JP4887341B2 - Information processing apparatus, information processing apparatus control method, and program - Google Patents

Description

  The present invention relates to a technique for obtaining an optimal solution when, for example, a product is efficiently cut from a coil that is a base material in the steel industry.

  Conventionally, when producing a coil manufactured according to an order (hereinafter referred to as a product coil), a certain actual product (an existing coil to be cut) is divided into a predetermined width and length according to the order. Disconnect. Here, the actual product (parent coil) is a coil having various widths, lengths, and thicknesses. At this time, it is devised to perform efficient plate cutting by finding an optimal solution of product coil allocation to the actual product and divided cutting (hereinafter referred to as plate cutting) of the allocated actual product.

  For example, Patent Document 1 discloses a plate cutting method. The technology disclosed in Patent Document 1 applies the one or more orders to a plurality of steel pieces, respectively, and creates a plan plan, under equipment constraints and constraints for eliminating redundant combinations, After enumerating all possible combinations by the branch and bound method, the billet that maximizes the target evaluation function is selected from the listed combinations using the 0-1 programming method under the constraints of the number of orders. By doing so, the plan is determined.

JP 2004-276034 A

  The technique disclosed in Patent Document 1 is a method of determining the number of patterns used by a mixed integer programming algorithm after generating an arrangement pattern. However, with respect to generation of an arrangement pattern, facility constraints and redundant combinations are used. Since all possible arrangement patterns are listed under the restriction to be excluded, if the number of arrangement patterns is large, there is a possibility that the optimal solution for the problem of determining the number of arrangement patterns to be used cannot be obtained in a practical time.

  Therefore, an object of the present invention is to make it possible to obtain an optimal solution with a smaller amount of calculation, without calculating the optimal solution for all the candidates to be assigned to the base material.

The information processing apparatus according to the present invention includes an initial block group determination unit that determines an initial block group that is a set of products assigned to a base material, and the length of the entire base material when the initial block group is used. An optimum solution calculating means for calculating the optimum solution of a method of assigning a product to the base material by calculating the number of uses of each block included in the initial block group by calculating a predetermined evaluation function to be represented; and the initial block group Additional block determination means for determining an additional block that reduces the value of the calculation result of the evaluation function when a block is added to the initial block group by performing a predetermined calculation for each block other than the additional blocks determining means, the value of the operation result of said evaluation function when adding a block is reduced to the initial block group Serial until additional block is eliminated, the initial blocks and for each block other than the additional blocks repeatedly said predetermined operation and run continue to determine the additional blocks, the optimal solution calculating section, the additional block determining means Each time the additional block is determined by the above, each block included in the initial block group and the number of times of use of the additional block are obtained to calculate the optimum solution of the product allocation method for the base material.
An information processing apparatus control method according to the present invention includes an initial block group determination step for determining an initial block group that is a set of products assigned to a base material, and the entire base material in the case where the initial block group is used. An optimal solution calculating step of calculating an optimal solution of a method of assigning a product to the base material by calculating a use number of each block included in the initial block group by calculating a predetermined evaluation function representing a length; and An additional block determination step for determining an additional block in which the value of the calculation result of the evaluation function is small when a block is added to the initial block group by performing a predetermined calculation on each block other than the initial block group; wherein the said additional block determination step, said evaluation function when adding a block to the initial block group Until said additional block value of the operation result is reduced is eliminated, it will determine the additional block repeatedly executes the predetermined operation for each block other than the initial block group and the additional block, the optimal solution calculating step Each time the additional block is determined by the additional block determining step , the optimal solution of the product allocation method for the base material is calculated by obtaining the number of times each block included in the initial block group and the additional block are used. It is characterized by doing.
The program of the present invention includes an initial block group determination step for determining an initial block group that is a set of products assigned to the base material, and a predetermined length that represents the length of the entire base material when the initial block group is used. An optimal solution calculating step for calculating the optimal solution of the product allocation method for the base material by calculating the number of times each block included in the initial block group is calculated, By performing a predetermined calculation for each block, the computer is caused to execute an additional block determination step for determining an additional block for which the value of the calculation result of the evaluation function is small when a block is added to the initial block group. the additional block determination step, the Review when adding a block to the initial block group Until said additional block value of the function of the operation result is reduced is eliminated, it will determine the additional block repeatedly executes the predetermined operation for each block other than the initial block group and the additional block, the optimal solution Each time the additional block is determined by the additional block determination step , the calculation step obtains the number of times each block included in the initial block group and the additional block are used, and the optimal solution of the method for assigning products to the base material. Is calculated.

According to the present invention, it is not necessary to calculate the optimal solution for all the blocks that are candidates to be assigned to the base material, and it is possible to obtain the optimal solution with a smaller amount of calculation.

  DESCRIPTION OF EXEMPLARY EMBODIMENTS Hereinafter, preferred embodiments to which the invention is applied will be described in detail with reference to the accompanying drawings.

  FIG. 1 is a block diagram showing a functional configuration of an optimum solution calculating apparatus according to an embodiment of the present invention. As shown in FIG. 1, the optimal solution calculation apparatus according to this embodiment includes an initial block group calculation unit 101, a dual problem calculation unit 102, and a reduced cost calculation unit 103.

  The initial block group calculation unit 101 inputs base material width information indicating the width of a coil serving as a base material, product information including size information indicating the size of the product and necessary number information indicating the number of necessary products, First, an initial block group that is a set (block) of products to be allocated to the base material is calculated. Here, the initial block group calculation unit 101 calculates, as an initial block group, a block group in which single types of products are arranged within the range of the width of the base material indicated by the base material width information.

First, the dual problem calculation unit 102 performs linear relaxation (integer variable X _{P) as} a main problem for minimizing the length of the entire base material when the initial block group calculated by the initial block group calculation unit 101 is used. Solve the dual problem for a problem that is relaxed to a real variable). Then, the dual problem calculation unit 102 calculates a block combination corresponding to a value in which the calculation result of the main problem and the calculation result of the dual problem match as a solution of the block allocation method for the base material.

  The reduced cost calculation unit 103 calculates the reduced cost for each block other than the initial block group among a plurality of types of blocks that are a set of products assigned to the base material, thereby adding an additional block to the initial block group To decide.

  When the additional block is determined by the reduced cost calculation unit 103, the dual problem calculation unit 102 has a value that matches the calculation result of the main problem and the calculation result of the dual problem when the additional block is added to the initial block group. Is calculated as a solution of the block allocation method for the base material.

  On the other hand, when it is determined by the reduced cost calculation unit 103 that there is no additional block, the dual problem calculation unit 102 determines the main problem and the dual problem for the initial block group or the block group of the initial block group and the additional block. The block allocation method corresponding to the values that are the same is calculated as the optimal solution.

The set covering problem calculation unit 104 obtains the number of times of use of the initial block group and each additional block, and calculates the optimum solution of the product allocation method for the base material.

  FIG. 2 is a block diagram showing a hardware configuration of the optimum solution calculating apparatus according to the present embodiment.

  The CPU 301 comprehensively controls each device and controller connected to the system bus. The ROM 303 or HD (hard disk) 309 stores a basic input / output system (BIOS) that is a control program for the CPU 301, an operating system program, a program for the processing shown in FIG. .

  In the example of FIG. 2, the HD 309 is configured to be arranged inside the optimum solution calculating device, but as another embodiment, a configuration corresponding to the HD 309 may be arranged outside the optimum solution calculating device. . Also, the program for performing the processing shown in FIG. 3 according to the present embodiment is recorded on a computer-readable recording medium such as a flexible disk (FD) or a CD-ROM, and is supplied from the recording medium. Alternatively, it may be configured to be supplied via a communication medium such as the Internet.

  The RAM 302 functions as a main memory, work area, and the like for the CPU 301. The CPU 301 implements various operations by loading a program necessary for execution of processing into the RAM 302 and executing the program.

  The HD 309 and the FD 308 function as an external memory. The CPU 301 implements various operations by loading a program necessary for execution of processing into the RAM 302 and executing the program.

  The disk controller 307 controls access to external memories such as the HD 309 and the FD 308. The communication I / F controller 306 is connected to the Internet or a LAN, and controls communication with the outside by TCP / IP, for example.

  The display controller 310 controls image display on the display 311.

  The KB controller 304 receives an operation input from the KB (keyboard) 305 and transmits it to the CPU 301. Although not shown, in addition to the KB 305, a pointing device such as a mouse can be applied to the optimum solution calculating apparatus according to the present embodiment as a user operation means.

  The initial block group calculation unit 101, dual problem calculation unit 102, and reduced cost calculation unit 103 illustrated in FIG. 1 are realized by, for example, a program stored in the HD 309 and loaded into the RAM 302 as necessary, and a CPU 301 that executes the program. It is the composition which is done.

  Next, the operation of the optimal solution calculation apparatus according to this embodiment will be described. FIG. 3 is a flowchart showing the operation of the optimum solution calculating apparatus according to this embodiment.

  First, the initial block group calculation unit 101 displays base material width information, product size information, necessary product number information, and upper limit value information on the number of slits in accordance with a user's operation using an input device such as a keyboard or a mouse. Input (step S201). In addition to the upper limit information on the number of slits, base material length upper limit information and the like may be used.

  Subsequently, the initial block group calculation unit 101 calculates, as an initial block group, a block group in which single types of products are arranged within the range of the base material width indicated by the base material width information (step S202).

  FIG. 4 is a diagram showing the base material and each product assigned to the base material. In the example shown in FIG. 4, the width of the base material 401 is 100, and four types of products are assigned to this base material. The first product 402 is a product having a length of 50 and a width of 50. The second product 403 is a product having a length of 40 and a width of 40. The third product 404 is a product having a length of 30 and a width of 30. The fourth product 405 is a product having a length of 15 and a width of 20. When the single types of products 402 to 405 are arranged within the range of the width of the base material, the products 501, 505, 508, and 511 in FIG. 5 are obtained. 501 in FIG. 5 is a block in which two products 402 are arranged in the width direction of the base material. 505 in FIG. 5 is a block in which two products 403 are arranged in the width direction of the base material. 508 in FIG. 5 is a block in which three products 404 are arranged in the width direction of the base material. 511 in FIG. 5 is a block in which five products 405 are arranged in the width direction of the base material. The initial block group calculation unit 101 calculates these blocks as an initial block group. More specifically, the initial block group calculation unit 101 reads the base material width information and the product size information temporarily stored in the RAM 302 into the CPU 301, divides the base material width by the width of each product, and the divided number. The initial block group is determined by arranging the separated products in the width direction of the base material. In this embodiment, the elements of the initial block group are configured by an arrangement pattern composed of a single type of material. However, the present invention is not limited to this. Such an initial block group may be used. In the following description, a set of an initial block group calculated by the initial block group calculation unit 101 and an additional block described later is denoted as P, and identification information of each block is denoted as p.

  Subsequently, the dual problem calculation unit 102 solves the dual problem for the problem in which the main problem that minimizes the length of the entire base material is linearly relaxed when the initial block group is assigned to the base material (step S203). The main problem is shown in the following equations 13 and 14.

Here, Formula 13 multiplies the usage count x _p of length h _p and block p of the block p, the value (initially initial blocks) each block to be assigned to the base material by summing all the This is an expression for minimizing the value (the length of the entire base material). Equation 14 multiplies the number of uses x _p of the block p by the number B _i ^{p of the} products i included in the block p, and adds the value to each block (initially a group of initial blocks) assigned to the base material. This is an expression for imposing a constraint that the combined value (number of products i allocated) is equal to or greater than the required number d _{i of} products i. The number of uses (integer solution) of each block that minimizes the length of the entire base material is calculated by Expression 13 and Expression 14.

  In the present embodiment, the problems shown in the following expressions 1 and 2 are solved by linearly relaxing the main problems shown in the expressions 13 and 14. Equation 1 corresponds to Equation 13, and Equation 2 corresponds to Equation 14.

Note that the use count x _p of the block p is a real number of 0 or more. More specifically, the dual problem operation unit 102 stores the necessary number information d _i of the product i temporarily stored in the RAM 302 and the number B _i ^p of the product i in the corresponding block p calculated in step S202. Are substituted into Equations 1 and 2, and further, the calculation of Equations 1 and 2 is performed while changing the number of uses x _p of the block p which is a variable. The dual problem for the main problem is as shown in Equation 3 and Equation 4.

Here Equation 3 multiplies the required number d _i Product i on dual variable y _i, the result is an equation for calculating a value obtained by adding for each product. Formula 4 multiplies the dual variable y _{i by} the number B _i ^{p of the} products i included in the block p, and the constraint that the sum of all the values for each product is less than the length h _{P of the} block p. It is a formula for imposing. In Expressions 3 and 4, the dual variable y _i is a value of 0 or more. More specifically, the dual problem operation unit 102 stores the necessary number information d _i of the product i temporarily stored in the RAM 302 and the number B _i ^p of the product i in the corresponding block p calculated in step S202. loading the CPU 301, they equation 3, by substituting for formula 4, while further changing the value of the dual variable y _p equation 3, the calculation of equation 4.

  Subsequently, the contracted cost calculation unit 103 calculates a minimum value of the contracted cost for additional block candidates other than the initial block group (step S204). The following equation 5 is an equation for obtaining the minimum value of the reduced cost, and equations 6 to 9 are constraint equations for obtaining the reduced cost. When calculating the minimum value of the reduced cost, the reduced cost calculation unit 103 calculates a candidate for an additional block that is a calculation target of the reduced cost each time. That is, the longest product in the length direction of the base material is set as one, and a block in which other products are arranged within a range not exceeding the length is calculated as an additional block candidate. It is assumed that only the same type of product is arranged in the length direction, and combinations of products having a remainder of 20 or more which is the minimum width of the product in the width direction of the base material are excluded from candidates for additional blocks. . In the example of the product shown in FIG. 4, 502, 503, 504, 506, 507, 509, and 510 in FIG. 5 can be calculated as additional block candidates, but in this embodiment, these blocks are used as additional block candidates. Rather than calculating all, the candidate for additional blocks is calculated one by one until the negative value is calculated as the minimum value of the contracted cost, and when the negative value is calculated as the minimum value of the contracted cost The remaining additional block candidates are not calculated.

  The calculation method of the additional block candidate will be specifically described. The reduced cost calculation unit 103 reads the base material width information and the product width information temporarily stored in the RAM 302 into the CPU 301, and the product is long in the length direction of the base material. We will target sequentially. When calculating the block 502 as a candidate for an additional block, the reduced cost calculation unit 103 first arranges the product 402 and then places the product 403 long in the length direction of the base material in the width direction of the base material. To do. In this state, the reduced cost calculation unit 103 determines that no more products can be arranged due to the limitation of the base material width, and calculates the block 502 as an additional block candidate. When calculating the block 503 as a candidate for an additional block, the reduced cost calculation unit 103 first arranges the product 402 and sets the product 404 that is long in the base material width direction next to the product 403 in the base material width direction. To place. In this state, since there are still 20 in the width direction of the base material, the product 405 can be arranged in the width direction. Further, since three products 405 can be arranged in the length direction, the reduced cost calculation unit 103 arranges one product 405 in the width direction of the base material and three products in the length direction. In this state, the reduced cost calculation unit 103 determines that no more products can be placed due to the limitation of the base material width, and calculates the block 503 as an additional block candidate. When 504, 506, 507, 509, and 510 in FIG. 5 are candidates for additional blocks, blocks are calculated by the same method.

  5 is a block in which one product 402 is arranged in the width direction of the base material and one product 403 is arranged in the width direction of the base material. In FIG. 5, reference numeral 503 denotes one product 402 in the width direction of the base material, one product 404 in the width direction of the base material, one product 405 in the width direction of the base material, and three in the length direction of the base material. It is a block arranged in two. 504 in FIG. 5 is a block in which one product 402 is arranged in the width direction of the base material, two products 405 are arranged in the width direction of the base material, and three are arranged in the length direction of the base material. 506 in FIG. 5 is one product 403 in the width direction of the base material, one product 404 in the width direction of the base material, one product 405 in the width direction of the base material, and 3 in the length direction of the base material. It is a block arranged in two. 507 in FIG. 5 is a block in which one product 403 is arranged in the width direction of the base material, two products 405 are arranged in the width direction of the base material, and three are arranged in the length direction of the base material. 509 in FIG. 5 is a product in which one product 404 is arranged in the width direction of the base material, three products 405 are arranged in the width direction of the base material, and two are arranged in the length direction. 510 in FIG. 5 is a block in which two products 404 are arranged in the width direction of the base material, two products 405 are arranged in the width direction of the base material, and two are arranged in the length direction.

bξ is the number in the length direction of the longest product in the length direction of the base material among the products included in the block p, and hξ is the length of the longest product in the length direction of the base material among the products included in the block p. It is. a _i is the number of products i in the width direction of the base material in the block p, and b _i is the number of products i in the length direction of the base material in the block p. The reduced cost calculation unit 103 calculates a value for which the reduced cost given by Expression 5 is the smallest for the candidate for the additional block. More specifically, the reduced cost calculation unit 103 stores the size information of the product i, the number information b _i in the length direction of the product i in the candidate for the additional block, the width of the product i, which are temporarily stored in the RAM 302. direction of number information a _i, a dual variable y _p calculated in the calculation step S203 is read in CPU 301, performs computation them by substituting for formula 5.

Expression 6 is an expression that imposes a restriction that the width of the block p is within the width W of the base material and that no more than a certain ratio is left in the width direction of the base material. The reduced cost calculation unit 103 temporarily stores the base material width information W, the width information w _i of the product i, the number information a _{i in} the width direction of the product i in the candidate for the additional block, the coefficient α ( For example, α = 0.9) is read into the CPU 301 and is substituted into Equation 6 for calculation.

Expression 7 is an expression that imposes a constraint that the total number a _i in the width direction of the product i in the block p is equal to or less than the upper limit value S of the slit. The reduced cost calculation unit 103 reads the number information a _{i in} the width direction of the product i in the additional block candidate and the upper limit value information S of the number of slits, which are temporarily stored in the RAM 302, into the CPU 301. Substitute and calculate.

Equation 8, a value obtained by multiplying the length of the number b _i and product i in the product i in the length direction of the base material in the block p is the number of longitudinal direction of the base material of the longest product ξ in the block p Bikushi And a length hξ of the product ξ, which is equal to or less than a value obtained by subtracting the length h _i of the product i from the value. The reduced cost calculation unit 103 reads the size information of the product i and the number information b _i in the length direction of the product i in the candidate for the additional block, which are temporarily stored in the RAM 302, into the CPU 301. Substitute and calculate.

Equation 9 is an equation to impose number in the width direction of the product i a _i, the number b _i in the longitudinal direction of the product i are both an integer of 0 or more as a constraint.

  The reduced cost calculation unit 103 calculates the minimum value of the reduced cost, which is a solution of Expression 5 that satisfies all of the constraints shown in Expression 6 to Expression 9, for the additional block candidates. If the minimum value of the reduced cost is a negative value, the candidate for the additional block is determined as a block (additional block) to be added to the initial block group. Here, a solution having a negative value means that the solution violates the constraint equation of Equation 4. Therefore, by adding an additional block corresponding to a solution having a negative value to the initial block group, the constraint equation of Equation 4 becomes an equation that imposes more severe constraints, and as a result, the value of the evaluation function of Equation 3 becomes smaller. Means that. By the way, as described above, since the coincidence between the value of the evaluation function of Equation 1 and the value of the evaluation function of Equation 3 is a necessary and sufficient condition for the optimal solution, an additional block corresponding to a solution having a negative value is set as an initial block. Adding to the group means that the value obtained by Equation 1 becomes smaller and the length of the entire base material becomes shorter.

  Subsequently, the dual problem calculation unit 102 determines whether or not an additional block has been determined by the reduced cost calculation unit 103 (step S205). When the additional block is determined, the dual problem calculation unit 102 determines that the value obtained by the evaluation function of Equation 1 and the value obtained by the evaluation function of Equation 3 match when the additional block is added to the initial block group. Is calculated as an optimal solution (step S203).

  Subsequently, the contracted cost calculation unit 103 calculates a new candidate for additional blocks, and the minimum value of the contracted cost that is a solution of Expression 5 that satisfies the constraints shown in Expressions 6 to 9 for the additional block candidates. Is calculated (step S204). Then, when the minimum value of the negative constrained cost is calculated for the additional block candidate, the constrained cost calculation unit 103 determines the additional block candidate as a new additional block for the initial block group. To do. If a new additional block is determined, the newly determined additional block is added to the block corresponding to the current optimum solution (here, the initial block group + additional block), and the processing from step S206 is performed. Will be repeated.

  On the other hand, when it is determined in step S205 that the additional block has not been determined, the set covering problem calculation unit 104 obtains the optimum number of times to use the initial block group and each additional block, and determines the optimal solution for the product allocation method for the base material. Calculate (step S207).

FIG. 6 shows the length h _p of each block p in a state where no additional block has been added to the initial block group, the number B _i ^p of products i in each block p, the required number d _i of each product _i , solution for variable x _p formula 1 is a diagram showing a solution for dual variable y _i of equation 3. In FIG. 6, the length h _p of each block p, the number B _i ^p of products i in each block p, the required number d _i of each product i, the solution of the variable x _{p in} Equation 1 and the dual variable in Equation 3 The solution of y _i is expressed as a matrix.

In FIG. 6, when only the initial block group is assigned to the base material, the length of the block 501 is 50, the length of the block 502 is 40, the length of the block 503 is 30, and the length of the block 504 is 15. It is shown that there is. FIG. 6 also shows that the number of products 402 in block 501 is 2, the number of products 403 is 0, the number of products 404 is 0, and the number of products 405 is 0. In the blocks 502, 503, and 504, the numbers of products 402, products 403, products 404, and products 405 are also shown. FIG. 6 also shows that the required number of products 402 is 10, the required number of products 403 is 15, the required number of products 404 is 25, and the required number of products 405 is 40. . Also, in FIG. 6, when only the initial block group is assigned to the base material, the solution of the variable x _{p in} Equation 1 is 5 for block 1, 15/2 for block 2, 25/3 for block 3, and block 4 Is shown to be 8. FIG. 6 also shows that the solution of dual variable y _i is 25 for product 1, 45/2 for product 2, 10 for product 3, and 3 for product 4 when only the initial block group is assigned to the base material. It is shown. FIG. 6 also shows that the value of the evaluation function of Equation 1 and the value of the evaluation function of Equation 3 are both calculated as 957.5.

FIG. 7 shows the length of the blocks 502, 503, 504, 506, 507, 509, 510, the number B _i ^p of the products i in each block, and the state in which no additional blocks are added to the initial block group. It is a figure which shows the calculation result of the reduced cost of step S204 when blocks 502, 503, 504, 506, 507, 509, 510 are calculated as candidates for additional blocks.

  In FIG. 7, the length of the block 502 is 50, the length of the block 503 is 50, the length of the block 504 is 50, the length of the block 506 is 40, the length of the block 507 is 40, and the length of the block 509 is 30, the length of block 510 is shown to be 30. FIG. 7 also shows that the number of products 402 in the block 502 is 1, the number of products 403 is 1, the number of products 404 is 0, and the number of products 405 is 0. Similarly, the numbers of products 402, 403, 404, and 405 are also shown for blocks 503, 504, 506, 507, 509, and 510. In FIG. 7, the value of the constrained cost obtained for the block 502 is 5/2, the value of the constrained cost obtained for the block 503 is 6, the value of the constrained cost obtained for the block 504 is 7, The reduced cost value determined for block 506 is 7/2, the reduced cost value determined for block 507 is 9/2, the reduced cost value determined for block 509 is 2, and the reduced cost value is determined for block 510. It is shown that the value of the saved cost is -2. Therefore, when the block 501 is calculated as an additional block candidate, the block 501 is determined as an additional block for the initial block group.

FIG. 8 shows the length h _p of each block p with the additional block 510 added to the initial block group, the number B _i ^p of the products i in each block p, the required number d _i of each product _i , the formula FIG. 4 is a diagram illustrating a solution of a variable x _p of 1 and a solution of a dual variable y _i of Equation 3. In FIG. 8, the length h _p of each block p, the number B _i ^p of products i in each block p, the required number d _i of each product i, the solution of the variable x _{p in} Equation 1, the dual variable in Equation 3 The solution of y _i is expressed as a matrix.

In FIG. 8, when the additional block 510 is added to the initial block group, the length of the block 501 is 50, the length of the block 505 is 40, the length of the block 508 is 30, the length of the block 511 is 15, The length of block 510 is shown to be 30. FIG. 8 shows that the number of products 402 in block 501 is 2, the number of products 403 is 0, the number of products 404 is 0, and the number of products 405 is 0. For blocks 505, 508, 511, and 510, the numbers of products 402, products 403, products 404, and products 405 are also shown. FIG. 8 shows that the required number of products 402 is 10, the required number of products 403 is 15, the required number of products 404 is 25, and the required number of products 405 is 40. . Further, FIG. 8 shows that when the initial block group and the additional block are assigned to the base material, the solution of the variable x _{p in} Equation 1 is 5 for block 1, 15/2 for block 2, and 5/3 for block 3. , 0 for block 4 and 10 for block 5. FIG. 8 also shows that when the initial block group and the additional block are assigned to the base material, the solution of the dual variable y _i is 25 for product 1, 45/2 for product 2, 10 for product 3, and 10 for product 4. It is shown to be 5/2. Further, FIG. 8 shows that the value of the evaluation function of Expression 1 and the value of the evaluation function of Expression 3 are both calculated as 937.5. Thus, compared with the example shown in FIG. 6, the length of the whole base material is shortened from 957.5 to 937.5.

FIG. 9 shows the length of the blocks 502, 503, 504, 506, 507, and 509, the number B _i ^p of the products i in each block, and the additional block 510 added to the initial block group. It is a figure which shows the calculation result of the reduced cost of step S204 when 503, 504, 506, 507, 509 is calculated as a candidate for an additional block.

  In FIG. 9, the length of the block 502 is 50, the length of the block 503 is 50, the length of the block 504 is 50, the length of the block 506 is 40, the length of the block 507 is 40, and the length of the block 509 is 30. FIG. 9 shows that the number of products 402 in the block 502 is 1, the number of products 403 is 1, the number of products 404 is 0, and the number of products 405 is 0. Similarly, the numbers of products 402, 403, 404, and 405 are also shown in blocks 503, 504, 506, 507, and 509. In FIG. 9, the value of the constrained cost obtained for the block 502 is 5/2, the value of the constrained cost obtained for the block 503 is 15/2, and the value of the constrained cost obtained for the block 504 is 10. Indicates that the value of the constrained cost determined for block 506 is 5, the value of the constrained cost determined for block 507 is 15/2, and the value of the constrained cost determined for block 509 is 5. Has been. As described above, since the contracted costs obtained for the additional block candidates are all positive values, there is no block determined as the additional block. Therefore, in this example, the block 501 is used five times, the block 505 is used eight times, the block 508 is used twice, the block 511 is used zero times, and the block 510 is used ten times. Is calculated as the optimal solution.

  In the embodiment described above, when the entire length of the base material can be shortened, an additional block is added to the initial block group so as to calculate the optimum solution of the product allocation method for the base material. It is composed. Therefore, it is not necessary to calculate the optimum solution for all the blocks that are candidates to be assigned to the base material, and it is possible to obtain the optimum solution with a smaller amount of calculation.

  In the above-described embodiment, the reduced cost is calculated using Equation 5, but when using Equation 5, the smaller the longer the block is used, the smaller the reduced cost tends to be calculated. It is in. Therefore, a more appropriate solution can be obtained by limiting the length of the block to be used to a certain length or less.

  As another embodiment, the reduced cost may be obtained using the following equation 10 instead of equation 5. When the reduced cost is obtained using Equation 10, a solution independent of the block length can be obtained. In addition, when Expression 10 is used, it is possible to obtain a solution that emphasizes the filling rate of the product in the block. Even when the reduced cost is obtained by Equation 10, a block corresponding to a negative reduced cost is determined as an additional block.

The reason why it is possible to obtain a solution that emphasizes the filling rate of the product in the block when using Equation 10 is that the solution of Equation 10 is obtained by maximizing the value of Equation 11 below. Here, y _i is a constant, a _i and b _i are the number of products i included in the block, and bξhξ is the length of the block. Therefore, maximizing Equation 11 means that the block length is as short as possible and many products are placed. In other words, the product filling rate in the block is increased.

As yet another embodiment, the term shown in Expression 11 in Expression 10 may be replaced with the following Expression 12. This is an equation when b _i is relaxed to a real variable and it is assumed that all b _i h _i have the same value for all _i satisfying a _i > 0. Therefore, in the case of this embodiment, it is necessary to maximize the following expression 12 when calculating the contracted cost. In the present embodiment, the process for obtaining the reduced cost is further simplified, and the processing speed can be increased.

  FIG. 10 is a diagram showing the results of the evaluation experiment. Here, as an example, the base material width is 200, the number of types of products is 30, the upper limit value of the number of slits is 5, and there is no upper limit value of the block length and the upper limit value of 10,000 is illustrated. ing.

  FIG. 10A shows the values (evaluation values) of Equation 1 (Equation 3) when the upper limit value of the block length is set and when the upper limit value of the block length is not set when Equation 5 is used as an equation for calculating the reduced cost. ), The product filling rate in each block, the calculation time of the optimal solution, and the number of additional blocks. As shown in FIG. 10A, when the upper limit value is set for the block length as compared to the case where the upper limit value is not set for the block length, the value (evaluation value) of Equation 1 (Equation 3) is It has become smaller (the length of the entire base material has been shortened), a good solution has been obtained, and the calculation time has been shortened.

  FIG. 10B shows the case where the upper limit value of the block length is set and the case where the upper limit value of the block length is not set when the formula obtained by applying the formula 12 to the corresponding term of the formula 10 is used as the formula for calculating the reduced cost. The value (evaluation value) of Equation 1 (Equation 3), the product filling rate in each block, the calculation time of the optimal solution, and the number of additional blocks are shown. As shown in FIG. 10 (b), compared to the example of FIG. 10 (a), when formula 12 is applied when calculating the reduced cost, it is set when the upper limit value of the block length is set. The calculation time is greatly shortened both in the case of not performing the calculation.

  The legend “before change” in the graphs 1001 and 1002 in FIG. 10 is a case where Expression 5 is used as an expression for calculating the reduced cost (FIG. 10A), and the legend “after change” indicates the reduced cost. This is a case where Expression 12 is applied to the corresponding term of Expression 10 as an expression for obtaining (FIG. 10B). The graph of 1001 in FIG. 10 shows the values (evaluation values) of Equation 1 (Equation 3) when the upper limit value is not set for the block length and when “before change” and “after change” are set. Represents. The graph of FIG. 1002 represents the calculation time of the optimal solution when no upper limit value is set for the block length and when “before change” and “after change” are set.

  In the above-described embodiment, the case where the product is efficiently cut off from the coil as the base material is taken as an example. However, the present invention is necessary for the film, paper, plate and the like as the base material. The same applies to the case of assigning products.

  Further, in the processing of the present embodiment shown in FIG. 3, when an additional block candidate having a negative value for the contracted cost is found, the processing is looped so that the additional block is always added. However, the present invention is not limited to this, and the loop may be terminated at an arbitrary timing, and the solution at that time may be obtained as the optimum solution. For example, it is conceivable to terminate the processing after a predetermined number of loops and use the solution at that time as the optimum solution.

It is a block diagram which shows the functional structure of the optimal solution calculation apparatus which concerns on embodiment of this invention. It is a block diagram which shows the hardware constitutions of the optimal solution calculation apparatus which concerns on embodiment of this invention. It is a flowchart which shows operation | movement of the optimal solution calculation apparatus which concerns on embodiment of this invention. It is a figure shown about each product allocated with respect to a base material and a base material. It is a figure which shows the block allocated with respect to a base material. The length h _p of each block p in a state where no additional block has been added to the initial block group, the number B _i ^p of products i in each block p, the required number d _i of each product i, and the variables of Equation 1 solution of x _p, illustrates a solution for dual variable y _i of equation 3. Step S204 in the case where each block is calculated as a candidate for an additional block in the state where the length of each block, the number B _i ^p of the products i in each block, and the additional block has not yet been added to the initial block group It is a figure which shows the calculation result of a contracted expense. The length h _p of the blocks p in the state in which additional blocks 510 to the initial block group is added, the number B _i ^p products i of the in each block p, the required number d _i of each product i, of the formula 1 variable x It is a figure which shows the solution of _{p and} the solution of the dual variable _yi of Formula 3. The length of each block, the number B _i ^p of products i in each block, and the constrain of step S204 when each block is calculated as a candidate for the additional block in the state where the additional block is added to the initial block group It is a figure which shows the calculation result of expense. It is a figure which shows the result of evaluation experiment.

Explanation of symbols

101: Initial block group calculation unit 102: Dual problem calculation unit 103: Reduced cost calculation unit 104: Set coverage problem calculation unit

Claims (7)

An initial block group determining means for determining an initial block group that is a set of products assigned to the base material;
Assigning products to the base material by calculating the number of times each block included in the initial block group is calculated by calculating a predetermined evaluation function that represents the length of the whole base material when the initial block group is used An optimal solution calculating means for calculating an optimal solution of the method;
An additional block determining means for determining an additional block that reduces the value of the calculation result of the evaluation function when a block is added to the initial block group by performing a predetermined calculation on each block other than the initial block group And
Each of the blocks other than the initial block group and the additional block until the additional block determining means eliminates the additional block in which the value of the calculation result of the evaluation function decreases when a block is added to the initial block group Repeatedly executing the predetermined operation to determine the additional block, and the optimum solution calculating means is included in the initial block group each time the additional block is determined by the additional block determining means. An information processing apparatus characterized in that an optimum solution of a method for assigning a product to the base material is calculated by obtaining the number of times the block and the additional block are used. Input means for inputting base material information including width information indicating the width of the base material and product information including size information indicating the size of a product allocated to the base material and necessary number information indicating the number of necessary products When,
The block calculating means according to claim 1, further comprising: a block calculating unit that calculates each block included in the initial block group and a block that is a candidate for the additional block based on the base material information and the product information. The information processing apparatus described.   The optimal solution calculation means calculates an optimal solution of a product allocation method for the base material by solving a main problem including the predetermined evaluation function and a dual problem for the main problem. The information processing apparatus according to 1 or 2.   The additional block determining means calculates a reduced cost of the main problem for each block that is a candidate for the additional block by using the solution of the dual problem, and the value of the calculation result of the evaluation function is reduced by the calculation result. The information processing apparatus according to claim 3, wherein the additional block is determined.   5. The apparatus according to claim 1, further comprising an upper limit setting unit configured to set an upper limit of a length of each block included in the initial block group and each block that is a candidate for the additional block. The information processing apparatus described in 1. An initial block group determination step for determining an initial block group that is a set of products assigned to the base material;
Assigning products to the base material by calculating the number of times each block included in the initial block group is calculated by calculating a predetermined evaluation function that represents the length of the whole base material when the initial block group is used An optimal solution calculating step for calculating an optimal solution of the method;
An additional block determination step for determining an additional block in which the value of the calculation result of the evaluation function is small when a block is added to the initial block group by performing a predetermined calculation on each block other than the initial block group Including
In the additional block determining step, each block other than the initial block group and the additional block until there is no additional block in which the value of the calculation result of the evaluation function becomes small when a block is added to the initial block group. The predetermined operation is repeatedly executed for determining the additional block, and the optimum solution calculating step is performed each time the additional block is determined by the additional block determining step. A method for controlling an information processing apparatus, comprising: calculating an optimum solution of a method of assigning a product to the base material by obtaining the number of times the block and the additional block are used. An initial block group determination step for determining an initial block group that is a set of products assigned to the base material;
Assigning products to the base material by calculating the number of times each block included in the initial block group is calculated by calculating a predetermined evaluation function that represents the length of the whole base material when the initial block group is used An optimal solution calculating step for calculating an optimal solution of the method;
An additional block determination step for determining an additional block in which the value of the calculation result of the evaluation function is small when a block is added to the initial block group by performing a predetermined calculation on each block other than the initial block group And let the computer run
In the additional block determining step, each block other than the initial block group and the additional block until there is no additional block in which the value of the calculation result of the evaluation function becomes small when a block is added to the initial block group. The predetermined operation is repeatedly executed for determining the additional block, and the optimum solution calculating step is performed each time the additional block is determined by the additional block determining step. A program characterized in that an optimum solution of a method for assigning a product to the base material is calculated by obtaining the number of times the block and the additional block are used.

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