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An investigation of dynamic group scheduling heuristicsin a job shop manufacturing cellFARZAD MAHMOODI a , KEVIN J. DOOLEY b & PATRICK J. STARR ba Dept. of Management , Clarkson University, The School of Management , Potsdam, NY,13699, USAb Dept. of Mechanical Eng , University of Minnesota, Industrial Eng. Division , 111 Church StSE, Minneapolis, MN, 55455, USA.Published online: 30 Mar 2007.

To cite this article: FARZAD MAHMOODI , KEVIN J. DOOLEY & PATRICK J. STARR (1990) An investigation of dynamic groupscheduling heuristics in a job shop manufacturing cell, International Journal of Production Research, 28:9, 1695-1711, DOI:10.1080/00207549008942824

To link to this article: http://dx.doi.org/10.1080/00207549008942824

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INT. J. PROD. RES., 1990, VOL. 28, No.9, 1695-1711

An investigation of dynamic group scheduling heuristics in a job shopmanufacturing cell

FARZAD MAHMOODlt, KEVIN 1. DOOLEyt, andPATRICK 1. STARRt

The objective of this study is to develop dynamic scheduling heuristics for cellularmanufacturing environments (group scheduling or family heuristics)and comparethem with existing family heuristics under various shop floor conditions. Theproposed family heuristics stress good due date performance while reducingoverall set-up time. Computer simulation is used to test three queue selection rulesin conjunction with three dispatching rules under eight experimental conditionsin a job shop cell. The results indicate that several of the proposed heuristicssubstantially improve the performance of the cell over the best previouslysuggested family heuristic under all experimental conditions.

1. IntroductionCellular manufacturing, one of the applications of group technology, involves

processing COllections of similar parts on dedicated clusters or 'cells' of dissimilarmachines. Cellular manufacturing provides an attractive alternative for manu­facturingjob shops (Burbidge 1975, Black 1983), and numerous case studies of actualimplementations indicate a substantial increase in efficiency (Allison and Vapor 1979,Droy 1984).

The general argument is that the total time required to set-up the machines isreduced since cells process similar parts. This provides the opportunity to reduce lotsizes, which leads to reduced work-in-process inventory and shorter manufacturinglead times. Furthermore, tool storage and control procedures are simplified. Otherbenefits mentioned in the literature are: reduced expediting, improved humanrelations, improved operator expertise, reduced material handling (Greene andSadowskis .1984), and better quality (Suresh and Meredith 1985). Possible dis­advantages are reduced machine utilization and shop flexibility (Greene andSadowski 1984).

To reduce the disadvantages of cellular manufacturing and enhance the possibilityof a successful implementation, many authors have proposed changes in cell operationin addition to the usual cell layout and grouping of parts. The most recommendedoperational change concerns scheduling rules which are based on the unique featuresof cellular manufacturing (Flynn 1987, Mosier and Taube 1985, Sinha and Hollier1984, Vaithianathan and McRoberts 1982, Ham et al. 1979). This is becausescheduling rules can embellish the advantages of cellular manufacturing by furtherreducing the overall machine set-up time and at the same time diminish its dis­advantages by adopting to a more diverse range of part families (Lee 1985).

Revision accepted October 1989.t Clarkson University, The School of Management, Dept. of Management, Potsdam, NY

13699, USA.t University of Minnesota, Dept. of Mechanical Eng.• Industrial Eng. Division, III

Church St SE, Minneapolis, MN 55455. USA.

0020-7543/90 ssoo © 1990 Taylor & Francis Ltd.

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Flynn and Jacobs (1986, 1987) demonstrated, via simulation, that althoughcellular manufacturing shops exhibit superior performance in terms of average set-uptime and average move time, the traditional job shop structure had superiorperformance in average queue lengths, average job waiting time, and average jobflow time. They concluded that a well-organized traditional job shop may be ableto achieve overall performance that, at least, is comparable to that of the same shopusing cellular layout. One of the major reasons for the apparent poor performanceof the simulated cellular shop was the fact that the study did not utilize groupscheduling heuristics. A later study (Flynn 1987) indicated that the use of a verysimple two-stage group scheduling heuristic considerably improved the performanceof the cellular manufacturing shop. However, the conclusions was that improvementwas not substantial enough to make cellular manufacturing a viable alternative tothe traditional job shop.

The motivation behind this research was to further develop the group schedulingconcept and discover under which conditions it compared favourably to existingtechniques. A review of existing research is presented in Section 2. The newlyproposed group scheduling heuristics are given in Section 3, followed by researchdesign and results in Sections 4 and 5.

2. Literature reviewAlthough the group scheduling area is one of the most important to prac­

titioners, it is the least addressed of all the topics of cellular manufacturing (Mosierand Taube 1985). Traditional job shop scheduling procedures are not directlyapplicable since these rules alone do not account for set-up similarities (and thusset-up savings). A group scheduling system requires a two-stage procedure thatattempts to avoid lengthy major set-ups in favour of quick minor set-ups. The firststage involves sequencing jobs within each subfamily (a subfamily is a grouping ofparts with similar set-up requirements), while the second stage consists of determiningthe sequence of subfamilies.

The research on group scheduling can be classified into two categories: schedulingflow-through cells and job shop cells. In a flow-through cell (in its pure form) all theparts have identical routes. In a job shop cell, parts may arrive and depart at differentworkcentres and have different routeings. This paper addresses the more general anddifficult job shop cell structure.

The literature addressing job shop group scheduling is sparse. Since job shopcells manufacture a variety of parts with different routeings, loading and dispatchingthese parts in the system becomes a difficult combinatorial problem. Thus, theapplication of the optimal seeking procedures is very limited. Simple analyticalsolution algorithms do not exist and only heuristic approaches have been employed.In fact, even the single stage group scheduling problem is NP-complete. This problemis parallel to the one machine scheduling problem in the case where set-ups aresequence-dependent, and is the production equivalent of the 'travelling salesman'problem (Foo and Wager 1983).

The first study in this area decomposed part family groups based on set-upsimilarities into subfamilies, such that scheduling of each of the subfamilies could betreated like a flow shop problem (Vaithianathan and McRoberts 1982). The per­formance of the resulting family oriented heuristics was compared with the per­formance of the single stage SPT (Shortest Processing Time) dispatching rule. Thefamily heuristics exhibited shorter flow times and a lower number of set-ups per job.

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Dynamic group scheduling heuristics 1697

However, even the best family heuristic displayed very unfavourable due date per­formance compared to the SPT dispatching rule. It is unclear under which conditionsthese conclusions were drawn.

A later study proposed two static heuristics to find near optimal sequences usingminimization of makespan as the only performance criterion (Sundaram 1983).Although the author reports favourable results, he made some limiting assumptions(e.g., all the jobs in a subfamily move from one workcentre to another at the sametime). Furthermore, the proposed heuristics were tested only on a single smallproblem.

In more recent studies, three queue selection rules were developed which focuson inducing efficiency in the cellular manufacturing shop (Mosier et al. 1984). Theserules were tested in conjunction with five dispatching rules in a simulation study ofa four-machine job shop cell which processed three subfamilies. Two of these rulesshowed notable improvements in shop performance. Overall, the family heuristicsexhibited good performance in terms of average job flow time and average latenessmeasures, but did not perform as well in terms of average tardiness and percent tardy,possibly because due dates were not explicitly considered.

Finally, a very simple queue selection heuristic that attempts to minimize thenumber of set-ups was proposed (Flynn 1987). This heuristic, which is based on the'repetitive lots' concept (Jacobs and Bragg 1988), chooses the subfamily whose firstjob arrived first. This queue selection heuristic was used in conjunction with theFCFS (First-Come-First-Served) dispatching rule. The resulting family-oriented rulewas compared with the single stage FCFS dispatching rule. The results exhibitedvery favourable performance by the family-oriented heuristic. No due date relatedperformance measures were reported.

In conclusion, although the reported heuristic rules reveal some insights, nonefocus explicitly on job due date performance; thus, reduction of set-up time is acquiredat the expense of due date performance. In practice, shop managers consider meetingthe due date the most important criterion. Recent job shop scheduling literatureconfirms the significance of good due date performance (Baker 1984). Finally, thereis a need for heuristics that perform well under various shop conditions. Such robustheuristics can significantly encourage industry to implement group scheduling pro­cedures.

It was not attempted to compare the performance of the family heuristics withthe performance of single stage dispatching rules, since this has been done in severalprevious studies (Mahmoodi et al. 1988b, Flynn 1987, Wemmerlov and Vakharia1986,Mosier et al. 1984). Such studies have generally concluded that family heuristicssignificantly outperform the single stage dispatching rules on all performance mea­sures, under all experimental conditions. The research reported here (Mahmoodi1989) was undertaken in order to develop alternative group scheduling heuristicsthat are dynamic, due date oriented, and robust to various experimental factors.

3. Group scheduling heuristicsAs discussed earlier, a group scheduling system consist of two stages. Dispatching

rules are used to perform the first stage of group scheduling. Such rules are utilizedat every workcentre. Three dispatching rules are considered:

(1) FCFS: This rule is a simple non-due-date oriented rule which assigns priorityto the jobs in the order they arrive and is most often used by practitioners.

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(2) SPT: This rule dynamically assigns priority to jobs with the most imminentprocessing times. This rule has exhibited very small mean flow times, but mayresult in large flow time variance.

(3) Two Class Truncated SPT (SI'): This rule dynamically assigns priority to jobswith zero or negative slack times and orders by SPT (Oral and Malouin 1973).Jobs with positive slack times are considered non-priority and are also orderedby SPT. Thus, it retains the performance of the SPT rule while minimizingthe extreme completion delays of a few jobs. Mathematically, SI' determinesthe job priority as:

S; = D; - L Pi j - TjEt/J

If S, ~ 0 Minimum Pij Priority QueueIf S, > 0 Minimum Pij Non-Priority Queue

Where:

S, = slack time of job i

D, = due date of job i

<p = set of uncompleted operations

Pij = processing time of job i on work centre j

T = present time

The queue selection heuristics are used to perform the second stage of groupscheduling (determine which subfamily queue to select first and when to process jobsfrom another subfamily queue or switch to another subfamily queue). Similar todispatching rules, the subfamily queue selection heuristics are applied at everyworkcentre. The subfamily of which the last processed job is a member is referredto as the current subfamily. Three such heuristics are considered:

(I) FCFAM: This heuristic chooses the subfamily queue whose first job (in thequeue) arrived first. This heuristic attempts to minimize the number of set-upsby not switching to another subfamily until all the jobs in the currentsubfamily are processed (exhaustive). FCFAM is dynamic, but has no regardsfor the job due date performance.

(2) DDFAM: This heuristic attempts to minimize the number of set-ups, whileconsidering the due date performance by choosing the subfamily queuewhose first job has the earliest due date. This rule is also dynamic andexhaustive.

(3) MSFAM: This heuristic attempts to minimize the number of set-ups and thetotal set-up time by taking advantage of sequence dependent set-up times.MSFAM chooses the subfamily queue that requires the least amount ofset-up time at each workcentre. This heuristic is also dynamic and exhaustive.MSFAM is similar to the Next Best rule (Wilbrecht and Prescott 1969).

The combination of the three dispatching rules and the three queue selection rulesresult in nine family heuristics. These are: FCFAM/FCFS, FCFAM/SPT, FCFAM/SI', DDFAM/FCFS, DDFAM/SPT, DDFAM/SI', MSFAM/FCFS, MSFAM/SPT,and MSFAM/SI'. For brevity, these combinations are referred to as: FCFCFS,FCSPT, FCSI, DDFCFS, DDSPT, DDSI, MSFCFS, MSSPT, and MSSI, re­spectively. Among these heuristics only the performance of FCFCFS heuristic hasbeen previously reported (Flynn 1987).

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Dynamic group scheduling heuristics 1699

4. Research design and experimental environmentThe vehicle for this study is a computer simulation model of a five-workcentre

job shop cell, each containing a single machine, as shown in Fig. I. The shop modelis intended to represent a typical job shop cell. This model was written in SIMANsimulation language (Systems Modelling Corp. 1987) using a combined process andevent orientation. All models utilized discrete event routines from the SIMANFORTRAN subprogram library, as well as user-written FORTRAN programs toperform the more detailed tasks.

The routeing for each job is generated when the job arrives at the shop. Jobs areallowed to enter at the first and second workcentres, must go through the thirdworkcentre, and exit from the fourth and firth workcentres (see Fig. I). This createsa bottleneck at the third workcentre. The cell size creates a reasonable level of jobrouteing diversity, and is consistent with the literature which indicates that theaverage number of workcentres per cell is approximately six (Greene 1980). Thereare also two motivating reasons for creating an unbalanced bottleneck workcentre.First, recent studies have indicated that job shops do have machine capacities whichare not balanced (e.g., Fry et al. 1988). Second, a simulation model with a bottleneckworkcentre simplifies control of the overall cell utilization.

The cell is assumed to be machine constrained only, and cycling is prohibited.These two assumptions are made to simplify the shop and are consistent with theprevious studies (Mosier et al. 1984). Finally, it is assumed that the cell has alreadybeen designed and set-up information is available.

4.1. Job characteristicsTo create a cellular manufacturing environment, a finite number of parts with

different routeings belonging to a few subfamilies is desired. This is achieved in thisstudy by creating three subfamilies and assigning either four or five operations toeach part. These combinations generate twelve distinct routeings. It is assumed thateach routeing corresponds to a part type, and each part type belongs to the samesubfamily at every workcentre. Thus, a total of 36 different parts are modelled (12parts in each subfamily). By design, the probability of each part being included inany of the subfamilies and having any of the possible routeings is equal.

The parts arrive according to a Poisson process and the due dates are assignedby the TWK rule (Conway et at. 1967). The processing times for all the fiveworkcentres are identical and follow a third order Erlang distribution with a meanof I h. While all 12 part types (in each subfamily) go through the bottleneckworkcentre, only 10 part types go through the other four workcentres. Thus, theaverage bottleneck workcentre utilization is 12/IOth of the other workcentre utiliza­tions.

Figure I. The job shop cell.

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Major set-up times are sequence-dependent and are generated using a secondorder Erlang distribution, with parameter specifications dependent upon the sub­family queue from which the job is selected. The ratio of the mean set-up time foreach of the three subfamilies at all the workcentres is in the proportion of 1:2:3. Thesecond order Erlang distribution was chosen because the histograms of actual servicetime data often have a shape similar to the density function of such a distribution(Law and Kelton 1982).The third order Erlang distribution was selected to representthe processing times, since they are generally less variable than the set-up times.

4.2. Experimental factorsThe proposed family heuristics were examined in an experimental design with

two levels for three factors: shop load (SL), due date tightness (DDT), and set-up torun-time ratio (SjR). Thus, a 9 x 23 full factorial experiment was carried out.

Different shop loads were achieved by varying the interarrival time (IT). The ITvalues were determined by pilot runs so that the 'high' level of shop load produceda bottleneck utilization of 87% and the 'low' level a utilization of 80%, under theFCFCFS family heuristic. The high level was chosen since it yields a bottleneckutilization under the single stage rules of 96%, while the low level was chosen toattain adequate average queue length at the various workcentres.

The due date tightness levels were established so that approximately 50% and20% of the jobs become tardy under the FCFCFS family heuristic for tight and loosedue dates, respectively. The average set-up to run-time ratios were set at 0.333 and0.667 for low and high settings. To maintain the same shop utilization for the twolevels ofSjR, the IT values were manipulated. Each combination ofSjR and SL levelsrequired a different IT values. Thus, four different IT values were utilized in this study.

4.3. Performance measuresThe performance of a cell should be measured in two dimensions: how well the

parts meet the promised due dates, and how efficiently the parts are processed throughthe cell. While the second dimension has always been considered in previous studies,the first dimension has been largely ignored. Due to the importance of meetingpromised due dates in practice (see Mahmoodi et al. 1988a), special attention is givento the due date performance of the heuristic rules. Three primary performancemeasures are considered (these values are averaged over all part types):

I. average job tardiness;2. average percentage of jobs tardy;3. average job time in system.

In addition to these primary measures, several other measures of shop per­formance were collected.

4.4. Data collectionThe system was started in an 'empty and idle' state and brought to steady state

by using the first 2000 has warm-up period. Statistics were collected for 8000 h afterthe warm-up period. Since it was desirable to be able to statistically distinguish theperformance of the heuristics, the common random numbers variance reductiontechnique was employed (Law and Kelton 1982). Thus, the random number seedsacross various models were fully synchronized so that a random number used for aparticular function in one model was used for the same function in all other models.

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Dynamic group scheduling heuristics 1701

Finally, the number of replicates was determined through several pilot runs. It wasconcluded that performing 50 replicates will achieve sufficient precision in estimatingthe mean differences of the performance measures.

5. Experimental resultsThe analysis of the scheduling heuristics is based on the three primary per­

formance criteria mentioned earlier. The purpose of the analysis is to study tworesearch questions. First, how do the family heuristics perform under variousexperimental conditions? Second, how much do the experimental factors impact theperformance of the heuristics?

Summary results for average time in system, average tardiness, and percent tardyfor different experimental conditions are presented in Tables I through 8. Theexperimental conditions are abbreviated as follows: HS and LS refer to high and lowset-up to run-time ratio, HL and LL refer to high and low load, and TO and LO referto tight and loose due dates, respectively.

FCFCFSFCSPTFCSIDDFCFSDDSPTDDSIMSFCFSMSSPTMSSI

Avg.TIS

15·9515·7015·6115·8815·5715-4815·2314·8914·92

Avg.tardiness

6·326·255·906·075·895·616·246·135·86

%tardy

50·9648·5949-4950·9148·2549·1145·8442-6143·76

Table I. Performance measures of various family heuristics under HS, H L. TD condition.

FCFCFSFCSPTFCSIDDFCFSDDSPTDDS)MSFCFSMSSPTMSSI

Avg.TIS

15·9515·7015·6315·9015'5015·4515·2314·8914·92

Avg.tardiness

5·365·254·915·084·844-465·655·685·38

%tardy

20·5018·5518·6118·9215·9616·6417-8215·2915-61

Table 2. Performance measures of various family heuristics under HS. HL. LD condition.

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Avg. Avg. %TIS tardiness tardy

FCFCFS 14·22 6·22 50·80FCSPT 14·00 6·28 47·66FCSI 13-93 5·80 49-47DDFCFS 14·17 6·01 50·67DDSPT 13'80 5·99 46·38DDSI 13'80 5·57 48·76MSFCFS 13·77 6·37 46·65MSSPT 1HI 6·47 42·00MSSI IH3 5·96 44·51

Table 3. Performance measures of various family heuristics under LS. H L. TD condition.

FCFCFSFCSPTFCSIDDFCFSDDSPTDDSIMSFCFSMSSPTMSSI

Avg.TIS

14·2214·0013-9014·1813·7613-7813·77IHIIHI

Avg.tardiness

5·535·695·105·385·424·896·196·515·88

%tardy

19·9117-6017·9418'4115·0916·2518·0015·1615·75

Table 4. Performance measures of various family heuristics under LS. HL. LD condition.

FCFCFSFCSPTFCSIDDFCFSDDSPTDDSIMSFCFSMSSPTMSSI

Avg.TIS

14·3114·2014·1414·3014·0514·0213'8713-6213-65

Avg.tardiness

5-615·595·355-415·275·065·545-435·27

%tardy

50·7549·2049·8351·1748·8449·7747·1444·5445-60

Table 5. Performance measures of various family heuristics under HS, LL, TD condition.

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Avg. Avg. %TIS tardiness tardy

FCFCFS 14·31 4·72 19·77FCSPT 14·20 4·64 18.23FCSI 14·14 4·42 18·35DDFCFS 14·35 4'46 18·74DDSPT 14·03 4·25 16·11DDSI 13-96 3-98 16·40MSFCFS 13·87 4·95 17·76MSSPT 13-62 4·94 15·50MSSI 13-63 4·74 15·83

Table 6. Performance measures of various family heuristics under HS, LL, LD condition.

FCFCFSFCSPTFCSIDDFCFSDDSPTDDSIMSFCFSMSSPTMSSI

Avg.TIS

12·2912·1012·0912·2511·9711·9612·0011·7211·76

Avg.tardiness

5·155·144·865·034·854·615·265·194·92

%tardy

50·6447·9049·4450·3847-4048·8747·2143·6345-49

Table 7. Performance measures of various family heuristics under LS, LL, TD condition.

FCFCFSFCSPTFCSIDDFCFSDDSPTDDS IMSFCFSMSSPTMSSI

Avg.TIS

12·2912·1012·0612·2311'9611·9512·0111·7211·73

Avg.tardiness

4·614·674·284·474·454·115·095·184·81

%tardy

20·3518·1818·5218·7615·9816·7518·7515·9316·40

Table 8. Performance measures of various family heuristics under LS, LL, LD condition.

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5.1. Statistical techniques utilizedHypothesis tests were conducted for the differences among mean responses of

various heuristics. A series of multiple comparison paired t-tests was required tostatistically rank the heuristics based on various performance measures. A pairedt-test does not assume that the mean responses of the heuristics are independent (dueto the use of common random numbers, they are not independent in this study), northat their variances are equal.

Generally, with N scheduling heuristics, K = N(N - 1)/2 pairwise comparisonsshould be conducted for each of the performance measures. Thus, according to theBonferroni inequality, if an overall significance level of 100(1 - O()% is desired, eachindividual test should be significant at 100(1 - 0(/K)% level. An overall significancelevel of 99% was selected (0( = 0.01). The robustness of the heuristics were exploredby examining the main and interaction effects of various experimental factors at 99%confidence intervals.

Typically similar studies have been unable to statistically distinguish the per­formance of the heuristics they considered. In this study, however, we were able tostatistically distinguish the performance of the heuristics, due to achieving highprecision (small variance) through:

(I) utilizing common random numbers variance reduction technique;(2) performing 50 replicates of each model;(3) executing long simulation runs.

5.2. Relative rankingWith nine family heuristics, 36 paired t-tests were performed at each experimental

condition for each of the three performance measures. The analysis indicated thatthere were some significant differences among the family heuristics (Mahmoodi 1989).

To simplify the analysis, the performance of each stage of the family heuristics(queue selection heuristics and dispatching rules) is examined separately. Suchanalysis is performed for each of the three performance measures, presented in TablesI through 8, in the following sections.

5.2.1. Average time in systemThe performance of the queue selection heuristics is examined first, by comparing

the family heuristics which utilize the same dispatching rules. The average time inthe system performance of MSFAM dominated all other heuristics under all experi­mental conditions. This was the case no matter what dispatching rule was utilized.Generally, DDFAM was the second best performing heuristic while FCFAM per­formed the worst.

The performance of various family heuristics indicated that different results areachieved by utilizing various dispatching rules. The results demonstrated that (withinthe same queue selection heuristic) the family heuristics that utilized FCFS tosequence jobs within the subfamily queues performed the worst. On the other hand,the family heuristics that employed SPT or SJX performed the same, in general.

Overall, the performance of the family heuristics with respect to this measure canbe classified into four or five groups, under all experimental conditions. MSSI andMSSPT were the best performing family heuristics under all experimental conditions.On the other hand, the worst performing heuristics were FCFCFS and DDFCFS.The range of average time in system was approximately 5-7% lower under the bestperforming heuristic than the worst performing one.

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5.2.2. Average tardinessThe average tardiness performance of DDFAM was superior to all other queue

selection heuristics under all experimental conditions. This was the case no matterwhat dispatching rule was utilized. FCFAM had a clear edge over MSFAM whendue dates were set loose, while its advantage diminished under tight due dates.MSFAM performed slightly better than FCFAM only when shop load and SIR werehigh and due dates were set tight.

The heuristics that utilized SI' to sequence jobs within the subfamily queuesperformed the best under all experimental conditions for average tardiness. On theother hand, the heuristics that utilized FCFS performed the worst under tight duedates, while the ones that employed FCFS and/or SPT had the worst performanceunder loose due dates.

Overall, the performance of the family heuristics can be classified into three tofive groups, under various experimental conditions. DDSI was the best performingheuristic under all experimental conditions. On the other hand, the worst performingheuristics were generally MSFCFS and/or MSSPT especially when due dates wereset loose. The range of average tardiness was approximately 11-25% lower underthe best performing heuristic than the worst performing one.

5.2.3. Percent tardyOn percent tardy, MSFAM again dominated the other queue selection heuristics

under all experimental conditions, no matter what dispatching rule was utilized. Thiswas not surprising since the heuristics that perform well on average time in systemgenerally display good performance on percent tardy as well. Generally, DDFAMoutperformed FCFAM especially when the due dates were loose. However, there wasnot a significant difference in the performance of DDFAM and FCFAM when shopload was high and due dates were tight.

The family heuristics that utilized SPT and FCFS to sequence jobs within thesubfamily queues performed the best, and the worst, respectively, under all experi­mental conditions. Overall, the performance of the family heuristics can be classifiedinto four to six groups, under various experimental conditions. MSSPT was the bestperforming heuristic under tight due dates; MSSI and MSSPT performed the bestunder loose due dates and high SIR, while DDSPT and MSSPT exhibited the bestperformance under loose due dates and low SIR. On the other hand, the worstperforming heuristics were FCFCFS under loose due dates, and FCFCFS and/orDDFCFS under tight due dates. The range of percent tardy was approximately12-26% lower under the best performing heuristic than the worst performing one.

5.3. Analysis of effectsThe main and interaction effects of the experimental factors were calculated for

the performance measures of the family heuristics, as displayed in Tables 9 through11. The value of the effect is the magnitude by which the performance measurechanged between the low and high level of the particular experimental variable.Blanks in the tables correspond to statistically insignificant effects. Since some of theinteraction effects are significant, the main effects must be interpreted with caution.Some dominant relationships among the factor settings of the experimental factorsare iden tified.

The average time in system performance of the heuristics was positively influencedby the SL and SIR factors. The performance of the heuristics that utilized MSFAM

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FCFCFSFCSPTFCSIDDFCFSDDSPTDDSIMSFCFSMSSPTMSSI

E(S/R) E(SL) E(DDT) E(S/R, SL) E(S/R, DDT) E(SL, DDT) E(S/R, SL, DDT)

1·88 /·78 -0'151·90 \·70 -0,201·89 1·66 -0,181·90 1·75 -0'191·92 1·65 -0,161·85 1-66 -0-18\·66 I-56 -0,201·69 1-48 . -0,211-70 1-48 -0.20

-.I

§;

Table 9. Summary results of the significant effects on 'various performance measures: Average time in system (TIS) measure.

E(S/R) E(SL) E(DDT) E(S/R, SL) E(S/R, DDT) E(SL, DDT) E(S/R, SL, DDT)

FCFCFS 0-13 0-84 0-77 -0-16 0·16FCSPT 0-86 0·75 -0-22 0·22FCS\ 0·14 0·70 0·80 -0'18 0·16DDFCFS 0·79 0·78 -0-15 0-19DDSPT -0'12 0·83 0·76 -0,23 0·28DDS\ 0·69 0·85 -0'18 0-26MSFCFS -0·13 0·90 0·38 -0,20 0-21MSSPT -0,29 1.01 0·23 -0,29 0-24MSSI 0·84 0·30 -0-22 0·21

Table 10. Summary results of the significant effects on various performance measures: Average tardiness measure.

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tl'-:ii

E(SjR) E(SL) E(DDT) EISjR, SL) E(SjR, DDT) E(SL, DDT) E(SjR, SL, DDT) '"3;:;.FCFCFS 30·66 <::::FCSPT 0·85 30·16

..,"FCSI 31·20 {;

DDFCFS 0·38 32·08 '"r,DDSPT 1·08 -0,66 31·93 0·58 ::-

'"DDSI 32·62 ?MSFCFS -0,51 -0·64 28·63 -0,39 ~MSSPT 0·31 -1,13 27·72 045 -0,65 <::::

::-MSSI -0·34 -0,92 28·94 -0,49 -0,32 '"'"..,

Table 11. Summary results of the significant effects 011 various performance measures: Percent tardy measure.~.

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1708 F. M ahmoodi et at

to select subfamily queues was slightly more robust to these factors than others. TheDDT factor did not significantly affect the average time in system of any heuristic.

The average tardiness performance of the heuristics was significantly influencedby the SL and DDT factors. The performance of the heuristics that utilized DDFAMand MSFAM was more robust to SL and DDT factors than others, respectively.About half of the heuristics were also significantly influenced by the SjR factor.Significant interactions between SjR and SL, and SjR and DDT also existed.

The percent tardy performance of all the family heuristics was significantlyinfluenced by the DDT factor. Many heuristics were also significantly influenced bythe SjR and SL factors. Although the performance of the heuristics that employedMSFAM was the most robust to the DDT factor, their performance was the leastrobust to SjR and SL factors. Overall, the percent tardy performance of the heuristicsthat employed FCFAM was the most robust to the experimental factors. In the nextsection, the results are summarized and discussed.

5.4. DiscussionFCFAM was overall the worst performing queue selection heuristic. This heuristic

performed poorly on average time in system, and percent tardy, especially when duedates were set loose. However, its performance was slightly more robust to theexperimental factors than the other heuristics.

DDFAM displayed excellent average tardiness and very good percent tardy(especially under loose due dates), as well as very good average time in system(especially under tight due dates) performance. Notably, this heuristic never demon­strated poor performance on any performance measure. Furthermore, DDFAM'ssuperior average tardiness performance was very robust to all experimental factors.

Finally, MSFAM exhibited the best performance on average time in system, andpercent tardy. Yet, it performed very poorly on average tardiness (especially underloose due dates), and its performance was very sensitive to the SjR factor. The latterwas expected, since MSFAM attempts to minimize the total set-up time by takingadvantage of sequence-dependent set-up times and, thus, it performs better when SjRis high.

The performance of the family heuristics also depended on the dispatching rulesthat they utilized. Generally, the family heuristics that utilized FCFS performedpoorly on average time in system and percent tardy. On the other hand, the familyheuristics that employed SPT demonstrated very good average time in system, andpercent tardy performance. However, their average tardiness performance was poor,especially when due dates were set loose. Finally, the family heuristics t hat utilizedSI' were among the best performing family heuristics. These heuristics performedwell on all performance measures, especially average tardiness, and average time insystem.

Recent studies have identified FCFCFS as the best performing family heuristic(Flynn 1987, Wemmerlov and Vakaria 1986). The results of this research are notable,since they indicate that several newly developed family heuristics outperformFCFCFS on all the performance measures. According to these results, MSSPT and/orMSSI exhibited the best performance on average time in system under all ex­perimental conditions. The range of average time in system was approximately 5-7%lower under these heuristics than FCFCFS.

MSSPT and MSSI were also among the best performing heuristics on percenttardy. This can be attributed to the outstanding average time in system performance

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Dynamic group scheduling heuristics 1709

of the MSFAM queue selection heuristic, as well as the SPT and SI' dispatchingrules. The range of percent tardy was about 12-26% lower under these heuristicsthan FCFCFS.

Finally, on average tardiness, DDSr demonstrated extreme robustness by domin­ating all other heuristics under all experimental conditions. This can be attributedto two factors. First, the SI' dispatching rule retains the sound performance of theSPT rule while minimizing the extreme completion delays of a few jobs. Second, thedue-date-oriented DDFAM queue selection heuristic further assists the adherence tothe due date constraints. The range of average time in system was approximately10--17% lower under DDsr than FCFCFS.

Table 12 exhibits the best performing heuristics on each of the performancemeasures, under each experimental condition. When a tie existed among the per­formance of several heuristics (the differences were not statistically significant), theheuristics were ranked in ascending order of the performance measure.

6. ConclusionsIn this study three queue selection heuristics and three dispatching rules were

utilized to form nine family heuristics. These heuristics were examined under eightexperimental conditions. Several major conclusions can be derived from the resultsof this study.

First, the performance of several newly developed family heuristics are sub­stantially better than the performance of FCFCFS (the best previously suggestedheuristic) on all performance measures. This is especially the case when due dateperformances are considered. In general, the family heuristics that utilized theDDFAM or MSFAM queue selection heuristics and the SI' or SPT dispatching rulesare among the best performing heuristics. Previous research has indicated that familyheuristics dominated all the one stage dispatching rules on all performance measures,

Average Average %TIS tardiness tardy

HS. HL, TD MSSI DDSI MSSPTMSSPT

LS, HL, TD MSSPT DDSI MSSPTMSSI

HS. LL. TD MSSPT DDSI MSSPTMSSI

LS. LL, TD MSSPT DDSI MSSPTMSSI

HS. HL, LD MSSI DDSI MSSPTMSSPT MSSI

LS. HL, LD MSSPT DDSI DDSPTMSSI MSSPT

HS, LL,LD MSSPT DDSI MSSPTMSSI MSSI

LS, LL. LD MSSPT DDSI MSSPTMSSI DDSPT

Table 12. Best performing family heuristics.

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1710 F. Mahmoodi et al.

under all experimental conditions. This study extends this result by demonstratingthat even better performances can be achieved by utilizing more effective familyheuristics.

Second, the results are especially significant since the performance of severalproposed heuristics are robust to a wide variety of different environments. Forexample, the DDSI heuristic displayed the best average tardiness performance, whileMSSPT was one of the best performing heuristics on average time in system andpercent tardy, under all experimental conditions. Such characteristics, along with thefact that the proposed heuristics are simple, can encourage the implementation byindustry.

Little research has been performed in the group scheduling area. This studyrevealed many insights regarding this vital field, but further research is needed. Astraightforward extension of this work is the development of family heuristics whichconsider other queue selection schemes and dispatching rule combinations. Specialattention should be given to non-exhaustive queue selection heuristics which mayhave great potential to perform well under a large variety of experimental conditions.

AcknowledgmentsThis research was partially supported by The School of Management of Clarkson

University and by the University of Minnesota CIM consortium.

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