JP5983976B1 - Member assignment system, member assignment program, recording medium and member processing apparatus - Google Patents

Abstract

An allocation calculation is performed to cut out not only rectangular but also polygonal products from k kinds of rectangular raw materials, and the yield is maximized. At that time, the calculation time is shortened by collecting the products having the same shape. Before starting the allocation calculation, a non-rectangular polygon product is processed so as to be regarded as the smallest rectangular product including the polygon. After starting the allocation calculation, it is determined whether or not other products can be allocated to the remaining raw materials cut out from the raw materials. At this time, a polygonal product is cut out from the rectangle including the polygon, and it is determined whether other products can be allocated to the remaining raw materials. In addition, products with the same shape are grouped together to reduce the number of assigned patterns. [Selection] Figure 1

Description

The present invention, in the case of cutting out the product in a variety of shapes from raw materials, their speed up processing for optimizing the blank layout, the member assignment system and member allocation program recording medium body and member machining device.

Several types of raw materials are prepared for pre-cutting of house structural materials according to specifications such as cross-sectional shape, tree type, grade, and layer. A member (product) with the required dimensions is cut out from there. Depending on the product specifications, the product dimensions, and the combination of the raw materials to be cut out, the amount of parts that are cut off from the raw materials and wasted differs. For linear materials such as columns and plates with a certain width, a technology that uses simplex arithmetic processing to search for optimum values for minimizing yield or cost by hill-climbing, random restart, annealing, etc. Has been developed (see Patent Document 1). Subsequently, when cutting out products with various vertical and horizontal dimensions from raw materials, a technology was developed to improve yield by executing predetermined arithmetic processing starting from the initial feasible solution obtained in advance by an existing method. (See Patent Document 2). Furthermore, a technique for obtaining an optimum combination of a product and a raw material for cutting the raw material vertically and horizontally and creating an instruction for a specific precut operation has been developed (see Patent Document 3 ).

JP 2009-98924 A Japanese Patent No. 3079189 Japanese Patent No. 5838047 Japanese Patent No. 3441420

The yield may be different between when each product is assigned to a raw material in a portrait orientation and in a landscape orientation. Furthermore, another product can be newly assigned to the remaining raw material from which the product is cut out. The optimization calculation for allocation including these has a problem that the number of products becomes extremely large when the number of products is large, and it takes a long time for the arithmetic processing.

  The present invention has been made in order to solve the above problems, and a member assignment system and a member assignment which can shorten the processing time for assignment calculation for cutting out products of various shapes from raw materials. It is an object to provide a program, a recording medium, and a member processing apparatus.

  The following configurations are means for solving the above-described problems.

<Configuration 1>
Each of the predetermined rectangular m products is obtained from each of the predetermined rectangular k kinds of raw materials, and the number of raw materials of each type required is obtained, and the combination of products assigned to the respective raw materials is optimized. ,
Accepts the input of the required horizontal data and vertical data of m products, and receives the m-th product horizontal vector wp whose product is the horizontal length and the m-th product vertical vector hp whose product is the vertical product. A product setting means for generating an m-th order product area vector sp having a product area as an element and an m-th order product request quantity vector b having a product request quantity as an element, and storing them in a storage device;
Accepts input of raw material data of k kinds of prepared rectangles, k-th raw material horizontal vector wm whose horizontal element is the raw material, k-th raw material vertical vector hm whose vertical element is the raw material, A raw material setting means for generating a k-th order raw material area vector sm having an area as an element and a k-th order raw material number vector nm having a raw material type number as an element, and storing them in a storage device;
The first evaluation condition (sp, aj) (inner product) ≦ S that the area of the allocated product is equal to or smaller than the area S of any one of the elements of the raw material area vector sm is assumed to be not overlapped with the adjacent product. Second evaluation condition, wpi + wpj ≦ wml or hpi + hpj ≦ hml,
Two-dimensional model condition generation means for generating a two-dimensional model condition including a third evaluation condition that the allocation pattern vector aj can be allocated by a predetermined allocation method, and storing the two-dimensional model condition in a storage device;
Initial setting means for receiving an input of an initial executable solution obtained by the predetermined allocation method, generating an m-th order initial allocation pattern vector and an initial allocation pattern matrix, and storing them in a storage device;
If the product horizontal data and product vertical data of the m products that are required are the same, the same product is combined into one element, and the product of less than m-th order including the same product horizontal data as the element A horizontal vector wp1, a product vertical vector hp1 less than m-order having the same product vertical length as an element, a product area vector sp1 less than m-th order having the same product area as an element, and a product less than m-th order Product resetting means for generating the requested quantity vector b1,
An initial allocation pattern vector is converted into an allocation pattern vector of less than m order corresponding to the same product, and an initial allocation pattern matrix is converted into an allocation pattern matrix corresponding to the allocation pattern vector of less than m order and stored in a storage device. Initial setting conversion means,
The product horizontal data included in the product horizontal vector wp1 less than the m-th order and the product vertical data included in the product vertical vector hp1 less than the m-th order are obtained. Compared with data and raw material longitudinal data, one or a plurality of products satisfying the two-dimensional model condition including the first evaluation condition, the second evaluation condition, and the third evaluation condition can be economically allocated. An allocation pattern vector generating means for enumerating allocation pattern vectors aj less than m-th order indicating the relationship between raw materials and products;
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;
Any one of the products included in the product horizontal vector wp1 less than the mth order and the product vertical vector hp1 less than the mth order is allocated to n raw materials arbitrarily selected from k kinds of raw materials. Then, in order to represent the number of used n raw materials used, an n-th order used number vector x whose elements are xi is defined, and the n-th order cost coefficient vector f corresponding to each of the n raw materials and the An objective function generating means for generating an objective function indicating the sum of products of the used number vectors x and storing the objective function in a storage device;
A first constraint condition expression Ax ≧ b1 is generated, in which the number of each product cut out with the selected allocation pattern from the allocation pattern matrix A must be equal to or greater than the quantity of each required product, and the storage device A constraint condition generating means to be stored in
Simplex operation processing means for receiving input of the initial executable solution, the objective function, and the constraint condition expression, and executing simplex operation processing;
Search control means for controlling arithmetic processing to search for and output the optimal solution,
This search control means
By the simplex operation process, when the value of xi is an integer greater than or equal to 0 and does not include any other value, the face material allocation data is output as the optimal solution, and otherwise The combination of the number of used raw materials that takes the value of the objective function in the range, with the objective function value of the initial feasible solution as the maximum value and the objective function value obtained as a result of the simplex operation processing as the minimum value. A raw material use matrix that enumerates and selects what kind of raw materials are selected and used for allocation to the constraint condition generation means by selecting the objective function close to the minimum value from among them Requesting the constraint condition generating means to generate a second constraint condition expression Cx = d, wherein the product of the number of used materials vector C and the raw material use quantity vector d is equal to
Under the constraint conditions of the first constraint condition expression and the second constraint condition expression, the simplex arithmetic processing means is requested to perform arithmetic processing, and the value of xi obtained by the simplex arithmetic processing is an integer of 0 or more, If the solution does not include any other solution, the face material allocation data is output with the solution as the optimal solution. In other cases, an executable solution with a non-integer solution is obtained by the simplex operation processing. Further, when an executable solution with a non-integer solution is obtained in the subsequent simplex operation processing, an evaluation formula Σ (the number of xi is an integer) for determining the number of xi that is an integer among xi is defined. If the value of the evaluation formula obtained by the non-integer solution obtained later is larger than the value of the evaluation formula obtained by the non-integer solution obtained earlier, Integer solution approaches integer solution and evaluates When the determination means determines that the non-integer solution does not approach the integer solution when the value of is reduced, when the determination unit determines that the non-integer solution does not approach the integer solution even when the simplex operation process is repeated, Change the constraint condition expression and control to repeat the simplex operation process,
A next candidate whose objective function value is close to the minimum value is selected from the listed combinations of the number of used raw materials, and a new second constraint condition expression Cx = A member assignment system that controls to repeat the operation of requesting generation of d and requesting simplex arithmetic processing means to perform arithmetic processing under the new constraint condition.

<Configuration 2>
When a polygon other than a square and a rectangle is included in the product to be cut out, for the corresponding polygon, the smallest rectangle including the polygon and having the horizontally long data and the vertically long data (referred to as a deemed rectangle), An assumed rectangle setting means for setting conditions to be included in the m products,
The allocation pattern vector generation means includes:
The remaining portion obtained by cutting out the product from the raw material is included in the raw material, and the remaining portion obtained by cutting out the polygon from the deemed rectangle is also included in the raw material to determine a combination of products to be allocated to the raw material. The member allocation system according to Configuration 1.

<Configuration 3>
The predetermined allocation method is a process in which products are arranged in order from the largest in the horizontal direction, raw materials are arranged in order from the largest in the horizontal direction, and the allocation is performed by the first fit method, or the products are arranged in the order from the largest in the vertical direction. Arrange the raw materials in descending order of the raw materials and execute the allocation by the first fit method, or arrange the products in order from the largest area, and arrange the raw materials in order from the largest area. The member allocating system according to any one of configurations 1 to 2, wherein the member allocating system is any one of processes for performing allocation by a first fit method.

<Configuration 4>
The allocation pattern vector generation means includes:
In the determination process of whether or not the two-dimensional model condition is satisfied, a determination result of whether or not the assignment can be performed by the predetermined assignment method is stored in a storage device,
Using this judgment result, after selecting the horizontal or vertical guillotine cutting direction from the raw material to which the product is assigned, the process of detecting all the cutting lines that can be cut and the cutting line in this direction are gone, Including allotted product position, raw material cutting position and cutting order for all raw materials, such as selecting the raw materials after cutting one by one and executing the process of detecting cutting lines in different directions in order, 4. The member assignment system according to any one of configurations 1 to 3, further comprising cutting data generation means for generating cutting procedure data.

<Configuration 5>
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,
Accepts input of length data of m required products, m-order product length vector wp having product length as an element, and m-order product request quantity vector b having product request quantity as an element Product setting means for generating and storing in a storage device;
Accepts input of k kinds of prepared raw material data, and generates k-th order raw material length vector wm having raw material length as an element and k-th order raw material number vector nm having raw material kind number as an element. Raw material setting means stored in the storage device;
A one-dimensional model condition (wp, aj) (inner product) ≦ wm is generated and stored in the storage device, assuming that the length of the assigned product is equal to or less than the length of any one of the elements of the raw material length vector wm One-dimensional model condition generating means for causing
Receives an input of an initial feasible solution obtained by pre-Me-determined allocation method, an initial setting unit that generates the m degree of the initial allocation pattern vector and the initial allocation pattern matrix, stored in the storage device,
When the required product length data of the m products is the same, the same products are grouped into one element, and a product length vector wp1 less than m-th order having the same product length as an element. Product resetting means for generating a product request quantity vector b1 of less than m-th order,
An initial allocation pattern vector is converted into an allocation pattern vector of less than m order corresponding to the same product, and an initial allocation pattern matrix is converted into an allocation pattern matrix corresponding to the allocation pattern vector of less than m order and stored in a storage device. Initial setting conversion means,
One or more satisfying the one-dimensional model condition by comparing the product length data included in the required product length vector wp1 of less than m order with the raw material length data of the k kinds of raw materials prepared An assignment pattern vector generation means for enumerating assignment pattern vectors aj less than m order, which indicate the relationship between raw materials and products that can economically assign products of the book;
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;
When any of the products included in the product length vector wp1 less than the m-th order is assigned to n raw materials arbitrarily selected from k kinds of raw materials, the selected n raw materials In order to express the number of used pieces, an n-th order used number vector x whose elements are xi is defined, and indicates the sum of products of the n-th order cost coefficient vector f corresponding to each of the n raw materials and the used number vector x. An objective function generating means for generating an objective function and storing it in a storage device;
A first constraint condition expression Ax ≧ b1 is generated, in which the number of each product cut out with the selected allocation pattern from the allocation pattern matrix A must be equal to or greater than the quantity of each required product, and the storage device A constraint condition generating means to be stored in
Simplex operation processing means for receiving input of the initial executable solution, the objective function, and the constraint condition expression, and executing simplex operation processing;
Search control means for controlling arithmetic processing to search for and output the optimal solution,
This search control means
By the simplex operation process, when the value of xi is an integer equal to or greater than 0 and does not include any other value, the assigned data is output as the optimal solution, and in other cases, List the combinations of the number of raw materials used that take the objective function value in the range, with the objective function value of the initial feasible solution as the maximum value and the objective function value obtained as a result of the simplex operation processing as the minimum value. , A material usage matrix C that selects an objective function close to the minimum value from among them and determines how many types of raw materials to select and use for allocation to the constraint generation means; The constraint condition generating means is requested to generate a second constraint condition expression Cx = d that the product of the number of used raw material vectors is equal to the raw material use scheduled quantity vector d.
Under the constraint conditions of the first constraint condition expression and the second constraint condition expression, the simplex arithmetic processing means is requested to perform arithmetic processing, and the value of xi obtained by the simplex arithmetic processing is an integer of 0 or more, When the solution does not include anything else, the assignment data is output as the optimal solution, and in other cases, the simplex operation process obtains an executable solution with a non-integer solution, Further, when an executable solution with a non-integer solution is obtained in the subsequent simplex operation processing, an evaluation expression Σ (the number of xi being an integer) for obtaining the number of xi that is an integer among xi is defined, If the value of the evaluation formula obtained by the non-integer solution obtained later is increased as compared with the value of the evaluation formula obtained by the non-integer solution obtained earlier, a non-integer solution is obtained. Approaches the integer solution, When the determination means determines that the non-integer solution does not approach the integer solution when it decreases, the second constraint condition determines that the non-integer solution does not approach the integer solution even if the simplex operation process is repeated. Control to repeat the simplex operation by changing the formula,
The next candidate whose value of the objective function is close to the minimum value is selected from the listed combinations of the number of used raw materials, and a new second constraint condition expression Cx = A member assignment system that controls to repeat the operation of requesting generation of d and requesting simplex arithmetic processing means to perform arithmetic processing under the new constraint condition.

<Configuration 6>
The member allocation according to Configuration 5, wherein the predetermined allocation method is a process in which products are arranged in order from the longest, raw materials are arranged in order from the longest, and the allocation is performed by the first fit method. system.

<Configuration 7>
A member assignment program for causing a computer to function as each means according to configurations 1 to 6.

<Configuration 8>
A computer-readable recording medium on which the member assignment program according to Configuration 7 is recorded.

<Configuration 9>
A member comprising a precut device that receives member assignment data output from the member assignment system according to any one of Structures 1 to 4 and cuts the m products from the k kinds of raw materials that are sequentially supplied. Processing equipment.

  When cutting out products of various shapes from raw materials, when using many raw materials and products of the same size, define an n-order number vector number x of elements xi and calculate xi to be 0 or more and a predetermined evaluation The calculation time can be greatly reduced by the formula.

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 the procedure which cuts out a product from a raw material, and a new raw material. It is a cross-sectional view of the main part of a member cutting means and a raw material. It is example explanatory drawing of arithmetic processing condition data. It is example explanatory drawing of the initial feasible solution calculated | required by the first fit. It is an example explanatory drawing of the optimal allocation pattern obtained as a result of the arithmetic processing. It is a top view of the example of the allocation pattern of an initial executable solution. It is a top view of the allocation pattern example of an optimal solution. It is data example explanatory drawing by calculation which shortens arithmetic processing time. It is data example explanatory drawing by calculation which shortens arithmetic processing time. It is data example explanatory drawing by calculation which shortens arithmetic processing time. It is data example explanatory drawing by calculation which shortens arithmetic processing time. It is a flowchart of the example of pre-processing for execution of a simplex operation process. It is a flowchart of an execution example of a simplex operation process.

  In the present invention, as described in Patent Document 3, based on a practical solution obtained by any existing 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 the required raw materials and products have several tens of vertical and horizontal dimensions, the number of combinations may exceed several hundred thousand. If the parameters for the arithmetic processing are made as they are based on the condition that any one of the m products is assigned to n raw materials arbitrarily selected from k kinds of raw materials, the optimal value Simplex operation processing for searching may take too long. Therefore, a constraint condition for arithmetic processing by the simplex method is newly added, and calculation is efficiently performed while narrowing down the comparison target range. Then, when an executable solution is obtained in the process of pivot calculation processing by the simplex method, a future evaluation is made using a predetermined evaluation formula. The search condition is changed according to the result to avoid unnecessary calculation processing. 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 products from raw 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 precut device 17, for example, a device as described in Patent Document 4 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 setting unit 21, a raw material setting unit 22, an initial setting unit 23, an allocation pattern vector generation unit 24, an allocation pattern matrix generation unit 25, a constraint condition generation unit 26, a cost coefficient vector. Computer programs such as generating means 27, objective function generating means 28, simplex operation processing means 29, search control means 30, and determining means 31 are installed. These computer programs cooperate to execute arithmetic processing. In this embodiment, a product resetting means 36, an initial setting converting means 37, a raw material use matrix generating means, a cutting data generating means 34, and an assumed rectangle setting means 35 are further provided.

  The storage device 40 has a product horizontal vector wp, a product vertical vector hp, a product area vector sp, a raw material horizontal vector wm, a raw material vertical vector hm, a raw material area vector sm, a required product quantity vector b42, as shown in the figure. Solution 44, raw material usage scheduled quantity vector d45, allocation pattern matrix 46, raw material usage matrix C47, first constraint condition expression 48, second constraint condition expression 49, objective function 51, combination list 52, member allocation data 53, and evaluation expression Data such as 54 is stored. These data are input from the outside in advance, or 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 2 , 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 (FIG. 1) 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 shown in FIG. 1 includes the ROM 112, RAM 113, and HDD 114 shown in FIG. The arithmetic processing unit 20 shown in FIG. 1 includes the CPU 111, the ROM 112, the RAM 113, and the like shown in FIG. Various data are mainly stored and stored 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 16 may have the same configuration. The network 14 may 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]
The number of products to be produced is m.
The product length is expressed in, for example, the unit m (meter).
An m-th product horizontal vector wp (row vector) is defined as follows.
wp = (wp1, wp2,…, wpm)
The m-th product vertical vector hp (row vector) is defined as follows.
hp = (hp1, hp2,…, hpm)
An m-th order product area vector sp (row vector) is defined as follows.
sp = (sp1, sp2, ..., spm)
Note that spi = wpi × hpi (i = 1, 2,..., M).

[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 Patent Document 3, bi = 1 is set on the assumption that the product shapes are all different. In the present invention, in order to handle the case where there is a product having the same shape, a special calculation is performed after bi is set to an arbitrary positive integer. For comparison with the present invention, the arithmetic processing of Patent Document 3 will be described first, and then an embodiment of the present invention will be described.
b = (b1, b2,..., bm) ^T
(The superscript T represents transposition. That is, b is a column vector. The same applies hereinafter.)
In the example of FIG. 3, the quantity m = 7 and b = (1,1,1,1,1,1,1) ^T.
The product setting means 21 accepts the input of the horizontally long data and the vertically long data for the required m products, and uses the product horizontally long vector wp, the product vertically long vector hp, the product area vector sp, and the product required quantity as elements. A product request quantity vector b42 is generated and stored in the storage device 40.

[Raw material data]
There are k types of raw materials. The vertical and horizontal dimensions of the raw material are expressed in, for example, the unit m (meter).
The k-th raw material horizontal vector wm (row vector) is defined as follows.
wm = (wm1, wm2,…, wmk)
A k-th raw material vertical vector hm (row vector) is defined as follows.
hm = (hm1, hm2,…, hmk)
A kth-order raw material area vector sm (row vector) is defined as follows.
sm = (sm1, sm2,…, smk)
Note that smi = wmi × hmi (i = 1, 2,..., K).
The k-th raw material number vector nm (row vector) is defined as follows.
nm = (1,2,..., k) This i-th element “i” represents a raw material number whose horizontal length is wmi, vertical length is hmi, and area is smi.
The raw material setting means 22 accepts the input of the horizontally long data and the vertically long data for the k kinds of prepared raw materials, and the k-th raw material horizontal vector wm, the k-th raw material vertical vector hm, and the k-th raw material area vector sm A k-th raw material number vector nm is generated and stored in the storage device 40.

[Raw material use planned quantity vector d]
The raw material use scheduled quantity vector d45 (column vector) indicates how many pieces of k lengths of materials are used for a feasible solution. This is defined as follows.
d = (d1, d2,..., dk) ^T
For example, in FIG. 3, when k = 3 and the raw materials are used in total of 1 sheet, 2 sheets, and 1 sheet, respectively,
d = (d1, d2, d3) ^T = (1, 2, 1) ^T
The raw material use scheduled quantity vector d45 is used in a second constraint condition expression described later.

[Use number vector x]
Any one of m products is assigned to n raw materials arbitrarily selected from k kinds of raw materials. At this time, an n-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 kinds of raw materials, the same raw material may be selected twice or more.
x = (x1, x2,..., xn) ^T
In Patent Document 3, since all the elements of the product request quantity vector b are set to bi = 1 on the assumption that the product shapes are all different, each element xi of the m-th order use number vector x is 0 ≦ xi ≦ 1. Thus, the case where xi is 0 or 1 is significant as a result of the member assignment. On the other hand, in the present invention, as will be described later, since bi is an arbitrary integer, calculation is performed with 0 ≦ xi ≦ N (N is an arbitrary integer). Further, when this condition is relaxed, 0 ≦ xi is satisfied, and therefore, in the present invention, a constraint condition expression is not necessary for executing the calculation.

In the symbol of FIG. 3C, the raw materials corresponding to wm1, hm1, and sm1 are represented as wm1.
When the above-described raw material usage scheduled quantity vector is d = (d1, d2, d3), for example, the raw materials are listed as (wm1, wm2, wm2, wm3). The required products are allocated to these four raw materials. At this time, x1 is set for the first wm1, x2 for the second wm2, x3 for the third wm2, and x4 for the fourth wm3. In the illustrated example, x1 = x2 = x3 = x4 = 1. When enumerating selected raw materials and unselected raw materials, the value of xi set to the selected raw materials is 1. The value of xi set to the raw material not selected is 0. The used number vector x is used in the constraint condition equation.

[Assignment pattern vector aj]
Data allocated so as to cut out one of the products of quantity m from any one raw material is represented by an m-th order allocation pattern vector aj (column vector). This is defined as follows.
aj = (a1j, a2j, ..., amj) ^T (j = 1,2, ..., n)
That is, there are n m-order vectors.
For example, the allocation pattern vector in the example of FIG. In addition, the figure of FIG.3 (c) is inconsistent with the following Formula.
If wp1 and wp6 are assigned to wm1,
(0,1,0,0,0,1,0) ^T
If wp1 is assigned to wm2, (1,0,0,0,0,0,0) ^T
If wp3 and wp5 are each assigned to wm2,

(0,0,1,0,1,0,0) ^T
If wp3 and wp7 are assigned to wm3,

(0,0,0,1,0,0,1) ^T

The above allocation pattern vector aj is generated so as to satisfy (Expression 1) and (Expression 2).
(Sp, aj) ≤ S (j = 1, 2, ..., n) (1 set)
S is the minimum value of smi that satisfies (Expression 1) and (Expression 2). However (i = 1,2, ..., k)
That is, (Expression 1) is a conditional expression that the area of the allocated product is equal to or less than the area of the raw material.
wpi + wpj = 〈wml or hpi + hpj = 〈hml ・ ・ ・ (2 formulas)
(I = 1,2, ..., m) (j = 1,2, ..., m) (l = 1,2, ..., k)
That is, it is a conditional expression that products assigned adjacent to the same raw material do not overlap each other.
Note that (sp, aj) on the left side of (Equation 1) is the sum of the areas of one product or a plurality of products assigned to the selected raw material. When the allocation pattern vector aj is generated, the raw material having the smallest area that can be allocated is selected. In actual machining, the cutting length and blade thickness for taking out the rectangle are considered, but are ignored here.

For example, if one product wp3 and one product wp5 are assigned, it is possible to assign to either raw material wm1 or wm2. Here, if the cost factor of wm1 is larger than the cost factor of wm2, the raw material is selected such that the allocation target is wm2. 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. As preparation for obtaining an optimal solution by the simplex method, an allocation pattern vector is enumerated based on the result of the simplex operation processing as necessary.

  The allocation pattern vector generation means 24 is the product horizontal data, product vertical data, product area data, raw material horizontal data, raw material vertical data, and raw material area data of k kinds of prepared raw materials. Are compared, a m-th order allocation pattern vector 46a indicating the relationship between the raw material and the product that can economically allocate one or a plurality of products is generated and stored in the storage device 40.

[Assignment pattern matrix]
When allocating any of the m products to n raw materials arbitrarily selected from k kinds 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. This is shown in FIG.
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. Therefore, 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.
.SIGMA.aij.xj.gtoreq.bi (j = 1, 2,..., N) (i = 1, 2,..., M)

  This constraint condition expression is expressed as Ax ≧ b. In the example of FIG. 3, the number of products produced and the number of required products are 7, and the equal sign is established. The constraint condition generation unit 26 generates a first constraint condition expression that the number of products 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. This is shown in FIG.
cj = (c1j, c2j,..., ckj) ^T (j = 1, 2,..., n)
However, c1j, c2j,..., Ckj are all 0 or 1.
As described above, the raw material use 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 example of FIG. 3 already described, 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 raw material usage matrix generation means 38 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 (i = 1, 2,..., K) (j = 1, 2,..., N)
Only one of the k numbers is 1 and all others are 0. Also, the minimum raw material that can be allocated is selected.

Further, as already defined, the used number vector x of n raw materials is x = (x1, x2,..., Xn). In addition, the raw material usage scheduled quantity vector d indicates the number of used raw materials. Therefore, the condition of the following formula must be satisfied.
.SIGMA.cij.xj = di (i = 1, 2,..., K) (j = 1, 2,..., N)
This second constraint condition expression is expressed as Cx = d.
This defines which number of raw materials are selected and used for actual allocation. The constraint condition generation unit 26 generates a second constraint condition expression that the product of the raw material usage matrix C generated by the allocation pattern matrix generation unit 25 and the raw material usage number vector x is equal to the raw material usage 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 in the example of Patent Document 3. 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 the example of Patent Document 3, this constraint condition is relaxed. That is, a constraint condition expression of 0 ≦ xi ≦ 1 is set. The constraint condition generation means 26 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.

(2D model conditions)
Since a two-dimensional model is targeted, new conditions are set. The area of the allocation product is less than or equal to the area S of the raw material. This is set as the first evaluation condition (sp, aj) (inner product) ≦ S. Adjacent products do not overlap. This is set as the second evaluation condition wpi + wpj ≦ wmi or hpi + hpj ≦ hmi. The allocation pattern vector aj must be assignable by a predetermined allocation method. This is the third evaluation condition. The two-dimensional model condition generation unit 32 generates these two-dimensional model conditions 63 and stores them in the storage device 40. The predetermined allocation method is, for example, the method shown in Patent Document 3 or Patent Document 4, or the First Fit method. If it cannot be allocated by a predetermined allocation method, the cutting procedure data 55 cannot be finally generated, so that it is not an executable solution.

[Cost factor vector]
Not only the price but also the transportation cost, storage cost, processing fee, etc. differ for each of the k types of raw materials. 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.

  An element of the cost coefficient vector is a cost (cost). If the cost is proportional to the area, it is agreed that the yield is highest and the total cost is lowest. However, if the price per unit area varies depending on the raw material, the cost factor is adjusted. The cost coefficient vector generation means 27 generates an nth-order cost coefficient vector f including a price component in each element of the raw material area vector sm. The element fi of the cost coefficient vector f is data whose unit is a circle. If the cost coefficient vector generating means 27 replaces the raw material area vector sm 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 products is assigned to n raw materials arbitrarily selected from k kinds 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 selected n raw materials is defined as follows.
Min Σfi ・ xi
The objective function generation means 28 generates an objective function indicating 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 the example simplified as in Patent Document 3 in order to execute arithmetic processing by the simplex method, the objective function and the constraint condition 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 indicates 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 usage matrix C, the raw material usage number vector x, and the raw material usage scheduled quantity vector d.
The third constraint condition expression indicates that xi is 0 or more and 1 or less. As already described, in the case of the present invention, this third constraint condition is not necessary.

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. The arbitrary method is the predetermined allocation method described above. In the initial feasible solution 44, whether or not the above two-dimensional model condition is satisfied is determined at the initial setting stage. The initial setting means 23 sets only those satisfying the two-dimensional model condition 63 as the initial executable solution 44. The initial feasible solution can be represented by a raw material use number vector x that designates an allocation pattern vector selected from the above allocation pattern matrix A. This will also be described more specifically in the third embodiment. Parameters input for the first simplex operation processing are data constituting the objective function Σfi · xi, the first constraint expression Ax ≧ b, and the third constraint expression 0 ≦ xi ≦ 1.

  The search control means 30 causes the simplex arithmetic processing means 29 to input parameters excluding the constraint condition of Cx = d and execute the first arithmetic processing. The simplex operation processing means 29 changes the basis variables 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 number of raw materials whose objective function value is F1 or more and less than F0, 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 determined as the optimum solution. In order to shorten the calculation time for the search process, control using an evaluation formula as will be described later is executed. When the optimum solution cannot be obtained, if the value of the objective function is the same as that of the next candidate in the list of combinations of the number of raw materials, it is selected as the next candidate. If not, the next smaller candidate is selected as the next candidate. 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 operation processing means 29 to execute the operation processing.

  In this way, the simplex operation process is repeated to search for the optimum solution. When a large number of combinations of the number of raw materials are generated, an upper limit is set for the number of selections of the number of raw material combinations. 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 required product quantity vector b is used, the product dimensions are not included in the parameters of the simplex arithmetic processing, and the calculation is complicated. do not become. In addition, since the parameters are set so that the used number vector x of the raw material in which each element takes only a value of 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 setting means 22 accepts raw material data. The input of all raw material data to be used is received from the terminal device 16, data corresponding to the raw material vector 43 is generated and stored in the storage device 40. That is, a k-th order raw material horizontal vector wm having the horizontal length of the raw material as an element, a k-th order raw material vertical vector hm having the vertical length of the raw material as an element, a k-th order raw material area vector sm having the raw material area as an element, A k-th order raw material number vector nm having the raw material type number as an element is generated and stored in the storage device 40. In step S12, the product setting unit 21 accepts input of data related to the product. The terminal device 16 accepts the input of the required horizontal data and vertical data of the m products, and receives the m-th product horizontal vector wp having the product horizontal length as an element and the m-th order having the product vertical length as an element. A product vertical vector hp, an m-th order product area vector sp having the product area as an element, and a product request quantity vector b having the product request quantity as an element are generated and stored in the storage device 40.

In step S13, receives an input of an initial setting means 23 is two-dimensional model satisfies been judged initial feasible solution 44. The result is stored in the storage device 40. In step S14, the allocation pattern vector generation means 24 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 as described later. 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 in step S23 the member assignment data and cutting procedure data are output and the process is terminated. If no, the process proceeds to step S22. In step S22, the search control means 30 controls the calculation by the simplex method according to the procedure shown in 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. Next, in step S33, a combination list of raw materials is generated within the set range of the objective function value. The results are stored in the storage device 40 side by side in ascending order of the objective function value. In step S34, the one with the smallest objective function value is selected from the combination list. Further, in step S35, a request is made to the constraint condition generation means 26, and a constraint condition is set as will be described later.

  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 the pivot calculation process 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.

(First fit)
According to the above-described method described in Patent Document 3, it is possible to assign the optimum yield by designating the portrait data and landscape data of the raw material, and the portrait data and landscape data of the product cut out from the raw material. That is, it is possible to obtain a combination of patterns that yields the maximum yield from a large number of patterns in which raw materials and products are combined in consideration of restrictions on the portrait, landscape, and area. Further, if the remaining raw material obtained by cutting out the product from the raw material includes a process for determining whether other products can be assigned, cutting procedure data for cutting out the product from the raw material can be generated.

  In one-dimensional allocation focusing only on the length in one direction, if the raw material length is equal to or greater than the sum of the allocated product lengths (ignoring the blade thickness), it can be determined that allocation is possible. However, in the two-dimensional allocation considering vertical and horizontal, it cannot be determined that allocation is possible immediately even if the raw material area is greater than the sum of the allocated product areas. Therefore, for example, in the mounting program, an appropriate order is assigned to the products. For example, the data is arranged in a vertically descending order, a horizontally descending order, an area descending order, and the like. Product data is extracted in this order.

FIG. 6 is an explanatory diagram of a procedure for cutting out products from raw materials and new raw materials.
This process is executed by the cutting data generating means 34 (FIG. 1). As shown in FIG. 6, with the lower left corner of the raw material as the origin, the product 62 taken out from the product data can be placed in the raw material 60 if possible, otherwise the next order product in the product data is taken out. If they can be placed, decide whether to start with a vertical or horizontal guillotine cut and select one. When starting with a longitudinal guillotine cut, as shown in FIG. 6A, the raw material 60 is cut in the vertical direction to obtain new separated raw materials 70 and 71.

  A product 62 is cut out from the raw material 70 to obtain a new raw material 72. For these two new raw materials 71 and 72, products in the next order are extracted from the product data, and the same allocation process is performed. Repeat this process until all products are gone.

  In this way, deciding the order of taking out products and taking them out and deciding the assignment from the assigned products is called first fit. Then, as described above, cutting the original raw material, regarding the separated material as a new raw material, and repeating the same allocation process is called recursive allocation. If recursive allocation processing is performed, the program can be simplified by executing a certain loop repeatedly until there is no product to be allocated.

(Guillotine cut)
When the products are all rectangular, the first fitting (recursive) allocation process, for example, arranges the products in the long and long order and then takes the first product and allocates it to the base material. The cutting data generating means 34 shown in FIG. 1 has a function of automatically selecting either vertical guillotine allocation or horizontal guillotine allocation. In the vertical guillotine assignment, first, the cut in the Y direction is performed, and then the cut in the X direction is performed. Then, the separated raw material is used as a new raw material, and the allocation is recursively advanced. In the horizontal guillotine allocation, as shown in the figure, the cut in the X direction is first performed and then the cut in the Y direction is performed.

(Non-guillotine cut constraint)
By using the above method, it is possible to perform allocation calculation including not only rectangular products but also polygonal products such as L-shape and U-shape, as shown in FIGS. 6B and 6C. Before starting the allocation calculation, these non-rectangular polygon products are processed so as to be regarded as the smallest rectangular product including the polygon. This minimum rectangle will be referred to as a “deemed rectangle”. The deemed rectangle setting means 35 shown in FIG. 1 has a function of setting a deemed rectangle and setting conditions so that the horizontally long data and the vertically long data are included in the m products.

  While proceeding with the allocation calculation, as described above, it is determined whether other products can be allocated to the remaining raw materials cut out from the raw materials. At this time, as shown in FIG. 6B, a polygonal product 63 is cut out from the deemed rectangle, and it is also determined whether other products can be allocated to the remaining new raw material 73. The same applies to the remaining new raw materials 74 and 75 obtained by cutting out the product 64 shown in FIG.

  In the process of cutting out the product from the raw material, the raw material to which the product has been assigned by the feasible solution is cut out. In the case of vertical guillotine, the product or the raw material including the product is cut out by vertical guillotine cutting first. Then, the raw material containing a product is selected one by one, and this time, a product or a material containing a product is cut out by a horizontal guillotine cut. In addition, a horizontal guillotine cut may be performed first and allocation calculation may be performed in the reverse procedure to the above. If the results are different, select the one with the higher yield.

  When cutting the raw material in a longitudinal guillotine, all cutting lines that can be cut are detected and cut in the same direction. This is because workability is better. When the cutting line in this direction disappears, the cut raw materials are selected one by one, and when viewed from the first raw material, the cutting line in the direction corresponding to the transverse guillotine cut is detected and cut. When viewed from the first raw material, the vertical guillotine cut and the horizontal guillotine cut are executed alternately. The cutting data generation means 34 (FIG. 1) generates such cutting procedure data 55 (FIG. 1), thereby minimizing the total number of times of cutting one raw material.

  Moreover, the number of cases of the allocation pattern can be increased by combining vertical guillotine and horizontal guillotine. This widens the search space and increases the calculation time, but has the effect that it is easy to find the optimal solution.

(Cutting blade for non-guillotine cutting)
FIG. 7 is a cross-sectional view of the main parts and raw materials of the member cutting means 121 (FIG. 2).
In the above processing, when a polygonal product is cut out from a deemed rectangle, a part that cannot be guillotine cut may occur. At this time, control is performed as shown in FIG. That is, the precut device 17 (FIG. 1) moves the cutting blade 65 in an inclined state so as to be at the left end of the drawing at the start of cutting. Then, immediately before the cutting blade 65 is stopped, the direction of the blade is directed in a direction perpendicular to the surface of the raw material 60. Thus, for example, the product 63 and the new raw material 73 can be cut out by cutting from point A to point B and from point C to point B in FIG. The other parts may be controlled similarly.

(Reduction of processing time)
8 to 10 are explanatory diagrams of data examples obtained by the arithmetic processing.
When the combination pattern is generated as described above, the calculation processing time may be long. A system configuration for shortening the calculation processing time according to the present invention will be described. FIG. 8 lists the length and the required number b for each of 15 products that may be cut vertically or horizontally from the raw material. In the above constraint expression Ax ≧ b and Cx = d, all the elements of b in 15 product types were 1. Even if products having the same length are listed as bi (i = 1 to k) = 1 as separate products in this way, versatile calculation processing can be performed as follows.

FIG. 9 shows the initial feasible solution obtained by the first fit based on the conditions of FIG.
The first and second products are assigned to the raw material a1. Similarly, 15 kinds of products are allocated to the raw material a7. Here, A is a 15 × 7 matrix, b is a 15 × 1 vector, C is a 1 × 7 matrix, and d is a 1 × 1 vector.

  In the initial feasible solution, x1 = 1, x2 = 1, x3 = 1, x4 = 1, x5 = 1, x6 = 1, x7 = 1 are all integers, so it is possible to assign at least this pattern. Yes. That is, a result that 15 kinds of products can be cut out from seven raw materials is obtained.

Next, a pattern is generated by the backtrack method, and an allocation pattern that can improve the initial execution solution based on a sensitivity analysis using a simplex multiplier is added to the allocation pattern of FIG. Actually, about 140 types of assignment patterns could be generated. Then, as described in Patent Document 3, the pivot operation is repeated until Σx ² (the sum of squares of x elements) increases until an integer solution (0, 1) is obtained. Thereby, an executable allocation pattern having the largest yield is automatically selected.

  FIG. 10 is an example of the optimal allocation pattern obtained as a result of the above arithmetic processing. FIG. 11 illustrates the allocation pattern of the above-described initial executable solution, and FIG. 12 illustrates the allocation pattern of the optimal solution. As shown in FIG. 10, the allocation patterns a5, a6, and a7 can be replaced with a8 and a9. As a result, a result that x1 = 1, x2 = 1, x3 = 1, x4 = 1, x8 = 1, and x9 = 1 can be assigned to the six raw materials was obtained.

  In the example of FIG. 11, four raw materials 60 having the same dimensions are shown. Two products of (1) are allocated to the raw material 60 of (a). Two products (2) and (7) are allocated to the raw material 60 of (b). The products (5) and (6) are allocated to the raw material 60 of (c). The products (3) and (4) are allocated to the raw material (d).

  When products having the same vertical and horizontal dimensions are arranged and optimized, the products (5), (6), and (7) can be assigned to the raw material 60 of (a) as shown in FIG. In addition, two products (2), (3), and (4) can be allocated to the raw material 60 of (b). As a result of this optimization processing, it is possible to assign the three raw materials and save one raw material.

  The processing so far is based on the method introduced in Patent Document 3 above. In this method, the elements A, b, and C are all 0 or 1. Therefore, the element of x is 0 or more and 1 or less (integer or real number). Subsequently, the arithmetic processing according to the present invention will be described.

FIG. 13 to FIG. 16 are explanatory diagrams of data examples according to calculation examples for shortening the calculation processing time.
The difference from the above-mentioned patent document 3 is that the element A and the element b are integers of 0 or more. As the allocation pattern vector, an integer of 0 or 1 or more is used, and in FIG. As shown in FIG. 14, the initial feasible solution shown in FIG. 9 is rewritten as a group of products having the same length. The first product is assigned to each of the raw materials a1, a2, a3, and a4.

  Up to this point, the initial executable solutions are x1 = 1, x2 = 1, x3 = 1, x4 = 1, x5 = 1, x6 = 1, x7 = 1. Here, as shown in FIG. 15, a1, a2, a3, and a4 which are the same allocation pattern vectors are deleted leaving a1. That is, A is a 7 × 4 matrix, b is a 7 × 1 vector, C is a 1 × 4 matrix, d is a 1 × 1 vector, and the size can be made smaller than the example of FIG. The obtained initial feasible solutions are x1 = 4, x5 = 1, x6 = 1, x7 = 1. Next, an allocation pattern is generated by the backtrack method + combination permutation, and an allocation pattern that can improve the initial solution based on sensitivity analysis using a simplex multiplier is added to A. The pivot operation by the picinplex operation is repeated until an integer solution (0 to N) is obtained.

At this time, in the above-described invention, the pivot operation is repeated as Σx ² increases. In the present invention, another evaluation formula is used. That is, the pivot operation is repeated in the direction in which the number of integer solutions increases. Thereby, a result as shown in FIG. 16 is obtained. This result corresponds to the allocation result shown in FIG.

  Here, the calculation process of the present invention will be verified. In the calculation of the present invention, about 30 patterns of assigned pattern vectors were generated, and the optimum value was selected from among them, and the result shown in FIG. 16 was obtained.

17 and 18 show a flowchart of a specific arithmetic processing method according to the present invention.
With reference to FIG. 17, the pre-processing for executing the simplex operation processing will be mainly described. First, in step S41, the product vector 41 is set. In other words, the product setting means 21 accepts the input of the required horizontal data and vertical data of the m products, and the m-th product horizontal vector wp having the horizontal length of the product as an element and the vertical length of the product as an element. The m-th order product vertical vector hp, the m-th order product area vector sp having the product area as an element, and the m-th order product request quantity vector b having the product request quantity as an element are generated. The product vector 41 obtained in this way is stored in the storage device 40.

  Next, the raw material vector 43 is set in step S42. That is, the raw material setting means 22 receives input of k kinds of rectangular raw material data prepared, and receives a k-th raw material horizontal vector wm having the horizontal length of the raw material as an element and a k-th order having the vertical length of the raw material as an element. A raw material longitudinal vector hm, a k-th order raw material area vector sm having the raw material area as an element, and a k-th order raw material number vector nm having the raw material type number as an element are generated. The raw material vector 43 thus obtained is stored in the storage device.

  In step S44, the initial setting means 23 receives an input of the initial executable solution 44 obtained by a predetermined allocation method, generates an m-th order initial allocation pattern vector 46a and an initial allocation pattern matrix 46, and stores them. Store in the device 40. The result is as shown in FIG.

In step S43, two-dimensional model condition generating means 32, the generation of the two-dimensional model conditions 63 including first evaluation condition and a second evaluation condition and the third evaluation condition. The first evaluation condition is a condition that the area of the allocated product is equal to or less than the area S of any raw material among the elements of the raw material area vector sm. The second evaluation condition is a condition that adjacent products do not overlap. The third evaluation condition is a condition that the allocation pattern vector aj can be allocated by a predetermined allocation method.

In step S45, a product having the same landscape data and portrait data is detected. In step S46, the product resetting means 36 resets the product vector 41. That is, the same product is grouped into one element. Then, a product horizontal vector wp1 of less than m-th order having the horizontal length of the same product as an element, a product vertical vector hp1 of less than m-th order having the vertical length of the same product as elements, and m having the area of the same product as elements. A product area vector sp1 less than the next order and a product request quantity vector b1 less than the mth order are generated.

  In step S47, the initial setting conversion means 37 resets the initial allocation pattern matrix 46. That is, the initial allocation pattern vector is converted into an allocation pattern vector of less than m order corresponding to the same product, the initial allocation pattern matrix is converted into an allocation pattern matrix corresponding to the allocation pattern vector of less than m order, and stored. The device 40 is stored. In this way, the data shown in FIG. 15 is obtained.

In step S48, the allocation pattern vector generation means 24 generates an allocation pattern vector 46a that satisfies the conditions. That is, the product horizontal data included in the product horizontal vector wp1 less than the required m-th order and the product vertical data included in the product vertical vector hp1 less than the m-th order are the raw material horizontal data of k kinds of raw materials prepared. And an allocation pattern vector aj of less than m order indicating the relationship between the raw material and the product that can economically allocate one or more products satisfying the above-mentioned two-dimensional model condition 63. Enumerate.

In step S49, the allocation pattern matrix generation means 24 generates an allocation pattern matrix 46 (A) in which the allocation pattern vectors 46a are arranged, and stores them in the storage device 40. In step S50, the objective function generation means generates an objective function Σfx. That is, in order to represent the number of used n raw materials to which a product is assigned, an n-th order used number vector x having elements xi is defined, and the n-th order cost coefficient vector f corresponding to each of the n raw materials is used. An objective function indicating the total sum of products of the number vectors x is generated and stored in the storage device 40.

  In step S51, the constraint condition generation unit 26 generates the first constraint condition expression Ax ≧ b1. That is, a first constraint condition expression is generated that stores the number of products cut out by the n number of allocation patterns selected from the allocation pattern matrix A so as to be equal to or greater than the quantity of each required product. Store in the device 40.

  In step S52, the simplex calculation processing means 29 receives the initial executable solution 44, the objective function 51, and the constraint condition expressions 48 and 49, and executes simplex calculation processing. In step S <b> 53, the search control means 30 executes a calculation process for searching for and outputting an optimal solution by search control.

  The search control means 30 performs control as shown in FIG. First, in step S61, it is determined whether or not the obtained xi is only an integer greater than or equal to 0 by simplex operation processing. When the result of this determination is yes, the process proceeds to step S72, and when the result is no, the process proceeds to step S62. If the value of xi is an integer greater than or equal to 0 and does not include any other value, the member assignment data 53 is output in step S72 with the solution as the optimum solution.

  In step S62, the search control means 30 sets the value of the objective function 51 of the initial executable solution 44 to the maximum value. In step S63, the value of the objective function 51 obtained as a result of the simplex operation process is set to the minimum value. Next, in step S64, combinations of the number of used raw materials taking the value of the objective function within the range are listed. In step S65, the objective function 51 having a value close to the minimum value is selected, and the constraint condition generation unit 26 is requested to generate the second constraint condition expression 49.

  In step S66, the constraint condition generation unit 26 generates the second constraint condition expression Cx = d. The second constraint condition formula defines how many kinds of raw materials are selected and used for allocation. This is an expression assuming that the product of the raw material use matrix C and the raw material use number vector is equal to the raw material use scheduled quantity vector d.

  The search control means 30 requests the simplex arithmetic processing means 29 for arithmetic processing. In step S <b> 67, the simplex arithmetic processing unit 29 executes arithmetic processing under the constraint conditions of the first constraint condition expression 48 and the second constraint condition expression 49.

  In step S68, the search control means 30 determines whether an executable solution with a non-integer solution has been obtained. If the result of this determination is yes, the process proceeds to step S69, and if no, the process returns to step S61. When an executable solution with a non-integer solution is obtained, an evaluation formula Σ (number of integers xi) is obtained in step S69.

  When an executable solution with a non-integer solution is obtained, and when an executable solution with a non-integer solution is obtained again in the subsequent simplex operation processing, whether or not the value of the evaluation expression has increased in step S70. Make a decision. When the result of this determination is yes, the process proceeds to step S67, and when no, the process proceeds to step S71. That is, as long as the value of the value formula increases, the simplex operation process is repeated to obtain an integer solution in which the value of xi is an integer equal to or greater than 0 and does not include any other value.

  When the value of the evaluation expression decreases without obtaining an integer solution, the restriction condition generation unit 26 is requested to change the second restriction condition expression 49 in step S71. Thus, the process returns to step S67, and an integer solution search is made again. Through the above processing, the optimum solution described with reference to FIGS. 14, 15, and 16 can be obtained.

(One-dimensional model)
The arithmetic processing described above can also be applied to the case where a bar-shaped product is allocated to a bar-shaped raw material that has only a length and does not have a problem with the width. In this case, the “m products” may be read as “m products”, and the “surface material assignment data” may be read as “assignment data”.

In one dimension, if the sum of the assigned product lengths is less than or equal to the raw material length (first evaluation condition), there is no overlap in the two dimensions (second evaluation condition), and how it is arranged (third evaluation condition) is automatic Therefore, only the first evaluation condition needs to be considered. Therefore, the first to third evaluation conditions are read as one-dimensional model conditions.

That is, the number of each type of raw material required when each of m products each having a predetermined length is cut out from k types of raw materials each having a predetermined length is obtained, and the combination of products assigned to each raw material is optimized. .

In the one-dimensional model, parameters for arithmetic processing are set as follows. Other settings are the same as those in the above embodiment. The same applies to the simplex operation processing and the evaluation formula setting.
(A) mth-order product length vector wp having the product length as an element
(B) mth-order product request quantity vector b having the product request quantity as an element
(C) k-th order material length vector wm having the length of the material as an element
(D) kth-order raw material number vector nm having raw material type numbers as elements
(E) First evaluation condition (wp, aj) ≦ wm
(The sum of the lengths of the assigned products is less than or equal to the length of one of the elements of the raw material length vector wm)

  In the case of assigning a bar-shaped product to a bar-shaped raw material, the processing elements are simplified. However, in the case of building materials, the types of raw materials and the lengths of products are often much larger than the face materials. Accordingly, since the number of cases becomes enormous, shortening of the arithmetic processing time as in the present invention is extremely effective.

  In the case of a one-dimensional model, products may be arranged in order from the longest, raw materials are arranged in order from the longest, and allocation may be executed by the first fit method. Similarly to the above-described embodiment, the remaining part obtained by cutting out the product from the raw material is also included in the raw material, and the combination of products to be allocated to the raw material may be determined.

  As described above, in the present invention, the n-order used number vector x whose element is xi is defined, and the value of xi is an integer equal to or larger than 0, so that an evaluation expression used for simplex operation processing is newly set. . This evaluation formula is used for the next calculation process with the prospect that if the calculation process is repeated to search for an executable solution with a better yield, no further results can be obtained by repeating the calculation. Used to determine when to move. Various evaluation formulas are conceivable, but depending on the setting method, the entire calculation processing time greatly affects.

The evaluation formula used in the present invention is the number of integers of the nth-order used number vector x. When all x are integers greater than or equal to 0, it becomes n (pieces). If even one is not an integer, it will be less than n. This evaluation formula is effective when searching by the hill-climbing method, random restart, or annealing method. That is, the search is continued as long as the number in which xi is an integer increases, and if it does not increase, the search is terminated, whereby an integer solution can be found in a short time. In practice, this method may not work if the order increases. However, it has been found that there is no practical problem with this evaluation formula because the allocation calculation processing of building materials falls within an appropriate order range.

  The calculation processing time between the method of the present invention and the calculation processing result of Patent Document 3 is compared. For example, the quantity of standard residential insulation products is 60-200. The number of shape types is 10-50. Arithmetic processing of the method of the present invention and the method of Patent Document 3 is executed by a general-purpose personal computer. In the two-dimensional model, when the number of products is about 200, compared to the conventional method, the method of the present invention can narrow down the allocation pattern matrix generated for searching to about 1/10 or more. . Thereby, the arithmetic processing time can be reduced to several ten. Since many building materials used in a house have the same size, the method of the present invention functions extremely effectively.

  The computer program executed by the above arithmetic processing unit 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.

DESCRIPTION OF SYMBOLS 10 Member allocation system 12 Computer 14 Network 16 Terminal device 20 Processing unit 21 Product setting means 22 Raw material 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 generation Means 28 Objective function generation means 29 Simplex arithmetic processing means 30 Search control means 31 Determination means 32 Two-dimensional model condition generation means 34 Cutting data generation means 35 Considered rectangle setting means
36 Product resetting means
37 Initial setting conversion means 38 Raw material use matrix generation means 40 Storage device 41 Product vector wp, hp, sp
42 Product requirement quantity vector b
43 Raw material vector wm, hm, sm
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 equation 49 Second constraint equation 50 Third constraint equation 51 Objective function 52 Combination list 53 Member allocation data 54 Evaluation equation 55 Cutting procedure data 60 Raw material 62 Product 63 Polygon 64 Polygon 65 Cutting blade 71 New New raw materials 72 New raw materials 73 New raw materials 74 New raw materials 75 New raw materials

Claims (9)

Each of the predetermined rectangular m products is obtained from each of the predetermined rectangular k kinds of raw materials, and the number of raw materials of each type required is obtained, and the combination of products assigned to the respective raw materials is optimized. ,
Accepts the input of the required horizontal data and vertical data of m products, and receives the m-th product horizontal vector wp whose product is the horizontal length and the m-th product vertical vector hp whose product is the vertical product. A product setting means for generating an m-th order product area vector sp having a product area as an element and an m-th order product request quantity vector b having a product request quantity as an element, and storing them in a storage device;
Accepts input of raw material data of k types of prepared rectangles, k-th raw material horizontal vector wm having the horizontal length of the raw material as an element, k-th raw material vertical vector hm having the vertical length of the raw material as an element, A raw material setting means for generating a k-th order raw material area vector sm having an area as an element and a k-th order raw material number vector nm having a raw material type number as an element, and storing them in a storage device;
The first evaluation condition (sp, aj) (inner product) ≦ S that the area of the allocated product is equal to or smaller than the area S of any one of the elements of the raw material area vector sm is assumed to be not overlapped with the adjacent product. Second evaluation condition, wpi + wpj ≦ wml or hpi + hpj ≦ hml,
Two-dimensional model condition generation means for generating a two-dimensional model condition including a third evaluation condition that the allocation pattern vector aj can be allocated by a predetermined allocation method, and storing the two-dimensional model condition in a storage device;
Initial setting means for receiving an input of an initial executable solution obtained by the predetermined allocation method, generating an m-th order initial allocation pattern vector and an initial allocation pattern matrix, and storing them in a storage device;
If the product horizontal data and product vertical data of the m products that are required are the same, the same product is combined into one element, and the product of less than m-th order including the same product horizontal data as the element A horizontal vector wp1, a product vertical vector hp1 less than m-order having the same product vertical length as an element, a product area vector sp1 less than m-th order having the same product area as an element, and a product less than m-th order Product resetting means for generating the requested quantity vector b1,
An initial allocation pattern vector is converted into an allocation pattern vector of less than m order corresponding to the same product, and an initial allocation pattern matrix is converted into an allocation pattern matrix corresponding to the allocation pattern vector of less than m order and stored in a storage device. Initial setting conversion means,
The product horizontal data included in the product horizontal vector wp1 less than the m-th order and the product vertical data included in the product vertical vector hp1 less than the m-th order are obtained. Compared with data and raw material longitudinal data, one or a plurality of products satisfying the two-dimensional model condition including the first evaluation condition, the second evaluation condition, and the third evaluation condition can be economically allocated. An allocation pattern vector generating means for enumerating allocation pattern vectors aj less than m-th order indicating the relationship between raw materials and products;
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;
Any one of the products included in the product horizontal vector wp1 less than the mth order and the product vertical vector hp1 less than the mth order is allocated to n raw materials arbitrarily selected from k kinds of raw materials. Then, in order to represent the number of used n raw materials used, an n-th order used number vector x whose elements are xi is defined, and the n-th order cost coefficient vector f corresponding to each of the n raw materials and the An objective function generating means for generating an objective function indicating the sum of products of the used number vectors x and storing the objective function in a storage device;
A first constraint condition expression Ax ≧ b1 is generated, in which the number of each product cut out with the selected allocation pattern from the allocation pattern matrix A must be equal to or greater than the quantity of each required product, and the storage device A constraint condition generating means to be stored in
Simplex operation processing means for receiving input of the initial executable solution, the objective function, and the constraint condition expression, and executing simplex operation processing;
Search control means for controlling arithmetic processing to search for and output the optimal solution,
This search control means
By the simplex operation process, when the value of xi is an integer greater than or equal to 0 and does not include any other value, the face material allocation data is output as the optimal solution, and otherwise The combination of the number of used raw materials that takes the value of the objective function in the range, with the objective function value of the initial feasible solution as the maximum value and the objective function value obtained as a result of the simplex operation processing as the minimum value. A raw material use matrix that enumerates and selects what kind of raw materials are selected and used for allocation to the constraint condition generation means by selecting the objective function close to the minimum value from among them Requesting the constraint condition generating means to generate a second constraint condition expression Cx = d, wherein the product of the number of used materials vector C and the raw material use quantity vector d is equal to
Under the constraint conditions of the first constraint condition expression and the second constraint condition expression, the simplex arithmetic processing means is requested to perform arithmetic processing, and the value of xi obtained by the simplex arithmetic processing is an integer of 0 or more, If the solution does not include any other solution, the face material allocation data is output with the solution as the optimal solution. In other cases, an executable solution with a non-integer solution is obtained by the simplex operation processing. Further, when an executable solution with a non-integer solution is obtained in the subsequent simplex operation processing, an evaluation formula Σ (the number of xi is an integer) for determining the number of xi that is an integer among xi is defined. If the value of the evaluation formula obtained by the non-integer solution obtained later is larger than the value of the evaluation formula obtained by the non-integer solution obtained earlier, Integer solution approaches integer solution and evaluates When the determination means determines that the non-integer solution does not approach the integer solution when the value of is reduced, when the determination unit determines that the non-integer solution does not approach the integer solution even when the simplex operation process is repeated, Change the constraint condition expression and control to repeat the simplex operation process,
A next candidate whose objective function value is close to the minimum value is selected from the listed combinations of the number of used raw materials, and a new second constraint condition expression Cx = A member assignment system that controls to repeat the operation of requesting generation of d and requesting simplex arithmetic processing means to perform arithmetic processing under the new constraint condition. When a polygon other than a square and a rectangle is included in the product to be cut out, for the corresponding polygon, the smallest rectangle including the polygon and having the horizontally long data and the vertically long data (referred to as a deemed rectangle), An assumed rectangle setting means for setting conditions to be included in the m products,
The allocation pattern vector generation means includes:
The remaining portion obtained by cutting out the product from the raw material is included in the raw material, and the remaining portion obtained by cutting out the polygon from the deemed rectangle is also included in the raw material to determine a combination of products to be allocated to the raw material. The member allocation system according to claim 1.   The predetermined allocation method is a process in which products are arranged in order from the largest in the horizontal direction, raw materials are arranged in order from the largest in the horizontal direction, and the allocation is performed by the first fit method, or the products are arranged in the order from the largest in the vertical direction. Arrange the raw materials in descending order of the raw materials and execute the allocation by the first fit method, or arrange the products in order from the largest area, and arrange the raw materials in order from the largest area. The member assignment system according to claim 1, wherein the member assignment system is one of processes for executing assignment by a first fit method. The allocation pattern vector generation means includes:
In the determination process of whether or not the two-dimensional model condition is satisfied, a determination result of whether or not the assignment can be performed by the predetermined assignment method is stored in a storage device,
Using this judgment result, after selecting the horizontal or vertical guillotine cutting direction from the raw material to which the product is assigned, the process of detecting all the cutting lines that can be cut and the cutting line in this direction are gone, Including allotted product position, raw material cutting position and cutting order for all raw materials, such as selecting the raw materials after cutting one by one and executing the process of detecting cutting lines in different directions in order, 4. The member allocation system according to claim 1, further comprising cutting data generation means for generating cutting procedure data. 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,
Accepts input of length data of m required products, m-order product length vector wp having product length as an element, and m-order product request quantity vector b having product request quantity as an element Product setting means for generating and storing in a storage device;
Accepts input of k kinds of prepared raw material data, and generates k-th order raw material length vector wm having raw material length as an element and k-th order raw material number vector nm having raw material kind number as an element. Raw material setting means stored in the storage device;
A one-dimensional model condition (wp, aj) (inner product) ≦ wm is generated and stored in the storage device, assuming that the length of the assigned product is equal to or less than the length of any one of the elements of the raw material length vector wm One-dimensional model condition generating means for causing
Receives an input of an initial feasible solution obtained by pre-Me-determined allocation method, an initial setting unit that generates the m degree of the initial allocation pattern vector and the initial allocation pattern matrix, stored in the storage device,
When the required product length data of the m products is the same, the same products are grouped into one element, and a product length vector wp1 less than m-th order having the same product length as an element. Product resetting means for generating a product request quantity vector b1 of less than m-th order,
An initial allocation pattern vector is converted into an allocation pattern vector of less than m order corresponding to the same product, and an initial allocation pattern matrix is converted into an allocation pattern matrix corresponding to the allocation pattern vector of less than m order and stored in a storage device. Initial setting conversion means,
One or more satisfying the one-dimensional model condition by comparing the product length data included in the required product length vector wp1 of less than m order with the raw material length data of the k kinds of raw materials prepared An assignment pattern vector generation means for enumerating assignment pattern vectors aj less than m order, which indicate the relationship between raw materials and products that can economically assign products of the book;
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;
When any of the products included in the product length vector wp1 less than the m-th order is assigned to n raw materials arbitrarily selected from k kinds of raw materials, the selected n raw materials In order to express the number of used pieces, an n-th order used number vector x whose elements are xi is defined, and indicates the sum of products of the n-th order cost coefficient vector f corresponding to each of the n raw materials and the used number vector x. An objective function generating means for generating an objective function and storing it in a storage device;
A first constraint condition expression Ax ≧ b1 is generated, in which the number of each product cut out with the selected allocation pattern from the allocation pattern matrix A must be equal to or greater than the quantity of each required product, and the storage device A constraint condition generating means to be stored in
Simplex operation processing means for receiving input of the initial executable solution, the objective function, and the constraint condition expression, and executing simplex operation processing;
Search control means for controlling arithmetic processing to search for and output the optimal solution,
This search control means
By the simplex operation process, when the value of xi is an integer equal to or greater than 0 and does not include any other value, the assigned data is output as the optimal solution, and in other cases, List the combinations of the number of raw materials used that take the objective function value in the range, with the objective function value of the initial feasible solution as the maximum value and the objective function value obtained as a result of the simplex operation processing as the minimum value. , A material usage matrix C that selects an objective function close to the minimum value from among them and determines how many types of raw materials to select and use for allocation to the constraint generation means; The constraint condition generating means is requested to generate a second constraint condition expression Cx = d that the product of the number of used raw material vectors is equal to the raw material use scheduled quantity vector d.
Under the constraint conditions of the first constraint condition expression and the second constraint condition expression, the simplex arithmetic processing means is requested to perform arithmetic processing, and the value of xi obtained by the simplex arithmetic processing is an integer of 0 or more, When the solution does not include anything else, the assignment data is output as the optimal solution, and in other cases, the simplex operation process obtains an executable solution with a non-integer solution, Further, when an executable solution with a non-integer solution is obtained in the subsequent simplex operation processing, an evaluation expression Σ (the number of xi being an integer) for obtaining the number of xi that is an integer among xi is defined, If the value of the evaluation formula obtained by the non-integer solution obtained later is increased as compared with the value of the evaluation formula obtained by the non-integer solution obtained earlier, a non-integer solution is obtained. Approaches the integer solution, When the determination means determines that the non-integer solution does not approach the integer solution when it decreases, the second constraint condition determines that the non-integer solution does not approach the integer solution even if the simplex operation process is repeated. Control to repeat the simplex operation by changing the formula,
The next candidate whose value of the objective function is close to the minimum value is selected from the listed combinations of the number of used raw materials, and a new second constraint condition expression Cx = A member assignment system that controls to repeat the operation of requesting generation of d and requesting simplex arithmetic processing means to perform arithmetic processing under the new constraint condition.
  6. The member according to claim 5, wherein the predetermined allocation method is a process in which products are arranged in order from the longest, raw materials are arranged in order from the longest, and allocation is performed by the first fit method. Allocation system.   A member assignment program for causing a computer to function as each means according to claim 1.   A computer-readable recording medium on which the member assignment program according to claim 7 is recorded. Accepting member allocation data output from the member assignment system according to any one of claims 1 to 4, the m pieces of products, characterized by comprising a precut device cut from sequentially the k kinds of raw materials supplied Member processing equipment.

Images