JP5838047B2 - Material assignment system - Google Patents

Description

  The present invention relates to a member assignment system, a member assignment program, a recording medium, a member assignment method, and a member processing apparatus for optimizing the planing of face materials.

  Several types of raw materials with a length of 3 to 6 meters 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. In fact, a large amount of waste can be reduced by improving yield by 1%. 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).

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

  The method described in the above-mentioned Patent Document 1 executes a predetermined calculation process in order to further improve the yield by some percentage starting from an initial executable solution obtained in advance by an existing method. The technique described in Patent Document 1 can also be used when a product (face material) having various vertical and horizontal dimensions is cut out from a raw material (face material). In this case, the techniques described in Patent Documents 2, 3 and the like can be used to obtain an initial executable solution. However, in order to apply the method of Patent Document 1 to the cutting of a face material, in order to extend the one-dimensional calculation to two dimensions, the development of a technique for selecting parameters specific to the face material and using them effectively Is required. In addition, since the face material is cut vertically and horizontally, a specific planing cannot be found only by obtaining an optimal combination of products and raw materials. In order to create an instruction for a specific pre-cut operation, it is necessary to specify the order of cutting and cutting at the final stage of the arithmetic processing.

  The present invention has been made to solve the above problems, and provides a member assignment system, a member assignment program, a recording medium, a member assignment method, and a member processing apparatus for cutting a face material from a raw material with a high yield. For the purpose.

<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 the product area as an element and a product request quantity vector b having the product request quantity as an element, and storing the product request quantity vector b 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;
Compared with the raw material horizontal data and raw material vertical data of the k types of raw materials prepared, the product horizontal data and product vertical data of the m products that are required,
M-th order indicating a relationship between raw materials and products that can economically allocate one or more products satisfying a two-dimensional model condition including the first evaluation condition, the second evaluation condition, and the third evaluation condition Allocation pattern vector generation means for enumerating the allocation pattern vectors aj of
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;
In order to represent the number of used n raw materials, when any one of m products is assigned to n raw materials arbitrarily selected from k types of raw materials, Define the n-th use number vector x of xi,
Objective function generating means for generating an objective function indicating the sum of products of the n-th order cost coefficient vector f and the used number vector x corresponding to each of the n raw materials, and storing the objective function in a storage device;
The number of products cut out by n allocation patterns selected from the allocation pattern matrix A has been relaxed as a first constraint condition Ax ≧ b, which must be equal to or greater than the quantity of each required product. A constraint condition generation means for generating a third constraint condition expression 0 ≦ xi ≦ 1 and storing it in a storage device;
Initial setting means for receiving an input of an initial executable solution obtained by the predetermined allocation method and storing it in a storage device;
Simplex operation means for receiving input of the initial executable solution, the objective function, and the constraint condition expression, and executing simplex operation processing;
Search control means for controlling arithmetic processing to search for and output the optimal solution,
This search control means
If the simplex operation processing results in a solution where the value of xi is either 0 or 1 and does not include anything else, the face material allocation data is output with the solution as the optimal solution, otherwise to the value of the objective function of the initial feasible solution to a maximum value, the value of the resulting objective function of the simplex operation processing as the minimum value, the number of used raw materials taking the value of the objective function of the range Raw materials that enumerate combinations, select the one whose objective function is close to the minimum value, and determine how many kinds of raw materials to select and use for the allocation to the constraint generation means Requesting the generation of the second constraint condition expression Cx = d, where the product of the use matrix C and the raw material use number vector is equal to the raw material use scheduled quantity vector d;
Under the constraint conditions of the first constraint condition expression, the second constraint condition expression, and the third constraint condition expression, the simplex operation means is requested to perform an operation process, and then the simplex operation process obtained results in the value of xi being 0. Or, if the solution is one that does not include anything else, the face material allocation data is output with the solution as the optimal solution, and in other cases,
When an executable solution with a non-integer solution is obtained by the simplex arithmetic processing, and further, an executable solution with a non-integer solution is obtained in the subsequent simplex arithmetic processing,
xi is defined numerical bets Ru evaluation formula .SIGMA.f (xi) between 0 and 1 while satisfying the constraint condition, seeking the value of the evaluation formula by the respective non-integer solution,
A function that the maximum value of the value of the evaluation equation is a constant value, the value of the evaluation formula by non-integer solutions obtained from later than the value of the evaluation formula by non-integer solutions previously obtained If it increases, the non-integer solution approaches the integer solution, and if the value of the evaluation formula decreases, it is determined that the non-integer solution does not approach the integer solution,
When it is determined that the non-integer solution does not approach the integer solution even if the simplex operation process is repeated, the second constraint condition expression is changed to control the simplex operation process to be repeated,
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 = It requests the production of d, member assignment system, characterized in that in this new constraint conditions, and controls so as to repeat the operation of requesting the arithmetic processing simplex operation means.

<Configuration 2>
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 the product area as an element and a product request quantity vector b having the product request quantity as an element, and storing the product request quantity vector b 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;
Compared with the raw material horizontal data and raw material vertical data of the k types of raw materials prepared, the product horizontal data and product vertical data of the m products that are required,
M-th order indicating a relationship between raw materials and products that can economically allocate one or more products satisfying a two-dimensional model condition including the first evaluation condition, the second evaluation condition, and the third evaluation condition Allocation pattern vector generation means for enumerating the allocation pattern vectors aj of
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;
In order to represent the number of used n raw materials, when any one of m products is assigned to n raw materials arbitrarily selected from k types of raw materials, Define the n-th use number vector x of xi,
Objective function generating means for generating an objective function indicating the sum of products of the n-th order cost coefficient vector f and the used number vector x corresponding to each of the n raw materials, and storing the objective function in a storage device;
The number of products cut out by n allocation patterns selected from the allocation pattern matrix A has been relaxed as a first constraint condition Ax ≧ b, which must be equal to or greater than the quantity of each required product. A constraint condition generation means for generating a third constraint condition expression 0 ≦ xi ≦ 1 and storing it in a storage device;
Initial setting means for receiving an input of an initial executable solution obtained by the predetermined allocation method and storing it in a storage device;
Simplex operation means for receiving input of the initial executable solution, the objective function, and the constraint condition expression, and executing simplex operation processing;
Search control means for controlling arithmetic processing to search for and output the optimal solution,
This search control means
If the simplex operation processing results in a solution where the value of xi is either 0 or 1 and does not include anything else, the face material allocation data is output with the solution as the optimal solution, otherwise to the value of the objective function of the initial feasible solution to a maximum value, the value of the resulting objective function of the simplex operation processing as the minimum value, the number of used raw materials taking the value of the objective function of the range Raw materials that enumerate combinations, select the one whose objective function is close to the minimum value, and determine how many kinds of raw materials to select and use for the allocation to the constraint generation means Requesting the generation of the second constraint condition expression Cx = d, where the product of the use matrix C and the raw material use number vector is equal to the raw material use scheduled quantity vector d;
Under the constraint conditions of the first constraint condition expression, the second constraint condition expression, and the third constraint condition expression, the simplex operation means is requested to perform an operation process, and then the simplex operation process obtained results in the value of xi being 0. Or, if the solution is one that does not include anything else, the face material allocation data is output with the solution as the optimal solution, and in other cases,
When an executable solution with a non-integer solution is obtained by the simplex arithmetic processing, and further, an executable solution with a non-integer solution is obtained in the subsequent simplex arithmetic processing,
xi is defined numerical bets Ru evaluation formula .SIGMA.f (xi) between 0 and 1 while satisfying the constraint condition, seeking the value of the evaluation formula by the respective non-integer solution,
A function minimum value of the evaluation equation is a constant value, the value of the evaluation formula by non-integer solutions obtained from later than the value of the evaluation formula by non-integer solutions previously obtained If it is decreasing, the non-integer solution approaches the integer solution, and if the value of the evaluation formula increases, it is determined that the non-integer solution does not approach the integer solution,
When it is determined that the non-integer solution does not approach the integer solution even if the simplex operation process is repeated, the second constraint condition expression is changed to control the simplex operation process to be repeated,
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 = It requests the production of d, member assignment system, characterized in that in this new constraint conditions, and controls so as to repeat the operation of requesting the arithmetic processing simplex operation means.

<Configuration 3>
In the member allocation system according to Configuration 1 or 2 ,
A member assignment system, characterized in that the evaluation formula values obtained by successively obtained non-integer solutions are determined according to a criterion for comparison using an annealing method.

<Configuration 4>
In the member allocation system according to any one of configurations 1 to 3 ,
The member allocation system according to claim 1, wherein the search control means sets an upper limit on the number of repetitions of the operation of requesting the simplex calculation means to perform calculation processing.

<Configuration 5>
In the member allocation system according to any one of configurations 1 to 4 ,
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. A member assignment system characterized by being one of processes for performing assignment by a first fit method.

<Configuration 6>
A member assignment program for causing a computer to function as each means according to configurations 1 to 5 .
<Configuration 7>
A computer-readable recording medium on which the member assignment program according to Configuration 6 is recorded.

<Configuration 8>
It is a method of optimizing the combination of products assigned to each raw material by obtaining the number of each type of raw material required when each of the predetermined rectangular m products is cut out from k kinds of raw materials of each predetermined rectangular shape. ,
The product setting means accepts the input of the required horizontal data and vertical data of m products, and the m-th product horizontal vector wp with the product horizontal length as the element and the m-th order with the product vertical length as the element Generating 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, and storing them in a storage device;
The raw material setting means accepts input of raw material data of k types of prepared rectangles, and the k-th raw material horizontal vector wm having the horizontal length of the raw material as an element and the k-th raw material vertical vector having the vertical length of the raw material as an element generating 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, and storing them in a storage device;
The two-dimensional model condition generation means determines that the area of the assigned product is the first evaluation condition (sp, aj) (inner product) that the area of the assigned product is equal to or less than the area S of any one of the elements of the raw material area vector sm ) ≦ S and the second evaluation condition that adjacent products do not overlap
wpi + wpj ≦ wml or
hpi + hpj ≦ hml
Generating a two-dimensional model condition including a third evaluation condition that the assignment pattern vector aj can be assigned by a predetermined assignment method, and storing the two-dimensional model condition in a storage device;
The allocated pattern vector generation means compares the product horizontal data and the raw material vertical data of the k kinds of raw materials prepared with the product horizontal data and the product vertical data of the m products requested, Listing m-th order allocation pattern vectors aj indicating the relationship between raw materials and products that can economically allocate a plurality of 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;
When the objective function generation means assigns any of the m products to n raw materials arbitrarily selected from k kinds of raw materials, the number of used n raw materials is determined. In order to express, an n-th order used number vector x of elements xi is defined,
Generating an objective function indicating 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, and storing the objective function in a storage device;
The first constraint condition expression Ax that the number of products cut out by the constraint condition generation means with the n number of allocation patterns selected from the allocation pattern matrix A must be equal to or greater than the quantity of each product that is determined. Generating a third constraint condition expression 0 ≦ xi ≦ 1 relaxed as ≧ b and storing it in the storage device;
An initial setting means for receiving an input of an initial executable solution obtained by the predetermined allocation method and storing it in a storage device;
A simplex computing means for receiving input of the initial executable solution, the objective function, and the constraint expression, and executing a simplex computing process;
The search control means is
If the simplex operation processing results in a solution where the value of xi is either 0 or 1 and does not include anything else, the face material allocation data is output with the solution as the optimal solution, otherwise to the value of the objective function of the initial feasible solution to a maximum value, the value of the resulting objective function of the simplex operation processing as the minimum value, the number of used raw materials taking the value of the objective function of the range Raw materials that enumerate combinations, select the one whose objective function is close to the minimum value, and determine how many kinds of raw materials to select and use for the allocation to the constraint generation means Requesting the generation of a second constraint condition expression Cx = d, wherein the product of the use matrix C and the raw material use quantity vector is equal to the raw material use scheduled quantity vector d ;
Under the constraint conditions of the first constraint condition expression, the second constraint condition expression, and the third constraint condition expression, the simplex operation means is requested to perform an operation process, and then the simplex operation process obtained results in the value of xi being 0. Or, if the solution is one that does not include anything else, the face material allocation data is output with the solution as the optimal solution, and in other cases,
When an executable solution with a non-integer solution is obtained by the simplex arithmetic processing, and further, an executable solution with a non-integer solution is obtained in the subsequent simplex arithmetic processing,
xi is defined numerical bets Ru evaluation formula .SIGMA.f (xi) between 0 and 1 while satisfying the constraint condition, determining a value of the evaluation formula by the respective non-integer solution,
A function that the maximum value of the value of the evaluation equation is a constant value, the value of the evaluation formula by non-integer solutions obtained from later than the value of the evaluation formula by non-integer solutions previously obtained If it increases, the non-integer solution approaches the integer solution, and if the value of the evaluation formula decreases, it is determined that the non-integer solution does not approach the integer solution,
When it is determined that the non-integer solution does not approach the integer solution even if the simplex arithmetic processing is repeated, the step of controlling the simplex arithmetic processing by changing the second constraint condition expression; and
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 allocating method comprising: a step of controlling to repeat the operation of requesting generation of d and requesting the simplex operation means to perform arithmetic processing under the new constraint condition.

<Configuration 9>
It is a method of optimizing the combination of products assigned to each raw material by obtaining the number of each type of raw material required when each of the predetermined rectangular m products is cut out from k kinds of raw materials of each predetermined rectangular shape. ,
The product setting means accepts the input of the required horizontal data and vertical data of m products, and the m-th product horizontal vector wp with the product horizontal length as the element and the m-th order with the product vertical length as the element Generating 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, and storing them in a storage device;
The raw material setting means accepts input of raw material data of k types of prepared rectangles, and the k-th raw material horizontal vector wm having the horizontal length of the raw material as an element and the k-th raw material vertical vector having the vertical length of the raw material as an element generating 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, and storing them in a storage device;
The two-dimensional model condition generation means determines that the area of the assigned product is the first evaluation condition (sp, aj) (inner product) that the area of the assigned product is equal to or less than the area S of any one of the elements of the raw material area vector sm ) ≦ S and the second evaluation condition that adjacent products do not overlap
wpi + wpj ≦ wml or
hpi + hpj ≦ hml
Generating a two-dimensional model condition including a third evaluation condition that the assignment pattern vector aj can be assigned by a predetermined assignment method, and storing the two-dimensional model condition in a storage device;
The allocated pattern vector generation means compares the product horizontal data and the raw material vertical data of the k kinds of raw materials prepared with the product horizontal data and the product vertical data of the m products requested, Listing m-th order allocation pattern vectors aj indicating the relationship between raw materials and products that can economically allocate a plurality of 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;
When the objective function generation means assigns any of the m products to n raw materials arbitrarily selected from k kinds of raw materials, the number of used n raw materials is determined. In order to express, an n-th order used number vector x of elements xi is defined,
Generating an objective function indicating 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, and storing the objective function in a storage device;
The first constraint condition expression Ax that the number of products cut out by the constraint condition generation means with the n number of allocation patterns selected from the allocation pattern matrix A must be equal to or greater than the quantity of each product that is determined. Generating a third constraint condition expression 0 ≦ xi ≦ 1 relaxed as ≧ b and storing it in the storage device;
An initial setting means for receiving an input of an initial executable solution obtained by the predetermined allocation method and storing it in a storage device;
A simplex computing means for receiving input of the initial executable solution, the objective function, and the constraint expression, and executing a simplex computing process;
The search control means is
If the simplex operation processing results in a solution where the value of xi is either 0 or 1 and does not include anything else, the face material allocation data is output with the solution as the optimal solution, otherwise to the value of the objective function of the initial feasible solution to a maximum value, the value of the resulting objective function of the simplex operation processing as the minimum value, the number of used raw materials taking the value of the objective function of the range Raw materials that enumerate combinations, select the one whose objective function is close to the minimum value, and determine how many kinds of raw materials to select and use for the allocation to the constraint generation means Requesting the generation of a second constraint condition expression Cx = d, wherein the product of the use matrix C and the raw material use quantity vector is equal to the raw material use scheduled quantity vector d ;
Under the constraint conditions of the first constraint condition expression, the second constraint condition expression, and the third constraint condition expression, the simplex operation means is requested to perform an operation process, and then the simplex operation process obtained results in the value of xi being 0. Or, if the solution is one that does not include anything else, the face material allocation data is output with the solution as the optimal solution, and in other cases,
When an executable solution with a non-integer solution is obtained by the simplex arithmetic processing, and further, an executable solution with a non-integer solution is obtained in the subsequent simplex arithmetic processing,
xi is defined numerical bets Ru evaluation formula .SIGMA.f (xi) between 0 and 1 while satisfying the constraint condition, determining a value of the evaluation formula by the respective non-integer solution,
A function minimum value of the evaluation equation is a constant value, the value of the evaluation formula by non-integer solutions obtained from later than the value of the evaluation formula by non-integer solutions previously obtained If it is decreasing, the non-integer solution approaches the integer solution, and if the value of the evaluation formula increases, it is determined that the non-integer solution does not approach the integer solution,
When it is determined that the non-integer solution does not approach the integer solution even if the simplex arithmetic processing is repeated, the step of controlling the simplex arithmetic processing by changing the second constraint condition expression; and
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 allocating method comprising: a step of controlling to repeat the operation of requesting generation of d and requesting the simplex operation means to perform arithmetic processing under the new constraint condition.

With respect to the face material, it is possible to improve the yield by using simplex calculation processing, and to create an instruction sheet including a cutting procedure for a pre-cut operation including specific planing.

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 an allocation pattern vector. It is explanatory drawing of the predetermined allocation method. It is the allocation processing operation | movement flowchart of the raw material kind by a FF method of several surface materials. It is the allocation processing operation | movement flowchart of the raw material kind by a FF method of several surface materials. It is explanatory drawing of the meaning of an evaluation type | formula. It is a flowchart of the main operation | movement of this invention. It is specific example explanatory drawing of the material to be allocated and the material to be used. It is explanatory drawing of the allocation pattern vector of 1-15 containing an initial feasible solution. It is explanatory drawing of 22698 types of allocation pattern vectors. It is explanatory drawing of the feasible solution which reached | attained. It is explanatory drawing of a non-integer solution. It is explanatory drawing of the comparative example of a non-integer solution and an integer solution. It is explanatory drawing of the yield improvement effect. It is a block diagram of a member processing apparatus. The allocation result by FF method is shown. The allocation result by FF method is shown. The allocation result by FF method is shown. The allocation result by FF method is shown. The allocation result by FF method is shown. The allocation result by FF method is shown. The allocation result by FF method is shown. The allocation result by the process of Example 2 is shown. The allocation result by the process of Example 2 is shown. The allocation result by the process of Example 2 is shown. The allocation result by the process of Example 2 is shown. The allocation result by the process of Example 2 is shown. The assignment result by the FF method when the product can be rotated 90 degrees vertically and horizontally is shown. The assignment result by the FF method when the product can be rotated 90 degrees vertically and horizontally is shown. The assignment result by the FF method when the product can be rotated 90 degrees vertically and horizontally is shown. The assignment result by the FF method when the product can be rotated 90 degrees vertically and horizontally is shown. The assignment result by the FF method when the product can be rotated 90 degrees vertically and horizontally is shown. The allocation result by the process of an Example in case the length and width of a product can rotate 90 degree | times is shown. The allocation result by the process of an Example in case the length and width of a product can rotate 90 degree | times is shown. The allocation result by the process of an Example in case the length and width of a product can rotate 90 degree | times is shown. The allocation result by the process of an Example in case the length and width of a product can rotate 90 degree | times is shown.

  In the present invention, based on a practical solution obtained by an existing arbitrary method, it is evaluated by a simplex method to obtain a further improved solution. The simplex method is known as a method for searching for an optimal solution of a linear programming problem. However, if there are several tens of types of product dimensions and raw materials required, 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 There is a possibility that the simplex operation processing for the search takes too much time. Therefore, in the present invention, a constraint condition for the arithmetic processing by the simplex method is added to efficiently calculate while narrowing down the comparison target range. 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. Therefore, the calculation processing time for searching can be greatly shortened. 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 the face material. The member assignment system 10 receives the condition data for precut from the terminal device 16, executes the calculation process, and returns the result. The terminal device 16 controls the precut device 17 using the returned member allocation data. As the pre-cut device 17, for example, a device as described in Patent Document 3 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.

  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 use scheduled quantity vector d45, allocation pattern matrix 46, raw material use matrix C47, first constraint condition equation 48, second constraint condition equation 49, third constraint condition equation 50, objective function 51, combination list 52, member Data such as allocation data 53 and evaluation formula 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 3, a keyboard 4, and a mouse 5 are connected to the input / output interface 115. A terminal device 16 is connected to the network interface 116 via the network 14. The above hardware is the same as that provided in a generally well-known personal computer. The terminal device 16 supplies the member allocation data 53 (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 this embodiment, in order to simplify the calculation, description will be made assuming that bi = 1. In practice, bi may be any positive integer.
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 third 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 order to simplify the calculation, since all the elements of the product request quantity vector b are set to bi = 1, each element xi of the m-th order use number vector x becomes 0 ≦ xi ≦ 1, and as a result of the member assignment It is meaningful when xi is 0 or 1.

In the symbols of Example 1 and 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. Accordingly, the number of each product cut out from the raw material selected from the allocation pattern matrix A with the corresponding allocation pattern must be equal to or greater than the quantity of each required product. The required quantity of each product corresponds to the product request quantity vector b. Therefore, the required number of products cannot be obtained unless at least the following formula is satisfied.
.SIGMA.aij.xj.gtoreq.bi (j = 1, 2,..., N) (i = 1, 2,..., M)

When the inequality sign is established, it is overmade. For convenience of calculation, the above inequality is used as a constraint. This constraint condition expression is expressed as Ax ≧ b.
In the example of FIG. 3, the number of products produced and the number of required products are 7, and the equal sign is established.
The constraint condition generating means 26 generates a first constraint condition expression that the number of each product cut out from the raw material selected from the allocation pattern matrix A with the corresponding allocation pattern is equal to or greater than the number of each required product. Then, it is stored in the storage device 40.

[Raw material use matrix C]
A k-th-order raw material usage vector cj indicating which raw material to be used out of k kinds of raw materials is defined as follows. 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 allocation pattern matrix generation means 25 generates a k × n-order raw material usage matrix C that enumerates raw material usage vectors cj indicating which raw material of k types of raw materials is used in each allocation pattern, Store in a storage device.

[Second constraint]
Since cj is a vector that designates one of k kinds of raw materials, the following equation is satisfied.
Σcij = 1 (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 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. This is because it has a meaning to determine which one of the many allocation pattern vectors listed is to be selected. Therefore, a constraint condition expression such as the following expression is established.
xi∈ {0,1}
In this embodiment, this constraint condition is relaxed. That is, a constraint condition expression of 0 ≦ xi ≦ 1 is set.
The constraint condition generation means generates a third constraint condition expression indicating that each element xi of the used number vector x is 0 ≦ xi ≦ 1, and stores it in the storage device.

(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 generating unit 31 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 the assignment method cannot be assigned by a predetermined assignment method, the cutting procedure data 54 cannot be generated in the end, 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.

  The element of the cost coefficient vector is the area. 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 order to execute arithmetic processing by the simplex method, an objective function and constraint conditions are defined as follows.
Min Σfi ・ xi
subject to Ax ≧ b
Cx = d
0≤xi≤1

The first expression is an objective function generated by the objective function generation means.
The second expression is a first constraint condition expression generated by the constraint condition generation means.
The third expression is a second constraint condition expression generated by the constraint condition generation means.
The fourth expression is a third constraint condition expression generated by the constraint condition generation means.
The objective function indicates the total cost of the n selected raw materials.
The first constraint condition expression 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.

  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 A46. 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 to input parameters excluding the constraint condition of Cx = d and execute the first arithmetic processing. The simplex operation processing means changes the basis variable of the simplex table so as to improve the value of the objective function and outputs a solution. The third constraint condition expression 0 ≦ xi ≦ 1 relaxes the constraint condition of xiε {0, 1}. Accordingly, the solution may include something other than an integer such as xi = 0.5. There may be a plurality of solutions having the same objective function value.

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

  Next, the search control means 30 enumerates combinations of the 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 calculation processing means to execute calculation processing.

  In this way, the simplex operation process is repeated to search for the optimum solution. When a large number of combinations of 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, the initial setting means 23 receives an input of the initial executable solution 44 determined to satisfy the two-dimensional model condition. 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. In the present invention, special control as described later is performed for the search operation in step S37.

6 to 11 are explanatory diagrams of specific calculation examples.
(Raw material data)
For example, five types of raw materials are prepared, and the raw material names are GG1 to GG5.
(Product data)
Seven products are required, and the product names are SS1 to SS7.

(Assignment pattern vector)
FIG. 6 is an explanatory diagram of an allocation pattern vector.
The above seven product names are listed in one vertical column from the top to the bottom on the left side of the figure. In addition, the names of raw materials are listed in one horizontal row from left to right in the uppermost row. The vertical column under each raw material name is an assigned pattern vector. For example, it is assumed that one with a product name of SS2 can be assigned to one with a raw material name of GG1. For example, it is assumed that one with a product name of SS3 and SS6 can be assigned to one with a raw material name of GG2. This table compares the dimensions of seven products with the dimensions of five raw materials in this way, and shows the relationship between raw materials and products that can be allocated economically to one or more products. The following 7th order allocation pattern vectors are listed. Here, x1 to x5 are allocation pattern vectors obtained from the initial executable solution. In the following, this table is expanded by the procedure as described in Patent Document 1, and the used number vector x of raw materials is obtained.

(Objective function)
In order to simplify the explanation, each element of the cost coefficient vector f is matched with the raw material area.
That is, the numerical value of the area is read as a circle as it is.
When the part of the raw material name in FIG. 6 is expressed by the area of the raw material, those numerical values are elements of the cost coefficient vector f. Therefore, the value of the objective function Σ (fi · xi) of the feasible solution that is input as the initial value in the first simplex operation processing is the sum of the areas of the used raw materials x1 to x5. In the following calculation, a solution to improve this is obtained, so the upper limit value of the objective function value is set to the sum obtained at this time.

  In the present invention, the objective function value when a solution by a simplex operation is obtained is set to the lower limit value of the optimum value. That is, since the objective is to improve the initial feasible solution, the initial value of the objective function value is set to the maximum value, and the objective function value obtained by the first simplex operation process is set to the minimum value. Assuming that there is an optimum value in this range, the search is performed again. Here, the cases where the objective function values are within this range by listing the raw materials in any number are listed. For example, calculation results to be aggregated while selecting combinations may be sorted in ascending order.

Since the specific simplex operation processing is as described in Patent Document 1, the description thereof is omitted. Thus, an allocation pattern that can save raw materials is found, and the result is output as member allocation data and transmitted to the terminal device.
For the two-dimensional model, even if only the data specifying the raw material to be used and the product to be cut out from each raw material is sent to the precut device, the precut control cannot be performed as it is. In the process of determining whether or not the two-dimensional model condition is satisfied when the initial feasible solution is obtained, it is determined whether or not allocation is possible using a predetermined allocation method. In this determination, the product allocation position, the raw material cutting position, and the cutting order are specifically confirmed. The result is stored in the storage device 40.

FIG. 7 is an explanatory diagram of a predetermined allocation method.
As the predetermined allocation method, for example, 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 executed by the first fit method (FF method). After that, arrange the products in descending order of the length, arrange the raw materials in order from the longest length, perform the allocation by the first fit method in the same way, arrange the products in order from the largest area, Are arranged in descending order of area, and allocation is performed by the first fit method. All this can be done to find the optimal allocation method.

  In this process, for example, in FIG. 7, it is assumed that a product 57 is assigned to a corner of a certain raw material 56. At this time, the raw material is cut at a cutting line 58 passing through one of the sides of the product 57. The raw material piece after cutting is cut along a cutting line 59 passing through the remaining side of the product 57. It is determined whether other products can be allocated to the remaining raw material pieces 60 and 61, and if not allocated, it is determined as a waste material. When the assignment is performed in this procedure, the product assignment position, the raw material cutting position, and the cutting order are automatically determined. This is stored in the storage device 40 as the determination result 64 together with the generation of the executable solution or during the determination process whether or not the two-dimensional model condition is satisfied. It is preferable to read the determination result 64 and generate cutting procedure data 54. This data can directly control the precut device. In addition, the work procedure manual can be printed and handed to the operator, and manual precutting can be performed.

(FF method)
FIG. 8 and FIG. 9 are flowcharts of the allocation processing operation for the face material having a plurality of raw material types by the FF method.
When assigning face materials using the first fit method (FF method), for example, as shown in the figure, the materials are assigned in order from the widest area. That is, first, in the first step S11, the raw materials are arranged in descending order of area, a list in reading order is created and stored in the storage device. In step S12, products are arranged in descending order of area, a list in reading order is created and stored in the storage device. Thereafter, the processing from step S3 to step S19 is repeated.

  In step S13, one raw material is selected according to the reading order list. In step S14, product allocation trial processing is performed on this raw material. Specific contents of the process in step S14 will be described later with reference to FIG. If the allocation of the product with the best yield is found in step S14 for one raw material selected in step S13, the yield is calculated in step S15.

  In step S16, it is determined whether or not all the raw materials have been selected. If the result of this determination is yes, the process proceeds to step S17, and if no, the process returns to step S13. That is, the processing from step S13 to step S16 is repeated for all types of raw materials. When the processing for all the raw materials is completed, the calculation results so far are compared in step S17, the allocation of the maximum yield is found, the combination of one material and product is determined, and this is adopted.

In step S18, the assigned product whose combination has been determined in step S17 is deleted from the reading order list. In step S19, it is determined whether the allocation process has been completed for all products. If the result of this determination is yes, the process proceeds to step S20, and if no, the process returns to step S13. In this way, the processing from step S13 to step S19 is repeated to assign all products to any material. When this is completed, the total yield is calculated in step S20. Thus, the allocation process by the FF method is completed.

FIG. 9 is an operation flowchart for performing a product allocation trial process on raw materials.
First, in step 21, it is determined whether there is an unassigned product in the product reading order list. If yes, then the process proceeds to step S22. If no, the process ends, and the process proceeds to step S15 in FIG. In step S22, one product is selected according to the reading order list. In step S23, it is determined whether the selected product can be assigned to the raw material or the remaining material.

  At first, raw materials are assigned, and after the second time, remaining materials are assigned. The determination in step S23 is whether the selected product can be assigned to the corner of the raw material or the remaining material. When yes, the process proceeds to step S24, and when no, the process proceeds to step S21. In step S24, the selected product is assigned to the corner of the raw material or the remaining material. Since both raw materials and remaining materials are rectangular (including squares), they are assigned to one of the four corners. In step S25, the product portion and the remaining material portion are divided by guillotine cutting (the cutter is not stopped halfway). Then, the process proceeds to step S21. This is repeated until the allocation to one raw material is completed, and when the allocation is completed, the process proceeds to step S15 in FIG.

(Allocation pattern vector generation)
In order to obtain an optimal solution, it is possible to automatically generate all the allocation patterns without overlapping each other by using the backtrack method, for example. But then
Even when the 25 products shown in FIG. 12 are assigned to two types of raw materials, the number of assigned patterns causes a combination explosion.

  In order to avoid this, a sensitivity analysis method using a simplex multiplier may be added to the two-dimensional model condition so as to rationally narrow down the number of assigned pattern vectors while ensuring an equivalent to the round robin. This contributes to a significant reduction in calculation time.

(Evaluation formula)
The simplex operation processing means 29 searches for combinations of allocation pattern vectors that satisfy the constraint conditions by a pivot operation using a known simplex tableau. Given the constraint that the combination of raw materials to be used is constant, the simplex operation processing means 29 finds an executable solution in which the value of x satisfies the constraint condition while gradually changing the combination of the allocation pattern vectors. There is no regularity in the order of appearance of non-integer solutions obtained in the process of this pivot operation. If the initial conditions at the start of the pivot operation are different, the pivot operation is executed in a completely different process, and the appearance order of the non-integer solutions also changes. There is no way to find the optimal initial condition to reach an integer solution in the shortest time. If you are unlucky, you may not be able to get an integer solution by repeating the pivot operation tens of thousands of times.

  A plurality of non-integer solutions may be obtained before an integer solution is obtained. Even if a large number of non-integer solutions are obtained, an integer solution may not be obtained until the end. If an integer solution is not obtained until the end, it means that there is no optimal solution for the combination of raw materials for which conditions are set. Repeating the pivot operation until the end is unreasonable considering the practical calculation time, so when the number of pivot operations reaches W, the search is terminated and another combination of raw materials is selected. It may be. However, the search strategy can be determined by monitoring the relative cost factor obtained from the simplex tableau when the non-integer solution is output. When the relative cost coefficients are all positive, it may be determined that there are no more feasible solutions. Further, if at least one relative cost coefficient includes 0 (zero), it can be determined that there are other feasible solutions. Therefore, the search should continue.

  However, even if the allocation pattern vector generation rationalization is attempted, if the number of allocation pattern vectors is large or the number of combinations of raw materials is large, the calculation processing time by the simplex calculation processing means 29 may become enormous. There is. Therefore, in the present invention, when a plurality of non-integer solutions are obtained, the result of the subsequent arithmetic processing is predicted using an evaluation formula defined below. That is, when a plurality of non-integer solutions are obtained as a result of the pivot operation processing, these non-integer solutions are compared by applying a specific evaluation formula, and if a certain criterion is satisfied, the pivot operation processing is continued. To do. If the determination criterion is not satisfied, the initial condition when starting the pivot calculation process is changed and the pivot calculation process is restarted. Alternatively, the arithmetic processing under the same constraint condition is stopped, and another raw material combination is set as the constraint condition.

  The evaluation formula 54 shown in FIG. 1 is data defined as Σf (xi). Σf (xi) is a function that has a constant maximum value when xi takes a numerical value between 0 and 1 while satisfying the constraint condition. For example, f (xi) can be defined as xi to the nth power (n> 1). Alternatively, Σf (xi) is a function whose minimum value is a constant value when xi takes a numerical value between 0 and 1 while satisfying the constraint condition. For example, f (xi) can be defined as sin πxi, or f (xi) can be defined as xi to the nth power (0 <n <1).

FIG. 10 is an explanatory diagram of the meaning of the evaluation formula.
The meaning of the evaluation expression will be described by defining f (xi) as the square of xi. This evaluation formula is for observing a change in the value of the element xi of the used number vector x of raw materials when a plurality of non-integer solutions are obtained. That is, it can be determined whether the pivot calculation is proceeding in a direction in which all xi included in each solution approach an integer. In general, the theory is as follows.

  For example, the number of used sheets x = (x1, x2). Also, the raw material combination C is (1, 1). The former is a column vector and the latter is a row vector. Since (Cx = d), x1 + x2 = 1. In this case, as shown in FIG. 10A, on the orthogonal coordinates of the x1 axis and the x2 axis, the feasible solution is on a straight line where the coordinate of the x1 axis cut edge is 1 and the coordinate of the x2 axis cut edge is 1. It can be said that there is. The white circles at both ends of the line are integer solutions, and the central black circle is a non-integer solution. In (b), the value of the evaluation formula is shown on the vertical axis, and the values of x1 and x2 are shown on the horizontal axis.

  FIG. 10B shows a solution space when the elements of the used number vector x are x1 and x2. The maximum value of the evaluation formula is 1, and the minimum value is 0.5. As the number of elements of the vector x increases, the solution space becomes more complicated than this figure. In addition, the output order of non-integer solutions and integer solutions obtained by pivot calculation is also complicated. Therefore, the value of the evaluation formula of the integer solution or the non-integer solution obtained by the executable solution that is sequentially output after starting the pivot operation under a certain condition changes as shown in FIG. Black circles are based on non-integer solutions, and white circles are based on integer solutions.

  Here, for example, it is assumed that the arithmetic processing by the simplex arithmetic processing means 29 is started and the executable solution R1 is obtained at a predetermined timing. After that, it is assumed that an executable solution R2 is obtained. Both are non-integer solutions. Comparing the values of both evaluation formulas, the value of the non-integer solution obtained later decreases. Even if the pivot calculation is further continued here, the value of the evaluation formula decreases, and it is determined that the integer solution is not immediately approached. Therefore, the initial condition is changed at this timing. That is, the starting point of the pivot calculation is changed.

  In this calculation processing, the objective function is Σfi · xi, the constraint condition is (Ax ≧ b), xi is 0 ≦ xi ≦ 1, and the constraint condition that the combination of raw materials is constant (Cx = d) is added. Then, the simplex operation processing means 29 was activated. Allocation pattern vectors and constraints cannot be changed. On the other hand, in the method of the present invention, since the cost coefficient value is not included in the constraint condition (Cx = d) and the used number vector x is used as the basis variable, the value of the cost coefficient fi is changed. There is no direct effect on the solution. In addition, if the value of the cost coefficient fi included in the objective function is changed, the starting point and order of the pivot calculation can be changed. For example, even if the calculation process is started with all the values of the cost coefficient fi set to 0, or the calculation process is started with all the values of the cost coefficient fi set to 1, the same result is finally obtained. . However, the pivoting process is different. That is, by changing the changeable setting conditions for the simplex calculation processing means 29, the pivot calculation is stopped when the executable solution R2 of FIG. 10C is obtained, and this time from the timing t1. It may be possible to resume the pivot operation. Of course, it suffices if the initial condition for starting the pivot calculation can be changed by any other method.

  When the pivot calculation is resumed from the timing t1, an executable solution R3 is obtained thereafter. After that, it is assumed that an executable solution R4 is obtained. Both are non-integer solutions. Here, when the value of both evaluation formulas is compared, the value increases. At this time, if the pivot calculation is further continued, the value of the evaluation formula increases and it is determined that there is a high possibility of approaching the integer solution. Such a determination is performed by the determination unit 31 shown in FIG. In the example of FIG. 10C, the integer solution indicated by the white circle can be safely reached thereafter.

  However, in practice, even if the arithmetic processing is continued under the same setting conditions, an integer solution is not always obtained. Therefore, for example, if the value of the evaluation formula increases and then begins to decrease without obtaining an integer solution, it is determined that the maximum value has been passed, and another setting curve is obtained to change the setting condition. For example, the pivot calculation may be repeated by sequentially switching the value of the cost coefficient fi from the state of all 0 to the state of all 1.

  When multiple non-integer solutions are obtained by the above processing, if it is determined that it is not possible to continue the pivot operation after that, the state is avoided and the pivot operation is started from another condition. In this way, the calculation processing time can be shortened. Further, for example, when the tendency of the value of the evaluation formula does not increase even when the initial condition is changed, it is determined that there is no integer solution under this constraint condition, and the constraint condition (Cx = It is preferable to change d) and restart the arithmetic processing.

  Continuing the pivot calculation only when the value of the evaluation formula increases can be called a hill-climbing method in the known local search method. And changing the initial condition at random can be called a random restart method. Furthermore, an integer solution can be searched by a known annealing method using the above evaluation formula. It is also effective to continue the pivot operation when the value of the evaluation formula once decreases and then increases when it is a non-integer solution and passes the local optimal solution. With the determination criteria as described above, the determination means 31 shown in FIG. 1 determines whether or not to continue the pivot calculation. The search control means 30 shown in FIG. 1 controls the search according to the determination by the determination means.

(Operation flow)
FIG. 11 is a flowchart of the main operation of the present invention.
A specific procedure of arithmetic processing using the evaluation formula will be described with reference to FIG. First, in step S51 in the figure, a combination of the number of raw materials is selected. Next, in step S52, a constraint condition is set using the above constraint equation. In step S53, initial conditions are set. This initial condition is a condition at the start of the pivot calculation. For example, all the cost coefficients are set to zero. In step S54, simplex operation processing is started. In step S55, a pivot calculation is executed. The pivot calculation is repeated, and an executable solution is output in step S56. In step S57, it is determined whether it is an integer solution. If the result of this determination is yes, the process ends because it is the optimal solution. If no, the process proceeds to step S58.

  In step S58, it is determined whether or not the pivot calculation is finished. This is a case where it is determined that there is no feasible solution as already described. If the result of this determination is yes, the process proceeds to the first step S51, and the constraint conditions are reset. If no, the process proceeds to step S59. In step S59, arithmetic processing for applying the non-integer solution to the evaluation formula is performed. The determination means 31 (FIG. 1) performs the calculation of steps S59-61. In step S60, determination is made by comparing the history of the values of the evaluation formula. That is, for example, for the previous non-integer solution, the value of the calculated evaluation formula is stored in the storage device and compared with the current one. Also, for the non-integer solution obtained several times in succession, the value of the calculated evaluation formula is stored in the storage device and compared with the current one. In step S61, it is determined whether or not to continue the pivot calculation using the determination criterion as described above. If the result of this determination is yes, the process proceeds to step S56, and steps S56 to 61 are repeated. On the other hand, when the answer is no, the process proceeds to step S62, and the cost coefficient is changed. Then, the process returns to step S54. That is, the pivot calculation is resumed under new initial conditions.

FIG. 12 is an explanatory diagram of specific examples of products to be allocated and materials to be used.
In the following specific example, as shown in this figure, 25 products are assigned products.
To simplify the vector display, products with the same portrait and landscape are assigned different product numbers. Two types of raw materials were prepared with the same horizontal length but different vertical lengths. The length was displayed in units of 0.1 mm. Therefore, “8222” means 822 mm. In the yield calculation, the price of raw materials was assumed to be proportional to the area. That is, the higher the yield, the lower the cost of the product. The area value shall be read as “circle”.

  As for the face material, the direction of the grain may be a problem when cutting off. That is, there are cases where the direction of the grain of the product is specified and the direction of the grain is free and may be rotated by 90 degrees. In this example, the product cannot be rotated 90 degrees. That is, the horizontal and vertical lengths of the raw material and the product are those in the required directions. The blade thickness when cutting the raw material is 0 mm. The raw material is not damaged at all and can be used according to dimensions.

  13 and 14 are explanatory diagrams of products and allocation pattern vectors. FIG. 13 shows 1 to 15 allocation pattern vectors including initial feasible solutions, and FIG. 14 shows 22698 types of allocation pattern vectors. The number at the top is for distinguishing each allocation pattern vector. In this table, only the product number of each product is shown because of space. The horizontal and vertical lengths of each product are as shown in FIG. 12 are initial executable solutions obtained by the FF method.

FIG. 15 is an explanatory diagram of the reached feasible solution.
Using the data in FIGS. 13 and 14, the pivot operation by the simplex operation processing means 29 is repeated. Repeated 6149 times counting from the beginning, a feasible solution as shown in FIG. 15 was obtained. That is, when the combinations of “14”, “2586”, “5392”, “7516”, and “8018” among the allocation pattern vectors shown in FIGS. 13 and 14 are combined, each of 25 types of products from five materials is combined. The solution that can be cut out one by one was obtained.

  As shown in FIG. 13, the initial feasible solution by the FF method is that 25 types of products can be cut out one by one from the seven materials “1” to “7”. Therefore, when compared with FIG. 15, it can be seen that a solution with significantly improved yield was obtained.

FIG. 16 is an explanatory diagram of a non-integer solution.
A non-integer solution as shown in FIG. 16 was obtained at the 256th time counting the pivot operation from the beginning. What is surrounded by the left frame is an allocation pattern vector. The uppermost part of the frame is an element of the used number vector x. That is, 0.5 means that 0.5 corresponding raw materials are used. This is a non-integer solution.

  What is surrounded by the right frame is an Ax element. Even if it is a non-integer solution, it means that one or more products are obtained (Ax ≧ b is established), but the meaning of the non-integer solution is that the product is divided and cut out, and when combined, it becomes the same shape as the original product .

  In the course of such arithmetic processing, Σf (xi) is calculated. If the value based on the evaluation formula continues to increase, the pivot calculation is repeated. As a result, an integer solution could be obtained at the 6149th time.

FIG. 17 is an explanatory diagram of a comparative example of a non-integer solution and an integer solution.
As shown in FIG. 17, when the objective function value was calculated for the non-integer solution of FIG. 16, the result was “3100000”. Predicting that this level of value would be obtained, the pivot operation was repeated to obtain the integer solution of FIG. The calculation result of the objective function value was “3100000” as described above. In view of the calculation processing time, it is preferable to set an upper limit on the number of times the pivot calculation is repeated, set this result as an optimum value, and end the calculation process.

FIG. 18 is an explanatory diagram of the yield improvement effect. FIG. 19 is a block diagram of the member processing apparatus.
For face materials, the member assignment data 53 must include a cutting procedure. In this specific example, first, products were arranged in order from the largest in the horizontal direction, and raw materials were arranged in order from the largest in the horizontal direction, and the allocation was executed by the first fit method. Moreover, the method of always always assigning a product to the lower left corner of the raw material, cutting the raw material along a line parallel to the side of the product, and assigning the remaining product to the remaining material as described in FIG. Therefore, the same procedure is executed for the allocation result obtained from the above optimum value, and cutting procedure data is generated when all products can be cut. The cutting procedure data may be in the form of NC data. Further, a work procedure manual printed with a plan drawing of FIG. 20 and later described later is suitable.

  The cutting procedure data was obtained by the above processing. This is supplied to the precut device 17 at the precut factory. The raw materials are selected in the order shown in FIG. 14 and cut according to the corresponding assignment pattern to obtain a product. In this embodiment, as shown in FIG. 18, when the product cannot be rotated, the yield of 59.5% in the case of the initial feasible solution can be improved to 78.6%. In addition, when rotation is possible, the yield of 78.6% in the case of the initial feasible solution could be improved to 87.1%.

  20 to 26 show the allocation results by the FF method. 27 to 31 show the allocation results by the processing of the embodiment. 32 to 36 show the assignment results by the FF method when the product can be rotated 90 degrees vertically and horizontally. FIG. 37 to FIG. 40 show the allocation results by the processing of the embodiment when the product can be rotated 90 degrees vertically and horizontally.

  As shown in FIGS. 20 to 26, when assigned by the FF method, five raw material numbers were used, and two raw material numbers were used, and a total of seven raw materials were used. As shown in FIGS. 27 to 31, in the method of the example, four raw material numbers were used and one of the second raw material numbers was used, and a total of five raw materials were used. On the other hand, when the product can be rotated 90 degrees vertically and horizontally, as shown in FIGS. 32 to 36, the use of the raw material number 1 in the FF method is reduced by one. In the example, as shown in FIGS. 37 to 40, the use of the raw material number 2 was reduced by one. In either case, it was confirmed that precutting was possible by the above procedure.

  In a pre-cut factory that allocates a large amount of products to a large amount of raw materials and cuts them, such a yield improvement can reduce the cost. In addition, if the amount of waste can be reduced, facilities and costs for waste disposal can be saved. In the above example, the types of raw materials and the types and quantities of products required were simplified, but handling a wide variety of raw materials and products further improved yields to a level that could not be achieved by conventional methods. I can expect.

  In addition, in order to obtain the minimum value of the total sum of the used raw material areas, first, simplex operation processing was executed under the constraints of the first constraint equation and the third constraint equation. At this time, if a feasible solution with a non-integer solution was obtained, the objective function value at that time was set to the minimum value of the total sum of the used raw material areas. However, as described above, a non-integer solution may be obtained multiple times under the same constraints. Therefore, there is a possibility that another new non-integer solution may be obtained, and it is preferable to repeat the simplex operation process under the constraint conditions as long as there is a combination that equals the objective function value by combining the number of raw materials. .

  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 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 assignment data 54 Evaluation equation 55 Cutting procedure data

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 the product area as an element and a product request quantity vector b having the product request quantity as an element, and storing the product request quantity vector b 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;
Compared with the raw material horizontal data and raw material vertical data of the k types of raw materials prepared, the product horizontal data and product vertical data of the m products that are required,
M-th order indicating a relationship between raw materials and products that can economically allocate one or more products satisfying a two-dimensional model condition including the first evaluation condition, the second evaluation condition, and the third evaluation condition Allocation pattern vector generation means for enumerating the allocation pattern vectors aj of
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;
In order to represent the number of used n raw materials, when any one of m products is assigned to n raw materials arbitrarily selected from k types of raw materials, Define the n-th use number vector x of xi,
Objective function generating means for generating an objective function indicating the sum of products of the n-th order cost coefficient vector f and the used number vector x corresponding to each of the n raw materials, and storing the objective function in a storage device;
The number of products cut out by n allocation patterns selected from the allocation pattern matrix A has been relaxed as a first constraint condition Ax ≧ b, which must be equal to or greater than the quantity of each required product. A constraint condition generation means for generating a third constraint condition expression 0 ≦ xi ≦ 1 and storing it in a storage device;
Initial setting means for receiving an input of an initial executable solution obtained by the predetermined allocation method and storing it in a storage device;
Simplex operation means for receiving input of the initial executable solution, the objective function, and the constraint condition expression, and executing simplex operation processing;
Search control means for controlling arithmetic processing to search for and output the optimal solution,
This search control means
If the simplex operation processing results in a solution where the value of xi is either 0 or 1 and does not include anything else, the face material allocation data is output with the solution as the optimal solution, otherwise to the value of the objective function of the initial feasible solution to a maximum value, the value of the resulting objective function of the simplex operation processing as the minimum value, the number of used raw materials taking the value of the objective function of the range Raw materials that enumerate combinations, select the one whose objective function is close to the minimum value, and determine how many kinds of raw materials to select and use for the allocation to the constraint generation means Requesting the generation of the second constraint condition expression Cx = d, where the product of the use matrix C and the raw material use number vector is equal to the raw material use scheduled quantity vector d;
Under the constraint conditions of the first constraint condition expression, the second constraint condition expression, and the third constraint condition expression, the simplex operation means is requested to perform an operation process, and then the simplex operation process obtained results in the value of xi being 0. Or, if the solution is one that does not include anything else, the face material allocation data is output with the solution as the optimal solution, and in other cases,
When an executable solution with a non-integer solution is obtained by the simplex arithmetic processing, and further, an executable solution with a non-integer solution is obtained in the subsequent simplex arithmetic processing,
xi is defined numerical bets Ru evaluation formula .SIGMA.f (xi) between 0 and 1 while satisfying the constraint condition, seeking the value of the evaluation formula by the respective non-integer solution,
A function that the maximum value of the value of the evaluation equation is a constant value, the value of the evaluation formula by non-integer solutions obtained from later than the value of the evaluation formula by non-integer solutions previously obtained If it increases, the non-integer solution approaches the integer solution, and if the value of the evaluation formula decreases, it is determined that the non-integer solution does not approach the integer solution,
When it is determined that the non-integer solution does not approach the integer solution even if the simplex operation process is repeated, the second constraint condition expression is changed to control the simplex operation process to be repeated,
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 = It requests the production of d, member assignment system, characterized in that in this new constraint conditions, and controls so as to repeat the operation of requesting the arithmetic processing simplex operation means. 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 the product area as an element and a product request quantity vector b having the product request quantity as an element, and storing the product request quantity vector b 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;
Compared with the raw material horizontal data and raw material vertical data of the k types of raw materials prepared, the product horizontal data and product vertical data of the m products that are required,
M-th order indicating a relationship between raw materials and products that can economically allocate one or more products satisfying a two-dimensional model condition including the first evaluation condition, the second evaluation condition, and the third evaluation condition Allocation pattern vector generation means for enumerating the allocation pattern vectors aj of
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;
In order to represent the number of used n raw materials, when any one of m products is assigned to n raw materials arbitrarily selected from k types of raw materials, Define the n-th use number vector x of xi,
Objective function generating means for generating an objective function indicating the sum of products of the n-th order cost coefficient vector f and the used number vector x corresponding to each of the n raw materials, and storing the objective function in a storage device;
The number of products cut out by n allocation patterns selected from the allocation pattern matrix A has been relaxed as a first constraint condition Ax ≧ b, which must be equal to or greater than the quantity of each required product. A constraint condition generation means for generating a third constraint condition expression 0 ≦ xi ≦ 1 and storing it in a storage device;
Initial setting means for receiving an input of an initial executable solution obtained by the predetermined allocation method and storing it in a storage device;
Simplex operation means for receiving input of the initial executable solution, the objective function, and the constraint condition expression, and executing simplex operation processing;
Search control means for controlling arithmetic processing to search for and output the optimal solution,
This search control means
If the simplex operation processing results in a solution where the value of xi is either 0 or 1 and does not include anything else, the face material allocation data is output with the solution as the optimal solution, otherwise to the value of the objective function of the initial feasible solution to a maximum value, the value of the resulting objective function of the simplex operation processing as the minimum value, the number of used raw materials taking the value of the objective function of the range Raw materials that enumerate combinations, select the one whose objective function is close to the minimum value, and determine how many kinds of raw materials to select and use for the allocation to the constraint generation means Requesting the generation of the second constraint condition expression Cx = d, where the product of the use matrix C and the raw material use number vector is equal to the raw material use scheduled quantity vector d;
Under the constraint conditions of the first constraint condition expression, the second constraint condition expression, and the third constraint condition expression, the simplex operation means is requested to perform an operation process, and then the simplex operation process obtained results in the value of xi being 0. Or, if the solution is one that does not include anything else, the face material allocation data is output with the solution as the optimal solution, and in other cases,
When an executable solution with a non-integer solution is obtained by the simplex arithmetic processing, and further, an executable solution with a non-integer solution is obtained in the subsequent simplex arithmetic processing,
xi is defined numerical bets Ru evaluation formula .SIGMA.f (xi) between 0 and 1 while satisfying the constraint condition, seeking the value of the evaluation formula by the respective non-integer solution,
A function minimum value of the evaluation equation is a constant value, the value of the evaluation formula by non-integer solutions obtained from later than the value of the evaluation formula by non-integer solutions previously obtained If it is decreasing, the non-integer solution approaches the integer solution, and if the value of the evaluation formula increases, it is determined that the non-integer solution does not approach the integer solution,
When it is determined that the non-integer solution does not approach the integer solution even if the simplex operation process is repeated, the second constraint condition expression is changed to control the simplex operation process to be repeated,
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 = It requests the production of d, member assignment system, characterized in that in this new constraint conditions, and controls so as to repeat the operation of requesting the arithmetic processing simplex operation means. In the member allocation system according to claim 1 or 2 ,
A member assignment system, characterized in that the evaluation formula values obtained by successively obtained non-integer solutions are determined according to a criterion for comparison using an annealing method. In the member allocation system in any one of Claims 1 thru | or 3 ,
The member allocation system according to claim 1, wherein the search control means sets an upper limit on the number of repetitions of the operation of requesting the simplex calculation means to perform calculation processing. In the member allocation system in any one of Claims 1 thru | or 4 ,
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. A member assignment system characterized by being one of processes for performing assignment by a first fit method. A member assignment program for causing a computer to function as each means according to claim 1 . A computer-readable recording medium in which the member assignment program according to claim 6 is recorded. It is a method of optimizing the combination of products assigned to each raw material by obtaining the number of each type of raw material required when each of the predetermined rectangular m products is cut out from k kinds of raw materials of each predetermined rectangular shape. ,
The product setting means accepts the input of the required horizontal data and vertical data of m products, and the m-th product horizontal vector wp with the product horizontal length as the element and the m-th order with the product vertical length as the element Generating 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, and storing them in a storage device;
The raw material setting means accepts input of raw material data of k types of prepared rectangles, and the k-th raw material horizontal vector wm having the horizontal length of the raw material as an element and the k-th raw material vertical vector having the vertical length of the raw material as an element generating 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, and storing them in a storage device;
The two-dimensional model condition generation means determines that the area of the assigned product is the first evaluation condition (sp, aj) (inner product) that the area of the assigned product is equal to or less than the area S of any one of the elements of the raw material area vector sm ) ≦ S and the second evaluation condition that adjacent products do not overlap
wpi + wpj ≦ wml or
hpi + hpj ≦ hml
Generating a two-dimensional model condition including a third evaluation condition that the assignment pattern vector aj can be assigned by a predetermined assignment method, and storing the two-dimensional model condition in a storage device;
The allocated pattern vector generation means compares the product horizontal data and the raw material vertical data of the k kinds of raw materials prepared with the product horizontal data and the product vertical data of the m products requested, Listing m-th order allocation pattern vectors aj indicating the relationship between raw materials and products that can economically allocate a plurality of 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;
When the objective function generation means assigns any of the m products to n raw materials arbitrarily selected from k kinds of raw materials, the number of used n raw materials is determined. In order to express, an n-th order used number vector x of elements xi is defined,
Generating an objective function indicating 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, and storing the objective function in a storage device;
The first constraint condition expression Ax that the number of products cut out by the constraint condition generation means with the n number of allocation patterns selected from the allocation pattern matrix A must be equal to or greater than the quantity of each product that is determined. Generating a third constraint condition expression 0 ≦ xi ≦ 1 relaxed as ≧ b and storing it in the storage device;
An initial setting means for receiving an input of an initial executable solution obtained by the predetermined allocation method and storing it in a storage device;
A simplex computing means for receiving input of the initial executable solution, the objective function, and the constraint expression, and executing a simplex computing process;
The search control means is
If the simplex operation processing results in a solution where the value of xi is either 0 or 1 and does not include anything else, the face material allocation data is output with the solution as the optimal solution, otherwise to the value of the objective function of the initial feasible solution to a maximum value, the value of the resulting objective function of the simplex operation processing as the minimum value, the number of used raw materials taking the value of the objective function of the range Raw materials that enumerate combinations, select the one whose objective function is close to the minimum value, and determine how many kinds of raw materials to select and use for the allocation to the constraint generation means Requesting the generation of a second constraint condition expression Cx = d, wherein the product of the use matrix C and the raw material use quantity vector is equal to the raw material use scheduled quantity vector d ;
Under the constraint conditions of the first constraint condition expression, the second constraint condition expression, and the third constraint condition expression, the simplex operation means is requested to perform an operation process, and then the simplex operation process obtained results in the value of xi being 0. Or, if the solution is one that does not include anything else, the face material allocation data is output with the solution as the optimal solution, and in other cases,
When an executable solution with a non-integer solution is obtained by the simplex arithmetic processing, and further, an executable solution with a non-integer solution is obtained in the subsequent simplex arithmetic processing,
xi is defined numerical bets Ru evaluation formula .SIGMA.f (xi) between 0 and 1 while satisfying the constraint condition, determining a value of the evaluation formula by the respective non-integer solution,
A function that the maximum value of the value of the evaluation equation is a constant value, the value of the evaluation formula by non-integer solutions obtained from later than the value of the evaluation formula by non-integer solutions previously obtained If it increases, the non-integer solution approaches the integer solution, and if the value of the evaluation formula decreases, it is determined that the non-integer solution does not approach the integer solution,
When it is determined that the non-integer solution does not approach the integer solution even if the simplex arithmetic processing is repeated, the step of controlling the simplex arithmetic processing by changing the second constraint condition expression; and
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 allocating method comprising: a step of controlling to repeat the operation of requesting generation of d and requesting the simplex operation means to perform arithmetic processing under the new constraint condition. It is a method of optimizing the combination of products assigned to each raw material by obtaining the number of each type of raw material required when each of the predetermined rectangular m products is cut out from k kinds of raw materials of each predetermined rectangular shape. ,
The product setting means accepts the input of the required horizontal data and vertical data of m products, and the m-th product horizontal vector wp with the product horizontal length as the element and the m-th order with the product vertical length as the element Generating 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, and storing them in a storage device;
The raw material setting means accepts input of raw material data of k types of prepared rectangles, and the k-th raw material horizontal vector wm having the horizontal length of the raw material as an element and the k-th raw material vertical vector having the vertical length of the raw material as an element generating 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, and storing them in a storage device;
The two-dimensional model condition generation means determines that the area of the assigned product is the first evaluation condition (sp, aj) (inner product) that the area of the assigned product is equal to or less than the area S of any one of the elements of the raw material area vector sm ) ≦ S and the second evaluation condition that adjacent products do not overlap
wpi + wpj ≦ wml or
hpi + hpj ≦ hml
Generating a two-dimensional model condition including a third evaluation condition that the assignment pattern vector aj can be assigned by a predetermined assignment method, and storing the two-dimensional model condition in a storage device;
The allocated pattern vector generation means compares the product horizontal data and the raw material vertical data of the k kinds of raw materials prepared with the product horizontal data and the product vertical data of the m products requested, Listing m-th order allocation pattern vectors aj indicating the relationship between raw materials and products that can economically allocate a plurality of 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;
When the objective function generation means assigns any of the m products to n raw materials arbitrarily selected from k kinds of raw materials, the number of used n raw materials is determined. In order to express, an n-th order used number vector x of elements xi is defined,
Generating an objective function indicating 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, and storing the objective function in a storage device;
The first constraint condition expression Ax that the number of products cut out by the constraint condition generation means with the n number of allocation patterns selected from the allocation pattern matrix A must be equal to or greater than the quantity of each product that is determined. Generating a third constraint condition expression 0 ≦ xi ≦ 1 relaxed as ≧ b and storing it in the storage device;
An initial setting means for receiving an input of an initial executable solution obtained by the predetermined allocation method and storing it in a storage device;
A simplex computing means for receiving input of the initial executable solution, the objective function, and the constraint expression, and executing a simplex computing process;
The search control means is
If the simplex operation processing results in a solution where the value of xi is either 0 or 1 and does not include anything else, the face material allocation data is output with the solution as the optimal solution, otherwise to the value of the objective function of the initial feasible solution to a maximum value, the value of the resulting objective function of the simplex operation processing as the minimum value, the number of used raw materials taking the value of the objective function of the range Raw materials that enumerate combinations, select the one whose objective function is close to the minimum value, and determine how many kinds of raw materials to select and use for the allocation to the constraint generation means Requesting the generation of a second constraint condition expression Cx = d, wherein the product of the use matrix C and the raw material use quantity vector is equal to the raw material use scheduled quantity vector d ;
Under the constraint conditions of the first constraint condition expression, the second constraint condition expression, and the third constraint condition expression, the simplex operation means is requested to perform an operation process, and then the simplex operation process obtained results in the value of xi being 0. Or, if the solution is one that does not include anything else, the face material allocation data is output with the solution as the optimal solution, and in other cases,
When an executable solution with a non-integer solution is obtained by the simplex arithmetic processing, and further, an executable solution with a non-integer solution is obtained in the subsequent simplex arithmetic processing,
xi is defined numerical bets Ru evaluation formula .SIGMA.f (xi) between 0 and 1 while satisfying the constraint condition, determining a value of the evaluation formula by the respective non-integer solution,
A function minimum value of the evaluation equation is a constant value, the value of the evaluation formula by non-integer solutions obtained from later than the value of the evaluation formula by non-integer solutions previously obtained If it is decreasing, the non-integer solution approaches the integer solution, and if the value of the evaluation formula increases, it is determined that the non-integer solution does not approach the integer solution,
When it is determined that the non-integer solution does not approach the integer solution even if the simplex arithmetic processing is repeated, the step of controlling the simplex arithmetic processing by changing the second constraint condition expression; and
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 allocating method comprising: a step of controlling to repeat the operation of requesting generation of d and requesting the simplex operation means to perform arithmetic processing under the new constraint condition.

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