constraint condition 0 ≦ xi ≦ 1 relaxed as ≧ b and storing it in the storage device;
An initial setting means for receiving an input of an initial executable solution obtained by an arbitrary method and storing it in a storage device;
A simplex computing means for receiving input of the initial executable solution, the objective function, and the constraint expression, and executing a simplex computing process;
The search control means outputs a member allocation data with the solution as the optimal solution when the value of xi is either 0 or 1 and does not include any other by the simplex operation processing, In other cases, the raw material which takes the value of the objective function in the range with the value of the objective function of the initial feasible solution as the maximum value and the value of the objective function obtained as a result of the simplex operation processing as the minimum value. Enumerating the combinations of the number of used and selecting the one whose objective function is close to the minimum value from among the combinations,
The search control means determines how many raw materials of which length to select and use for allocation to the constraint generation means. The product of the raw material use matrix C and the raw material use number vector x is the raw material use. Requesting generation of a second constraint condition expression Cx = d that is equal to the planned quantity vector d ;
The search control means requesting a simplex computing means to perform arithmetic processing under the constraint conditions of the first constraint condition expression, the second constraint condition expression, and the third constraint condition expression ;
When the search control means obtains a simplex operation process , and the solution is a solution that does not include any other value when the value of xi is 0 or 1, member assignment data is determined with that solution as the optimum solution. Otherwise, select the next candidate whose objective function is close to the minimum value from the listed combinations of the number of used raw materials , and A member assignment comprising: a step of requesting the generation of a new second constraint condition expression Cx = d, and a control to repeat the operation of requesting a calculation process to the simplex operation means under the new constraint condition Method.

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