New dispatching rules for shop scheduling: A step forward

This article was downloaded by: [Texas A & M International University]On: 07 October 2014, At: 23:01Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number:1072954 Registered office: Mortimer House, 37-41 Mortimer Street,London W1T 3JH, UK

International Journal ofProduction ResearchPublication details, including instructions forauthors and subscription information:http://www.tandfonline.com/loi/tprs20

New dispatching rules forshop scheduling: A stepforwardM. S. Jayamohan & ChandrasekharanRajendranPublished online: 14 Nov 2010.

To cite this article: M. S. Jayamohan & Chandrasekharan Rajendran (2000) Newdispatching rules for shop scheduling: A step forward, International Journal ofProduction Research, 38:3, 563-586, DOI: 10.1080/002075400189301

To link to this article: http://dx.doi.org/10.1080/002075400189301

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of allthe information (the “Content”) contained in the publications on ourplatform. However, Taylor & Francis, our agents, and our licensorsmake no representations or warranties whatsoever as to the accuracy,completeness, or suitability for any purpose of the Content. Anyopinions and views expressed in this publication are the opinions andviews of the authors, and are not the views of or endorsed by Taylor& Francis. The accuracy of the Content should not be relied upon andshould be independently verified with primary sources of information.Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilitieswhatsoever or howsoever caused arising directly or indirectly inconnection with, in relation to or arising out of the use of the Content.

This article may be used for research, teaching, and private studypurposes. Any substantial or systematic reproduction, redistribution,

http://www.tandfonline.com/loi/tprs20

http://www.tandfonline.com/action/showCitFormats?doi=10.1080/002075400189301

http://dx.doi.org/10.1080/002075400189301

reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of accessand use can be found at http://www.tandfonline.com/page/terms-and-conditions

Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4

http://www.tandfonline.com/page/terms-and-conditions

http://www.tandfonline.com/page/terms-and-conditions

int. j. prod. res., 2000, vol. 38, no. 3, 563± 586

New dispatching rules for shop scheduling: a step forward

M. S. JAYAMOHAN{ andCHANDRASEKHARAN RAJENDRAN{*

This paper provides a set of new dispatching rules for the minimization of variousperformance measures such as mean, maximum and variance of ¯ ow time andtardiness in dynamic shops. A static rule which minimizes the number of tardyjobs is also proposed. To evaluate these proposed rules, their relative performanceis analysed in open job shops and reported in comparison with the standardbenchmark rules such as the SPT (shortest process time) and EDD (earliestdue-date), popular rules like ATC (apparent tardiness cost) and MOD (modi® edoperational due-date), and the best performing rules in current literature such asRR, PT ‡ WINQ, PT ‡ WINQ ‡ SL and AT-RPT. Thereafter, a comparativeanalysis of the relative performance of these rules is carried out in job shops (withno machine revisitation of jobs) and ¯ ow shops (with missing operations on jobs)in dynamic environments. Based on the simulation study and analysis of results indi� erent manufacturing environments viz. job shops and ¯ ow shops, observationsand conclusions are made, highlighting some interesting aspects about the e� ectof routeing on the individual performance of rules.

1. Introduction

The problem of scheduling has been addressed by researchers over the last threedecades and they are yet to arrive at a conclusive solution to the problem. Theproblem, as it exists, is one in which a set of competing jobs, each of which hasone or more operations to be performed in a speci® ed sequence on pre-de® nedmachines, with corresponding process times, is to be processed over a period oftime. The objective of the problem is to determine job schedules which can minimizeone or more measures of performance.

Two types of manufacturing systems, viz. ¯ ow shops and job shops, have beenwidely researched. In the case of ¯ ow shops, the problem of scheduling is generallyaddressed by assuming the availability of the jobs at the beginning of the schedulingperiod, i.e. static ¯ ow shop scheduling problem, whereas in the case of job shops, theproblem is generally investigated by assuming a dynamic arrival of jobs during thescheduling period. While the use of heuristic algorithms is mostly resorted to in thecase of static scheduling problems, dispatching rules are made use of in the case ofdynamic scheduling problems. Dispatching rules are more popular in many real-lifemanufacturing systems than heuristics, mainly because dispatching rules are simpleto implement and use in any shop ¯ oor, and most real-life systems have dynamic jobarrivals.

International Journal of Production Research ISSN 0020± 7543 print/ISSN 1366± 588X online # 2000 Taylor & Francis Ltdhttp://www.tandf.co.uk/journals/tf/00207543.htm l

Revision received March 1999.{ Industrial Engineering and Management Division, Department of Humanities and

Social Sciences, Indian Institute of Technology Madras, Chennai 600 036, India.* To whom correspondence should be addressed. e-mail: [email protected]

Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4

The problem of scheduling in ¯ ow shops is generally investigated with a staticarrival of jobs. Hence, the solution methodology is directed towards the developmentof exact and approximation techniques (Baker 1974, French 1982, Pinedo 1995). Inpractical situations when the scheduler is faced with the task of dynamic arrivalpatterns for jobs, dispatching rules are used to arrive at good schedules. While weencounter many studies in dynamic job shops (see the survey articles of Blackstoneet al. 1982, Haupt 1989, Ramasesh 1990), very limited studies have addresseddynamic ¯ ow shop scheduling problems (Scudder and Ho� mann 1987, Hunsuckerand Shah 1994, Rajendran and Holthaus 1999). A comparative analysis of perform-ances of dispatching rules in job shops and ¯ ow shops could reveal some interestingresults regarding the in¯ uence of routeing of jobs and shop characteristics. Hencethis study is also carried out on dynamic ¯ ow shops and job shops.

The paper initially provides an up-to-date literature review of research on jobshop and ¯ ow shop scheduling in dynamic environments, followed by a brief surveyof some existing rules. Subsequently, new rules are presented. An extensive simula-tion study is carried out to evaluate the relative performances of the existing and theproposed dispatching rules.

2. Literature review

A dispatching rule, in general, is used to select the next job from a set of waitingjobs to be processed at a machine when the machine becomes free. The practicaldi� culty of selection occurs because there are n! ways of selection from n jobswaiting at a facility, and dynamic shop conditions can in¯ uence the performanceof a rule. Mostly, the dispatching rules address the problem of reducing the inven-tory and tardiness related costs. It is customary to have surrogate measures of thesecosts through ¯ ow time and tardiness of jobs (Blackstone et al. 1982).

Dispatching rules can be classi® ed into ® ve categories: (1) rules involving processtimes; (2) rules involving due-dates; (3) simple rules involving neither process timesnor due-dates; (4) rules utilizing shop ¯ oor conditions and (5) rules involving two ormore of the ® rst four classes. It is worth noting that so far no rule has been found toperform well for all criteria relating to ¯ ow time and tardiness. In general, process-time based rules fare well under tight load conditions and due-date based rules farewell under light load conditions (Conway 1965, Rochette and Sadowski 1976,Blackstone et al. 1982). In most of the studies, it is notable that a process timerule, viz. the SPT (shortest process time) fares quite well for reducing mean ¯ owtime and hence is used as a common benchmark rule (see Conway 1965, Rochetteand Sadowski 1976, Blackstone et al. 1982, Haupt 1989). Among the due-date basedrules, the EDD (earliest due-date) rule is the most popular in view of its ease ofimplementation. The WINQ (work content in the queue of the next operation of thejob) rule utilizes shop ¯ oor conditions existing as the base for the rule (Haupt 1989).Survey articles by Day and Hottenstein (1970), Panwalker and Iskander (1977),Blackstone et al. (1982), Haupt (1989) and Ramasesh (1990) provide a good insightinto various rules in job shop scheduling.

It is customary in contemporary research that in ¯ ow shop scheduling problemsall jobs are assumed to be available at the beginning of the scheduling period. Hencemany optimization algorithms and heuristics have been proposed for solving theseproblems (e.g. Ignall and Schrage 1965, Campbell et al. 1970, Nawaz et al. 1983,Rajendran 1994, Ishibuchi et al. 1995). However, when job arrivals are dynamic, theuse of dispatching rules has to be resorted to (Hunsucker and Shah 1992, 1994).

564 M. S. Jayamohan and C. Rajendran

Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4

Hunsucker and Shah’s studies were limited by the selection of dispatching rules suchas FIFO, SPT and LPT, and e� cient rules such as MOD (Baker and Kanet 1983)and ATC (Vepsalainen and Morton 1987) were not included. Moreover, a compre-hensive set of measures involving mean and variance of ¯ ow time, and mean andvariance of tardiness of jobs was not considered. In comparison to these studies, thestudy by Rajendran and Holthaus (1999) appears more complete with the considera-tion of many dispatching rules such as COVERT (see Russell et al. 1987), RR(Raghu and Rajendran 1993, 1995) and PT ‡ WINQ (Holthaus and Rajendran1997). From a relative evaluation of many dispatching rules from the literaturesurvey, it appears that there is a scope to develop e� cient dispatching rules thatcould address a number of performance measures such as the minimization of mean,maximum and variance of ¯ ow time and tardiness of jobs, and also minimizing thepercentage of tardy jobs.

In the next section, the details of some existing rules and the new dispatchingrules are presented.

3. Identi® cation of best existing rules and development of new dispatching rules

To understand the various rules in this study, we present the terminology used inthis paper as follows:

½ time at which the dispatching decision is made.T ij process time for the imminent operation j of job i.mi total number of operations on job i.Di due date of job i.

ODDij operational due-date for operation j of job i.W i; j‡ 1 total work content of all jobs in the queue of next operation of job i.

Ai time of arrival of job i on the shop ¯ oor.Zi priority index of job i at the instant ½ (the job with the least Zi is chosen

for loading).Z 0

i priority index of job i at the instant ½ (the job with the largest Z 0i is

chosen for loading).Ci; j¡ 1 Completion time of the previous operation (i.e. operation j ¡ 1) of job i.

c due-date allowance factor.

Basically, the due-date allowance factor is used to vary the tightness of due-datesetting. When the TWK (Total Work content) method of due-date setting (seeBlackstone et al. 1982) is used, Di is set equal to

Ai ‡Xm i

jˆ 1T ij… † c:

After a detailed review of the literature, the following rules are identi® ed for theirperformance evaluation in the present study.

3.1. Best performing existing rules3.1.1. SPT (shortest process time) rule

This rule, which is probably one of the simplest and oldest in design, is commonlyused to minimize mean ¯ ow time and percentage of tardy jobs (see Conway 1965,Rochette and Sadowski 1976, Blackstone et al. 1982, Haupt 1989). Its priority index

565Dispatching rules for shop scheduling

Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4

is given as follows:Zi ˆ T ij : … 1†

The job with the minimum value of Zi is chosen for loading.

3.1.2. PT ‡ WINQ (process time plus work in the next queue) ruleThis rule, proposed by Holthaus and Rajendran (1997), is found to yield excellent

results for minimizing mean ¯ ow time of jobs. When the utilization level of the shopis high and the due-date setting is tight, the rule also minimizes mean tardiness andpercentage of tardy jobs. The priority index for job i is given as follows.

Zi ˆ T ij ‡ W i; j‡ 1: … 2†

The job with the minimum value of index is chosen for loading.

3.1.3. ATC (apparent tardiness cost) ruleThis rule proposed by Vepsalainen and Morton (1987), is a very popular bench-

mark rule in literature in view of reducing the percentage of tardy jobs and meantardiness (Pinedo 1995). This rule is obtained as an extension to the popular ruleCOVERT (Carroll 1965) by a suitable introduction of an exponential look-aheadfeature (instead of the linear look-ahead in COVERT) that scales the slack accordingto the expected number of competing jobs. Note that the priority index of job i,according to the COVERT rule (see Russell et al. 1987 for details), is given as follows.

Z 0i ˆ

… 1=T ij †Xmi

qˆ j‡ 1W 0

iq ¡ si… † Xm i

qˆ j‡ 1W 0

iq; if 0 si <Xmi

qˆ j‡ 1W 0

iq;

0 if siXmi

qˆ j‡ 1W 0

iq;

… 1=T ij † ; if si < 0:

8>>>>>>><

>>>>>>>:

… 3†

Note that W 0iq denotes the expected waiting time of job i for its operation q, and si

denotes the slack of job i, where si ˆ Di ¡ ½ ¡Pm i

qˆ j T iq. The job with the largestvalue of Z 0

i is chosen for loading.The priority index given by the ATC rule is as follows:

Z 0i ˆ … 1=T ij † exp ¡ max Di ¡

Xmi

qˆ j‡ 1

… W 0iq ‡ T iq† ¡ ½ ¡ T ij … k Tbar† ; 0

… 4†

where k is the exponential look ahead parameter to scale the slack according to theexpected number of competing jobs and Tbar is the average processing time of theimminent operations of the competing jobs at the service facility. The job with themaximum value of Z 0

i is taken for loading. In this study, parameter values are set inaccordance with the recommendations and observations of Vepsalainen and Morton(1987), Anderson and Nyirenda (1990) and Jensen et al. (1995). Values of k ˆ 2 forstatic shops (see Vepsalainen and Morton 1987) and k ˆ 3 for dynamic shops wererecommended as parameter values in the rule. This exponential look ahead works byensuring timely completion of short duration jobs (steep increase of priority close tothe due date) and by extending the look-ahead far enough to prevent long tardy jobsfrom overshadowing long clusters of shorter jobs (see Vepsalainen and Morton(1987) for details).


Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4

3.1.4. MOD (modi® ed operational due-date)This rule was popularized by Baker and Kanet (1983) by using the concept of

operational due-date (ODD), proposed earlier by Baker and Bertrand (1982). Thepriority index of the job i is given as follows:

Zi ˆ max fODDij ; ½ ‡ T ijg … 5†

where ODDij is obtained as below:

ODDij ˆ Ai ‡ cXj

kˆ 1

T ik : … 6†

The job with minimum value for Zi is chosen for loading. This is a popular bench-mark rule for tardiness related measures.

3.1.5. EDD (earliest due-date) ruleThis rule is perhaps the most commonly used in industry for easy implementation

and practice on the shop ¯ oor. The priority index of the rule is as follows:

Zi ˆ Di : … 7†

This rule is known to minimize the values of maximum tardiness and variance oftardiness, and hence is used as a benchmark for those performance criteria in manystudies.

3.1.6. ODD (operational due-date) ruleThe job with the least ODDij is chosen for loading. This rule was ® rst proposed

by Kanet and Hayya (1981). The rule is expected to fare well with respect to themeasures of tardiness like the maximum and variance of tardiness of jobs. Theperformance of this rule as a progress milestone is discussed in detail by Baker(1984).

3.1.7. RR (Raghu and Rajendran 1993, 1995) ruleOne of the most promising rules, this rule yields low values of mean tardiness

(performing better than rules by Anderson and Nyirenda (1990)) and mean ¯ ow time(better than the SPT rule). The priority index of the job i is

Zi ˆ … si exp … ¡ ² † T ij † =RPT i ‡ exp … ²† T ij ‡ W 0 0nxt … 8†

where si denotes the slack of the job given by

si ˆ Di ¡ ½ ¡ RPT i : … 9†

Here, RPT i denotes the total remaining process times for the job, ² is the utilizationlevel of the machine on which the job is to be loaded and W 0 0

nxt is the probable waitingtime of job i at the machine of its next operation, taking into account the relativepriority of the job when it enters the queue of the next operation. The job withminimum value for Zi is taken up for loading. A detailed description of the rule isavailable in Raghu and Rajendran (1993) and Holthaus and Rajendran (1997). Inthe works of Holthaus and Rajendran (1997) and Rajendran and Holthaus (1999),this rule was found to be superior to COVERT in minimizing mean tardiness of jobs.


Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4

3.1.8. PT ‡ WINQ ‡ SL (process time ‡ work in next queue ‡ slack) ruleThis rule, proposed by Holthaus and Rajendran (1997), is found to be a very

good rule for minimizing maximum tardiness and variance of tardiness of jobs.Priority index of job i is given as follows:

Zi ˆ T ij ‡ W i; j‡ 1 ‡ min … si ; 0† … 10†

The job with the minimum value of Zi is taken for loading. A detailed description ofthe rule is available in Holthaus and Rajendran (1997) and Rajendran and Holthaus(1999), where the rule is clearly proved to be superior to the slack-per-remaining-operations rule and the COVERT rule with respect to minimizing the maximumtardiness and variance of tardiness of jobs.

3.1.9. AT -RPT (arrival time-total remaining process times) ruleThis rule has been proposed by Rajendran and Holthaus (1999) and has been

found to be e� ective in minimizing the maximum ¯ ow time and variance of ¯ ow timeof jobs. This rule is shown to perform better than the rule by which the job with theearliest arrival time in the queue (or the FIFO rule) is chosen; and the AT (or thearrival time) rule, where the job with the earliest arrival time in the shop in the queueis chosen next for loading. The priority index for the rule is given as follows:

Zi ˆ Ai ¡Xmi

qˆ jT iq … 11†

and the job with minimum value of Zi is taken up for loading.In addition to these nine existing rules, we have also considered some other

existing rules such as NOP (choosing the job with the least number of operationsremaining), LWKR (choosing the job with the least work remaining), and MWKR(choosing the job with the most work remaining). In fact, these rules have beenconsidered in the study by Waikar et al. (1995). In view of the research worksdone subsequently by Holthaus and Rajendran (1997), and Rajendran andHolthaus (1999) wherein the rules PT ‡ WINQ, PT ‡ WINQ ‡ SL and AT-RPThave been proposed, we conducted some pilot studies considering NOP, LWKR,MWKR, SPT, PT ‡ WINQ and AT-RPT rules. The results of this experimentalinvestigation have shown that while the PT ‡ WINQ rule is superior to NOP andLWKR rules for minimizing mean ¯ ow time, mean tardiness and the number oftardy jobs, the AT-RPT rule performs better than the MWKR rule in terms ofminimizing the maximum ¯ ow time and variance of ¯ ow time of jobs. Hence, wehave chosen not to include NOP, LWKR and MWKR rules in the present study. Asno additional signi® cant information is conveyed from these results, we are notreporting them in detail.

3.2. Proposed new rules3.2.1. Proposed rule I (FDD)

A new concept of ¯ ow due-date (FDD) is proposed in this paper. FDDij of job ifor operation j is computed as follows:

FDDij ˆ Ai ‡Xj

qˆ 1T iq: … 12†


Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4

The priority index given by this proposed rule is as follows:

Zi ˆ FDDij : … 13†

The job with the minimum value of Zi is taken for loading. In case of any tie, use theFIFO (® rst-into the queue-® rst-out) rule for breaking it. This rule is expected to yieldminimum values for maximum ¯ ow time and variance of ¯ ow time too. Note thatwhen the allowance factor (i.e. c) is equal to 1, we have FDDij ˆ ODDij . Basicallythis rule de® nes a milestone for every operation of a job, and hence attempts toensure the timely completion of operations, thereby minimizing the maximum ¯ owtime and variance of ¯ ow time of jobs.

3.2.2. Proposed rule II (PT ‡ PW)The priority index by this proposed rule is as follows:

Zi ˆ T ij ‡ … ½ ¡ Ci; j¡ 1† ; or simply Zi ˆ T ij ¡ Ci; j¡ 1: … 14†

The component ½̀ ¡ Ci; j¡1’ refers to the waiting time of job i at the current operation.This rule attempts to yield low values of mean ¯ ow time and percentage of tardy jobs, bye� ectively utilizing the present waiting time of jobs when the dispatching decision is tobe made. The job with the minimum value of Zi is taken for loading. In case of anytie, use the FIFO rule for breaking it. Since the ¯ ow time of a job is governed by itsprocess time and waiting time, and the rule seeks to load the job with the least sum ofprocess time and waiting time, we expect the rule to yield minimum value of mean¯ ow time of jobs.

3.2.3. Proposed rule III (PT ‡ PW ‡ FDD)The priority index for the job i using this rule is as follows:

Zi ˆ T ij ‡ … ½ ¡ Ci; j¡ 1† ¡ … ½ ¡ FDDij † ; or simply Zi ˆ T ij ¡ Ci ; j¡ 1 ‡ FDDij :

… 15†

The addition of the component FDDij attempts to overcome the de® ciency of theproposed rule II in terms of rendering some jobs to be resident for a very long spanof time in the job shop. It can be noted that the component `¡ … ½ ¡ FDDij † ’ isintroduced to incorporate this consideration in rule III and it serves to hasten thejob that has waited for a long time beyond the ¯ ow due-date at the current opera-tion. Consequently, this rule is expected to improve the performance with respect tomaximum and variance of ¯ ow time of jobs as well, and also improve the perform-ance measures related to tardiness. The job with the minimum value of Zi is chosenfor loading. In case of any tie, use the FIFO rule for breaking it.

3.2.4. Proposed rule IV (PT ‡ PW + ODD†

The priority index for this proposed rule is as follows:

Zi ˆ T ij ‡ … ½ ¡ Ci; j¡ 1† ¡ … ½ ¡ ODDij † ; or simply Zi ˆ T ij ¡ Ci ; j¡ 1 ‡ ODDij :

… 16†

This rule is a modi® cation of rule III with a focus on tardiness related measures,since ODDij is added to the priority index given by rule II. The job with the mini-mum value of Zi is selected for loading. In case of any tie, use the FIFO rule forbreaking it. It is evident that the rule is both process-time based and due-date based.


Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4

It can also be seen that the term `¡ … ½ ¡ ODDij † ’ serves to hasten the job that haswaited for a long time beyond the operational due-date at the current operation.

3.2.5. Proposed rule V (OPFSL K/PT; FDD)This proposed rule uses `negative slack’ with respect to FDDij , computed at the

operation level. We call this version of slack, operational ¯ ow slack. We would liketo have the operational ¯ ow slack proportional to the process time so as to minimizethe maximum ¯ ow time of jobs. We convert the negative slack to a positive value inorder to overcome the anomalies of negative ratio rules (see Kanet 1982).

The priority index of the job i using this rule is given by

Z 0i ˆ max f ½ ‡ T ij ¡ FDDij ;0g =T ij : … 17†

The job with the maximum value of Z 0i is chosen for loading. In case of any tie, break

it by choosing the job with the minimum value of FDDij . This rule seeks to reduceboth maximum and variance of ¯ ow time, and consequently the maximum andvariance of tardiness of jobs as well.

3.2.6. Proposed rule V I (OPSL K/PT; ODD)This rule is also proposed similar to the above rule except that it tries to reduce

the maximum tardiness and variance of tardiness by using the operational due dateof job i for operation j (i.e. ODDij).

The priority index of job i is as follows:

Z 0i ˆ max f ½ ‡ T ij ¡ ODDij ; 0g =T ij : … 18†

The job with the maximum value of the priority index is chosen for loading. In case ofany tie, break it by choosing the job with the minimum ODDij . This rule seeks to main-tain the operational slack, when job i becomes tardy, proportional to the process time.The rule tries to achieve the minimization of maximum and variance of tardiness of jobs.

3.2.7. Proposed Rule VII (AV PRO)It is well known that the SPT rule is good for reducing the percentage of tardy

jobs. Hence, an attempt is made to extend the SPT rule to develop a single priorityindex for a job which can be expected to outperform the SPT rule. The priority indexfor job i is proposed as follows:

Zi ˆXm i

qˆ 1

T iq=mi : … 19†

The job with the minimum value of Zi is chosen for loading. In case of any tie, usethe FIFO rule for breaking it. This rule is expected to reduce the percentage of tardyjobs. This rule is a static rule in the sense that the priority index of a given job, oncecomputed, remains the same throughout the shop.

In all cases, if the priority index of job i yielded by a rule is indicated by Zi, the jobwith the minimum value of Zi is chosen for loading; and if the index of job i yielded bya rule is indicated by Z 0

i , the job with the maximum value Z 0i will be chosen for loading.

To explain further, we present a simple numeric example to illustrate the pro-posed rules.

Suppose we have job i with the data: Ai ˆ 100, c ˆ 3, mi ˆ 3, T i1 ˆ 10, T i2 ˆ 20,T i3 ˆ 10 and Di ˆ 220. We obtain ODDi1 ˆ 100 ‡ 3 10 ˆ 130, ODDi2 ˆ 190 and


Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4

ODDi3 ˆ 220. We also compute FDDi1 ˆ 100 ‡ 10 ˆ 110, FDDi2 ˆ 130 andFDDi3 ˆ 140. Let ½ ˆ 200 and j ˆ 2, i.e. job i is waiting in the queue to undergoits second operation. Let Ci; j¡ 1 be equal to 180. It means that job i has been in queueof the current operation for 20 time units after having completed its ® rst operation at180 time units.

The values of priority indices yielded by the proposed rules are given below.

1. FDD rule: Zi ˆ FDDi2 ˆ 130: 2. PT ‡ PW rule: Zi ˆ 20 ‡ … 200 ¡ 180† ˆ 40.3. PT ‡ PW ‡ FDD rule: Zi ˆ 20 ‡ … 200 ¡ 180† ¡ … 200 ¡ 130† ˆ 20 ¡ 180 ‡

130 ˆ ¡ 30.4. PT ‡ PW ‡ ODD rule: Zi ˆ 20 ‡ … 200 ¡ 180† ¡ … 200 ¡ 190† ˆ 20 ¡ 180 ‡

190 ˆ 30.5. (OPFSLK/PT; FDD) rule: Z 0

i ˆ max f200 ‡ 20 ¡ 130; 0g =20 ˆ 4:5.6. (OPSLK/PT; ODD) rule: Z 0

i ˆ max f200 ‡ 20 ¡ 190; 0g=20 ˆ 1:5.7. AVPRO rule: Zi ˆ … 10 ‡ 20 ‡ 10† =3 ˆ 13:33.

Note that while the job with the least Zi is chosen for loading when the rules FDD,PT + PW, PT + PW + FDD, PT + PW + ODD and AVPROare operational, thejob with the largest Z 0

i is chosen for loading when the rules (OPFSLK/PT; FDD)and (OPSLK/PT; ODD) are implemented. Details of tie-breaking have been givenseparately for each proposed rule.

In all, we have included nine existing rules, and proposed seven new dispatchingrules in our study.

4. Experimental design for the simulation study

Based on the routeing patterns existing in the shop, job shops can be classi® ed intoone of the two categories: open or closed. If jobs on arrival follow one of the ® xedrouteings, it is called a closed job shop, and if the jobs have no restriction on routeings,it is an open job shop. Our study focuses on open job shop con® gurations with theusual standard assumptions (Haupt 1989, Ramasesh 1990, Raghu and Rajendran1993, Holthaus and Rajendran 1997). Some of these assumptions are listed below.

1. A machine can process only one job at a time.2. An operation cannot be pre-empted, implying no job pre-emption.3. The process times of jobs are deterministic, and include times such as set-up

times and removal times.4. There are no machine breakdowns; machines are always available for pro-

cessing jobs.5. There are no other limiting resources such as labour or material.

We assume the presence of ten machines in the shop. In the ® rst phase of thestudy that deals with the conventional open job shops, the number of operations foran entering job is randomly sampled in the range 5± 9, and corresponding machinevisitations are randomly generated among ten machines. It is to be noted that no twoconsecutive operations can be performed on the same machine and that a machinecan be visited by a job for a later operation. In the second phase of the study,involving the comparison of the performance of job shops with no machine revisita-tion and ¯ ow shops with missing operations, we assume the presence of 10 machines.In this case, as for the job shop, the number of operations is randomly sampled fromthe set {5, 6, 7, 8, 9}, and the corresponding machine visitations are randomly


Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4

generated with no machine being revisited. For example, if we have the number ofoperations for an entering job as 7; we randomly sample seven machines to be visitedby the job as {7± 4± 5± 6± 10± 2± 9}, avoiding any revisitation of a machine. In thecase of ¯ ow shop with missing operations, the machine visitation order will be{2± 4± 5± 6± 7± 9± 10}, in order to maintain the unidirectional routeings of jobs. In ouropinion, as per the second phase of the study, such an approach to generate machinevisitations in ¯ ow shops and job shops helps us to have the same experimental set upfor both job shops and ¯ ow shops, so as to draw a meaningful comparison of theperformances of dispatching rules in these two manufacturing systems. Note that bymissing operations in ¯ ow shops, we mean that a job may not be processed on allmachines and it may skip some machines in the ¯ ow line.

In all our experimental studies, process times are sampled from a discrete uni-form distribution in the range 1± 50. The total work-content method of due-datesetting is utilized (see Blackstone et al. 1982) with allowance factors of 3, 5 and 7to represent tight and loose due-date settings. In the studies by Kanet and Hayya(1981) and Ragatz and Mabert (1984), the TWK method is seen to be superior toother due-date setting methods. The job arrivals are generated using an exponentialdistribution for inter-arrival times. Two levels of machine utilization are tested in theexperiments, viz. 85% and 95%. Thus, in all we have three due-date settings and twodi� erent utilization levels, thereby making six di� erent simulation experiments forevery dispatching rule.

In our study, each simulation experiment consists of 20 replications (or runs). Ineach replication, the shop is continually loaded with job-orders that are numberedon their arrival. In order to ascertain when the system attains steady state, we haveobserved shop parameters such as utilization level values, mean ¯ ow time of jobs,etc. It has been observed that steady state has been reached in the shop after thearrival of about 500 job orders. Typically, the total sample size of a job shopsimulation study is of the order of tens of thousands of job completions (Conwayet al. 1960, Blackstone et al. 1982). For a given sample size, it is preferable to have asmaller number of replications and a larger run length (Law and Kelton 1984).Following these guidelines, we have ® xed the number of replications and runlength as 20 and 1500 completed jobs respectively. As for the computation of sta-tistics from a given replication, we have collected data from job orders numbered 501to 2000, and the shop is continually loaded with jobs until the completion of these1500 numbered job orders. This procedure helps us to overcome the problem ofcensored data (see Conway 1965). The statistical analysis of the experimental datawith single factor ANOVA with randomized block design and Duncan’s multiplerange test (see Montgomery 1991, Lorenzen and Anderson 1993) has shown that thissample size yields a variance which results in a type I error of at most 1%. Duncan’smultiple range test has been used to identify the best (marked with * in the tables)and second best set of rules (marked with { in the tables), after conducting the test onthe ® ve best performing rules in each category of performance measures. A ¯ owchart of the job shop simulation experiment is shown in ® gure 1.

The simulation program has been written in C‡ ‡ and implemented using anIBM RS-6000 system, working in a UNIX environment.

5. Results and discussion

The performance of the 16 rules under study is evaluated with respect to mean¯ ow time, maximum ¯ ow time, variance of ¯ ow time, mean tardiness, maximum


Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4


Figure 1. Flow chart for job shop simulation experiment.

Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4

tardiness, variance of tardiness and percentage of tardy jobs. The results have beenobtained by taking the mean of the values obtained for the 20 replications carriedout.

After a detailed statistical analysis of the absolute values of the best ® ve perform-ing rules with respect to a given performance measure, we have tabulated sometypical results in tables 1± 12 (see Appendix) for di� erent utilization levels anddue-date settings. While statistical tests are carried out using the absolute values,results of relative evaluation are presented in the tables. The relative evaluation iscarried out as follows.

For a given performance measure, say, the minimization of mean ¯ ow time, let Fk

be the ¯ ow time yielded by dispatching rule k, where k ˆ 1 refers to the SPT rule, k ˆ 2indicates the ATC rule, k ˆ 3 indicates the MOD rule, and so on. The relative per-formance evaluation of rule k is given by … … Fk ¡ min fFi ; i ˆ 1; 2; . . . ; 16g †

100† = min fFi ; i ˆ 1; 2; . . . ; 16g . It is evident that the percentage relative deviation ofthe value of a given performance measure yielded by the best performing rule will beequal to zero. This method of relative evaluation is carried for all measures of perform-ance, except for measuring the percentage of tardy jobs in which case the absolutevalues are presented.

We now address the relative performance of some good performing rules asfollows: (1) overall performance of the rules (in conventional open job shops, jobshops with no machine revisitation and ¯ ow shops with missing operations), and (2)comparative performance of rules in ¯ ow shops and job shops.

5.1. Overall performance of the rules5.1.1. Mean ¯ ow time

The proposed rule PT ‡ PW appears to be the leader (or not signi® cantly worsethan the best performing rule) in almost all cases irrespective of the nature of theshop, level of utilization in the shop and due-date setting. This rule performs betterthan the PT ‡ WINQ rule which is identi® ed as the best from the literature to date.The reason for the good performance of the PT ‡ PW rule is that it seeks to hastenthe job with the least process time plus the waiting time, thereby leading to theminimum sum of ¯ ow time of jobs. The PT ‡ PW ‡ ODD, PT ‡ PW ‡ FDD andPT ‡ WINQ rules emerge to be the next best performing rules in most cases.

5.1.2. Maximum ¯ ow timeAmong the various rules tested, the new dispatching rules (OPFSLK/PT; FDD)

and FDD emerge as the best, in that order, for minimizing the maximum ¯ ow time.The reason for the good performance of the FDD rule is that the rule seeks tominimize the deviation of job completion from its ¯ ow due-date, and consequentlythe maximum ¯ ow time of a job is minimized. The (OPFSLK/PT; FDD) rule per-forms very well because the rule seeks to obtain the deviation of the job completiontime, beyond the job’s ¯ ow due-date, proportionate to the job process time, andconsequently the maximum ¯ ow time of jobs is minimized. The existing AT± RPTrule ranks third in minimizing the maximum ¯ ow time of jobs.

5.1.3. Variance of ¯ ow timeThe AT± RPT rule emerges as the best in minimizing the variance of ¯ ow time of

jobs. The proposed FDD rule and the (OPFSLK/PT; FDD) rule are the next best in


Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4

almost all cases. The reason for the good performance of these proposed rules are thesame as ascribed to their performances with respect to maximum ¯ ow time of jobs.

5.1.4. Mean tardinessWhen the utilization level is high, the best performing rule in this category is the

PT ‡ PW ‡ ODD rule, followed by PT ‡ PW ‡ FDD and PT ‡ PW rules in thatorder as the next best performing rules. When the utilization level is less, the bestperforming rules are PT ‡ PW ‡ ODD, PT ‡ WINQ ‡ SL and PT ‡ PW ‡ FDD.The reason for the good performances of PT ‡ PW ‡ ODD and PT ‡ WINQ ‡ SLrules is that these rules make use of process time and due-date information. Thereason for the good performance of PT ‡ PW ‡ FDD rule is that the component¯ ow due-date, FDD can be viewed as a rather t̀ight due-date setting’ (though seenwith respect to ¯ ow time), apart from having the component of process time. Thegood performance of the pure process-time based rule, i.e. the PT ‡ PW rule, at highutilization levels is expected, as in the case of other process-time based rules (seeBlackstone et al. 1982, Haupt 1989). It can also be seen that the performance of theslack-based rules is good at lower utilization levels. Note that the relative perform-ance values do not always give a complete picture on the performance of rules,especially when the utilization level is lower and due-date tightness is loose. Thisis mainly because the percentage of tardy jobs is small in this setting, thereby bring-ing down the absolute values of mean tardiness to very small values, and causingwide variation in the relative values even for small changes in absolute values. Forexample, with respect to mean tardiness, the absolute values for PT ‡ WINQ ‡ SLand RR rules are 7.59 and 31.74, and their relative performance values reported are0.00% and 318.12% respectively. This may lead us to the impression that RR rule isa bad performer at this setting, which in reality is not absolutely correct.

5.1.5. Maximum tardinessThe PT ‡ WINQ ‡ SL rule is the best rule (or signi® cantly not worse than the

best performing rule) in this category in almost all cases. This is followed by(OPSLK/PT; ODD) and ODD rules in that order. The negative slack in thePT ‡ WINQ ‡ SL rule serves to enhance its performance at higher utilizationlevels where more jobs are expected to be tardy than at lower utilization levels.We also observe that all three rules mentioned above make use of due-date informa-tion and hence their performances are good. The rule ODD seeks to minimize thedeviation of completion times of a job from its operation due-date, and hence goodperformance for this rule is observed. The rule (OPSLK/PT; ODD) seeks to main-tain the negative slack of a job (after converting it into a positive value) propor-tionate to its process time, resulting in minimization of maximum tardiness of jobs.

5.1.6. V ariance of tardinessThe rule PT ‡ WINQ ‡ SL, followed by ODD and (OPSLK/PT; ODD) rules in

that order, emerge to be the best for this purpose. The behaviour of these rules isattributed to the reasons of good performance with respect to minimizing the maxi-mum tardiness. Generally, the performance pattern of the dispatching rules for thisobjective is similar to the rules’ performances with respect to the maximum tardiness.


Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4

5.1.7. Percentage of tardy jobsThe proposed rule PT ‡ PW appears to be the best rule for this category, fol-

lowed by AVPRO, PT ‡ PW ‡ ODD and PT ‡ WINQ rules. This observation is inconformance with the literature ® ndings (see Blackstone et al. 1982, Haupt 1989)that process-time based rules perform very well with respect to minimizing theproportion of tardy jobs. The SPT rule, reported in the literature as the best rulefor minimizing the percentage of tardy jobs, does not emerge to be the best in thecurrent study.

On the whole, we feel that PT ‡ WINQ ‡ SL and (OPSLK/PT; ODD) rules canbe termed as the best for minimizing a number of tardiness-related measures simul-taneously. Similarly, (OPFSLK/PT; FDD) and FDD rules may be considered as thebest for minimizing many ¯ ow-time related measures at the same time. Even thoughwe state the above rules to be the best, it is actually for the practitioner (or thedecision maker) to decide ® nally on the dispatching rules on the basis of the pre-ference structure for objectives.

5.2. A comparative analysis on the relative performances of some rules in ¯ owshops with missing operations and job shops

It is interesting to note that there are di� erences in the performances of rules injob shops (with no machine revisitations of jobs) and ¯ ow shops (with missingoperations on jobs). For example, the relative performance of the SPT rule isbetter in ¯ ow shops than job shops. The reason is that the waiting times of di� erentjobs do not di� er very much (when the SPT rule is used) in ¯ ow shops due to theunidirectional routeing of jobs, as opposed to the case of job shops. For the samereason, the di� erence in the performances of PT ‡ PW and SPT is not signi® cant in¯ ow shops. The performance of PT ‡ WINQ ‡ SL rule is better in job shops than¯ ow shops. The reason is that the component `WINQ’ is a more active contributor tothe priority index in job shops than in ¯ ow shops. This contribution is once againdue to the non-unidirectional routeing in job shops, and the contribution of thecomponent WINQ is not quite signi® cant in ¯ ow shops. Consider one of the pro-posed rules, viz. the PT ‡ PW rule. The relative performance of the rule is better injob shops than ¯ ow shops. As observed in the case of the SPT rule in ¯ ow shops, thecomponent `PW’ is not a signi® cant contributor in the case of ¯ ow shops, whereasthe component serves e� ectively to enhance the performance of the PT ‡ PW rule injob shops. Again, for similar reasons, the relative performance of the PT ‡ PW ruleis better in job shops than in ¯ ow shops with respect to the objective of minimizingthe number of tardy jobs. This observation is in line with the known observation thatthe process-time based rules are quite e� ective in minimizing the number of tardyjobs (see Blackstone et al. 1982, Haupt 1989). We also observe that the performancesof the rules viz. PT ‡ PW, FDD, (OPFSLK/PT; FDD), PT ‡ PW ‡ ODD, ODDand (OPSLK/PT; ODD) rules are indeed consistently very good with respect to themeasures that they seek to minimize in both job shops and ¯ ow shops. In otherwords, these rules seem to be quite robust in the sense that their performances arenot a� ected by the routeing pattern of jobs, utilization level of shops and tightness ofdue-date settings. This brings out the utility of concepts of ¯ ow due-date and opera-tional due-date in the development of dispatching rules. We are of the opinion thatthe development of any new rules should consider the use of job due-date and ¯ owdue-date to minimize the measures related to tardiness and ¯ ow time of jobs.


Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4

6. A compilation of ® ndings of the study

A compilation of the best performing rules summarized on the basis of overallperformance in di� erent experimental settings is given in table 13. On the whole, theproposed rule PT ‡ PW emerges to be very good for minimizing mean ¯ ow time ofjobs, followed by PT ‡ PW ‡ ODD, PT ‡ PW ‡ FDD and PT ‡ WINQ rules. Forthe minimization of maximum ¯ ow time and variance of ¯ ow time, FDD and(OPFSLK/PT; FDD) rules lead the rest, followed by the AT± RPT rule. For mini-mizing mean tardiness, PT ‡ PW ‡ ODD, PT ‡ PW ‡ FDD and PT ‡ WINQ ‡ SL(in some cases) rules are identi® ed as the best. For minimizing maximum tardinessand variance of tardiness, the PT ‡ WINQ ‡ SL rule proves to be the best, followedby (OPSLK/PT; ODD) and ODD rules. For minimizing the percentage of tardyjobs, the PT ‡ PW rule, followed by AVPRO, PT ‡ PW ‡ ODD and PT ‡ WINQrules, are identi® ed to be the best. As mentioned earlier, the use of concepts such as¯ ow due-date and operational due-date has been found to quite useful in developinge� ective dispatching rules in scheduling.

7. Conclusion

Even though extensive research has been carried out on job shop scheduling forthe last three decades, the problem still appears open for further studies. With theproposition of the new concept of ¯ ow due-date, which yields consistently excellentresults individually and in conjunction with other pieces of information using joband operational due-dates, it leaves a lot to be explored, making the research on jobshop scheduling g̀reener’ to look at.

It can be noted that a lot of work has been carried out on the study of dispatchingrules in the area of dynamic job shops, but there has been relatively few attempts inthe ® eld of dynamic ¯ ow shops. This study is also an attempt in that direction toexplore and compare the relative performances of dispatching rules in job shops withno machine revisitations of jobs and ¯ ow shops with missing operations of jobs. Theproposed rules have been found to be quite e� ective in minimizing mean ¯ ow time,maximum ¯ ow time, variance of ¯ ow time, mean tardiness, maximum tardiness,variance of tardiness and percentage of tardy jobs, separately or more than one ata time. The ® rst part of the study explains the new set of rules in detail along withbest performing existing rules identi® ed from the literature. The simulation study inthe ® rst phase of the work has evaluated the performances of rules in a conventionalopen job shop environment. The second simulation study has compared the rules injob shops with no machine revisitation of jobs and ¯ ow shops with missing opera-tions. The set of best performing rules for every measure has been identi® ed. It isfound from the study that some of the proposed and existing rules perform very wellunder di� erent experimental conditions. As extensions of the present work, futureresearch could look into the cases where jobs have di� erent weights (or penalties) for¯ ow time and tardiness. Further research can also be directed toward the minimiza-tion of earliness of jobs, apart from the minimization of ¯ ow time and tardiness ofjobs. The problem of minimizing both earliness and tardiness of jobs assumes sig-ni® cance in the context of Just-In-Time manufacturing. The authors of the presentwork are also investigating such problems of dynamic job shop scheduling.

Acknowledgement

The authors are thankful to the referees for their constructive suggestions andcomments to improve the earlier version of the paper.


Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4

Appendix


Variance VarianceDispatching Mean Maximum of Mean Maximum of Percentagerule ¯ ow time ¯ ow time ¯ ow time tardiness tardiness tardiness tardy

SPT 72.86 848.50 13967.52 263.09 1244.83 25622.32 54.13ATC 316.34 1327.12 30849.10 918.93 1969.59 58632.90 45.10{MOD 95.64 841.08 13727.97 258.74 1233.03 25176.27 57.26RR 67.72 246.14 1644.02 176.64 354.75 2845.63 80.48PT ‡ WINQ 57.70{ 851.25 14253.28 143.10{ 1375.64 31224.26 45.14{PT ‡ WINQ‡ SL 51.74{ 28.42 44.20 125.44{ 0.00* 0.00* 93.79AT± RPT 129.16 11.79{ 15.04{* 345.74 64.52 147.30 99.20EDD 123.62 47.90 113.42 329.78 58.47 129.32 99.15FDD 66.25 3.34* 0.72* 166.58 13.71*{ 27.07{ 95.78ODD 76.88 16.79{ 32.94{ 196.09 16.79{ 29.08{ 98.04PT ‡ PW 4.33* 543.39 6489.47 34.85*{ 796.64 11557.97 39.36{PT ‡ PW ‡ FDD 4.06* 160.96 903.66 8.41* 242.63 1557.04 57.74PT ‡ PW ‡ ODD 0.00* 169.00 971.10 0.00* 253.09 1669.35 46.12{OPFSLK/PT; FDD 64.70 0.00* 0.00* 194.85 10.68*{ 23.57{ 94.11OPSLK/PT; ODD 72.95 15.63{ 31.31{ 184.85 15.60{ 28.30{ 97.88AVPRO 96.30 1302.49 31422.52 292.48 1911.40 58143.39 35.86*

* and { indicate the best and second best performing subsets respectively.

Table 1. Relative performance of rules in a conventional open job shop (utilization: 95%TWK: 3).


SPT 66.65 848.50 13967.52 389.09 1707.94 40272.89 31.00ATC 271.39 1331.01 31396.87 1303.66 2731.76 95904.23 29.30MOD 100.53 799.93 12509.97 345.24 1625.62 36743.33 32.81RR 64.37 129.93 608.87 158.74 252.06 1505.32 66.16PT ‡ WINQ 53.63{ 851.25 14253.28 141.77{ 1712.41 40783.47 26.32{PT ‡ WINQ‡ SL 45.49{ 28.54{ 51.82{ 72.87{ 0.00* 0.00* 64.45AT-RPT 121.79 11.79*{ 15.04*{ 406.60 110.67 299.19 90.69EDD 111.63 57.43 155.46 355.04 77.51 176.22 90.23FDD 60.90 3.34* 0.72* 209.54 38.89{ 92.55{ 72.30ODD 81.38 34.30{ 85.42{ 215.41 41.39{ 84.87{ 84.09PT ‡ PW 0.98* 543.49 6489.47 51.69*{ 1088.74 17698.54 21.33*PT ‡ PW ‡ FDD 0.71* 160.96 903.66 0.24* 342.00 2327.59 22.04{PT ‡ PW ‡ ODD 0.00* 167.68 960.47 0.00* 351.19 2431.36 19.72*OPFSLK/PT; FDD 58.63 0.00* 0.00* 175.54 34.06{ 79.11{ 69.09OPSLK/PT; ODD 78.67 34.52 87.72 202.93 40.87{ 85.86{ 83.76AVPRO 89.99 1302.49 31422.52 459.35 2621.39 92194.12 22.21{



Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4



SPT 33.51 421.24 3947.17 193.46 850.30 10027.25 34.52ATC 122.45 767.64 11113.06 827.05 1583.33 30948.97 34.72MOD 39.65 388.44 3418.54 167.06 788.41 8757.99 34.57RR 34.61 48.71 160.52 122.79 106.30 357.10 54.47PT ‡ WINQ 17.37{ 396.88 3602.32 135.47 808.91 9208.10 27.45{PT ‡ WINQ‡ SL 22.85{ 11.12{ 35.34{ 47.90{ 0.00* 0.00* 53.85AT± RPT 78.34 9.17{ 32.77{ 382.44 83.60 199.20 84.88EDD 69.62 43.88 120.41 318.50 64.47 142.23 83.17FDD 33.48 0.00* 0.00* 112.47 24.67{ 51.92{ 63.21ODD 41.53 16.79 43.35 142.45 14.36*{ 22.48*{ 71.42PT ‡ PW 0.00* 253.66 1746.55 53.25{ 511.88 4121.89 24.46*{PT ‡ PW ‡ FDD 2.32* 119.33 566.99 5.37* 255.81 1321.46 28.93{PT ‡ PW ‡ ODD 0.31* 113.20 529.38 0.00* 242.27 1215.84 22.13*OPFSLK/PT; FDD 29.08 0.22* 2.08* 98.25{ 26.37{ 44.74{ 60.32OPSLK/PT; ODD 40.20 16.53{ 43.22{ 133.92 13.87*{ 22.26*{ 71.00AVPRO 38.36 740.88 10758.64 276.34 1477.34 27987.38 26.13{




SPT 33.51 421.24 3947.17 1430.57 2114.37 49336.00 14.06ATC 106.30 865.25 13976.99 5694.20 4485.90 208740.52 17.35MOD 60.04 329.68 2544.17 848.35 1671.28 31661.51 10.30{RR 32.99 46.91 150.48 318.12 221.44 1189.30 20.86PT ‡ WINQ 17.37{ 396.88 3602.32 1088.93 2000.52 44530.38 11.53PT ‡ WINQ‡ SL 22.24{ 28.91{ 93.47{ 0.00* 0.00* 0.00* 6.97*AT± RPT 78.34 9.17{ 32.77{ 1536.89 299.17 1365.23 43.25EDD 65.71 59.47 185.97 815.94 159.26 527.82 29.82FDD 33.48 0.00* 0.00* 301.98 145.10{ 490.61{ 17.72ODD 50.39 43.05{ 129.04 375.76 88.19{ 239.97{ 21.81PT ‡ PW 0.00* 253.66 1746.55 557.58 1271.49 18970.11 9.66{PT ‡ PW ‡ FDD 2.32* 119.33 566.99 243.87{ 673.84 5976.67 7.21*{PT ‡ PW ‡ ODD 3.12* 120.39 573.16 247.96{ 677.17 6028.56 6.44*OPFSLK/PT; FDD 29.08 0.22* 2.08* 306.32 151.94{ 435.85{ 17.68OPSLK/PT; ODD 49.78 43.22 130.07 354.81 84.12{ 225.94{ 21.48AVPRO 38.36 740.88 10758.64 2221.74 3658.06 142562.54 13.23



Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4



SPT 144.45 853.18 16328.69 709.47 1498.44 32073.18 55.87ATC 609.55 1749.30 54666.58 3637.84 3020.48 107872.10 45.20MOD 150.78 860.03 15019.81 637.91 1493.66 32128.63 59.80RR 107.39 126.14 1263.59 301.55 240.53 933.68 79.59PT ‡ WINQ 88.70{ 848.20 15842.06 329.85 1487.51 33473.92 42.13{PT ‡ WINQ‡ SL 95.39{ 14.94{ 33.74{ 466.33 0.00* 0.00* 98.27AT± RPT 232.89 16.61{ 0.00* 1284.90 93.66 29.79 100.00EDD 228.61 52.68 152.45 1259.36 82.55 19.90 100.00FDD 125.30 1.58* 6.28* 643.54 27.55{ 15.96{ 99.67ODD 145.95 19.15{ 29.16{ 766.52 26.35{ 3.40*{ 100.00PT ‡ PW 6.03* 211.78 2312.09 95.91{ 394.49 2866.12 27.73*PT ‡ PW ‡ FDD 9.75* 66.23 353.60 34.00{ 127.00 474.39 47.40PT ‡ PW ‡ ODD 0.00* 91.20 611.31 0.00* 155.92 742.13 28.73*OPFSLK/PT; FDD 106.69 0.00* 17.11{ 533.86 18.27{ 16.81{ 98.33OPSLK/PT; ODD 141.74 19.42 65.90 741.42 28.74{ 9.11*{ 99.93AVPRO 141.38 1549.63 48304.58 854.46 2687.51 101502.8 34.93{


Table 5. Relative performance of rules in a job shop with no revisitation (utilization: 95%TWK: 3).


SPT 138.21 853.18 16328.69 1258.11 2169.91 44359.81 32.20ATC 533.42 1786.62 56929.90 7260.10 4547.00 172755.5 32.47MOD 163.31 848.20 14408.29 1489.80 2158.85 43416.08 35.73RR 95.79 69.54 393.53 391.43 234.12 558.98 52.67PT ‡ WINQ 83.88{ 848.20 15842.06 438.22 2150.87 45960.35 23.93{PT ‡ WINQ‡ SL 89.90{ 17.83{ 73.45{ 401.32 0.00* 0.00* 62.33AT± RPT 224.40 16.61{ 0.00* 2169.27 148.87 82.96 99.00EDD 219.01 63.69 212.78 2091.66 120.37 148.49 99.60FDD 119.56 1.59* 6.28* 774.33 53.00{ 47.36{ 78.47ODD 154.88 47.82 107.50 1193.59 63.52{ 31.35{ 96.33PT ‡ PW 3.32* 211.78 2312.09 164.31{ 573.64 3665.94 13.27{PT ‡ PW ‡ FDD 6.95* 66.24 353.60 0.00* 170.57 471.01 11.53*PT ‡ PW ‡ ODD 0.00* 110.30 776.78 2.92* 255.13 993.53 7.60*OPFSLK/PT; FDD 105.78 0.00* 17.11{ 626.50 41.41{ 42.43{ 73.87OPSLK/PT; ODD 151.30 48.20 123.56 1143.18 59.39{ 31.92{ 95.87AVPRO 135.22 1549.63 48304.58 1800.59 3877.90 140105.4 20.93{



Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4



SPT 34.72 314.07 4212.68 349.31 787.21 7228.63 25.87ATC 115.00 711.27 11023.75 1729.93 1900.93 37254.34 29.93MOD 46.76 310.19 2434.56 329.10 777.21 7063.37 24.33RR 34.96 63.38 237.77 153.26 96.51 212.67 30.60PT ‡ WINQ 19.61{ 251.31 1645.78 257.64 625.35 4795.84 19.33{PT ‡ WINQ‡ SL 26.57{ 5.78*{ 29.67{ 66.39{ 0.00* 0.00* 27.33AT± RPT 87.23 23.44{ 8.13{ 834.39 130.93 241.74 74.20EDD 81.61 51.94 132.45 708.20 120.93 228.01 72.13FDD 35.54 0.00* 0.00* 159.44 13.49* 18.30{ 41.13ODD 44.41 20.29{ 23.41{ 212.52 39.53{ 66.30{ 43.73PT ‡ PW 0.00* 199.37 1465.8 99.31{ 523.49 3578.38 14.20*{PT ‡ PW ‡ FDD 6.98*{ 48.69 113.46 13.90* 144.65 456.84 16.93{PT ‡ PW ‡ ODD 2.28* 105.86 316.17 0.00* 287.21 1323.64 9.33*OPFSLK/PT; FDD 30.83 0.18* 4.21*{ 150.74{ 28.14{ 48.94{ 39.60OPSLK/PT; ODD 44.48 19.57{ 20.29{ 214.78 37.91{ 61.63{ 44.33AVPRO 38.53 363.12 1397.51 526.61 943.72 10267.94 22.33{




SPT 34.72 314.07 4212.68 7283.33 2558.87 59235.93 7.53ATC 118.85 902.89 14980.90 49991.66 8341.13 598999.20 13.87MOD 67.08 289.9 1741.58 3328.33 2342.74 50401.59 4.20{RR 35.18 67.36 201.44 311.67{ 338.55 1299.68 10.47PT ‡ WINQ 19.61{ 251.31 1645.78 5846.67 2218.55 44823.89 6.47PT ‡ WINQ‡ SL 29.11{ 38.14{ 76.57{ 0.00* 0.00* 0.00* 1.53*AT± RPT 87.23 23.44{ 8.13*{ 9125.00 584.68 3300.41 26.20EDD 79.92 78.27 234.65 3973.33 355.65 1440.42 14.80FDD 35.54 0.00* 0.00* 863.33 165.32{ 459.61{ 5.73ODD 50.73 58.79 99.07 1253.33 159.68{ 450.14{ 7.13PT ‡ PW 0.00* 199.37 1465.80 2615.00 1718.55 27786.60 4.13{PT ‡ PW ‡ FDD 6.98* 48.69 113.46 635.00{ 465.32 2523.44 2.60*{PT ‡ PW ‡ ODD 6.00* 139.40 457.07 971.67 900.00 8324.53 1.73*OPFSLK/PT; FDD 30.83 0.18* 4.21*{ 853.33 167.74{ 487.43{ 5.13OPSLK/PT; ODD 50.12 56.45 93.78 1200.00 184.68{ 560.67{ 7.00AVPRO 38.53 363.12 1397.52 12263.33 3170.97 91625.54 8.20



Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4



SPT 8.85*{ 707.01 27059.02 11.52{ 914.12 36931.12 50.93ATC 170.87 1257.73 84615.71 265.46 1623.69 115521.30 45.13MOD 10.53{ 734.47 29275.76 9.67*{ 947.19 40058.38 53.13RR 18.18 270.45 6971.49 45.50 185.97 282.38 84.63PT ‡ WINQ 0.00* 1037.10 61330.17 1.97* 1339.34 83596.28 40.93PT ‡ WINQ‡ SL 50.49 9.36 33.76 68.11 1.02* 3.04*{ 99.93AT± RPT 70.40 4.77*{ 0.00* 98.75 16.54 11.49 100.00EDD 70.49 19.26 34.07 98.89 10.54 0.00* 100.00FDD 53.95 0.54* 5.90*{ 73.44 5.48*{ 7.04*{ 99.87ODD 51.61 8.20{ 27.85{ 69.83 1.58* 3.10*{ 100.00PT ‡ PW 12.74{ 1264.45 96844.98 25.10 1624.90 130905.40 36.60*{PT ‡ PW ‡ FDD 24.05 1258.78 95199.98 31.32 1630.19 131308.90 72.20PT ‡ PW ‡ ODD 3.32* 1210.98 87838.78 0.00* 1554.95 119075.30 59.47OPFSLK/PT; FDD 53.79 0.00* 7.39*{ 66.94 6.13{ 14.49 100.00OPSLK/PT; ODD 44.81 7.62{ 35.47{ 59.38 0.00* 8.79*{ 99.93AVPRO 17.50 1251.59 92404.00 30.72 1599.07 123587.20 33.00*


Table 9. Relative performance of rules in a ¯ ow shop with missing operations (utilization:95% TWK: 3).


SPT 8.85{ 707.01 27059.02 108.05 1111.15 47575.45 28.00{ATC 157.10 1322.97 93745.83 591.60 2057.97 166583.60 28.80MOD 27.89 849.98 35158.39 108.14 1322.87 62976.02 32.40RR 3.31* 97.67 303.76 0.00* 42.42 445.02 68.67PT ‡ WINQ 0.00* 1037.10 61330.17 92.66{ 1627.61 108264.30 23.60{PT ‡ WINQ‡ SL 53.32 16.53 64.42 170.64 0.00* 4.90*{ 99.07AT± RPT 70.40 4.77*{ 0.00* 243.74 28.96 44.81 99.87EDD 77.05 26.21 58.07 248.16 14.20{ 0.00* 100.00FDD 53.95 0.54* 5.90*{ 188.37 14.42 32.00 99.33ODD 48.58 13.32{ 55.32 154.95 1.01* 14.10{ 99.93PT ‡ PW 12.74{ 1274.88 96844.98 146.29 1978.70 170722.30 23.00*{PT ‡ PW ‡ FDD 24.05 1264.44 95199.98 144.58 1985.13 171826.10 36.93PT ‡ PW ‡ ODD 7.36*{ 1258.78 99409.87 85.84*{ 1971.15 172945.80 24.13{OPFSLK/PT; FDD 53.79 0.00* 7.39*{ 172.16 12.79{ 39.01 99.27OPSLK/PT; ODD 45.14 13.54{ 61.26 143.71 0.56* 21.01{ 99.87AVPRO 17.50 1251.59 92404.00 159.00 1929.69 158306.70 19.93*



Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4



SPT 11.85{ 254.35 1662.37 67.47 582.08 4180.40 20.40{ATC 79.86 568.95 6589.97 629.20 1282.82 17578.71 27.93MOD 19.02 234.51 1407.15 26.6{ 538.57 3649.20 19.87{RR 29.65 66.45 136.44 43.44 54.48 100.16 46.60PT ‡ WINQ 0.00* 291.90 2126.59 34.03{ 637.11 4945.34 14.80*{PT ‡ WINQ‡ SL 28.56 15.86 40.52 48.67 7.68*{ 8.07*{ 47.60AT± RPT 52.85 12.41*{ 8.83*{ 229.62 72.76 118.26 66.20EDD 49.54 26.24 50.27 175.33 29.98 33.54 65.60FDD 26.77 2.11* 7.94*{ 55.96 12.07{ 14.88{ 46.33ODD 22.38 14.01{ 37.79 18.11{ 1.10* 1.19* 39.87PT ‡ PW 5.65*{ 322.95 2496.54 98.25 737.66 6324.57 18.60{PT ‡ PW ‡ FDD 8.33*{ 361.52 3021.91 41.91 758.87 6806.74 23.00PT ‡ PW ‡ ODD 3.07* 306.50 2265.31 0.00* 632.54 4865.47 13.60*OPFSLK/PT; FDD 32.84 0.00* 0.00* 105.34 21.76{ 32.27 53.20OPSLK/PT; ODD 21.32 11.81*{ 33.49{ 11.29*{ 0.00* 0.00* 38.13AVPRO 17.37 377.89 2910.38 155.07 775.14 7100.40 18.27{




SPT 11.85{ 254.35 1662.37 1461.81 1246.06 15430.30 6.47ATC 66.75 916.31 15589.99 7905.12 4327.56 161195.20 11.00MOD 34.83 230.06 1304.64 640.55 1020.08 10313.27 3.40*{RR 27.78 132.95 454.08 412.87 678.87 7603.20 12.13PT ‡ WINQ 0.00* 291.90 2126.59 1247.24 1326.77 17422.15 4.53{PT ‡ WINQ‡ SL 25.70 40.22 113.87 133.46{ 9.45*{ 12.91*{ 5.47AT± RPT 52.85 12.41*{ 8.83*{ 1569.29 215.35 691.81 22.40EDD 44.59 49.62 123.30 445.28 64.17 124.00 10.60FDD 26.77 2.11* 7.94*{ 293.31 76.38 166.33 9.13ODD 18.52 29.55{ 83.04{ 0.39* 0.00* 0.11* 3.27*{PT ‡ PW 5.65*{ 322.95 2496.54 2123.62 1605.51 24744.11 7.40PT ‡ PW ‡ FDD 8.33*{ 361.52 3021.91 1242.52 1547.24 23545.56 6.00PT ‡ PW ‡ ODD 2.60* 324.68 2594.51 883.86 1326.38 17390.44 2.53*OPFSLK/PT; FDD 32.84 0.00* 0.00* 658.66 79.92 205.15 13.87OPSLK/PT; ODD 18.34 29.55{ 81.51{ 0.00* 0.00* 0.00* 3.20*AVPRO 17.37 377.89 2910.38 2743.31 1650.79 26937.66 8.27



Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4


List of best performing rules under di� erent experimental conditions

Due-datePerformance measures allowance (c) Utilization level 95% Utilization level 85%

PT ‡ PW PT ‡ PWc ˆ 3 PT ‡ PW ‡ ODD PT ‡ PW‡ ODD

PT ‡ PW‡ FDD PT ‡ PW ‡ FDD

PT ‡ PW PT ‡ PWc ˆ 5 PT ‡ PW ‡ ODD PT ‡ PW‡ ODD

PT ‡ PW‡ FDD PT ‡ PW ‡ FDD

(OPFSLK/PT; FDD) (OPFSLK/PT; FDD)c ˆ 3 FDD FDD

AT± RPT AT± RPT

(OPFSLK/PT; FDD) (OPFSLK/PT; FDD)c ˆ 5 FDD FDD

AT± RPT AT± RPT

AT± RPT AT± RPTc ˆ 3 FDD FDD

(OPFSLK/PT; FDD) (OPFSLK/PT; FDD)AT± RPT AT± RPT

c ˆ 5 FDD FDD(OPFSLK/PT; FDD) (OPFSLK/PT; FDD)

PT ‡ PW ‡ ODD PT ‡ PW‡ ODDc ˆ 3 PT ‡ PW‡ FDD PT ‡ PW ‡ FDD

PT ‡ PW PT ‡ WINQ‡ SL

PT ‡ PW ‡ ODD PT ‡ WINQ‡ SLc ˆ 5 PT ‡ PW‡ FDD PT ‡ PW‡ ODD

PT ‡ PW PT ‡ PW ‡ FDD

PT ‡ WINQ‡ SL PT ‡ WINQ‡ SLc ˆ 3 (OPSLK/PT; ODD) (OPSLK/PT; ODD)

ODD ODD

PT ‡ WINQ‡ SL PT ‡ WINQ‡ SLc ˆ 5 (OPSLK/PT; ODD) ODD

ODD (OPSLK/PT; ODD)

PT ‡ WINQ‡ SL PT ‡ WINQ‡ SLc ˆ 3 ODD ODD

(OPSLK/PT; ODD) (OPSLK/PT; ODD)PT ‡ WINQ‡ SL PT ‡ WINQ‡ SL

c ˆ 5 ODD (OPSLK/PT; ODD)(OPSLK/PT; ODD) ODD

AVPRO PT ‡ PW‡ ODDc ˆ 3 PT ‡ PW PT ‡ PW

PT ‡ PW ‡ ODD AVPRO

PT ‡ PW ‡ ODD PT ‡ WINQ‡ SLc ˆ 5 PT ‡ PW PT ‡ PW‡ ODD

AVPRO PT ‡ PW

Table 13. A compilation of overall performance of rules.

Mean ¯ ow time

8>>>>>><

>>>>>>:

Maximum ¯ ow time

8>>>>>><

>>>>>>:

Variance of ¯ ow time

8>>>>>><

>>>>>>:

Mean tardiness

8>>>>>><

>>>>>>:

Maximum tardiness

8>>>>>><

>>>>>>:

Variance of tardiness

8>>>>>><

>>>>>>:

Percentage of tardy jobs

8>>>>>><

>>>>>>:

Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4

References

Anderson, E. J. and Nyirenda, J. C., 1990, Two new rules to minimize tardiness in a jobshop. International Journal of Production Research, 28, 2277± 2292.

Baker, K. R., 1974, Introduction to Sequencing and Scheduling (New York: Wiley).Baker, K. R., 1984, Sequencing rules and due-date assignments in a job shop. Management

Science, 30, 1093± 1104.Baker, K.R. and Bertrand, J.W.M., 1982, A dynamic priority rule for sequencing against

due-dates. Journal of Operations Management, 3, 37± 42.Baker,K.R. and Kanet, J.J., 1983, Job shop scheduling with modi® ed due dates. Journal of

Operations Management, 4, 11± 22.Blackstone, J. H., Phillips, D. T. and Hogg, G. L., 1982, A state of the art survey of

dispatching rules for manufacturing job shop operations. International Journal ofProduction Research, 20, 27± 45.

Campbell,H.G.,Dudek,R. A. and Smith,M.L., 1970, A heuristic algorithm for the n-job,m-machine sequencing problem. Management Science, 16, B630± B637.

Carroll, D. C., 1965, Heuristic sequencing and multiple component jobs. Unpublished PhDdissertation, Massachusetts Institute of Technology, Cambridge, MA.

Conway, R. W., 1965, Priority dispatching and job lateness in a job shop. Journal ofIndustrial Engineering, 16, 123± 130.

Conway, R. W., Johnson,B.M. and Maxwell,W.L., 1960, An experimental investigationof priority dispatching. Journal of Industrial Engineering, 11, 221± 230.

Day, J. E. and Hottenstein, M. P., 1970, Review of sequencing research. Naval ResearchL ogistics Quarterly, 17, 11± 39.

French,S., 1982, Sequencing and Scheduling: An Introduction to the Mathematics of the JOBShop (Chichester: Ellis Horwood).

Haupt, R., 1989, A survey of priority rule based dispatching. O. R. Spektrum, 11, 3± 16.Holthaus, O. and Rajendran, C., 1997, E� cient dispatching rules for scheduling in job

shop. International Journal of Production Economics, 48, 87± 105.Hunsucker, J. L. and Shah. J. R., 1992, Performance of priority rules in a due date ¯ ow

shop. OMEGA, 20, 73± 89.Hunsucker, J. L. and Shah. J.R., 1994, Comparative performance analysis of priority rules

in a constrained ¯ ow shop with multi-processors environment. European Journal ofOperational Research, 72, 102± 114.

Ignall,E. and Schrage.L., 1965, Application of branch-and-bound technique to some ¯ owshop scheduling problems. Operations Research, 13, 400± 412.

Ishibuchi, H., Misaki, S. and Tanaka, H., 1995, Modi® ed simulated annealing algorithmsfor the ¯ ow shop sequencing problems. European Journal of Operational Research, 81,388± 398.

Jensen, J. B, Philipoom, P. R. and Malhotra, M. K., 1995, Technical note: evaluation ofscheduling rules with commensurate customer priorities in job shops. Journal ofOperations Management, 13, 213± 228.

Kanet, J. J., 1982, On anomalies in dynamic ratio type scheduling rules: a clarifying analysis.Management Science, 28, 1337± 1341.

Kanet, J. J. and Hayya, J. G., 1981, Priority dispatching with operation due-dates in a jobshop. Journal of Operations Management, 2, 167± 176.

Law, A. M. and Kelton, W. D., 1984, Con® dence intervals for steady state simulation: I, asurvey of ® xed sample survey procedures. Operations Research, 32, 1221± 1239.

Lorenzen, T. J. and Anderson, V. L., 1993, Design of Experiments: A No-Name Approach(New York: Marcel Dekker).

Montgomery, D. C., 1991, Design and Analysis of Experiments, 3rd edn (New York: Wiley).Nawaz, M., Encore, Jr. E. E. and Ham, I., 1983, A heuristic algorithm for the m-machine,

n-job ¯ ow shop sequencing problem. OMEGA, 11, 91± 95.Panwalker, S. S. and Iskander, W., 1977, A survey of scheduling rules. Operations

Research, 25, 49± 61.Pinedo,M., 1995, Scheduling Theory, Algorithms and Systems (Englewood Cli� s, NJ: Prentice

Hall).Ragatz,G.L. and Mabert,V.A., 1984, A simulation analysis of due date assignment rules.

Journal of Operations Management, 5, 27± 39.


Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4

Raghu, T. S. and Rajendran, C., 1993, An e� cient dispatching rule for scheduling in a jobshop. International Journal of Production Economics, 32, 301± 313.

Raghu, T.S. and Rajendran, C., 1995, Due-date setting methodologies based on simulatedannealing-an experimental study in a real-life job shop. International Journal ofProduction Research, 33, 2535± 2554.

Rajendran, C., 1994, A heuristic for scheduling in ¯ ow shop and ¯ ow line-based manu-facturing cell with multi-criteria. International Journal of Production Research, 32,2541± 2558.

Rajendran, C. and Holthaus, O., 1999, A comparative study of dispatching rules indynamic ¯ ow shops and job shops. European Journal of Operational Research, 116,156± 170.

Ramasesh,R., 1990, Dynamic job shop scheduling: a survey of simulation research. OMEGA,16, 43± 57.

Rochette, R. and Sadowski, R. P., 1976, A statistical comparison of the performance ofsimple dispatching rules for a particular set of job shops. International Journal ofProduction Research, 14, 63± 75.

Russell, R. S., Dar-el, E. M. and Taylor III, B. W., 1987, A comparative analysis of theCOVERT job sequencing rule using various shop performance parameters.International Journal of Production Research, 25, 1523± 1540.

Scudder,G.D. and Hoffmann, T. R., 1987, The use of cost-based priorities in random and¯ ow shops. Journal of Operations Management, 7, 217± 232.

Vepsalainen, A. P. J. and Morton, T. E., 1987, Priority rules for job shops with weightedtardiness costs. Management Science, 33, 1035± 1047.

Waikar, A. M., Sarker, B. R. and Lal, A. M., 1995, A comparative study of some prioritydispatching rules under di� erent shop loads. Production Planning and Control, 6, 301±310.

586 Dispatching rules for shop scheduling

Dow

nloa

ded

by [

Tex

as A

& M

Int

erna

tiona

l Uni

vers

ity]

at 2

3:01

07

Oct

ober

201

4

Documents

New dispatching rules for shop scheduling: A step forward