Computers ind. Engng Vol. 12, No. 3, pp. 167-171, 1987 0360-8352/87 $3.00 + 0.00 Printed in Great Britain. All rights reserved Copyright © 1987 Pergamon Journals Ltd

A N E X P E R T S Y S T E M F O R T H E S E L E C T I O N O F S C H E D U L I N G R U L E S IN A J O B S H O P

S. M. ALEXANDER Department of Industrial Engineering, University of Louisville, KY 40292, U.S.A.

(Received for publication 4 November 1986)

Abstract--This paper presents a conceptual framework for the application of expert systems for the selection and development of scheduling rules for a job shop. A portion of the framework is illustrated using an expert system developed using MI TM.

INTRODUCTION

Over the past three decades several authors have provided surveys of scheduling and priority rules [1-3]. However, it is difficult for a practitioner to select from among these rules. This is because the number of priority and scheduling rules are extensive (Panwal- kar and Iskander [1] for instance, list over a 100 rules). Also, the practitioner must interpret the literature to match his scheduling objectives with the rules. This is not a trivial task since the simulation experiments, cited in the literature, which evaluate the various scheduling rules utilizing different performance criteria, have different operating conditions and often give conflicting results [1,4]. Expertise is therefore necessary to interpret the literature and to select or develop appropriate scheduling rules to meet the scheduling objectives of the practitioner. This paper presents a conceptual expert system framework for providing this expertise.

In the next section, the background of the scheduling domain is provided. This background information is used as the basis for building the knowledge base for the expert system. Following this section the framework for the expert system is illustrated. A portion of the framework was developed using the development tool MI T M [5] and is implemented on an IBM PC.

DOMAIN INFORMATION

The goal of the expert system is to recommend a scheduling rule to the user. Gere [6] defines a scheduling rule to be a combination of one or more priority rules and one or more heuristics (rules of thumb). Hence, the sub-goals of the expert system are to select appropriate priority rules and heuristics based on the situation.

Numerous priority rules are provided in the literature. These rules could be static or dynamic based on whether the values of the rules change over time (Jackson [3]). The rules could also be local (i.e. the rules utilize only local information) or global (i.e. the rules utilize other information such as that from jobs in other queues) [7]. Panwalkar and Iskander [1] classify priority rules as simple priority rules, combinations of simple priority rules, and weighted priority indexes. Simple priority rules are those rules that are usually based on specific job parameters such as due-date, processing time, etc. A combination of simple priority rules are usually applied by dividing a job queue into groups and applying different rules to different groups. Weighted priority indexes are obtained by combining the simple priority rules using different weights.

Heuristic rules are usually developed for a specific shop and may include complex considerations such as anticipated machine loading and alternate routings, etc.

The development of scheduling rules utilizing priority rules and heuristics of course depend on the schedule objectives. Some common schedule objectives are to: minimize the number of late jobs, maximize machine utilization, minimize queue length, minimize

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168 S . M . ALEXANDER

job waiting time, minimize set-up time, and minimize average tardiness. Schedule objectives vary from situation to situation. The measure of performance of a schedule could be based on a single criterion, such as minimizing mean tardiness, though it is often based on multiple criteria. The literature tends to support the use of weighted priority indexes for multi-criteria performance measures. However, there is little guidance available for the selection of weighting factors other than through the utilization of simulation and search techniques [8,9].

Two criteria that are of primary interest in scheduling and which seem to be prevalent in almost all schedule objective functions are shop time and due-date performance [4]. The shop time, or flow time, is the time a job spends in the shop from order release to completion. The literature repeatedly indicates that the mean flow time is minimized by using the shortest processing time (SPT) priority rule, though slight improvements can be obtained by modifying this rule [10]. Minimizing mean flow time has the added benefit of minimizing in process inventory [11].

Due-date performance is measured by values such as, the proportion of jobs tardy, mean tardiness and conditional mean tardiness (the tardiness averaged over the number of jobs tardy). There have been a considerable number of simulation experiments conducted to determine the best priority rules for optimizing the above measures of performance. These experiments indicate that SPT is an effective priority rule for minimizing the proportion of jobs tardy [11-15]. For minimizing conditional mean tardiness, ratio based priorities, such as the smallest critical ratio, which is the ratio of the remaining allowance of the job to the remaining work and the smallest operational critical ratio, have been found effective [13,14]. The literature reveals mixed results in suggesting priority rules for minimizing mean tardiness. Baker [4] suggests that the mixed results are due to varying levels of due-date tightness in the experiments. Baker's [4] experiments reveal that the earliest operation's modified due-date rule provides robust performance in terms of minimizing mean tardiness over all levels of due-date tightness. The operation's modified due-date is its original due-date or its early finish

Simulation model

generator

Search Algorithm

Optimal'welghts

Priority index elements; objective function.

Global Date Base

• Facts supplied by user

• Intermediate conclu- sions

• Welghts for priority index calculation.

Knowledge Base

• Facts

• Rules

• Priority rule selection

• Heuristics

• Combining priority rules and heuristics

• Metafacts

I Inference Mechanism

• makes conclusions • questions user

l I User

Fig. 1. A framework for an expert system for the selection of scheduling rules.

Scheduling rules in a job shop 169

time, whichever is larger. The literature also indicates that the operation due-dates should be set to indicate the work content of individual operations and should not be equally spaced [4,14]. Baker's experiments also indicate that the remaining allowance per operation rule may be desirable if due-dates are kept loose (i.e. the congestion of work in the shop is small and tardiness is consistently low) [4].

THE F R A M E W O R K

The expert system framework for the selection of scheduling rules in a job shop is shown in Fig. 1. The knowledge base consists of rules, facts and metafacts. Facts and rules provide factual and inferential knowledge. Metafacts provide information on how the consultation with the user should proceed. The rules include those obtained from the literature for selecting priority rules. If the user desires, the system will display refer- ences from which the priority rules were derived. The system could also display draw- backs or disadvantages of utilizing any priority rule directly as a scheduling rule, on a query from the user. Appropriate references will be included with this display. This display is triggered by an MI statement of the form shown below:

when found (priority-rule = known) = [references]

(The above statement directs the expert system to ask the user if he desires to see the references from which the priority rules were derived. If the user's response is yes then the appropriate references will be displayed. The user interface is built using MI metafacts such as question [references]. This allows the questions to the user to be in plain English.)

The knowledge base also includes heuristics or rules of thumb developed for the specific job shop. Owing to the expert system architecture it is relatively easy to add and remove heuristics from the knowledge base. This makes the framework adaptable to a variety of job shops. Rules are also included in the knowledge base for combining the different priority rules and heuristics to form scheduling rules. A simple example of this, using MI and its English translation, is shown on Table 1.

Table 1. An example rule for combining priority rules and heuristics

Presupposition (Scheduling-rule = Priority-rule = known If Queue > Q and Alternate-Routing = yes Scheduling-rule = Move job with lowest priority to an alternate route.

If alternate-routing = no then scheduling-rule = Priority-rule.

English Translation: If a priority rule has been determined and if the number of jobs in queue at the machine under consideration is greater than a critical value (Q), attempt to move jobs with a low priority to an alternate route.

The inference paradigm is backward chaining. Here an hypothesis is made and tested against the facts collected by the expert system. The inference strategy can, however, be changed. In order to illustrate the inference process a sample trace of a search session is shown in Table 2. Table 2 shows that even though the goal of the expert system is to determine a scheduling rule, the normal backward chaining inference process is changed and the system first seeks information on performance criteria and due-date tightness. In MI, this process is made possible through the use of metafacts.

If the scheduling objectives are based on multiple criteria then priority rules are first

170 S. M. ALEXANDER

Table 2. A sample trace of a search session

Ml>go. Seeking performance-criteria. Which performance criteria or objective(s) would you like your schedule to minimize? mean-flow-time in-process-inventory proportion-of-jobs-tardy mean-tardiness Conditional-mean-tardiness. > > proportion-of-jobs-tardy.

performance-criteria = proportion-of-jobs-tardy cf. 100.

Found performance-criteria. Seeking due-date. Are the due-dates for the jobs tight or loose? (Tight due-dates imply that a large percent of the jobs are expected to be tardy owing to high shop utilization.) tight loose > > loose

due-date = loose cf. 100. Found due-date. Seeking scheduling-rule.

kb--7: if priority-rule = X1 then scheduling-rule = f(X1, Job-shop-environment)

Seeking priority-rule.

kb--9: if performance-criteria =

proportion-of-jobs-tardy and due-date = loose

then priority-rule = Remaining allowance per

operation (A/OPN). Already sought performance-criteria. Already sought due-date. priority-rule =

Remaining allowance per operation (A/OPN)cf. 100. kb-10 succeeded. Found priority-rule.

Remaining allowance per operation (A/OPN)cf. 100.

obtained for the single criteria. These rules are combined to form a weighted priority index of the form shown below:

n

Wp [priority-rule (p)] p = l

where n = No. of criteria

0 < W p < l

EW~=I p = l

where Wp are the weights assigned to priority rule(p). Since there is no guidance in the literature for selecting weights, the weights are selected by simulation and search [9] (Fig. 1). A standard objective function can be supplied by the expert system or the user can input his own objective function. A generic simulation model generator can be used to build a simulation model for a variety of job shops. A simulation model generator is

Scheduling rules in a job shop 171

defined by Mathewson [16] as, "An interactive software tool that translates the logic of a model described in a relatively general symbolism into a code of a simulation language and so enables a computer to mimic model behavior ." Essentially, the user need only input the characteristics of the system on prompts f rom the user interface of the generator . The simulation model is built by the generator. Haddock and Davis [17] describe four main advantages for using a simulation model generator. These are:

• it assists the user in inputting data and model building;

• it provides for bet ter model experimentat ion;

• it reduces t ime required to redefine the model;

• it encourages the user to test different design and control alternatives.

Hence, by providing an interface between the simulation model generator and the expert system, scheduling rules can be developed for a variety of job shops. This would keep the f ramework adaptable to different job shop environments, A search technique such as pat tern search [18] can be utilized for determining optimal weights for calculating the weighted priority index.

CONCLUSION

The expert system f ramework suggested and partially implemented for selecting scheduling rules is feasible and useful. The f ramework is feasible because the domain is defined and small, and involves structured selection.

The f ramework is useful because it enables the practit ioner to utilize the fruits of scheduling research. The practit ioner would just have to specify his objectives or select an objective function; the expert system f ramework would select or develop appropriate scheduling rules. The expert system f ramework also allows the knowledge base to be easily modified and tuned to the unique requirements of a particular shop.

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