adaptive scheduling in dynamic flexible manufacturing systems: a dynamic rule selection approach

486 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 13, NO. 4, AUGUST 1997

Adaptive Scheduling in Dynamic FlexibleManufacturing Systems: A Dynamic Rule

Selection ApproachSang Chan Park, Narayan Raman, and Michael J. Shaw

Abstract—This paper develops an adaptive scheduling policyfor dynamic manufacturing systems. The main feature of thispolicy is that it tailors the dispatching rule to be used at a givenpoint in time to the prevailing state of the system. The inductivelearning methodology used for constructing this state-dependentscheduling policy also provides an understanding of the relativeimportance of the various system parameters in determining theappropriate dispatching rule. Experimental studies indicated thesuperiority of the suggested approach over the alternative ap-proach involving the repeated application of a single dispatchingrule for randomly generated test problems as well as a realsystem, and under both stationary and nonstationary conditions.In particular, its relative performance improves further whenthere are frequent disruptions, and when disruptions are causedby the introduction of tight due date jobs and machine break-downs—two of the most common sources of disruptions in mostmanufacturing systems. From an operational perspective, themost important characteristics of the pattern-directed scheduling(PDS) approach are its ability to incorporate the idiosyncraticcharacteristics of the given system into the dispatching ruleselection process, and its ability to refine itself incrementally on acontinuing basis by taking new system parameters into account.

Index Terms—Adaptive scheduling, dispatching rule selection,dynamic manufacturing system, inductive learning.

I. INTRODUCTION

OPERATION SCHEDULING is an important aspect ofthe real-time control of dynamic manufacturing systems.

The ability of a system to meet its job due dates, for example,depends critically upon establishing an efficient sequence ofoperations at each machine. In dynamic systems, schedulingdecisions are usually implemented through dispatching rulesthat assign priority indices to the various jobs waiting ata machine; the job with the highest priority is selected forimminent processing. Given its importance, there has beensignificant research done in identifying dispatching rules that

Manuscript received February 13, 1995; revised December 6, 1995. Thework of N. Raman and M. J. Shaw was supported by the Research Boardof the University of Illinois. The work of M. J. Shaw was also supported bythe Decision Risk and Mangement Science Program of the National ScienceFoundation #SBR93-21011. This paper was recommended for publication byAssociate Editor A. Kusiak and Editor A. Desrochers upon evaluation of thereviewers’ comments.

S. C. Park is with the Department of Industrial Management, KoreaAdvanced Institute of Science and Technology, Yusong-gu, Taejon, Korea.

N. Raman is with Bell Laboratories, Lucent Technologies, Holmdel, NJUSA.

M. J. Shaw is with the Beckman Institute for Advanced Science andTechnology, University of Illinois, Urbana, IL 61801 USA.

Publisher Item Identifier S 1042-296X(97)05906-5.

are superior. The major finding is that there is no one rule thatclearly dominates others.

In order to explain the somewhat inconsistent results ob-tained by various researchers, Baker [1] proposes that therelative effectiveness of any rule depends upon the systemparameters incorporated in the study. For the objective ofminimizing mean job tardiness, he identifies due date tightnessand system utilization levels as two parameters that couldresult in crossovers among the various dispatching rules in adynamic job shop. His results suggest that it may be possibleto improve system performance by implementing a schedulingpolicy rather than a single dispatching rule. Such a policyshould be adaptive in that it should be able to identify thecurrentstateof the manufacturing system, and should then beable to decide upon the appropriate dispatching rule to be used.

While such an adaptive policy is conceptually appealing,its effectiveness depends upon three critical elements: 1) anefficient characterization of any given manufacturing state; 2)the completeness of the set of scheduling rules considered; and3) the correctness of the decision that maps the manufacturingstate into the appropriate dispatching rule. Identifying themajor descriptions of past research to determine the ma-jor parameters that influence system performance, any realmanufacturing system is additionally likely to possess someidiosyncratic characteristics as well. These characteristics maybe important descriptors of a manufacturing state in that sys-tem, but usually are difficult to predicta priori. Consequently,the scheduling approach should be able to incorporate suchsystem-dependent characteristics readily.

Second, there is a need for specifying the set of “good”dispatching rules that a given manufacturing state will bemapped into. In order for the scheduling policy to be compre-hensive, we need to identify all dispatching rules which canpotentially be appropriate. Panwalker and Iskander [27] givea list of over 100 dispatching rules that have been consideredin prior research. Third, the scheduling policy needs a setof decision rules in order to determine the dispatching ruleappropriate for a given state of the system. Clearly, in orderto be implementable in real time, such a scheduling policyshould be computationally efficient. This requires that the setof dispatching rules be compact, essentially consisting onlyof dominant rules. In addition, the mapping rules should beparsimonious.

All three elements of the adaptive policy are likely to beproblem specific. The set of important system attributes, the

1042–296X/97$10.00 1997 IEEE

PARK et al.: ADAPTIVE SCHEDULING IN DYNAMIC FLEXIBLE MANUFACTURING SYSTEMS 487

set of dispatching rules as well the set of mapping rules dependupon the type of manufacturing system considered, such asflow shops, job shops, etc., and the scheduling objective, suchas minimizing flow time, minimizing earliness, etc.

A practical consideration for many manufacturing systemsis their ability to withstand constant disruptions such as theunexpected arrival of “hot” jobs with shorter due dates, ma-chine breakdowns, etc. Consequently, an important measure ofthe effectiveness of any scheduling approach is its robustnessin the face of such disruptions. While there is some recentresearch dealing with the generation of robust schedulingrules, it has largely addressed static systems only. Previousinvestigations of scheduling rules in dynamic systems havelargely considered their performance of any dispatching ruleobserved under these conditions will continue to hold whenthere are frequent disruptions.

This paper proposes an adaptive approach in which thedispatching rule selected at a given point in time is determinedby the existing state of the system. The required mapping rulesare constructed through an inductive learning approach. Thisapproach utilizes a set of training examples to construct theknowledge base in the form of a decision tree. There are twomajor advantages in using inductive learning. First, it can bereadily modified to incorporate system-specific attributes. Inso doing, it satisfies a major requirement of any schedulingapproach that can be implemented in a real system. Second,it has the capability of incremental learning that enables it toaccommodate new attributes as well as new dispatching rulesas they become available. It is, therefore, able to constantlyimprove upon its performance. While, theoretically, these twofeatures can be incorporated in many other approaches, suchas regression, the cost of doing so is usually quite high becauseit entails generating the dependence relationship afresh. Ininductive learning, however, the acquisition of incrementalknowledge can be incorporated in a modular fashion.

The proposed pattern-directed scheduling (PDS) method-ology is general enough to be used in a wide variety ofmanufacturing scenarios. In this paper, we illustrate the useof this approach for solving the mean tardiness problem in adynamic flexible manufacturing system (FMS). The extensiveprior research done on the tardiness problem provides a rich setof dispatching rules that can be used both for developing thePDS approach as well as providing a benchmark for evaluatingthis approach. In addition, an FMS typically provides a largernumber of distinct system states available. The experimentalresults obtained in this study show that the PDS approachis superior to the conventional approach involving a singlescheduling rule. Furthermore, its effectiveness increase in thepresence of random system disruptions.

This paper extends the adaptive scheduling methodologyproposed in Parket al. [29]. The analysis of PDS performanceover varying conditional factors of the manufacturing environ-ment is reported in Shawet al. [44]. The test-bed for the PDShas been extended from FMS to Flexible Flow Systems (FFS)under the minimizing flow time objective [30], [33], [31]. Themodel management aspects of scheduling decision supportsystem has been discussed in [33]. In this paper, first, weaugment the dispatching rule selection tree with a meta-tree in

order to reduce system nervousness. This meta-tree comprisesdecision rules that map the current state of the system to asmoothing constant which, in its turn, determines the thresholdlevel required for effecting any change in the dispatchingrule used. Second, we propose a systematic approach forincorporating incremental learning toward rule refinement inthe decision trees. Third, we extend the investigation ofthe relative performance of the proposed methodology tononstationary systems that are subject to frequent disruptions.Finally, PDS has been implemented in ancillary company thatmanufactures fuel delivery systems for passenger cars and lighttrucks to discuss the efficacy of using PDS approach in a realmanufacturing facility.

This paper is organized as follows. In Section II, we presentthe sets of system parameters and dispatching rules consideredin this study, and discuss the relevant results from previousresearch. In Section III, we first overview a generic inductivelearning approach, and subsequently, discuss the refinementsdeveloped in this study for the mean tardiness problem.We conclude this section with a discussion of the decisiontree generated and its ability to synthesize insights into theproblem. Section IV deals with the experimental evaluationof the proposed PDS approach. We compare the relativeperformance of PDS with those of some of the well-knownscheduling methods in a laboratory setting on some sampleproblems generated randomly. Next, in Section V we showthat the superiority of the PDS policy over the conventionalscheduling rules is carried to a real system as well. The majorresults of this paper are summarized in Section VI.

II. A DAPTIVE SCHEDULING

In this section, we develop the set of dispatching rules tobe considered in this study, as well as the set of system statedescriptors. In so doing, we also review the relevant resultsin dynamic scheduling.

A. Dispatching Rules

Dispatching rules differ in how they assign priority indicesto waiting jobs. Rules that have been found to be effective inprevious studies include 1) the Earliest Due Date (EDD) rule[2]; 2) the Shortest Processing Time (SPT) rule [2], [9]; 3)the Modified Job Due Date (MDD) rule [3], [38], and 4) theModified Operation Due Date (MOD) rule [1], [38]. While anumber of other rules have been proposed in the literature, wehave selected four rules that have been found to be effectivefor the objective of minimizing mean tardiness in the past [1].

B. System State Descriptors

The set of important system parameters to be considered isbased upon past research, and it includes both system and jobcharacteristics. These are now discussed.

1) Flow Allowance: This measures the lead time permittedto any job, and is, therefore, a measure of due date tightness. Atany point in time the (remaining) flow allowance, of jobis expressed as where and respectively,refer to the due date and the remaining processing time ofInthis study, the system descriptor is the average


flow allowance of all jobs currently in the system. To calculatethe expected value in the presence of nonparallel alternativemachines, we assume that each remaining operations of jobsare carried out by the best machine (since the processingtimes vary for each alternative machines). The impact ofonthe selection of the best dispatching rule has been discussed,among others, by [1] and [2].

2) System Utilization:From basic queuing theory, it isknown that job flow time, and therefore job tardiness aswell, depends upon the system utilizationAs documentedin Baker’s study, can increase or decrease the effectiveaverage due date tightness of jobs in a given system, In thispaper, is measured at any instant as the time-averaged valueof the ratio of the number of busy machines to the totalnumber of machines.

3) Contention Factor:The contention factor of any op-eration in any job is the number of alternative machinesavailable for processing it. It is well known that providingparallel servers can reduce system congestion and job flowtime. Wayson’s study [49] indicates that the contention factoralso alters the relative ordering of the various dispatching rulesin terms of their performance. At any instant, contention factor

for the system is the average of the contention factors of allunstarted operations.

4) Buffer Size:Many FMS’s are tightly constrained interms of the available buffer space When this constraintis binding, and particularly in the presence of job shop-like random material flows, various machines in the systemare likely to go through phases of blocking and starvingwhich adversely affect the system performance. The overallperformance of a dispatching rule is, therefore, likely to alsodepend upon its ability to minimize such instances. Conwayetal. [10] discuss the importance of buffer placement and its rolein determining job flow time, and therefore, job tardiness aswell. Note that is a design attribute; unlike other attributes,its value remains unchanged throughout the manufacturingprocess.

5) Relative Machine Workloads:It is well known that bot-tlenecks impact system performance critically. Ramanet al.[38] show that relative workload distribution can also impactthe selection of an appropriate scheduling rule. Two measuresare used in this study to determine relative machine workloads.

measures the ratio of the maximum work-load at any machine to the average workload. At any instant,these workloads reflect the remaining processing to be doneon the available jobs. The other measure is the normalizedstandard deviation of relative workload, expressed as the ratioof the standard deviation of individual machine workloadsto the average machine workload

6) Machine Homogeneity:This measures the variability inthe number of operations that individual machines can process.Machine homogeneity is expressed as the ratio of thestandard deviation of the number of operations that eachmachine can process to the average number of operationsthat a machine can process. In earlier studies [29], [44], thisparameter is found to play an important part for selecting theappropriate scheduling rule. is also a measure of machineflexibility [5]. In addition, higher values of generally lead

to lower coefficient of variation of processing times with aconsequent reduction in job flow time [45].

We make two observations here. First, the metrics used todescribe each parameter are clearly not unique. For example,machine homogeneity can possibly be expressed in severalother ways. Second, these metrics are not independent fromeach other. For example, impacts both and At higher

values, the number of operations waiting at any machineis higher. This tends to bring down the instantaneous valuesof both the standard deviation and the average number ofoperations that a machine can process. Similarly, becausethe utilization of the bottleneck machine is strictly less than100%, cannot increase indefinitely without a correspondingdecrease in as well.

C. Previous Results

Previous research on the dependence of scheduling ruledominance upon system parameters has considered three at-tributes: 1) flow allowance; 2) relative machine workloads; and3) contention factor. As mentioned earlier, this research haslargely considered stationary systems operating in the steadystate.

1) Flow Allowance: In the context of a job shop withbalanced machine workloads, Baker [1] shows that EDD issuperior when due dates are set loosely, and SPT performswell when they are tightly set. MOD performs the best for alarge range of intermediate values of MDD rates a closesecond to MOD across a wide range ofalthough it neveractually dominates it at any specific value of

2) Relative Machine Workloads:Ramanet al. [38] extendBaker’s investigation to also understand the impact of im-balance of machine workloads (which leads to one or morebottlenecks in the system) as well as variability in due dateassignment on the performance of dispatching rule. Theyshow that while MOD retains its effectiveness under balancedworkloads, there are crossovers between MOD and MDDwhen machine workloads are unbalanced. In particular, MDDis superior when due date tightness is low to moderatelyhigh, and when there is a greater variability in the due dateassignment. They also find that using an adaptive schedulingprocedure, which selects the dispatching rule based on machineworkloads, results in lower mean tardiness. In particular, theshop performance improves significantly if the dispatching ruleused at the bottleneck machine(s) is MDD, and MOD is usedat other machines.

3) Contention Factor:Shawet al. [44] find that, in the caseof balanced workloads, the relative performance of EDD andMDD improves with an increase in the contention factor. EDDremains the best rule at large values ofMDD is superiorto MOD at intermediate values, and MOD is the best rule atlow values. Furthermore, asincreases, the crossover betweenMOD and MDD, and between MDD and EDD occurs atincreasingly lower values of For a given value of thistrend is also observed asdecreases.

It is important to note that, in all these studies, a singlecross-over point exists between two dispatching rules whichreduces the number of system states to map to dispatching


rules. This result is significant in than it helps reduce thedimensionality of the state table (i.e., the number of differentconditions generated under the proposed inductive learningapproach) that is required for mapping the set of system statesto dispatching rules, because otherwise, the number of requiredmapping rules could increase exponentially with the numberof dispatching rules considered.

III. CONSTRUCTING A PATTERN-DIRECTED

SCHEDULING APPROACH

Given the set of dispatching rules, and the set of sys-tem descriptors, the third element of the adaptive schedulingpolicy, namely the set of transformation rules is developedthrough inductive learning. In this section, we first review thebasic concepts of inductive learning and next recapitulate theconstruction of the adaptive scheduling policy developed in[44].

A. Inductive Learning

Inductive learning can be defined as the process of inferringthe description (that is, the concept) of a class form the descrip-tion of individual objects of the class [44]. A concept to belearned in scheduling, for example, can be the most appropriatedispatching rule (a class) for a given manufacturing pattern.

A set of training examples is provided as input for learningthe concept representing each class. A given training exampleconsists of a vector of attribute values and the correspondingclass. A concept learned can be described by a rule determinedby inductive learning. If a new input data case satisfies theconditions of this rule, then it belongs to the correspondingclass. For example, a rule defining a concept can be thefollowing:

IF ( ) AND )THEN

where represents the th. attribute, and definethe range for and denotes the class. Shawet al.[44] employ inductive learning to derive selection heuristicsfor selecting the appropriate dispatching rules in a flexiblemanufacturing system. In this instance, the IF–THEN ruleis treated as aselection heuristicwhich is a conjunction ofattribute conditions collectively defining thepattern, andrepresents the best scheduling rule for that pattern.

An instance that satisfies the definition of a given conceptis called a positive example of that concept; an instancewhich does not do so is anegativeexample. In the dynamicscheduling problem, because there are several dispatchingrules which can potentially be selected, multiple conceptsneed to be learned, In this situation, the training examplessupporting the use of a given dispatching rule are treated as thepositive examples of that rule; training examples supportingany other rule are treated as negative examples.

Generalization and specialization are essential steps for theinductive learning process. A generalization of an exampleis a concept definition which describes a set containing thatexample. In other words, if a concept descriptionis moregeneral that the concept descriptionthen the transformation

form to is called generalization; a transformation formto is specialization. For a set of training examples, the

generalization process identifies the common features of theseexamples and formulates a concept definition describing thesefeatures; the specialization process on the other hand, helpsrestrict the coverage of features for a concept description.Thus, inductive learning can be viewed as the process ofmaking successive iterations of generalizations and specializa-tions on concept descriptions as observed form examples. Thisprocess continues until an inductive concept description whichis consistent with all the training examples is found. Thusthe generalization to specialization relations between conceptdescriptions provide the basic structure to guide the search ininductive learning. For a given problem, applying the inductivelearning process can contribute to one s understanding of thedecision process on the following three dimensions [44]: 1)Predictive validity: the ability to predict the decision outcomefor a given data base; 2)Structural validity: the ability tocapture the underlying structure of the decision process; and3) Identifying validity: the ability to infer the most criticalattributes in the decision process.

These features of inductive learning make it useful in deal-ing with the scheduling problem. If we can make an inductivelearning system observe the effects of various schedulingdecisions on the manufacturing processes and the resultingscheduling performance, then it can: 1) predict the schedulingoutcome for a given manufacturing process in a specified setof manufacturing conditions (predictive validity), 2) capturethe underlying decision structure of the scheduling process(structural validity), and 3) identify the critical manufacturingattributes for the scheduling decision process (identifyingvalidity).

The input to an inductive learning algorithm consists ofthree steps: 1) A set of positive and negative examples; 2) a setof generalization and other transformation rules; and 3) criteriafor successful inference. Each training example consists of twocomponents—a data case consisting of a set of attributes, eachwith an assigned value; and the classification decision made bya domain expert according to the given data case. The outputgenerated by this inductive learning algorithm is a set of deci-sion rules consisting of inductive concept definition for eachof the classes. Learning programs falling into this category in-clude AQ15 [25], PLS [39], and ID3 [35]. These programs arereferred to as similarity-based learning methods. Shawet al.[43] compare the above three inductive learning programs interms of their algorithmic designs and classification accuracy.They find that ID3 and PLS are able to classify more accuratelythan AQ15; they are also more efficient computationally andare better able to handle noisy data. In this research, we useC4.5 [36] which is a refinement of the ID3 program. The learn-ing process in C4.5 follows a sequence of specialization stepsguide by aninformation entropy functionfor evaluating classmembership. The concept description generated by a learningprocess can be represented by adecision tree. The nodes of thetree represent conditions set of attribute values; each branchcorresponds to a disjunctive normal form expression.

The resulting decision tree from the inductive learningemployed to map system states to a dispatching rule is a


partition of the state space into a number of hyperrectangles(open or closed) each associated with the best dispatching rule.The surface of this description space is a hyperplane that isorthogonal to the axis of the given attribute and parallel to allother axes. Suppose the intended division of the descriptionspace is by an oblique hyperplane, C4.5 has to improve theapproximation of such oblique division by a collection ofrectangles at the expense of a substantial increase in thenumber of rectangles. This is a limitation of C4.5, and theremedy would be to look for some arithmetic combination ofthe attributes. To incorporate general arithmetic combinationswould require, yet, the kind of extensive search carried outby programs like BACON [22], MARS [15], and ABACUS[13]. Even the limited generalization to linear combinationscan slow down the process of building trees by an order ofmagnitude [37].

There are a large variety of discriminant analysis methodsfor generating hyperplanes [11], [18]. Classical statistical dis-criminant analysis methods include Fisher’s original method[14] and the logistic model [42]. To overcome the typesof assumptions often hard to satisfy in classical statisticalprocedures, mathematical programming models are developed[7], [17], [20]. In addition, Koehler and Majthay [21] attemptto generalize the ID3 by merging linear discriminant methodsin their NEWQ algorithm.

From the previous PDS experience [28], the quality ofthe decision tree we obtained from inductive learning wasrelatively satisfactory. Since this paper extends the features andefficacy of dynamic scheduling capability of PDS, we leavethe employed inductive learning algorithm C4.5 untouched.Perhaps, in subsequent studies, it is worth while to compare theimproved performance of PDS using the knowledge obtainedfrom hybrid of inductive learning and linear or nonlineardiscriminant analysis methods generating general hyperplanes.

B. Pattern-Directed Scheduling

Because the proposed scheduling approach determines thescheduling rule on the basis of dynamically changing manufac-turing patterns, i.e., the combination of system attributes, werefer to it aspattern-directed scheduling(PDS). In the generalcase, it can be represented by the 5-tuple .

denotes the set of scheduling objectives;is the set ofmanufacturing patterns, each pattern described by a conjunc-tion of system attributes; represents the set of candidatescheduling rules; denotes the set of transformation heuristicsfor selecting best scheduling rule. Each rulein is in theform is the set of possible systemstates when which can be supportedby occurs, the decision rule selected by is activated.

There are rich collections of literatures of control theoreticmodels of FMS which share the ideas of this study. Thecontrol theory paper by Rishel [40] describes that the solutionof the optimization problem divides the continuous part ofthe state space into regions each of which is associated witha different feedback law. Olsder and Suri [26] proposeda dynamic programming model to describe the disruptivenature of machine failures while showing that the state spaceis divided into regions, and that the optimal decision is

determined by the region that the state is currently locatedin. Kimemia and Gershwin [19] modeled the behavior ofthe FMS between failures and repairs as a continuous-time,mixed state dynamic programming problem. The solutionhas three components: the long-term calculation of valuefunction which is equivalent to determining the regions in statespace; the mid-term calculation of the current production ratewhich is performed by determining which region the state iscurrently in; and the short-term dispatch of parts [16]. Notethat the bulk of the stochastic dynamic programming/controltheory literature dealing with the planning and scheduling ofstochastic dynamic systems deals with flexible flow systems inwhich all parts follow the same route through the systems (orthere is at least a dominant processing route). In these systems,the scheduling decision (typically made at the lowest levelof a hierarchical policy such as one proposed by Kimemiaand Gershwin) relates only to the dispatching of parts intothe system. On the other hand, in the system studied here,we consider multiple and random part processing routes. Thisrequires us to in address the sequences in which parts areproduced at each machine in the system.

The features of PDS’s dynamic rule change and rule refine-ment are similar to that of reinforcement learning. Reinforce-ment learning often involves two difficult subproblems: tem-poral credit assignment problem and generalization problem orstructural credit assignment problem [23]. PDS’s adjustmentof scores of each dispatching rule is similar to the temporalcredit assignment problem that figures out how to assign creditor blame to each individual situation to adjust its decisionmaking and improve its performance. The rule refinement partof the PDS shares an idea with the generalization problemthat a learning agent must guess about the new situationsbased on experience with similar situations when the problemspace is too large to explore. Rich literatures can be found inreinforcement learning area [4], [46], [8], [24], [23], [48].

The design of the PDS approach comprises three stages: 1)The learning stage; 2) the schedulingstage; and 3) the rulerefinementstage. These are now described.

C. The Learning Stage

The learning stage consists of two elements: 1) the trainingexample generator and 2) the learning module. The trainingexample generator provides the set of positive and negativeexamples pertaining to the various scheduling rules studied.An example can be represented as a 4-tuplewhere represents a scheduling objective, anddenotesthe dispatching rule that performs the best among all rules in

for this objective under the pattern If follows that isa positive example of and a negative example of all rulesin Because the analytical evaluation of dispatchingrules in dynamic systems is hard to carry out, we use computersimulation for the purpose of generating training examples.Although it is desirable for the set of examples generatedinitially to be as comprehensive as possible, the size of the statespace clearly precludes its complete coverage. However, aswe discuss later, the criticality of this requirement is mitigatedbecause of rule-refinement.


Fig. 1. Ther-tree.

The learning module employs an inductive learning algo-rithm on the training examples to generate the set of heuristicselection rules that describe the dependence between manu-facturing patterns and the dispatching rules. This dependenceis typically expressed as

Pattern Dispatching rule

An example of such a heuristic selection rule derived from anexperiment described in Parket al. [29] is as follows:

IF

THEN

This rule requires that if the current system attributes indi-cate unbalanced machine workload, a normalized workloadstandard deviation equal to 0.519, flow allowance

less than 3, and system utilization level less than93%, the appropriate dispatching rule to apply is the shortestprocessing time rule. The subscriptis used to accommodatethe situations when there are several patterns which ar allsuitable for applying the same rule.

These selection rules are typically stated in the form of a de-cision tree, henceforth the-tree, whose leaf node correspondsto a scheduling rule while the path from the root node to thisleaf gives the conjunction of various system attributes thatcollectively represent the manufacturing pattern. The-treegenerated in this study is shown in Fig. 1. As Shawet al. [44]note, an important aspect of the-tree is its ability to highlightthe relative importance of the system parameters in influencingthe selection of the appropriate dispatching rule. The higherthe parameter in this tree, the greater is its contribution indetermining the dispatching rule.

D. The Scheduling Stage

The selection rules obtained in the learning stage are hybridswith manufacturing patterns as preconditions, and the appro-priate dispatching rule as the resulting action. The schedulingstage implements the heuristic selection rules in real time.Whenever a scheduling decision is to be made, the current stateof the system is observed, the existing pattern is compared withthe preconditions of the matching hybrid, and the associateddispatching rule is used for assigning priorities to the waitingjobs.

Preliminary experiments with the PDS approach indicatedthat, in order to be effective, it should be able to filter outtransient patterns [44]. Overreaction to these patterns leadsto system nervousness and performance degradation. Manyproduction systems may always be in transient state becausethey constantly switch from one group of orders to anothergroup which may have a totally different characteristics. Evenin such a case, filtering scheme provide the best dispatchingrule to stick to use so that the relative performance is asgood as that of the best dispatching rule. If transient patternsbecomes permanent,however, PDS’s filtering scheme providesnecessary adjustment of the dispatching rule to use, thusopportunistically performs better that sticking to the singledispatching rule.

The implemented system incorporates two procedures to inorder to minimize overreaction to transient patterns: 1) treepruning; and 2) the use of a smoothing mechanism. Treepruning aims at improving the parsimony of the heuristicselection rules. Starting with the initial, and possibly large,tree, it discards one or more subtrees and replaces themwith the most frequent class (more specifically, the bestdispatching rules dominant in numbers of supporting trainingexamples) because it would leads to a lower predicted errorrate—the ratio of the number of erroneous examplesoverthe number of correctly classifying examples Pruningalways increases error for classifying training examples withan expectation to result in better prediction accuracy for theunseen test examples. The stopping condition of this pruningprocess is when it hits the upper limit of the probability oferror, which is obtained by naively observing E


events in N trials which follows the binomial distribution [37].CF is a given confidence level.

Smoothing is achieved by using a procedure which main-tains a cumulative score of the number of occasions a givendispatching rule is favored. When a scheduling decision isto be made, the rule with the maximum cumulative scoreis selected provided this score is above a certain threshold.Suppose that the dispatching rule being used currently iswith a cumulative score of At the point of scheduling, thisscheme will select rule if it exists, where

and

and is a smoothing coefficient; otherwise it will continue us-ing rule Clearly, higher values lead to increased robustnessat the expense of system responsiveness. Experimentation withvarious values revealed that it should be allowed to adapt tothe prevailing pattern instead of fixing it at a predeterminedvalue. This is done by generating a decision tree, henceforththe -tree, for selecting the appropriate value ofin a mannersimilar to the generation of the-tree. the -tree generated inthis study is shown Fig. 2.

The implementation of PDS in real time requires sequentialconsideration of these two trees. Whenever a scheduling deci-sion is required, PDS first selects the appropriatevalue fromthe current manufacturing pattern and-tree, and determinesthe required smoothing threshold. The-tree is next queried toupdate the scores for all scheduling rules, and in conjunctionwith the specified threshold, to determine the appropriatescheduling rule to use. Suppose, the current manufacturingpattern is described by 70% system utilization, 0.47 machinehomogeneity, flow allowance factor of 3, and 0.2, thevalue of becomes 0.8. In this case, the suggested best rulewill be MDD. However, if the current rule being used is MODand its cumulative score is 5 whereas that of MDD is 2, norule change occurs but the score of MDD becomes 3. Nexttime, the same manufacturing pattern exists, the score of MDDbecomes 4 and the rule changes to MDD from MOD (0.8*

).It is important to note here that, because the training exam-

ples are driven by simulation experiments, the appropriatenessof a dispatching rule for a given pattern is determined byits steady state average performance over the length of thesimulation run. Its implementation during real time schedulingis, however, based on the pattern which is observed at theinstant a scheduling decision is to be made. while a dispatchingrule may perform well in the long run for a given setof attributes, it need not necessary be effective when it isapplied on a rolling basis on transient patterns. This is animportant structural limitation is partially mitigated by theuse of smoothing constant which helps in smoothing out thetransient patterns.

E. The Rule Refinement Stage

The rule refinement stage provides a control mechanism forthe purpose of insuring an acceptable scheduling performancelevel. This stage monitors the quality of the schedules gener-ated at the second stage by comparing its performance with

Fig. 2. The�-tree.

those obtained by repeatedly applying each dispatching rulein individually, under a variety of scenarios. Higher meantardiness values under PDS indicate deficiencies that needcorrection. These deficiencies could be caused, for example,by not considering a large enough set of training examples. Asnoted earlier, it is difficult for the set of training examples to becomprehensive in view of the vastness of the system attributespace. Consequently, the heuristic selection rules imbedded inthe -tree and -trees are overgeneralized to some extent. Ifthis results in performance degradation, then these trees needto be refined.

Formally, let denote the set of training examples gener-ated until stage An example is tuple where

represents a pattern, is the set of allpatterns investigated through stageand is the dispatchingrule found appropriate for Let denote the set of rulesimbedded in the-tree through stage and let Forany rule let be the set of supportingtraining examples, where is the set of patterns considered


Fig. 3. Layout of the Test System.

in these examples and is the resulting dispatching rule. Theinductive learning algorithm insures that

and

Note, however, that as a result of the imbedded generalizationin the algorithm, the system attribute state space covered by

is such that

If is not a complete representation of then overgen-eralization occurs resulting in a prediction error.

The rule refinement procedure identifies all such instancesof incomplete representations, and augments the decision treeby generating additional rules appropriately. The metric usedfor rule refinement isprediction accuracy that measures theproportion of testing instances in which the scheduling ruleselected by the -tree turns out be the one that performs thebest among all rules in when implemented individually. Ona random sample of test problems, ifis found to be less than

the prespecified target prediction accuracy level, then thelearned rules are refined following a three-step process. First,the deficient rules in the-tree are identified; next, additionaltraining examples are generated in order to specifically addresspreconditions manifest in the deficient rules. In the final step,the inductive learning algorithm is employed to update the treeon the basis of the additional information provided by theseexamples. The process of generating the testing instances,evaluating on these instances, and refining the tree is carriedout iteratively until the desired prediction accuracy is achieved.This method is formally stated below; a detailed descriptionfollows subsequently.

Algorithm Refine Rule

Step 1. Initialization: Set at the initial decisiontree, and the patterns considered for constructing this tree.Go to Step 2.

Step 2. Testing Example Generation:

a) For each determine andDetermine the set of testing patterns suchthat

b) Generate set consisting of testing examples ob-tained by performing simulation runs on for eachdispatching rule in Go to Step 3.

Step 3. Termination:

a) Determine the prediction accuracyby using onb) IF THEN stop or go to Step 2 for evaluating

next testing set. ELSE, go to Step 4.

Step 4. Iteration:

1) For each determine the set of testing patternsfor which is not found to be the best dis-

patching rule. Letbe the corresponding set of testing examples wheredenotes the subset of patterns for which the best dis-patching rule was found to be

and is the number of such subsets.2) For each generate a set of rules using the

inductive learning algorithm with as the set oftraining examples.

3) Identify suspicious regions and

Step 5. Additional Training Example Generation:Generateset consisting of additional training examples obtainedby performing simulation runs on for each dispatchingrule in

Step 6. Refined Rule Generation:Generate a set of rulesusing the inductive learning algorithm with

as the set of training examples, and go to Step 3.The testing examples used in Step 2 of this procedure

considers the subspace that is not covered by the trainingexamples in order to check the occurrence of any incompleterepresentations. Such an occurrence is indicated if, for anysubspace, the dispatching rule found dominant in the testingexamples is different from the one indicated by the current


Fig. 4. Initial r-tree for the Test System.

-tree. If the proportion of such occurrence is higher than theacceptable level, this subspace is divided in Step 4 into smallersubspace; each of these smaller subspace being dominated inthe testing examples by a different dispatching rule. The-tree is accordingly updated, and at the next iteration, the testingexamples used address the possibility of overgeneralization forthe new rules added at the current iteration. The attribute sub-space covered by the testing examples consequently reducesat each iteration, thereby guaranteeing the convergence of thisalgorithm. (Also see [6], [34], [41], [47], [32], and [12].)

For example, the initial decision tree in Fig. 4 was obtainedfrom 37 training examples (Step 1) among which followingthree training examples belong to the first rule:

RULE 1: IF contention-factor 2.139 AND 0.298THEN

Training examples for RULE 1 (erroneous example isincluded):

flow-allowancecontention-factorsystem-utilization

Then following 5 testing examples are generated (Step 2).Testing examples for RULE 1:


Since the error (Step 3) is higher than the threshold (totalprediction error should be calculated for the overall testingexamples), Step 4 is initiated. In Step 5, following 3 additionaltraining examples are added in regard to Rule 1.

Fig. 5. Ther-tree after Rule Refinement for the Test System.

TABLE IIMPACT OF RULE REFINEMENT

Additional training examples for RULE 1:


The resulting -tree after refinement is shown in Fig. 5 (Step6). Note that new -tree correctly predicts previous testingexamples.

IV. EXPERIMENTAL STUDY

Three sets of experiments were conducted to evaluate theperformance of the PDS approach. The first set addresses


TABLE IIPERFORMANCE OF PDS UNDER STATIONARY CONDITIONS


TABLE IIISUMMARY OF RESULTS FOR THENONSTATIONARY SYSTEM

the performance improvement obtained by rule refinementfor randomly generated problems in a dynamic stationaryFMS. The second set considers a nonstationary FMS that issubject to random system “disruptions” in the form of machinebreakdown, increase in job arrival rate, introduction of tightdue date jobs. The levels of disruptions are controlled by themagnitude the duration and the frequency As in thefirst set, the problems considered here are randomly generated.The third set addresses the efficacy of using the PDS approachin the context of a real manufacturing facility that producesfuel-delivery subsystems to auto companies. In this section,we discuss the first two sets of experiments; the third set isdealt with in Section V.

The PDS system is implemented on VAX 8800 VMSenvironment, IBM 3090 CMS environment, and DecStation5000/200 Ultrix environment. Simulation module was writtenin SLAM II simulation language. Inductive learning modulewas written in C (at this moment, learning module is off-line).Each simulation run and knowledge induction takes less than2 minutes.

A. The Stationary System

In the first set of experiments, we consider an FMS withfour workcenters. Each workcenters is provided with a bufferof size ranging from 9 to 16; we also consider the case inwhich the buffer size is unlimited. Jobs arrive at the systemfollowing a Poisson process. Upon its arrival, each job isassigned the number of required operations randomly from auniform distribution The nominal operation processingtime is sampled from an exponential distribution with a meanof 100. Since workcenters are not identical, the penalty beingprocessed at the less desirable machine is given as 10%of the given operation processing time. Each operationisassigned a contention factor selected randomly from theuniform distribution . Operation-to-machine assignmentis varied in individual experiments to yield varying valuesof in the range (0.00, 0.82). Each arriving jobis assigneda due date where and denote,respectively, the arrival time, total processing time and theflow allowance of . is sampled from a uniform distribution

Job inter-arrival times are varied to yield overallsystem utilization of 50%, 70%, 80%, and 90%, respectively.

The nominal operation times are varied randomly in order toyield values of in the range (1.4, 3.1) and in the range(0.19, 1.2). No workcenter breakdowns are considered in thisset. The set of dispatching rules considered includes SPT,EDD, MOD, and MDD.

The experimental results are shown in Tables I and II.Table I shows the stagewise improvement in prediction ac-curacy that results from rule refinement given a targetprediction accuracy 0.9. It can be seen from this tablethat successive application of algorithmRefineRule improveboth the average and the worst-case performance of

Table II gives the mean tardiness values obtained undereach dispatching rule and the PDS approach. In this table,BEST refers to the dispatching rule among all rules inthatperforms the best for the corresponding scenario. Across thevarious scenarios considered, PDS results in mean tardinessvalues that are on average lower than EDD by 8.6%, MOD by29.8%, MDD by 7.8%, and BEST by 4.4%. Relative to BEST,it produces lower mean tardiness values in 12 cases, the samevalues in 41 cases, and larger values in 5 cases. It is importantto note that, in a dynamic system, the BEST scheduling rulecannot be determineda priori. The results shown in Table Iindicate that, even if this rule were known, its performancewould still be inferior to that of PDS.

B. The Nonstationary System

In the second set of experiments, we introduce disruptionsin the base system described in Section IV-A. Four types ofdisruptions are considered: 1) machine breakdowns, this resultsin a negative change in values; we also consider positivechanges in to reflect the availability of an additional machineafter repair; 2) sudden increase in job arrival rate, this results inan increase in system utilization; 3) arrival of rush jobs withshorter due dates, this decreases the average flow allowancewe also include positive shifts in to represent job with looserdue dates; and 4) shifting bottlenecks resulting from a changein the mix of jobs arriving at the system, this leads to a shiftin the relative machine workloads With each disruption,we associate three parameters—the magnitude of shift in theaverage value denoted by the duration of disruption, andthe number of disruptions during the length of the simulationrun. and are related to the total length of the simulationrun according to where measures thelength during which the system is in its original steady state.A total of 71 combinations of these three parameters andthe four types of disruptions were considered; the results aresummarized in Table III. The individual combinations and thedetailed experimental results are shown in Tables IV throughVII; in these tables, indicates the percentage improvementobtained by using the PDS approach over the best among theindividual dispatching rules.

Table III indicates that the relative superiority of PDSincreases further in a nonstationary system. In fact, it yieldedlower mean tardiness values than each of the dispatching rulesin all 71 instances. It also performs substantively better thanthe BEST rule across all four types of disruptions. (It is inter-esting to note that, among the dispatching rules, MDD clearly


TABLE IVPERFORMANCE OF PDS UNDER SHIFT IN FLOW ALLOWANCE

appears to be the most robust.) These results also indicate that,even more so in a nonstationary system, the ability to merelya priori predict which dispatching rule is likely to perform thebest is not good enough; the overall system performance canbe improved by systematically adapting to these disruptionsas they occur.

Among the four types of disruptions studied, the relativeperformance of PDS is best under shift in flow allowanceTable IV indicates that in this case, generally increases withan increase in the duration of the disruption. It is seen toincrease with the frequency of disruptions as well, especiallyat higher values. is also sensitive to is higher fornegative values, and larger increases inresult in lower

The relative performance of PDS is markedly superior forshifts in the contention factoras well. As seen from Table V,

increases with an increase in and generally, with anincrease in as well. As indicated in Table VI, the impact of

on is less pronounced. In this case,is seen to dependupon the magnitude of disruption; the difference betweenPDS and the best rule is higher when the disruption resultsin increasingly higher utilization. Table VII shows that, withrespect to disruptions in relative loading values increaseswith an increase in especially at higher values. The impactof other parameters is somewhat mixed.

Overall, in the nonstationary case, PDS performs betterwhen there are a large number of switches in scheduling


TABLE VPERFORMANCE OF PDS UNDER SHIFT IN CONTENTION FACTOR

rules. While this result appears to contradict the study ofShawet al. [44] who found that PDS performs best when thenumber of dispatching rule changes is in the medium range,it must be understood that the underlying cause for theseswitches is different in these two studies. In the stationarysystem operating under steady state conditions considered byShawet al., instances that resulted in a large number of ruleswitches were those in which tardiness values were small anddifferences between the various rules were marginal. On theother hand, for the nonstationary system addressed in thisstudy, an increase in the number of rule switches is associatedwith higher disruption frequencies.

PDS is generally superior as the system becomes moreconstrained because of disruptions especially in regard to

tighter due dates and higher system utilization.This is animportant result in that the disruptions faced by real systemsare largely of these two types. However, the implementationof PDS in real time is likely to further improve the ability of aflexible manufacturing system to effectively meet other typesof disruptions as well.

V. IMPLEMENTATION OF PDS IN A REAL SYSTEM

In this section, we discuss the implementation of the PDSapproach in an auto ancillary company that manufacturesfuel delivery systems for passenger cars and light trucks.This facility produces 41 different products on two identicalmanufacturing lines. Although the operations are driven by amonthly production schedule, there are frequent changes in this


TABLE VIPERFORMANCE OF PDS UNDER SHIFT IN SYSTEM UTILIZATION

TABLE VIIPERFORMANCE OF PDS UNDER SHIFT IN RELATIVE WORKLOADS

schedule that result in expediting some orders and delayingthe due dates of other orders.

Fig. 3 gives the layout of the facility. Each manufacturingline consists of two stages—tube cutting and tube forming.The processing time for the tube cutting operation is 36

seconds (The actual processing time values are suppressed;the numbers shown here are representative of the actualfigures.) for all products at each of the two cutters availableon each line. Tube forming is done on one of 11 identicalmachines available; the tube forming time depends upon the


tube geometry and it varies from 60 seconds to 105 seconds.Formed tubes are subsequently sent to the welding stagecomprising two welding machines. The welding time is 30seconds for small tubes and 42 seconds for large ones.

Depending upon the composition of the orders, the systemutilization varies form 30% to 80%. A range of due datetightness is achieved by allowing flow allowance factor to varybetween 2 and 12. The size of buffer available at each benderis 120 while it is virtually unrestricted for cutters and welders.Machine workloads and the average contention factor at anypoint in time depend upon the composition of jobs present inthe system at that instant. Based on the processing times andthe past demand data, the relative machine workloadis seento vary between 1.2 and 3.0, while varies between 0.1and 0.8. The contention factor for the overall system rangesbetween 1.9 and 2.6.

For the purpose of this set of experiments, the thresholdlevel of prediction accuracy was set to 0.9. The-tree turnsout to be a singleton with performing the best in 20of 21 training examples. The-tree generated initially from37 training examples comprised 6 selection rules as shown inFig. 4. When tested on 18 scenarios, it yielded a predictionaccuracy of 77.8%. At this stage, 12 new training exampleswere added for the purpose of rule refinement. Augmentingthe -tree appropriately resulted in 8 selection rules and0.944; since the desired prediction accuracy was achieved, nofurther refinement was carried out. The final-tree is shownin Fig. 5.

Similar to the computational study described in Section IV,two sets of experiments were conducted to evaluate PDSrelative to other scheduling rules. The first set evaluated PDSunder stationary operating conditions. In order to capture theimpact of frequent changes in order due dates, the secondset of experiments allowed random shifts in the mean flowallowance value. The experimental results for these two setare shown in Tables VIII and IX, respectively.

Table VIII confirms the overall superiority of PDS observedin the earlier experiments for the stationary case. Relative tothe BEST rule, PDS is found to be better in 6 of 21 problems,equal in 11 problems, and worse in 1 problem. On average,it improves the mean tardiness values obtained under STP by16.3%, EDD by 4.6%, MDD by 1.7%, MOD by 20.5%, andBEST by 0.8%.

Table IX shows that PDS continues to be increasinglysuperior in the nonstationary case. It is better than the BESTrule in all 11 cases. Relative to PDS, SPT yields 4.6% higherthan mean tardiness, and the corresponding figures for EDD,MDD, MOD, and BEST are 6.0%, 7.2%, 6.2%, and 1.3%,respectively. Furthermore, its performance tends to improvewith an increase in the frequencyof disruptions.

VI. CONCLUSION

This paper develops an adaptive scheduling policy fordynamic manufacturing systems. The main feature of thispolicy is that it tailors the dispatching rule to be used ata given point in time to the prevailing state of the system.The rule selection logic is imbedded in a decision tree that

TABLE VIIIPERFORMANCE OFPDS FOR THE TEST SYSTEM: THE STATIONARY CASE

is generated by applying an inductive learning algorithm on aset of training examples. The inductive learning methodologyalso enhances one s understanding of the real time schedulingdecision along three dimensions. First, it provides predictivevalidity by increasing the decision maker s ability to predict theappropriate dispatching rule for a given state of the system.In so doing, this study extends Baker’s [1] work regardingthe dependence of dispatching rule performance in systemparameters. Second, it lends structural validity through thedecision rules that map system parameters to the dispatchingrule. Third, it provides identifying validity by highlightingthe critical system attributes; the higher an attribute is in thedecision tree, the more important it is for determining thedispatching rule.

Experimental studies dealing with a stationary FMS con-firm the superiority of the suggested PDS approach over thealternative approach that involves the repeated application ofa single dispatching rule previously found in Shawet al. [44].In addition, this study shows that, for randomly generated testproblems as well as a real system, the relative performance im-proves further when the system is nonstationary. In particular,PDS performs better when there are frequent disruptions, andwhen disruptions are caused by the sudden introduction of ur-gent jobs and machine breakdowns—two of the most commonsources of disruptions in most manufacturing systems.

From an operational perspective, the most important char-acteristics of the PDS approach are its ability to incorporatethe idiosyncratic characteristics of the given system into thedispatching rule selection process, and its ability to refine itselfincrementally on a continuing basis. The first characteristichighlights the fact that the decision trees are system specific,and emphasize the need, on a part of the decision maker, topursue ascheduling policy(such as PDS) instead of using asingledispatching rule.The second characteristic insures that


TABLE IXPERFORMANCE OF PDS FOR THE TEST SYSTEM: THE NONSTATIONARY CASE

decision trees are self correcting and current. As discussedearlier, all selection rules imbedded in the tree are overgener-alized to some extent. If this results in inferior performance,then the trees need to be augmented with additional rules.Furthermore, while the set of system parameters and the setof dispatching rules considered for generating the trainingexamples need to be comprehensive, they change over time asnew parameters are added, and new dispatching rules becomeavailable. The built-in rule refinement procedure, when usedin conjunction with periodica posterioricomparisons of PDSwith other dispatching rules, insures that the selection rulebase is maintained efficiently.

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Sang Chan Parkreceived the M.B.A. degree fromthe University of Minnesota, Minneapolis, and thePh.D. degree in MIS from the University of Illinois,Urbana-Champaign.

After six years serving at the School of Business,University of Wisconsin, Madison, as an AssistantProfessor in MIS, he joined the Department ofIndustrial Management, Korea Advanced Instituteof Science and Technology. His research interestincludes the application of artificial intelligence,especially machine learning methodologies, to the

design of knowledge-based systems for various management principles. Hehas expanded his research domain into Total Quality Management/QualityInformation Systems, and CALS as well. He has published in the areasof FMS scheduling, process planning, library information systems, BPR,construction management, workflow analysis, and financial engineering. Hehas contributed papers to the IEEE TRANSACTIONS ON SYSTEMS, MAN, AND

CYBERNETICS, Information Processing and Management, theCanadian Journalof Civil Engineering, Annals of OR, the European Journal of OR, DSS,International Journal of Technology Management, and theIIE Transactions.

Narayan Raman received the Bachelor’s degreein mechanical engineering from the Indian Instituteof Technology, the PGDM (M.B.A.) degree fromthe Indian Institute of Management, and the Ph.D.degree from the University of Michigan, Ann Ar-bor.

He is a Member of Technical Staff of LucentTechnologies Bell Laboratories, Holmdel, NJ. Hehas worked in the areas of new product develop-ment, manufacturing, material planning and pur-chasing. His current research interests are in the

areas of supply chain design, planning and scheduling flexible manufacturingsystems, design of production flow lines, and simultaneous determination ofproduct design and process flexibility for new product introduction.

Dr. Raman is a member of INFORMS and a member of the Editorial Boardof the International Journal of Flexible Manufacturing Systems.

Michael J. Shaw is a Professor of informationsystems with the Department of Business Admin-istration, University of Illinois, Urbana-Champaign.He has been a faculty member since 1984. He isalso a senior research scientist with the NationalCenter of Supercomputing Applications (NCSA)and a research faculty member at the BeckmanInstitute for Advanced Science and Technology. Hisresearch concerns information technology, manu-facturing decision support, business process design,intelligent decision support systems, and electronic

commerce. He has published widely in academic journals.Dr. Shaw served as Guest Editor of Special Issues forIIE Transactions

(on System Integration), theDecision Support Systems Journal(on MachineLearning Methods), theGroup Decision and Negotiation Journal(on Enter-prise Integration), theInternational Journal of Flexible Manufacturing Systems(on Information Technology for Manufacturing Enterprises), theAnnals ofOperations Research(on Artificial Intelligence for Management Science),and theJournal of Organizational Computing(on Enterprise Modeling andKnowledge Management). He is currently on the Editorial Boards of theInformation Systems Research, IIE Transactions, International Journal ofFlexible Manufacturing Systems, Decision Support Systems, InternationalJournal of Business Studies, and the International Journal of IndustrialEngineering. He was a Fulbright Research Fellow visiting National TaiwanUniversity in 1996. He is currently a member of the Board of Directors ofINFORMS.

adaptive scheduling in dynamic flexible manufacturing systems: a dynamic rule selection approach

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