JPH08180100A - Method and device for scheduling - Google Patents

Abstract

PURPOSE: To calculate a (quasi) optimum solution at high speed by generating an efficient neighborhood and combining it with an approximate solution concerning a job shop scheduling question accompanied with the allocation of machines. CONSTITUTION: After an initial solution is generated by an initial solution generating means 1, the neighborhood to improve a target function is generated by a neighborhood generating means 2. In that case, when a block on a critical path is composed of operations more than three, the top or bottom is exchanged with the preceding or following operation. Besides, when the block is composed of two operations, the top and bottom are exchanged. Further, the top of the block is moved to the other machine. While utilizing the generated neighborhood, an optimizing means 3 searches the solution so that the target function can be optimum (quasi optimum).

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a scheduling method and apparatus for assigning a job consisting of a plurality of operations to a machine and determining scheduling.

[0002]

2. Description of the Related Art Scheduling is a work necessary for the entire manufacturing industry, and it is difficult to do it manually, so there is a great need for automation. As a formulation of the scheduling problem, the job shop model is general,
Widely used. An example of job shop scheduling is shown in FIG.

FIG. 1 shows a case where operations (jobs) 1 to 3 of jobs 1 to 3 are executed by a machine 1 to 3 including a press machine (1), a press machine (2) and a punching machine.
As shown in the figure, each of the jobs 1 to 3 is composed of a plurality of operations (work), ..., ..., and a machine for executing the operations and a processing time are given in advance.

The scheduling problem is that in the above-mentioned job shop model, the execution order of operations in each machine is determined so as to optimize a given objective function. Various functions are used as this objective function, but here, as a typical one, the total required time (time at which execution of all jobs is completed)
What minimizes is explained.

The above problem has a large number of combinations ((n!) ^M for the number of jobs n and the number of machines ^m ) and is difficult to solve exactly. Therefore, an approximate solution method such as a hill climbing method, a simulated annealing method, a tabu search method, etc., for generating a temporary initial solution and improving the solution is used.

In the hill-climbing method, as shown in FIG. 7 (an example in which the objective function is maximized is shown in FIG. 7), an initial solution x1 is obtained, and (x1 + Δx), (x1-Δ) near x1 are obtained.
The optimum solution is obtained by searching x) and moving x in the direction in which the value of the objective function f (x) is improved. In this method, as shown in the figure, when there is a local optimum solution, the search operation stops at the local optimum solution.
For this reason, it is necessary to find a true optimal solution by taking measures such as trying various initial solutions.

The simulated annealing method prevents the search operation from being caught and stopped by the above-described local optimum solution. That is, in FIG. 7, starting from the initial solution x1, the x is moved in the direction in which the value of the objective function f (x) is improved.
Even when the value of (x) is not improved, x is moved in a direction in which it is not improved with a predetermined probability so that a true optimal solution is finally obtained.

The tabu search method is the same as the above-mentioned hill-climbing method, in which the original x is not returned in order to avoid cycling in the above-mentioned hill-climbing method. As described above, in the approximate solution method, the current solution is changed to generate a new solution (hereinafter referred to as “neighborhood”), and when it is improved, a new solution is moved (in the case of the hill climbing method). ).

Conventionally, in order to solve the above-mentioned scheduling problem, the above-mentioned approximate solution method has been used, and after obtaining an initial solution, the neighborhood is obtained by changing the order of operations, for example, to obtain an optimum solution.

[0010]

As described above, when the scheduling problem is solved by the approximate solution method, changing the order of operations continuously performed by a certain machine corresponds to the neighborhood. However, there is a problem in that the number of this neighborhood is large and the processing efficiency is poor.

For this reason, a method of generating a neighborhood using a critical path has been proposed. FIG. 8 is a diagram for explaining the generation of the neighborhood by changing the above-mentioned critical path, which shows the scheduling of the operations of, the dotted arrows show the order of processing, and FIG. Before changing the order of the operations on the critical path, FIG. 7B shows the order after changing.

Note that, as shown in FIG.
A set of operations that are continuously executed by a certain machine in a path is called a block, and the rightmost operation of each block is called top and the leftmost operation is called bottom. In FIG. 9A, the operation →→→ is a critical path, and the order of the operations on the critical path is exchanged (in the figure, for example, with operation), a neighborhood is generated. To be done.

For example, by exchanging the order with the operation of FIG. 10A, the neighborhood shown in FIG. 9B is generated, and in this example, the total required time is 30 hours to 2 hours.
It is 5 hours, which is shorter than the total required time shown in FIG. In the example in the figure, the critical path is changed by exchanging the order of operations.
→→

By the way, in the conventional job shop scheduling, one machine is preliminarily determined to execute each operation. However, in the actual problem, there are many machines that can execute a certain operation, and their execution performances are often different, and the conventional method cannot solve such a problem well. The present invention has been made in view of the above-mentioned problems of the prior art, and an object of the present invention is to generate an efficient neighborhood for a job shop scheduling problem involving machine allocation. It is an object of the present invention to provide a scheduling method and apparatus that can obtain a suboptimal solution at high speed by combining it with an approximate solution method such as a hill climbing method or a simulated annealing method.

[0015]

FIG. 1 is a diagram illustrating the principle of the present invention. In the figure, 1 is a means for generating an initial solution, 2 is a neighborhood generating means, and the neighborhood generating means 2 is a critical
The neighborhood of the solution is generated by exchanging the execution order of the operations of the top and / or the bottom of the block on the path and moving the other machine of the top.

3 is an optimizing means for searching for an optimum solution,
Starting from the initial solution, an optimum solution (quasi-optimal solution) for (sub-) optimizing the objective function is searched using the neighborhood generated by the neighborhood generating means. In order to solve the above-mentioned problems, the invention of claim 1 of the present invention assigns an operation to a machine as shown in FIG. 1 and determines the execution order of the operation in the machine so that a given objective function becomes optimum. In the scheduling method, the neighborhood search is performed by exchanging the execution order of the top and / or bottom operations of blocks on the critical path on the same machine, and the given objective function is optimized. is there.

According to a second aspect of the present invention, in the first aspect of the invention, the neighborhood search is performed by moving the operation of the top of the block on the critical path to another machine. According to a third aspect of the present invention, in a scheduling device that allocates an operation to a machine and determines an execution order of the operation in the machine so that a given objective function is optimal, a means for generating an initial solution and a critical solution. A neighborhood generating means for generating the neighborhood of the current solution by exchanging the execution order of the top and / or bottom operations of blocks on the path on the same machine, or by moving the top operation to another machine , And an optimization means for obtaining an optimal solution or a suboptimal solution of the given objective function, the optimization means starting from the initial solution,
The neighborhood generated by the neighborhood generating means is used to search for an optimum solution or a sub-optimal solution.

[0018]

In FIG. 1, when determining the execution order of the operations in the machine, first the initial solution is generated by the initial solution generation means 1, and then the neighborhood generation means 2 is used in the following manner according to the block length. Generate a neighborhood that improves the function. That is, paying attention to the top / bottom of the block on the critical path, and when the block is composed of three or more operations, the top or bottom is exchanged with the operation before or after one. Also, if the block consists of two operations, swap the top and bottom. Then move the top of the block to another machine.

By generating the neighborhood as described above,
Move the operation on the critical path appropriately /
Compared with the case of exchanging, it is possible to prevent the number of neighbors from increasing and to efficiently generate neighbors. The optimizing means 3 searches for a solution in which the objective function is optimum (suboptimal) by using the neighborhood generated as described above.

In the inventions of claims 1 to 3, the neighborhood is generated as described above to obtain the optimum solution (suboptimal), so that the optimum solution (suboptimal solution) is obtained at high speed. be able to.

[0021]

FIG. 2 is a diagram showing a system configuration of an embodiment of the present invention. In FIG. 2, 11 is a set of jobs as shown in FIG. 6, 12 is a processor, and 13 is a scheduling result. . The processing device 12 includes a scheduler 121. After the scheduler 121 calculates a temporary initial solution as shown in the figure, the operation on the critical path is moved to generate a neighborhood, and the hill climbing method / simulated annealing is performed. A quasi-optimal solution is calculated by an approximate solution method such as a method to obtain a schedule result.

FIG. 3 is a diagram showing a processing procedure in the above scheduler. In the scheduler 121, a quasi-optimal solution is obtained by the following procedure. That is, step S
In step 1, an initial solution S is generated, and in step S2, it is determined whether or not a termination condition (the number of iterations, the evaluation value of the solution, etc.) is satisfied. The neighborhood S ′ of the initial solution S is generated by exchanging the order of top / bottom operations on the path.

Next, in step S5, it is determined whether or not the neighborhood S'fulfills the acceptance condition (in the case of the hill climbing method, the evaluation value is better than S). If the acceptance condition is not satisfied, the process returns to step S4 and the above process is repeated. If you meet the acceptance conditions,
The process proceeds to step S6, the above S'is taken as a new solution, and the process returns to step S2.

In step S2, if the termination condition is satisfied, the process goes to step S3 to output the solution S and terminate. Next, S ′ in the vicinity of S in step S4 above
An example of the present invention will be described for the generation of In this embodiment, in order to shorten the length of the critical path,
Taking advantage of the need to accelerate the end time of the top of any block, the position of the operation on the critical path is changed depending on the block, and the neighborhood is generated as follows. It also introduces a neighborhood that modifies the machine that performs the operation.

At this time, if the machine is changed appropriately, the number of neighbors increases too much and the efficiency is poor.
Efficiently generate the neighborhood by moving the top of the block to another machine. (A) When the block length is 3 or more (a1) The top of the block is exchanged with the previous operation.

That is, as shown in FIG. 4A, when a block is composed of operations T, T2, T3, ..., B2, B, and the top of the block is operation T, operations T and T2 are exchanged, It moves as shown in FIG. It should be noted that FIG. 4 represents each operation by arranging them in the vertical direction, and time advances in the direction of the arrow in the figure. (a2) Swap the bottom of the block with the next operation.

That is, the bottom operations B and B2 are exchanged from the state shown in FIG. 4A, and the operation is moved as shown in FIG. 4A2. Since the processing time of the operation B2 is shifted by exchanging the operations B and B2, the operation B and the next operation C may be connected as shown in FIG. (a3) Move the top of the block to another machine. (B) When the block length is 2. (b1) Replace the top and bottom of the block.

That is, when the block is composed of operations T and B as shown in FIG. 4B, the operation T at the top and the operation B at the bottom are exchanged as shown in FIG. 4B1. (b2) Move the top of the block to another machine. (C) When the block length is 1. (c1) Move the top of the block to another machine.

Here, in the above (a) to (c), the insertion position of the operation when the operation is transferred to another machine is determined as shown in FIG. In FIG. 5, before the movement, as shown in FIG.
It is assumed that there are operations T, P, and O1 to O4 above, respectively, the operations T and P belong to the same job, and the operation T cannot be executed before the immediately preceding operation P.

As in FIG. 4, FIG. 5 represents each operation by arranging them in the vertical direction, and time advances in the direction of the arrow in the figure. In the above case, the operation T is moved to the machine M3 as follows. In the figure, when the operation T on the machine M1 is moved to the machine M3, the operation T cannot be executed earlier than the end time t1 of the operation P as described above. If it moves after O3, its start time will be later than t1.

If the operation O2 is moved to, the start time is t1. Even if the operation O1 is moved to, the start time is t1 and the execution of O2 is delayed. Therefore, the operation T is moved after the operation O2 as shown in FIG. As described above, in this embodiment, focusing on the top and bottom of the block, the neighborhood is determined by exchanging the position of the top or bottom in the block on the critical path / moving the top to another machine. Therefore, in a job shop scheduling problem involving machine assignment, it is possible to efficiently find a neighborhood that shortens the length of the critical path, and obtain a suboptimal solution in a short time.

[0032]

As described above, according to the present invention, the top of the block on the critical path and / or
Alternatively, the execution order of the bottom operation is exchanged on the same machine, or the top operation is moved to another machine to generate a neighborhood, so
It is possible to efficiently generate neighborhoods for a job shop problem that involves machine assignment, and by combining it with an approximate solution method such as a hill climbing method or a simulated annealing method, a fast optimal solution (suboptimal solution) can be obtained. ) Can be asked.

[Brief description of drawings]

FIG. 1 is a principle diagram of the present invention.

FIG. 2 is a diagram showing a system configuration of an embodiment of the present invention.

FIG. 3 is a diagram showing a processing procedure in an embodiment of the present invention.

FIG. 4 is a diagram for explaining replacement of top / bottom operation.

FIG. 5 is a diagram illustrating movement of the top operation to another machine.

FIG. 6 is a diagram illustrating an example of job shop scheduling.

FIG. 7 is a diagram illustrating an approximate solution method such as a mountain climbing method.

FIG. 8 is a diagram illustrating generation of a neighborhood by changing a critical path.

[Explanation of symbols]

 1 means for generating an initial solution 2 neighborhood generating means 3 optimizing means 11 job set 12 processor 13 scheduling result

Claims (3)

[Claims] 1. A scheduling method for allocating a plurality of operations to a machine and determining the order of execution of the operations in the machine so that a given objective function is optimal, the top and / or bottom of blocks on a critical path. Scheduling method characterized by performing a neighborhood search by exchanging the execution order of the operations on the same machine and optimizing a given objective function. 2. The scheduling method according to claim 1, wherein the neighborhood search is performed by moving the operation of the top of the block on the critical path to another machine. 3. A scheduling device for allocating a plurality of operations to a machine and deciding the execution order of the operations in the machine so that a given objective function is optimized, means for generating an initial solution, and a critical path. A neighborhood generating means for generating the neighborhood of the current solution by exchanging the execution order of the top and / or bottom operations of the block of the same machine on the same machine or by moving the top operation to another machine. And an optimization means for obtaining an optimal solution or a suboptimal solution of the objective function, the optimization means starting from the initial solution and utilizing the neighborhood generated by the neighborhood generation means A scheduling device which searches for an optimum solution.