JPH01277902A - Scheduling problem solution backup system - Google Patents

Abstract

PURPOSE:To efficiently lead out a valid schedule solution by combining two stages of allocation techniques based on determinate allocation of jobs to machines and the successive improvement. CONSTITUTION:A job allocator 12 of a processor 11 of a CPU/memory successively allocates jobs in accordance with determinate procedures based on a problem 10 to mechanically allocate jobs at a high speed. In this case, when scheduling is not successful, restriction conditions of all jobs are relaxed to generate the all job allocated state. A job modifier 13 extracts already allocated jobs and job groups, which can be exchanged between arbitrary machines, based on the all job allocated state and calculates the evaluation value for the state, where jobs and job groups are exchanged, to successively improve allocation in such direction that restriction conditions are satisfied furthermore, thereby generating a schedule solution. A valid schedule solution is efficiently led out by this system of two stages.

Description

[Detailed Description of the Invention] [Summary] The present invention relates to a scheduling problem solving support system in which a computer processes a scheduling problem that can be understood in the framework of allocating jobs to machines so as to satisfy predetermined constraints.

The purpose is to provide a means to efficiently derive a reasonable schedule solution.

By sequentially assigning jobs to machines in a deterministic manner and relaxing the constraints if the scheduling is not successful.

a first processing means for generating allocation status of all jobs;
Based on the allocation status of all jobs generated by the first processing means, allocated jobs or job groups that can be exchanged between arbitrary machines are extracted.

By calculating the evaluation value of the state in which jobs or groups of jobs are exchanged between these machines, improvements are made in a direction that further satisfies the constraint conditions.

and second processing means for generating a schedule solution.

[Industrial application field]

The present invention satisfies certain constraints.

This invention relates to a scheduling problem solving support system that uses computers to process scheduling problems that can be understood in the framework of assigning jobs to machines.

Many scheduling problems can be considered as "problems of allocating jobs to machines." 6 A machine is a target that is restricted by a job for a certain period of time and executes an assigned job. For example, when freight is transported between required points by truck, the truck or the like that transports the freight is a machine, and the freight transport request is a job.

Such a scheduling problem is one of the problems to which planning-type expert systems and the like are applied, but it is difficult to generate a solution quickly because of the characteristics of this type of problem, such as the tendency to become a combinatorial problem.

There is a need for technical means to solve this problem and enable the construction of a practical system.

[Conventional technology]

For example, given n offices and m trunks,
Let us consider the processing of a scheduling problem in which a trunk operation plan is created to realize the required number of flights between these offices.

In that case, the geographical relationship of each business office (route connecting the business offices, time required for operation between them, etc.), and the time required for loading, unloading, etc. at each business office.

Business hours of business offices, requests for arrival and unloading times of cargo, etc. for each business office, and other constraints are given as constraints.

The solution to this problem is 1.For example, each track TI, T2゜...
However, the daily schedule includes which office to leave from, what time to arrive at which office, how many minutes to work there, and what time to leave for other offices, etc. It is necessary to find this solution so as to satisfy the above-mentioned constraints.

In general, such scheduling problems can be thought of as a problem in which a truck is considered a "machine" and a job is assigned to two machines, with the operation from one business office to another as a "job" to be processed by that machine. be able to.

When solving this type of problem, one problem is expressed as a formula and the solution is found mathematically. There are analysis methods such as so-called operation research, but in real-life problems like the one mentioned above, unless the two problems are significantly simplified.

It is extremely difficult to express it mathematically, so
It is often not applicable in practice.

Furthermore, even if it is possible to convert the formula into 5 formulas, if the constraints change, it will generally be necessary to reconsider the structure of the formula.
It is often difficult to respond to changes in circumstances.

On the other hand, a method that exhaustively searches for all combinations of job assignments to one machine on the five time axes that satisfy the constraint conditions is also considered, but the search space is wide. Therefore, it is generally difficult to obtain a schedule solution within a practical processing time.

[Problem to be solved by the invention]

Therefore, the present inventors have proposed two types of first-order techniques as systems/methods for quickly obtaining solutions to scheduling problems.

One of them is to perform deterministic scheduling using heuristics, separating the selection of one machine and job, and reducing the calculation time by limiting the prespace to a subspace ( Patent application 1986-267561
issue).

The other method is to create a new state by relaxing the constraints and allocating all jobs to machines and sequentially exchanging jobs or job groups that can be exchanged between the five machines according to the calculation results of evaluation values. Then, a schedule solution that finally satisfies all the constraints is found (Japanese Patent Application No. 274089/1989).

In the former method, jobs are assigned to machines definitively, so it is difficult to deal with the increase in machines and jobs.

It is possible to avoid an increase in calculation time due to combinatorial problems. However, in some cases, the rate of generation of complete solutions that satisfy all constraints may be poor.

On the other hand, the latter method is based on sequential improvement.

By initially assigning all jobs to machines.

The number of exchanges of jobs or groups of jobs may increase significantly, making it difficult to generate solutions quickly, especially for scheduling problems that handle large-scale data.

The present invention aims to solve the above-mentioned problems, and aims to provide a means for efficiently deriving a reasonable schedule solution by combining the two methods described above and performing two-step control, taking advantage of the advantages of both methods. There is.

[Means to solve the problem]

FIG. 1 is a diagram for explaining the present invention in detail.

In FIG. 1, 10 is a problem that is input as a scheduling target, 11 is a processing device consisting of a CPU, memory, etc., 12 is a job allocator that selects jobs and assigns them to machines using heuristics, and 13 is a state. 14 is a schedule solution output unit that outputs the obtained schedule solution, and 15 is a schedule solution for the given time period B10.

The job allocator 12 uses heuristics to allocate zips to machines on the time axis, given a zip 9 machine and a time uio defined by constraints. Jobs are assigned to machines according to the following steps and scheduled.

In general, if all zips satisfy the constraint conditions and are allocated to each machine, scheduling is considered successful, and the result is set as schedule solution 15.

When the constraint conditions cannot be met during definitive job assignment and unassigned jobs remain 5
By relaxing the given constraints, unallocated jobs are assigned to machines without satisfying the constraints, the assignment status of all jobs is generated, and the result is notified to the Jilib modifier 13. - If the zip allocator 12 is unable to derive a schedule solution and notifies all job allocation state information whose constraint conditions are not satisfied, the job modifier 13 uses the all job allocation state as an initial state and performs a process between different machines. Extract replaceable assigned jobs or job groups,
By calculating the evaluation value of the state in which jobs or groups of jobs are exchanged between these machines, improvements are made in a direction that satisfies the constraints even more, and processing is performed to generate a schedule solution. The schedule solution obtained is outputted via the schedule solution output unit 14.

[Effect]

In the present invention, a schedule solution is generated through two-step control: deterministic scheduling using heuristics by the zip allocator 12, and scheduling based on a sequential improvement method by the job modifier 13.

In the job 70 caterer 12, jobs are assigned to machines definitively, so even if the number of jobs increases, the processing time for all jobs only increases linearly. In addition, even if a schedule solution cannot be reached, to some extent,
Generate an allocation state close to the solution and exit. Therefore, if the job modifier 13 sequentially improves the state generated by the 8 job allocator 12, the 8
By improving the state close to the solution, it becomes possible to arrive at the schedule solution with fewer state evaluations and fewer zip changes.

In other words, if an initial state is generated using only the job modifier 13 and the initial state is successively improved, as the number of jobs increases, the number of exchange executions and other problems will increase. , and zip allocate 12, it is possible to reduce the number of exchange executions and realize high-speed solution generation even for scheduling problems that involve handling large-scale data.

〔Example〕

FIG. 2 is a processing flow of a job allocator according to an embodiment of the present invention, FIG. 3 is a processing flow of a job modifier according to an embodiment of the present invention, FIG. 4 is an example of processing by a job modifier, and FIG. Figure 5 is an example of scheduling data for detailed explanation of the present invention, Figure 6 is an example of job and machine description, Figure 7 is an explanatory diagram of forced allocation by zip allocation, and Figure 8 is an example of application of the present invention. An example of the scheduling result is shown below.

In the scheduling problem of creating a daily trunk transportation plan, for example, m trucks are designated as machines, and n locations are to be transported between offices.

A job such as "flight from office P to office Q" is specified. In addition, time required between offices and other constraints are set.

For the input of such a scheduling problem.

The job allocator 12 shown in FIG. 1 performs definitive scheduling by the processing shown in FIG. 2. In the following description, ``■'' to ``0'' correspond to the processes ``■'' to ``■'' shown in FIG. 2.

■ Select a machine of interest that can be assigned 1 at the present time. Note 2: If there is no machine that can be assigned, focus on the machine that will be released from the job the earliest, and advance time until it is released.

That machine is set as the featured machine.

Next, a job set to be allocated as candidates is selected, and in this embodiment, two time spans are used to target appropriate jobs.

Two time parameters are used: the maximum required time and the minimum possible time. The required maximum time is such that no matter which job is printed, the machine can be assigned after that time, and the minimum possible time is such that the idle time of the two machines is reduced.

This time is determined based on the relationship between the allowable play time and the frequency of job occurrence. These times are given as constants depending on one problem, but it is preferable to select appropriate values by tuning through two trials.

■ A set Jsl of jobs whose final job allocation start time is within the required maximum time from the current time (hereinafter referred to as maximum required jobs) based on the target machine.
Extract.

(2) Also, with the 8 machines of interest as a reference, a set Js2 of jobs (hereinafter referred to as the minimum possible jobs) whose first time of the possible allocation start time of the 9 jobs is included within the minimum possible time from the current time is extracted.

(2) Next, it is determined whether an i-machine other than the machine of interest is capable of processing the set Jsl of the maximum required jobs. Here, the following judgment is made.

Assume that there are jobs J to J4 as the maximum required jobs, as shown in FIG. 2 fal. first.

The 0th order job J that associates the slowest (empty machine M) with job J1 among the machines that can process the first job J1
□ is similarly associated with machine M8. Zip J,
The same applies to Finally, regarding Zip J4, if there is a machine Ml that can be assigned to a machine other than the machine of interest.

This means that the required maximum zip can be processed by a machine other than the target machine.

■ Set Js of the maximum required jobs for machines other than the focused machine
If it is not possible to process l, use this set Js as a 2 selection job.
Adopt l.

■ Set Js of the maximum required jobs for machines other than the focused machine
Since it is better to start the machine of interest as soon as possible, the minimum possible job set Js2 is adopted as the selected job.

■ Determine the job to be assigned to the machine of interest from among the selected jobs. Along with considering constraints.

Evaluate the elements of the selection job set and assign the best job.

■ Determine whether it was possible to allocate a job that satisfies the constraint conditions, and if a solution that satisfies the constraint conditions cannot be obtained, move to process @.

■ Determine whether all jobs have been scheduled. When the schedules for all jobs are completed, it means that the necessary schedule solution has been obtained, and the result is notified to the schedule solution output unit 14 shown in FIG. 1.

Finish the process.

0 If there are jobs remaining to be processed 5 Check whether it is necessary to generate a new job in response to the passage of one hour or changes in conditions. If job generation is not required,
Return control to process ■.

Repeat the same process 0 For example, if the end of business hours approaches and a truck is at a business office without a garage, it is necessary to create a job to move the truck to a business office with a garage. Become.

■ If it is necessary to generate a job, generate the job, set it in an internal table (not shown), and process it.■
Control is returned to and the process is repeated in the same way.

■ If the constraint conditions are not met and jobs cannot be assigned, the constraint conditions are relaxed and the unassigned jobs are forcibly assigned to the machine. and.

The result is notified to the zip modifier 13 shown in FIG. 1, and the processing of the job allocator 12 is ended.

In job modifier 13, zip allocator 12
In response to the notification from 2, for example, processes Φ to 2 shown in FIG. 3 are executed.

■ First, the receiver obtains information on the allocation status of all jobs whose constraint conditions are not satisfied. With this as the initial state, improvements are made sequentially through the following processes.

■ Checks the current allocation state based on constraints, and if all constraints are satisfied.

The state is determined to be a schedule solution, and information on the state is outputted via the schedule solution output unit 14 shown in FIG.

■ If the status does not satisfy the constraint conditions, search for a mutually interchangeable subset of the jobs assigned to any machine based on the assignment status of the job, and select it as a swap candidate. do.

As an interchangeable subset, 2. For example, jobs assigned to two different machines, each job sequence consisting of one or more jobs following jobs with the same starting office, or from jobs with the same starting office. , you can select columns for each job up to jobs that have the same arrival office. In addition, cases in which a job or a sequence of jobs assigned to a machine is simply moved to another machine, including the case where one subset is empty, are also swap candidates.

■ When a swap candidate is retrieved, an evaluation value related to the constraint condition is calculated for the state obtained by exchanging the job subset of the candidate between the corresponding machines. For example, the excess time of each flight can be taken as this evaluation value.

■ Check whether the evaluation value of the condition obtained after the exchange is improved from the evaluation value of the current condition before the exchange.

Judgment is made based on the judgment conditions. If it is determined that there is no improvement, the process returns to process (2) and searches for another swap candidate.

■ If swapping provides an improvement, swap the swap candidate zip or zip group.

After updating the state to a new state, control is returned to process (2) to check whether the disconnected state has become a solution. Thereafter, the process ``■'' or ``process ■'' is repeated to improve the status one by one and obtain a schedule solution.

The successive improvement process by the zip modifier 13 will be explained according to a specific example shown in FIG.

Note that to simplify the explanation, job 70 will be used here.
This will be explained as a process independent of the process by the controller 12.

For example, as shown in Figure 4 (a), there are four sales offices, office A to office ri, and there are four flights (two round trips) between office A and B, and flights between all other offices. Assume that each job has two flights. Assume that there are three trucks (Tl, T2, T3) that are machines that execute the job.

It is also assumed that a first-order constraint condition is given.

(l) Track TI, T2. T3 is each office A.

It is initially placed in B and C.

(2) Travel time between each office is 50 minutes.

(3) What is the required flight time to allocate to each trunk?

Must be less than 200 minutes.

(4) Operate all trucks.

(5) Each truck must be deployed to offices A, B, and C upon completion.

Here, the evaluation value is the value of the time exceeding 200 minutes out of the total research time required for the flight assigned to each truck.

The ninth-order condition is specified as the determination condition.

One of the current evaluation values of the swap candidate is eI+ and the other is C2, and the new evaluation values after the exchange are ne, , ne, respectively.
As z.

wax (e+ + ex) > wax (ne+,
nflx ) or ((e, =ne, ) and (e
, >net ) 1 or ((e, =ne, ) and (1lll >nel ) 1, the condition is said to be improved.

Here, the exchange of a subset of jobs in the swap candidates is a loop swap performed on a sequence of jobs that constitute a path with the same starting point and arrival point.

Everything after a certain starting point? There are two types of tail swaps that are performed on the rows of jobs that make up the database, and paths that meet these conditions and have the same starting point are searched from different job sets and used as swap candidates.

Scheduling is done with the above conditions in mind.

For example, as shown in FIG. 4(b) (al~(C1), a schedule solution is obtained through sequential improvement.

That is, 9. If the initial state that the zip modifier processes is like falO1, for example, as a swap candidate between trunks TI and T2.

The part shown in the dotted line frame in the figure is taken up and is the target of loop swap. Note that trunks T2 and T3, to which no jobs are assigned, have offices B to B, respectively.
It can be seen that there is a dummy flight from office C to office C.

(The evaluation value in the state of al is 50X12-200=400 for track T1, and -200 for T2.Here, if the above loop swap is performed, the evaluation value is 2.O for trunk Tl. , 200 for trunk T2. Therefore, it is determined that an improvement can be obtained according to the above-mentioned judgment conditions, and the replacement is executed.
Obtain the disconnected state of Cbl.

Next, if we search for a swap candidate between tracks T2 and T3 with a large interval between evaluation values and select the tail swap in the part indicated by the dotted line in The value is track T2.
It becomes 0 for both T3. Therefore, it can be seen that an improvement can be obtained under the 1 judgment condition, and the replacement is executed. This results in state 5(C). Since this state satisfies all five constraints, it becomes a schedule solution.

In the present invention, the initial state of fal shown in FIG. 4(B) is generated in advance by the job allocator 12 shown in FIG. schedule solution can be obtained quickly.

Next is a similar kind of scheduling problem.

An example of a scheduling problem that is needed in practice will be explained.

This is a question of planning a day's land transportation using a trunk.

The data given as scheduling data is, for example, data as shown in FIGS. 5(A) to 5(D).

For example, as shown in FIG. 5(A), the office information for scheduling is 5 for each office.

Information includes business hours, availability of nighttime facilities (garage), initial number of trucks, loading and unloading times, and inspection times.

In addition, as information on the number of trunk flights, 2, for example, Fig. 5 (B)
As shown in , information on the required number of truck flights from the departure office to the destination office is input information. Here, the number surrounded by O marks indicates the departure time or the number of flights including scheduled flights with a fixed departure time.

This regular flight information is input separately, for example, as information shown in FIG. 5(C).゛In addition, the time required by truck from the departure office to the destination office is 2
For example, it is given as information as shown in FIG. 5(D).

In solving such scheduling problems, the trunk is treated as a machine, and the task of moving the trunk according to the number of flights is treated as a job. Summarize.

In the job representation shown in FIG. 6(a), the earliest start time is the earliest time at which this job can be started. Latest start time is the latest time this job can start.

The earliest end time and latest end time are the earliest time and latest time at which this job can be completed, respectively. Job size is the time required for a machine to perform that job.

Regarding each machine, as shown in Figure 6 (b).

It is summarized in the description of information such as job processing performance, operation start time, latest operation end time, and initial placement position.

The description shown in Figure 6 is as shown in Figure 5 (A) to CD).
In order to input the information shown in , the user may do it himself or, in the user interface section, based on the input information through a menu or the like.

It may also be automatically generated within the system.

Various constraint conditions can be described in 9, for example, production rules.

In the initial state in the morning, the job allocator 12 shown in FIG. 1 allocates each job using the heuristics it has as internal knowledge.

For example, one trunk at the second office is set as the machine of interest and is the first scheduling target. Here, the job set of 2 allocation candidates is transportation to the first office,
Transportation to the third office, transportation to the fourth office, etc., the maximum required time is 1, for example 2 hours, and the minimum possible time is 3
You can set it as you like, such as 0 minutes.

Initially, there are four trunks at the second office, so the machines other than the machine of interest are the remaining three trucks. In addition, the scheduling of each track is progressing,
Once trunks arriving from other offices become available within the required maximum time.

The truck is also counted as one of the counter machines.

Through the process explained in accordance with FIG. 2, it is determined whether to adopt the maximum necessary job or the minimum possible job as the selection zip for the machine of interest.

A job is assigned to the machine of interest (trunk) to determine which office it should go to. Thereafter, in the fifth step, a currently allocatable track is selected as the machine of interest, a job is selected in the same way, and scheduling proceeds.

As a result, if all jobs can be allocated so as to satisfy the constraint conditions, then this becomes a schedule solution. However, job J23 shown in FIG. 7(a). J26
．． If there remain jobs that satisfy the constraint conditions and cannot be allocated, as in...1 For example, relax the time constraints and consider only the start and end states of unallocated jobs, as shown in Figure 7. As shown in (b), the job is forcibly pushed into a connectable position, thus creating an all-job allocation state, and the job modifier 13 shown in FIG. 1 is activated.

The job modifier 13 performs sequential improvements similar to the example shown in FIG. 4 through the processing shown in FIG.

Find a schedule solution that satisfies all constraints. That is, the machine (Ml.

M2. ), a partial sequence exchange operation is performed on the job sequence assigned to the job sequence, and convergence to the layer state is attempted.

By the above two-step control scheduling process,
Finally, a scheduling result as shown in FIG. 8, for example, is obtained. In this result, Trunk A, who is initially at the 2nd office, leaves for the 1st office at 4:00, and after arriving at the 1st office at 5:00, the working time is 50 minutes. Finally, I returned from the first office to the second office at 5:50. Furthermore, as a regular flight from the 9th office to the 2nd office, this trunk A leaves the 9th office at 16:10. Similarly, for other trunks, the departure time from the office where you are currently located,
The target business office, etc. can be obtained.

Of course, the present invention is applicable not only to such truck transportation planning but also to other scheduling problems.

Similarly applicable.

For example, the actual processing times etc. for each problem based on the following transportation plan scheduling data were as follows.

(1) Scheduling data Here, the numbers in parentheses in the Jisib column are.

This is the number of jobs (referred to as fixed jobs) that have a fixed start time, such as regular flights. In Area 8.

This means that 16 of the 49 jobs are fixed jobs.

(2) Results of scheduling using heuristics (3) Results of scheduling started from a random initial state using only the sequential improvement method The number of operations is the number of times jobs or job groups are exchanged. A schedule solution has been obtained except for the area, but as the number of jobs increases, the processing time increases rapidly.

(4) Results of scheduling performed by combining a method using heuristics and a sequential improvement method according to the present invention As is clear from this scheduling experiment example, according to the present invention, the generation rate of schedule solutions is high. At the same time, especially when the number of jobs increases, the number of operations for sequential improvement is considerably reduced compared to when performing only one improvement, so it can be expected that the processing time will also be significantly shortened.

〔Effect of the invention〕

As explained above, according to the present invention, schedule solutions can be generated at a high generation rate even for scheduling problems that handle large-scale data.
Furthermore, the calculation time for scheduling can be significantly reduced.

[Brief explanation of the drawing]

FIG. 1 is a diagram explaining the principle of the present invention. FIG. 2 is a processing flow of a job allocator according to an embodiment of the present invention. FIG. 3 is a processing flow of a job modifier according to an embodiment of the present invention. FIG. 4 is an example of processing using a job modifier. FIG. 5 is an example of scheduling data for explaining the present invention in detail. Figure 6 is an example of job and machine description. FIG. 7 is an explanatory diagram of forced allocation by the job allocator. FIG. 8 shows an example of a scheduling result according to an application example of the present invention. In the diagram, 10 is the problem and 11 is the processing bag! 112 is a job allocator, and 13 is a job modifier 1 year. Reference numeral 14 represents a schedule solution output unit, and 15 represents a schedule solution.

Claims (1)

[Scope of Claims] A scheduling problem solving support system that uses a computer to process a scheduling problem that can be understood in the framework of allocating jobs to machines so as to satisfy predetermined constraints, using a deterministic procedure. , a first processing means (12) that sequentially allocates jobs to machines and generates an allocation state of all jobs by relaxing constraint conditions when the scheduling is not successful; Based on the allocation status of all jobs generated by the processing means (12) of No. 1, allocated jobs or job groups that can be exchanged between arbitrary machines are extracted, and the jobs or job groups are exchanged between these machines. a second processing means (13) that generates a schedule solution by calculating an evaluation value of a state in which the constraint condition is satisfied by successively improving the constraint condition; Problem solving support system.