JP2007206980A - Method for making lot plan, apparatus for making lot plan, and computer program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To make a lot plan for strictly optimizing performance function, set by a plurality of orders. <P>SOLUTION: First, variables for making the lot plan, upper and lower bounds of the variables, a constraint among the variables, and the performance function are set up. Next, real values of the variables are calculated to optimize the performance function, and the variables and the performance value are stored as an optimum solution, when the performance value is better than the performance value already obtained and the values of the variables are integers. When the variables are not integers, the lot plan for optimizing the performance value by repeating the process of fixing the values of variables to the integers are proposed. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a method for automatically collecting a plurality of raw materials into a plurality of lots based on the specifications of a plurality of orders (orders) given in the manufacturing industry, and preparing a production plan. The present invention relates to a technique that can be used when planning a casting plan (cast plan) of a continuous casting machine in the industry or when planning a rolling lot plan of a rolling mill.

  When planning production plans for factories in the manufacturing industry, when ordering multiple orders, manufacture multiple orders in an appropriate scale and an appropriate number of multiple lots from the standpoints of preventing quality degradation and setup change costs. Often to do.

  For example, in a steelmaking plant, as shown in the cross-sectional view of the continuous casting machine in FIG. 4, the refined molten steel 10 is conveyed in a ladle 11 and poured into a ladle 12. The molten steel in the ladle 12 is continuously poured from above by a dipping nozzle 19 into a mold 14 controlled to a predetermined size via a tundish 13 which is an intermediate container, and the steel whose surface has solidified from below the mold. Is withdrawn continuously. Then, the steel material moves while being supported by the support roll 15, and the inside is gradually cooled and solidified by the water ejected from the spray nozzle 16, and is cut into a predetermined length by a cutting machine 17 to be slab, billet, Alternatively, a steel piece called bloom is continuously cast. In the present application, these steel pieces are collectively referred to as a slab 18.

  The casting unit that is one cup of the molten steel pan 11 is called a charge, but with a continuous casting machine, multiple charges can be continuously cast continuously (continuous continuous casting is abbreviated as continuous continuous casting, abbreviated. Called continuous casting). The mold is usually configured to surround the periphery with four mold walls. When casting slabs 18 having different widths, the width of the mold 14 (distance between mold walls: casting width) can be changed during successive casting. This continuous casting unit is called a cast. In many cases, one cast is usually composed of 2 to 15 charges due to a refractory melt or quality problem.

  In this way, at the break between cast and cast, after replacing the mold 14, the tundish 13, and the immersion nozzle 19, a jig called a dummy bar (not shown) is inserted into the mold, and the dummy bar is pulled out from the bottom of the mold, It is necessary to start pouring the molten steel into the mold. For this reason, it takes a considerable amount of time to change the setup, and the quality of the casting at the beginning and end of the cast decreases, such as a decrease in manufacturing stability and the inclusion of impurities. It is desirable to increase the number of cast charges) as much as possible. However, continuous casting of charges with different casting widths and molten steel components (also called steel types) reduces the quality of the cuts in the charge, lowers the yield, and cannot continuously cast when the casting widths and molten steel components differ greatly. There are problems such as. Therefore, it is necessary to plan an appropriate cast in consideration of the casting width of each charge and the molten steel composition. In other words, it is necessary to appropriately compile orders called charges into consideration in the order of casting into lots called casts, and to create a production plan (cast plan) that improves both production capacity and yield.

  Conventionally, as a method for drafting a cast plan, it is common that an expert performs almost manually. However, in order to make an appropriate cast plan, even a skilled person who has long experience generally takes several hours to make a cast plan for one week at the beginning of the week, for example. Therefore, in the second half of the week, there is a problem that the deviation from the actual operation is widened, and it is not possible to review the cast plan while knowing that it is not an appropriate cast plan. There is also a problem in that there are variations in technology among skilled workers, and it is difficult to say that the cast plans of skilled workers are necessarily appropriate.

  In order to solve such a problem, in Patent Document 1, after making an initial cast plan manually or by an expert system, in each cast, a group of charges of the same molten steel component and the same size are grouped into one group. There is disclosed a technique for making a cast plan in a procedure in which exchange is possible and the means for exchanging different cast groups is repeated until the value of the set evaluation function is not improved.

  Moreover, in patent document 2, after consolidating a plurality of charges into a plurality of groups having the same molten steel component and refining method, the groups are ordered (sorted) by the molten steel component and the refining method, so that the groups can be cast one after another. A method for creating a cast plan by repeatedly dividing and integrating is disclosed.

  Further, in Patent Document 3, after making an initial cast plan by an appropriate method, two arbitrary charges are exchanged using the simulated annealing method so that the value of the set evaluation function becomes small, A technique for creating a cast plan that minimizes the value of the evaluation function is disclosed.

Japanese Patent Laid-Open No. 7-88605 JP 11-314146 A Japanese Patent Laid-Open No. 2004-348436

  However, in the method disclosed in Patent Document 2, only a limited casting plan that continuously casts a charge in which the molten steel component and the refining method are close can be obtained. Even if the molten steel component and the refining method are close, the casting width is different. For example, there is a problem of being divided into two casts. In addition, since the methods disclosed in Patent Document 1 and Patent Document 3 are both search methods, there is no guarantee of optimality, and only a minimal solution. In addition, since the neighborhood solution is generated only by exchanging two groups or charges, there is a problem that only a cast plan with a slightly improved initial cast plan can be obtained. In other words, the cast plan largely depends on the initial cast plan, and it is difficult to make a good cast plan.

  The present invention has been devised in order to solve the problem, and continuously processes a plurality of raw materials while changing the processing conditions according to the manufacturing conditions based on the specifications and quantities of a plurality of orders (orders). An object of the present invention is to obtain an optimal manufacturing plan by considering manufacturing conditions larger and more flexibly than in the prior art when planning a manufacturing plan in a manufacturing process in which lots or a plurality of lots are processed together.

  In the lot planning method of the present invention, one lot or a plurality of raw materials are continuously processed in a manufacturing plant while changing the processing conditions according to the manufacturing conditions based on the specifications of a plurality of orders (orders) and the status of the manufacturing process. In a method for drafting a manufacturing plan to be processed in batches, an order input step of inputting a plurality of orders from an external input device and / or an external storage device, and a plurality of orders among the plurality of orders according to the number of the input multiple orders A variable setting step for setting a variable x representing the continuous production relationship for two orders, a variable y representing the production order within the lot of each order, and a variable z representing the upper limit value of the number of orders to which each order belongs. And upper limit values of the variables x, y, and z according to manufacturing conditions predetermined for each input order. An upper / lower limit setting step for setting both upper and lower limit constraints of the lower limit value, a constraint equation represented by the variable x with respect to an order manufactured before each order, and an order manufactured after each order The constraint equation represented by the variable x, the constraint equation represented by the variables x and y regarding the production order in the lot of the two orders, and the variables x and z regarding the upper limit value of the order number of the lot to which each order belongs A constraint equation setting step for setting a constraint equation represented by the variables y and z with respect to the production order of each order and the upper limit value of the number of orders of the lot to which the order belongs, An evaluation function setting step for setting an evaluation function represented by the variable x for judging pass / fail, the upper and lower limit constraints, and each constraint equation set in the constraint equation setting step; Optimal for calculating the values of the variables x, y, and z that optimize the value of the evaluation function set in the evaluation function setting step under the condition that both are satisfied and the value of the variable x is an integer The method includes a solution calculation step and a lot plan output step of outputting a lot plan to an external output device or an external storage device based on the value of the variable x calculated in the optimal solution calculation step.

  In the lot planning method of the present invention, the optimal solution calculating step uses a branch and bound method to relax the condition that the value of the variable x is an integer, Satisfying and calculating the values of the variables x and y and z that optimize the value of the evaluation function, and fixing the values of some or all of the variables x having non-integer values to integer values, Repeated multiple times.

  The lot planning apparatus according to the present invention continuously processes one or more lots of raw materials in a manufacturing plant while changing the processing conditions according to the manufacturing conditions based on the specifications of a plurality of orders (orders) and the manufacturing process. In an apparatus for drafting a manufacturing plan to be processed collectively, an order input means for inputting a plurality of orders from an external input device and / or an external storage device, and a continuation of two orders among the plurality of orders with respect to the plurality of orders A variable setting means for creating a variable x representing a manufacturing relationship, a variable y representing a production order within a lot of each order, and a variable z representing an upper limit value of the number of lots to which the order belongs, and the plurality of orders, The upper and lower limits of the variables x, y, and z or any one of the upper and lower limits, manufactured before each order The constraint equation represented by the variable x for the order to be produced, the constraint equation represented by the variable x for the order produced next to each order, and the variables x and y for the production order in the lot of the two orders Constraint formula expressed, constraint formula expressed by the variables x and z regarding the upper limit value of the order number of lots to which each order belongs, and manufacturing order of each order and upper limit value of the order number of lots to which the order belongs Restriction condition setting means for setting a constraint expression represented by the variables y and z, evaluation function setting means for setting an evaluation function represented by the variable x for determining the quality of a lot plan, and the constraint condition setting means The variables x, y, and x satisfying each constraint condition set in (1) and optimizing the value of the evaluation function set by the evaluation function setting means under the condition that the value of the variable x is an integer. And an optimum solution calculating means for calculating the value of z and a lot plan output means for outputting a lot plan to an external output device or an external storage device based on the value of the variable x calculated by the optimum solution calculating means. It is characterized by having.

  The computer program according to the present invention collects raw materials into one lot or a plurality of lots to be continuously processed while changing the processing conditions according to the manufacturing conditions based on the specifications of a plurality of orders (orders) and the status of the manufacturing process in the manufacturing plant. In order to create a manufacturing plan to be processed, an order input process for inputting a plurality of orders from an external input device and / or an external storage device, and two orders among the plurality of orders according to the number of the input orders A variable setting process for creating a variable x representing the continuous manufacturing relationship of the variable, a variable y representing the production order in the lot of each order, and a variable z representing the upper limit of the number of orders of the lot to which the order belongs, and the input Depending on the manufacturing conditions predetermined for each order, both the upper and lower limits of the variables x, y and z Or any one upper / lower limit constraint, a constraint equation represented by the variable x with respect to an order manufactured before each order, a constraint equation represented by the variable x with respect to an order manufactured next to each order, A constraint expression represented by the variables x and y regarding the production order within the lot of orders, a constraint expression represented by the variables x and z regarding the upper limit value of the number of orders to which each order belongs, Constraint condition setting processing for setting a constraint expression represented by the variables y and z with respect to the manufacturing order and the upper limit value of the number of orders of the lot to which the order belongs, and the variable x for determining the quality of the lot plan. The evaluation function setting means that satisfies the respective constraint conditions set in the evaluation function setting process for setting the evaluation function and the constraint condition setting process, and the value of the variable x is an integer An optimal solution calculation process for calculating values of the variables x, y, and z that optimize the set evaluation function value, and a lot plan based on the value of the variable x calculated in the optimal solution calculation process And a lot plan output process for outputting the data to an external output device or an external storage device.

  The present invention is a manufacturing process in which a plurality of raw materials are processed collectively into one lot or a plurality of lots to be processed continuously, while changing the processing conditions according to the manufacturing conditions based on the specifications and quantities of a plurality of orders (orders). In order to obtain an optimal manufacturing plan in consideration of the manufacturing conditions larger and flexibly than in the past, this is a method of preparing a lot plan by optimizing the value of an evaluation function for determining the quality of the lot plan. As a result, unlike the conventional search method, a strict optimum solution can be calculated, so that quality and yield can be increased to the limit.

  Hereinafter, the best mode for carrying out the lot planning method of the present invention will be described with reference to the drawings.

  FIG. 1 is a flowchart showing a processing procedure when all calculations related to the lot planning method of the present invention are realized by a computer, and is executed by a program stored in a memory in the computer main body.

  First, information on the planned order 1 is read into the memory of the computer in order input step 2 from an external storage device such as a hard disk connected to the computer or an external input device such as a keyboard.

  For order 1 to be planned, at least as production conditions, for each order, a condition related to the upper limit of the number of orders of the lot to which the order belongs, a condition related to the possibility of production when manufacturing sequentially with other orders, The conditions relating to the manufacturing position (order) are described.

  The following Table 1 is a simple example of the planned order 1 and describes the raw material type, manufacturing method, and manufacturing conditions of ten orders (in this case, representing charge). For example, in the No. 1 order (charge), the molten steel component (steel type) is A as the raw material type, and the production method is specified to be manufactured (cast) with a narrow width. In addition, as the manufacturing conditions, the upper limit of the number of orders (charges) of the lot (cast) to which the No. 1 order (charge) belongs is 6 orders (charges), and it is manufactured continuously with orders (charges) with different steel types. (Casting) possible (manufacturing (casting) is always possible with orders with the same steel grade), and No.1 order (charge) must be manufactured within the sixth in the lot. Represents.

  Next, according to the order number (quantity) of the order 1 to be planned, the number of orders representing the continuous manufacturing relationship between the two orders as a variable required for creating a lot plan in the variable setting step 3 X Variable x having the number of orders (two-dimensional array variable x (i, j), x (i, j) = 1 when manufacturing No.j order next to No.i order , Otherwise defined as x (i, j) = 0) and a variable y (a one-dimensional array variable y (i) having the number of orders representing the production order within the lot of the order, No. i And y (i) = k when an order is manufactured at the kth of a lot), and a variable z (one-dimensional array variable z (i) representing the upper limit of the number of orders of the lot to which the order belongs, Set z (i) = h when the lot to which No. To create the storage area in the memory.

  Next, in the upper and lower limit setting step 4, based on the manufacturing conditions specified for each order in the information of the planning target order 1, the upper limit constraint and the lower limit constraint for each of the variables x, y, and z ( (Also called upper and lower limit constraints) are set and stored in the memory.

  Next, in the constraint formula setting step 5, the variable values and the lot plan are necessary for making the lot plan correspond one-to-one, and the constraint formula for the variables for creating an executable lot plan is prepared. Store (equalities or inequalities) in memory. Here, the constraint equation between the variables is set based on the information of the above-mentioned planning target order 1 and the common manufacturing constraint of the manufacturing process itself (for example, when all charges have the same casting position constraint) May be set based on the above-mentioned planned order 1).

  Next, in the evaluation function setting step 6, a predetermined function with the variable x as an argument is set as an evaluation function that is determined from the viewpoint of improving production capacity and preventing quality deterioration, and determining the quality of the lot plan. And store it in the memory.

  Next, in the optimal solution calculation step 7, the upper and lower limit constraints of the variable set in the upper and lower limit setting step 4, the constraint equation set in the constraint equation setting step 5, and the value of the variable x are integers (the variable y And z are real numbers), and the value of the variable that optimizes the value of the evaluation function set in the evaluation function setting step 6 (hereinafter referred to as evaluation value) is calculated.

  Finally, in the lot plan output step 8, the lot plan 9 corresponding to the value of the variable x calculated in the optimum solution calculation step 7 is output to an external display device such as a display or an external storage device such as a hard disk.

  The form for carrying out the present invention is not limited to the above. As shown in FIG. 5, the plan target order 1 stored in the external storage device is input by the order input means 30, and the plan target order 1 Variable setting means 31 for setting variables x, y, and z for creating a lot plan according to the number of orders and manufacturing conditions, and constraint condition setting means 32 for setting the constraint conditions for the variables x, y, and z, The evaluation function setting means 33 for setting the evaluation function represented by x is implemented, and the optimum solution calculation means 34 calculates the values of the variables x, y, and z that optimize the value of the evaluation function. The lot plan output means 35 may output the lot plan 9 indicated by the value of the variable x to the external storage device.

<First Embodiment>
Hereinafter, a manufacturing plan in a manufacturing process in which a plurality of raw materials are processed collectively into one lot or a plurality of lots to be processed continuously while changing the processing conditions according to the manufacturing conditions based on the specifications and quantities of a plurality of orders (orders). As an example of the planning method, a method for planning a casting plan (cast plan) of a continuous casting machine in the metal product manufacturing industry will be described. In the present embodiment, what corresponds to each of the plurality of raw materials is a steel type, and the molten steel in a casting unit for each molten steel pan, that is, the charge is cast on the slab of each custom-made item (order). In the description, “order” is described as “charge” and “lot” as “cast”.

  Table 1 shows the charge for planning corresponding to order 1 for planning (charge = casting unit for one full molten steel pan). Each row after the second row in Table 1 represents one charge, the first column from the left is the identification number (No.) of the charge, and the second column is a symbol (steel type) representing the steel type (molten steel component) of the charge. The third row is the casting width (width) of the charge, the fourth row is the upper limit (maximum continuous casting) of the number of consecutive castings of the cast including the charge (the number of casting charges), and the fifth row is the different charge. The steel type charge indicates whether or not continuous casting is possible (different steel type continuous casting), and the sixth column represents the upper limit on the casting order in the cast when casting the charge (casting position). For example, No.5 charge is steel grade B, cast with medium width, cast including No.5 charge must be limited to 6 charges, and different steel grades are possible, but by the third cast It means that it must be cast.

  In the case of such a small and simple cast plan example, the cast plan can be easily drafted manually, and Table 2 shows an example of the cast plan. Each row after the second row in Table 2 below represents one cast (the first row represents the casting number of the charge), the No. 1 cast casts No. 5 charge first, then No. It is planned to cast .6 charge, No.3 charge, No.4 charge, No.1 charge and finally No.2 charge. Here, No.5 and No.6 charges are cast in the first and second casts because the casting position of No.5 and No.6 charges is limited to 3, and the cast is third. This is because it must be cast by the time.

  The lot plan creation method of the present invention relates to a method for automatically creating a cast plan as shown in Table 2 under the respective production constraints for a plurality of steel grades as shown in Table 1 and a plurality of widths as target charges for planning. The processing flow is represented by a flowchart in which “order” in FIG. 1 is replaced with “charge” and “lot” is replaced with “cast” as described above.

(Order entry step)
First, in order input step 2, information on the plan target charge as shown in Table 1 is transferred to the computer via an external storage device such as a hard disk connected to the computer, an external input device such as a keyboard, or a network in the manufacturing plant. Read into memory.

(Variable setting step)
Next, in variable setting step 3, since it is a cast lot plan composed of 10 plan target charges based on the information on the plan target charge, a variable representing the continuous manufacturing relationship between two charges (orders) X is a 10 × 10 two-dimensional array variable, and a charge (order) cast (lot) is a variable that represents the production order in a cast (lot). A region of a one-dimensional array variable of size 10 is secured in the memory as a variable z representing the upper limit (maximum number of continuous castings) of the number of charges (orders) of lot.

  Here, x (i, j) which is the i-th row and j-th column component of the two-dimensional array variable x is a variable meaning a continuous casting relationship between two charges, and No. i charge is followed by No. i. jThis variable is 1 when casting a charge and 0 otherwise. Y (i) which is the i-th component of the one-dimensional array variable y is a variable representing the casting order of No.i charge. For example, if y (i) = 3, the No.i charge is within the cast. It means to cast third. Z (i) that is the i-th component of the one-dimensional array variable z is a variable that means the maximum number of continuous castings of the cast to which the No. i charge belongs. For example, if z (i) = 4, No. This means that the cast to which i-charge belongs can only cast up to 4 charges continuously. More specifically, z (i) is the minimum value among the maximum continuous castings of all charges cast by the cast to which the No. i charge belongs.

For example, if the cast plan in Table 2 is represented by the variable,
x (5,6) = 1, x (6,3) = 1, x (3,4) = 1, x (4,1) = 1, x (1,2) = 1
x (7,8) = 1, x (8,9) = 1, x (9,10) = 1
y (1) = 5, y (2) = 6, y (3) = 3, y (4) = 4, y (5) = 1, y (6) = 2, y (7) = 1, y (8) = 2, y (9) = 3, y (10) = 4
z (1) = 6, z (2) = 6, z (3) = 6, z (4) = 6, z (5) = 6, z (6) = 6, z (7) = 4, z (8) = 4, z (9) = 4, z (10) = 4
(The values of all other variables are 0.) The variable values and the cast plan have a one-to-one correspondence, and determining these variables is the creation of a cast plan.

(Upper / lower limit setting step)
Next, in the upper / lower limit setting step 4, the upper and lower limit constraints of each variable x (i, j), y (i), z (i) are stored in the memory as manufacturing constraints based on the information on the charge to be planned. Set / Remember. In the case of the present embodiment, equations (1) to (12) are obtained.
0 ≤ x (1-6, 1-6) ≤ 1 (1)
0 ≤ x (1-6, 7-10) ≤ 0 (2)
0 ≤ x (7-10, 1-6) ≤ 0 (3)
0 ≤ x (7-10, 7-10) ≤ 1 (4)
0 ≤ x (i, i) ≤ 0 ∀i (5)
1 ≤ y (1-4) ≤ 6 (6)
1 ≤ y (5-6) ≤ 3 (7)
1 ≤ y (7-8) ≤ 2 & (8)
1 ≤ y (9-10) ≤ 6 (9)
4 ≤ z (1-6) ≤ 6 & (10)
4 ≤ z (7-8) ≤ 4 (11)
4 ≤ z (9 to 10) ≤ 6 (12)
Here, since x (i, j) is 0 or 1 for the above constraint content, the upper and lower limit constraints of Equation (1) and Equation (4) are basically set. However, No. 7 to No. 10 charges of steel grade C cannot be cast continuously with different steel grades, and No. 1 to No. 6 charges of steel grade A or steel grade B cannot be cast continuously. And set the constraints of equation (3). In addition, since it is impossible to cast the same No. i charge after the No. i charge, the equation (5) is naturally set.

  Equations (6) to (9) are upper and lower limit constraints set for casting position constraints, and Equations (10) to (12) are upper and lower limit constraints set for maximum continuous casting constraints. ) To (9) are the casting positions in Table 1, and the upper limits in Equations (10) to (12) are the maximum continuous castings in Table 1. Regarding the lower limit, since the casting position of the charge cast at the beginning of casting is 1, all the lower limits of Equations (6) to (9) are 1, and the maximum continuous casting value in Table 1 is the minimum value. Is 4, and the value of the variable z (i) is 4 or more. Therefore, the lower limit values of the equations (10) to (12) are all 4.

(Constraint equation setting step)
Next, in the constraint formula setting step 5, the variable relating to the charge (order) manufactured before each charge (order), which is the relationship between the charge based on the information on the charge to be planned and the restrictions on the manufacturing process. a constraint expression (13) represented by x, a constraint expression (14) represented by the variable x with respect to a charge (order) manufactured next to each charge (order), and casting of two charges (order) Regarding the production order in (lot), the constraint equation (15) expressed by the variables x and y and the upper limit value of the number of charges (orders) of the cast (lot) to which each charge (order) belongs (maximum number of continuous castings) ) And the constraint equation (16) represented by the variables x and z, and the production order of each charge (order) and the charge (order) of the cast (lot) to which the charge (order) belongs The constraint equation (17) represented by the variables y and z is set / stored in the memory with respect to the upper limit value (maximum number of continuous castings).
Σj {x (j, i)} ≤ 1 ∀i (13)
Σj {x (i, j)} ≤ 1 ∀i (14)
y (j) ≥ y (i) + 1 − K (i, j) × {1-x (i, j)} ∀i, j (≠ i) (15)
z (j) ≤ z (i) + H (i, j) x {1-x (i, j) -x (j, i)} ∀i, j (≠ i) (16)
y (i) ≤ z (i) (17)

Here, Σj {x (j, i)} in Equation (13) and Equation (14) represents the sum of variables in parentheses {} for all subscripts j. Further, K (i, j) in equation (15) is an arbitrary constant that satisfies equation (18),
K (i, j) ≥ upper limit of y (i) − lower limit of y (j) + 1 (18)
In the case of this embodiment, since the lower limit value of y (j) is all 1, it may be given by equation (19) (the upper limit value of y (i) is indicated by the right side value of equations (6) to (9). )
K (i, j) = upper limit of y (i) (19)
Further, H (i, j) in the equation (16) is an arbitrary constant that satisfies the equation (20).
H (i, j) ≥ upper limit value of z (j) − lower limit value of z (i) (20)
In this embodiment, since the lower limit value of z (i) is all 4, it may be expressed as equation (21) (the upper limit value of z (j) is indicated by the right side value of equations (10) to (12). )
Upper limit value of H (i, j) ≥ z (j) − 4 (21)

  In the constraint equation of Equation (13), for example, if x (5,6) = 1, x (∀j ≠ 5,6) = 0, No.6 charge is not the top charge, and No There will be no charge cast before the .6 charge other than the No. 5 charge. When x (xj, 5) = 0, No. 5 charge is the first charge of the cast.

  In the constraint equation of Equation (14), for example, if x (1,2) = 1, x (1, ∀j ≠ 2) = 0, and No.1 charge is not the top charge, and No There will be no charge cast after the .1 charge other than the No. 2 charge. When x (2, (j) = 0, No. 2 charge is the final charge of the cast.

In the constraint equation of Equation (15), for example, if x (1,2) = 1, the value of the variable y (2) representing the casting position of No. 2 charge needs to satisfy Equation (22). Therefore, it is guaranteed that y (1) +1 or more.
y (2) ≥ y (1) + 1-K (1,2) x {1-1} = y (1) + 1 (22)
That is, in general, if x (i, j) = 1, it is guaranteed that y (j) ≧ y (i) +1. Therefore, in the cast plan of x (9,7) = 1, x (7,8) = 1, Equation (23) and Equation (24) are obtained,
y (7) ≥ y (9) + 1 (23)
y (8) ≥ y (7) + 1 (24)
Also, from equation (9), y (9) is 1 or more, so as in equation (25), y (8) is 3 or more,
y (8) ≥ y (9) + 2 ≥ 3 (25)
Violates equation (8), which is the restriction on the casting position of No.8 charge. Therefore, when all of the upper and lower limit constraint equations (1) to (9) and the constraint equations (13) to (15) are satisfied, a cast plan that violates the casting position constraint as in the above example is obtained. I can't.

In the constraint expression of Expression (16), for example, x (7,8) = 1, x (8,9) = 1, x (9,10) = 1 (other than those related to No. 7 to No. 10) In the cast plan in which all variables x (i, j) are 0), equations (26) to (31) are obtained, and z (7) to z (10) are all 4 or less.
z (7) ≤ z (8) + H (8,7) x {1-0-1} = z (8) ≤ 4 (26)
z (8) ≤ z (7) + H (7,8) x {1-1-0} = z (7) ≤ 4 & (27)
z (8) ≤ z (9) + H (9,8) x {1-0-1} = z (9) ≤ 6 (28)
z (9) ≤ z (8) + H (8,9) x {1-1-0} = z (8) ≤ 4 (29)
z (9) ≤ z (10) + H (10,9) x {1-0-1} = z (10) ≤ 6 (30)
z (10) ≤ z (9) + H (9,10) x {1-1-0} = z (9) ≤ 4 (31)
Therefore, according to the constraint equation (17), the casting positions of y (7) to y (10) are all limited to 4 or less, that is, the cast length (number of consecutive castings) is also limited to 4 charges or less.

  As described above, when all of the upper and lower limit constraint equations (1) to (12) and the constraint equations (13) to (17) are satisfied, the constraint on the casting position (relating to the casting order in the cast of the charge). The cast plan that satisfies both the (restriction) and the maximum continuous casting restriction (restriction on the cast length to which the charge belongs) can be obtained.

(Evaluation function setting step)
Next, in the evaluation function setting step 6, the evaluation function of Expression (32) is stored in the memory as the evaluation function represented by the variable x for determining the quality of the cast (lot) plan.
J = Σi [1-Σj {x (i, j)}] + G (i, j) × ΣiΣj {x (i, j)} (32)
The first item on the right side of the evaluation function in Expression (32) represents the number of casts. The smaller the number of casts, the smaller the value of the evaluation function in Expression (32) (referred to as evaluation value). On the other hand, the second item on the right side represents an evaluation value related to continuous casting. Here, G (i, j) represents the evaluation value when continuously casting No. j charge after No. i charge, depending on the steel type and casting width of No. i charge and No. j charge. This is a constant set in advance. For example, G (i, j) = 0.1 if either steel grade and width of No.i charge or No.j charge are different, and G (i, j) = 0 if steel grade and width are the same. Set.

(Optimal solution calculation step)
Next, in the optimal solution calculation step 7, the upper and lower limit constraint equations (1) to (12) and the constraint equations (13) to (17) are satisfied, and the value of the evaluation function of equation (32) is minimized. Integer values of variables x (i, j), y (i), and z (i) (hereinafter referred to as optimal solutions) are obtained. Here, since the cast plan has a one-to-one correspondence with the variable x (i, j), all x (i, j) may be integers, and y (i) and z (i) are not necessarily It does not have to be an integer value, and may be a real value as long as the upper and lower limit constraints and the constraint equation are satisfied.

  FIG. 2 is a flowchart showing the processing procedure of the optimal solution calculation step 7 using a branch and bound method, which is one of integer programming methods (Non-Patent Document “Hiroshi Konno” Course / Mathematical Programming 6 Integer Programming) Law "published by Sangyo Tosho Co., Ltd., pp.21-28, July 13, 1986, first edition.)

  First, in initialization step 20, the best solution used in the subsequent calculations is set to empty, the unprocessed node set is set to 0, and the current node is set to 0. Here, the best solution is a memory area for storing values of variables and evaluation values that are candidates for the optimum solution in the optimization calculation step 7 to be described later, and nodes are upper and lower limit values of variables and constraint expressions. The memory area to be stored, the unprocessed node set is a set of nodes whose variable values are not determined, and the current node is a currently processed node for determining the variable values.

  Next, in relaxation solution calculation step 21, the upper and lower limit constraints of equations (1) to (12) and the constraint equations of equations (13) to (17) are satisfied, and the evaluation function of equation (32) Real values (hereinafter referred to as relaxation solutions) of variables x (i, j), y (i), and z (i) that minimize the value are obtained by linear programming.

  Next, in the termination determination step 22, if there is no relaxation solution or the evaluation value of the relaxation solution is worse than the evaluation value of the best solution, the process proceeds to the node determination step 25. If not (if there is a relaxed solution and the evaluation value of the relaxed solution is better than the evaluation value of the best solution), the process proceeds to the feasibility determination step 23.

  In the feasibility determination step 23, the value of the relaxation solution is examined to determine whether x (i, j) is an integer. If they are all integers, the best solution storage step 27 stores the relaxation solution in the memory as the best solution. On the other hand, if there is a variable other than an integer, in node creation step 24, select one variable from non-integer variables x (i, j) and fix the value of that variable to 0. A node with a new constraint to be added and a node with a new constraint fixed to 1 are created and added to the unprocessed node set.

  In the node determination step 25, the current node is deleted from the unprocessed node set, and when there are no unprocessed nodes, the process is terminated and the currently stored best solution is output as the optimum solution. If there is still an unprocessed node, in node selection step 26, one arbitrary node is selected from the unprocessed nodes, and the process returns to the relaxation solution calculation step 21 as the current node.

  Thereafter, in the relaxed solution calculation step 21, in addition to the upper and lower limit constraints of the equations (1) to (12) and the constraint equations of the equations (13) to (17), they are newly added in the node creation step 24. Variable x (i, j that satisfies the constraint (set / stored as upper and lower bound constraints) that fixes the value of variable x (i, j) to an integer value and minimizes the value of the evaluation function in expression (32) ), y (i), real value of z (i).

  By repeating the above processing until there is no unprocessed node, the last remaining best solution is output as the optimum solution.

  FIG. 3 shows how nodes are created in the optimum solution calculation step 7. After the processing of the initialization step 20, as shown in FIG. 3A, the best solution has not yet been found and is empty, and the unprocessed node set is only node 0. Next, assuming that the current node is node 0 and performing relaxation solution calculation step 21, a relaxation solution of evaluation value J = 0.3 (x (1,2) = 1, x (2,1) = 0.7, x (2.6) = 0.3, ...). In node creation step 24, select one arbitrary variable from non-integer variables, for example x (2,1), and add a new constraint to fix the value of x (2,1) to 0 Create node 1 and node 2 with new constraints fixed to 1 and add node 1 and node 2 to the unprocessed node set. In node determination step 25, node 0 which is the current node is deleted, and it is confirmed whether the unprocessed node set is empty. The state of the nodes at this time is shown in FIG. 3B, and there are two unprocessed node sets, node 1 and node 2. When node 1 is selected as the current node in node selection step 26 and steps from relaxation solution calculation step 21 to node determination step 25 are performed, a node is created as shown in FIG. Thus, when the best solution has not yet been found and there is a relaxed solution, the number of nodes in the unprocessed node set increases by one. However, when the best solution in which the values of the variables are all integers is found, if the evaluation value of the relaxed solution is worse than the evaluation value of the best solution, the number of nodes in the unprocessed node set is decreased by one, and the best solution Unless a better relaxation solution is found, the number of nodes in the unprocessed node set continues to decrease, eventually the unprocessed node set becomes empty, and the optimal solution calculation step 7 ends.

  Here, in the node creation step 24, a constraint that newly fixes the value of the variable that was a non-integer is added to an integer, and the value of the variable that optimizes the evaluation function is obtained again in the relaxation solution calculation step 21 . For this reason, the value of the evaluation function after adding a new constraint is equal to or larger than that before the addition. In other words, it is guaranteed that the evaluation value of the upper node ≦ the evaluation value of the lower node (in the example of FIG. 3C, the evaluation value of node 0 ≦ the evaluation value of node 1 ≦ the evaluation value of node 3). The When a feasible solution in which the values of the variables x (i, j) are all integers is calculated at a certain node and the best solution is obtained, the value of the evaluation function of the best solution is set as the upper limit value, and the evaluation value is Even if a bad node is deleted, there is no better solution than the evaluation value of the best solution at a node lower than the deleted node. Therefore, if node creation and deletion are repeated until there are no unprocessed nodes, it is guaranteed that the best solution remaining at the end is the optimal solution.

(Lot plan output step)
Finally, in the lot plan output step 8, a cast (lot) plan corresponding to the value of the variable x of the optimal solution obtained in the optimal solution calculation step 7 is output to a display device such as a display or an external storage device such as a hard disk. .

<Other embodiments>
The lot planning apparatus of the present invention is a means as shown in FIG. 5 by a program stored in a memory in the computer main body in order to execute the processing described in the first embodiment on the computer. It can be realized as a configuration. Each of the means in FIG. 5, that is, the order input means 30, the variable setting means 31, the constraint condition setting means 32, the evaluation function setting means 33, the optimum solution calculating means 34, and the lot plan output means 35 are respectively described in steps 2 to 2. The operation described in 8 is performed. The program is one of the present inventions.

  The present invention is useful when planning a production lot plan so that the value of an evaluation function set from a plurality of orders is optimized.

It is a flowchart showing an example of the process sequence of the lot planning method of this invention. 10 is a flowchart illustrating an example of a processing procedure of an optimal solution calculation step 7. It is a conceptual diagram showing the mode of node creation of the optimal solution calculation step 7. It is sectional drawing of a continuous casting apparatus. It is a block diagram of the lot planning apparatus of this invention.

Explanation of symbols

1 Planned order
2 Order entry step
4 Variable setting steps
5 Constraint formula setting step
6 Evaluation function setting step
7 Optimal solution calculation step
8 Batch planning output step
9 lot planning
10 Molten steel
11 Molten steel pan
12 Ladle
13 Tundish
14 Mold
15 Support role
16 spray nozzle
17 cutting machine
18 Slab
19 Immersion nozzle

Claims (4)

A production plan that processes raw materials in batches or batches that are continuously processed while changing the processing conditions according to the manufacturing conditions based on the specifications of the multi-order product (order) and the status of the manufacturing process. In the method of planning,
An order input step of inputting a plurality of orders from an external input device and / or an external storage device;
According to the input number of the plurality of orders, a variable x representing a continuous production relationship for two orders in the plurality of orders, a variable y representing a production order in the lot of each order, and a lot to which each order belongs A variable setting step for setting a variable z representing the upper limit value of the order number of
An upper and lower limit setting step for setting upper and lower limit constraints for both the upper limit value and the lower limit value of the variables x, y, and z in accordance with manufacturing conditions predetermined for each input order; ,
Constraint expression expressed by the variable x for orders manufactured before each order, constraint expression expressed by the variable x for orders manufactured next to each order, production order in lots of two orders , The constraint equation represented by the variables x and y, the constraint equation represented by the variables x and z regarding the upper limit of the number of orders to which each order belongs, and the production order of each order and the lot to which the order belongs A constraint equation setting step for setting a constraint equation represented by the variables y and z with respect to the upper limit value of the order number of
An evaluation function setting step for setting an evaluation function represented by the variable x for determining the quality of the lot plan;
The evaluation function set in the evaluation function setting step under the condition that both the upper and lower limit constraints and the respective constraint expressions set in the constraint equation setting step are satisfied and the value of the variable x is an integer. An optimal solution calculating step of calculating values of the variables x, y, and z that optimize the value of
A lot plan planning method comprising: a lot plan output step for outputting a lot plan to an external output device or an external storage device based on the value of the variable x calculated in the optimal solution calculation step. The optimal solution calculation step uses a branch and bound method, relaxes the condition that the value of the variable x is an integer, satisfies both the upper and lower limit constraints and the constraint equations, and optimizes the value of the evaluation function The step of calculating the values of the variable x and y and z and the step of fixing a part or all of the variables x having non-integer values to integer values is repeated a plurality of times. The lot planning method according to 1. Develop a production plan that processes raw materials in batches or batches that are processed continuously while changing the processing conditions according to the manufacturing conditions based on the specifications of the multi-order product (order) and the status of the manufacturing process. In the device to
Order input means for inputting a plurality of orders from an external input device and / or an external storage device;
For the plurality of orders, a variable x representing a continuous production relationship for two orders in the plurality of orders, a variable y representing a production order in the lot of the order, and an upper limit value of the number of orders of the lot to which the order belongs Variable setting means for creating a variable z to be represented;
From the plurality of orders, the upper and lower limit constraints of the upper and lower limits of the variables x, y, and z or any one of the upper and lower limit constraints, the constraint equation represented by the variable x with respect to the orders manufactured before each order, Constraint expression expressed by the variable x with respect to the order produced next to each order, constraint expression expressed by the variables x and y with respect to the production order within the lot of the two orders, the order of the lot to which each order belongs The constraint equation represented by the variables x and z for the upper limit value of the number and the constraint equation represented by the variables y and z for the production order of each order and the upper limit value of the number of orders of the lot to which the order belongs are set. A constraint condition setting means,
Evaluation function setting means for setting an evaluation function represented by the variable x for determining the quality of the lot plan;
The variable x that satisfies each constraint condition set by the constraint condition setting means and optimizes the value of the evaluation function set by the evaluation function setting means under the condition that the value of the variable x is an integer. an optimum solution calculating means for calculating values of y and z;
A lot plan planning device comprising: a lot plan output unit that outputs a lot plan to an external output device or an external storage device based on the value of the variable x calculated by the optimal solution calculation unit. Develop a production plan that processes raw materials in batches or batches that are processed continuously while changing the processing conditions according to the manufacturing conditions based on the specifications of multiple orders (orders) and the status of the manufacturing process. In a computer program to
Order input processing for inputting a plurality of orders from an external input device and / or an external storage device;
In accordance with the number of the input orders, a variable x representing a continuous production relationship for two orders in a plurality of orders, a variable y representing a production order in the lot of orders, and the number of orders of the lot to which the order belongs. A variable setting process for creating a variable z representing the upper limit value of
Depending on the manufacturing conditions predetermined for each input order, both the upper and lower limits of the variables x, y, and z or any one upper / lower limit constraint, manufactured before each order. The constraint equation represented by the variable x for the order to be produced, the constraint equation represented by the variable x for the order produced next to each order, and the variables x and y for the production order in the lot of the two orders Constraint formula expressed, constraint formula expressed by the variables x and z regarding the upper limit value of the order number of lots to which each order belongs, and manufacturing order of each order and upper limit value of the order number of lots to which the order belongs A constraint condition setting process for setting a constraint expression represented by the variables y and z;
An evaluation function setting process for setting an evaluation function represented by the variable x for determining the quality of the lot plan;
The variable x that satisfies each constraint condition set in the constraint condition setting process and optimizes the value of the evaluation function set in the evaluation function setting process under the condition that the value of the variable x is an integer. an optimal solution calculation process for calculating values of y and z;
A computer program for causing a computer to execute a lot plan output process for outputting a lot plan to an external output device or an external storage device based on the value of the variable x calculated in the optimal solution calculation process.

Images