Simulation studies in job shop scheduling—II

Comput. & Indus Engng V o l 8. No 2, PD 95 105. 1984 printed in Great Brttain

SIMULATION

STUDIES

0360 8352/84 S3 00 + 00 P e r g a m o n Press ktd

IN JOB SHOP

SCHEDULING--II

P E R F O R M A N C E OF PRIORITY RULES ALl S. KIRAN Department of Industrial and Systems Engineering, University of Southern CaLifornia, Los Angeles, CA 90007, U.S.A.

and MILTON L. SMITH Department of Industrial Engineering,Texas Technical University, P.O. Box 4130, Lubbock, TX 79409, U.S.A. (Received for publication 28 September 1983)

Abstract--Major simulation studies of dynamicjob shop scheduling problem and approaches taken to model dynamic job shops have been consideredin Part I[25] of this paper. In Part II we focus our attention on basic results on relativeeffectivenessof priority rules in job shop simulation literature. Information on surveyedarticles also is provided in the Appendix. RESULTS FOR COMPLETION TIME BASED CRITERIA The Shortest Processing Time (SPT) rule is superior to other simple priority rules for job-completion times based and in process jobs-based criteria. However, some weighted priority rules are found slightly more effective than the SPT rule for average flow time and average number of jobs in. the shop; Conway[7, 10] reported that a weighted priority rule consisting of SPT and A W I N Q (Anticipated Work In Next Queue) gave better results than SPT for average flow time, and another weighted priority rule consisting o f SPT and L W K R gave better results for average number of jobs in the shop. SPT could not show the same superiority for other criteria in this group. FISFS is best among the simple rules for variance of flow times, shortest setup time is best for total or average setup times, and a heuristic rule[l 2, 13] based on job pooling is better than SPT in balancing the workload among the machines. Simplicity of SPT led to attempts to find rules combining SPT with FCFS to yield better performance for variance of flow times without increasing the average flow time. These attempts included: (1) Alternatingly use SPT and FCFS in predetermined time intervals[5]. (2) Use SPT until waiting time of a job reaches a certain limit in the queue; use F C F S for jobs with long times in queue (truncated SPT)[3, 7, 10, 273]. (3) Use FCFS until queue length reaches a certain limit; use SPT to reduce queue length (relief SPT)[3, 7, 10]. The last combination effectively reduces flow time variance without increasing average flow time [3, 5, 10]. RESULTS RELATED TO DUE DATES Panwalkar et a/.[29] reported that meeting due dates is the most important goal followed by minimization of setup times and minimization of inprocess inventory (in that order) in industrial scheduling. SPT, S/OPN, SLACK and S/RPT are superior to other simple priority rules in terms of all measures of due date performance. Among these dominant simple rules, SPT and S/OPN are slightly better than SLACK and S/RPT. A consensus appears to be that SPT gives best results for average lateness, and S/OPN is the best rule in minimizing variance of lateness distribution; however the superiority of SPT and S/OPN are highly dependent on shop and job parameters for remaining due date performance measures such as fraction of tardy jobs and mean tardiness. In general, high utilization, tight due dates and due dates independent of processing times favor the superiority of SPT: S/OPN is more successful in moderate utilizations, less tight and/or T W K due date assignments[I, 2, 3, 7, 8, 10, 13, 14, 17].

96

A S. KIRANand M. L SMITH

Relative success of SPT and S/OPN for due date based criteria formed a basis to develop a number of combination rules, weighted priority rules and heuristics. Conway{7, 10] developed a weighted priority rule by combining SPT and S/OPN with different:, weights and found the weighted priority rule superior to SPT or S/OPN alone for avoiding tardy jobs. Eilon & Cotterill[15] tested several SPT based combination rules and found that tardiness of very long jobs was reduced using a two-class SPT rule which gives priority to the jobs with negative anticipated slack. Oral & Maulin[27] improved this rule by combining S/OPN and SPT; the resulting SPT-T rule was found to reduce maximum tardiness, and skewness and kurtosis of the tardiness distribution; however the SPT-T rule was dominated by SPT for average tardiness[27]. Carroll[6] and Oldziey[28] developed look ahead heuristics which also consider processing time, job slack and current load of the machines. Oldziey compared his rule with SPT, S/OPN and MOST and found that the heuristic is better than simple rules for average tardiness, percentage of late jobs and mean tardiness of tardy jobs. Carroll tested the COVERT (i.e. c[t, where c is a function of job tardiness and t is imminent processing time of the job) rule and found that it was superior to S[OPN and to SPT for average tardiness. Gere[19] compared several different types of heuristics with simple priority rules and concluded that heuristics are generally better than simple rules but the computation load is prohibitive for application of heuristics in practical problems. However, this conclusion was reached before low cost computers were available. HoUoway & Nelson[21] and Nelson et all26] developed three different loading heuristics which are based on heuristics solutions of static problems at predetermined intervals and reported improved performance in percentage of tardy jobs, variance of tardiness distribution and average and maximum tardiness. RESULTS FOR COST BASED CRITERIA The main objective in many industrial systems is to minimize total cost, and this objective is considered mostly in recent studies[l, 4, 24, 31, 32]. Jones[24] investigated the cost of idle machines, cost of carrying work in-process, cost of long promises, cost of missed due dates and total cost using SPT and S/OPN and showed the relations between shop parameters and costs. Ulgen[32] investigated effectiveness of simple priority rules according to setup cost, in-process inventory cost, storage cost, penalty cost and several different cost functions composed of two or more of these four costs. His findings, in general, are similar to those of other researchers' findings in that SPT and JV reduce in-process inventory cost, S/OPN gives best results for earliness and tardiness costs and SST is best for setup cost among simple priority rules. Furthermore SST is the best rule for minimizing the total of these four costs as well as several combinations of the four. Aggarwal et al.[I] compared a weighted priority rule with SPT, SST and S/OPN and found that the weighted rule is best for total of in-process inventory, utilization, lateness and setup costs. Shue & Smith[31] used sequential application of simple priority rules. The sequential approach considers all waiting jobs; the first simple rule allows a subset of jobs to be considered by the second rule; the third rule selects one job for the machine. It is concluded that any sequential rule performs better than its components. They reported superiority of S/OPN-JV-SST for setup, in-process inventory and late penalty costs; however, this may not be valid for other shop parameters and cost structures. Hoilier[20] and Berry[4] investigated cost functions and priority rules in batch type manufacturing shops. Berry concluded that SPT is not successful in batch type manufacturing even for in-process inventory cost because of its high flow time variance which causes high in-process inventory costs. RESULTS FOR SOME EXTENTIONS OF THE BASIC MODEL Effects of customer requested due date changes are investigaed in[l !, 14, 17, 22, 32]. In all these studies, it was found that customer requested due date changes adversely

Simulation studies in job shop scheduling--ll

97

affected due date performance of all priority rules, but the rules which use due date information are more responsive to due date changes. The effect of loose due dates for soine jobs are also investigated bu Ulgen[32]. Looser due dates denote the jobs that are prrduced for inventory and are allowed longer time in the shop. Ulgen concluded that the tardiness penalty might be decreased by earlier release of such jobs, but the increase of in-process and finished goods inventory costs offset the benefits of doing this. Expediting in the shop is investigated in[22, 32]. According to time based criteria, Hottenstein concluded that "shops in general are no better or worse off by using expediting" [22]. He also concluded that the shop performance with expediting may change with load level, shop configuration, due date procedure and expediting procedure. Expediting may be useful for tardiness related criteria especially in moderate loads and customer requested earlier due dates. These results are confirmed by Ulgen for cost based criteria: expediting reduced the tardiness cost but increased the in-process inventory cost[32]. Periodic release of jobs has a widespread use in job shop simulation research because of its easier application on the computers, but only a few researchers investigated its impact on shop performance[12,18,21,30,32]. Periodic release does not affect relative effectiveness of priority rules[ 18, 32]. The other conclusions are, somehow, conflicting in related literature: (1) Mean and variance of inventory level are higher with the increase in release period [30]. (2) Utilization is higher than average at the beginning of the scheduling period but is lower at the end[30]. (3) The decrease in in-process inventory and storage costs is more than offset by the increase in penalty cost due to tardiness under the cost structure assumed for the shop[32]. (4) Fewer jobs are tardy for periodic release; however the jobs that are tardy have longer periods of tardiness [32]. (5) Due date performance is improved when periodic release is combined with a scheduling rule[21]. Very few studies have been performed for job pooling, Ulgen[32] found the optimal pool size is zero (i.e. no job pooling) under the conditions and cost structure assumed in his model. On the other hand, Irastorza & Deane[23] reported that job pooling has a positive effect on shop and work load balance measures but no significant effect or worse results on variance of lateness distribution and average tardiness. CONCLUSIONS

Numerous studies have been conducted on the effectiveness of priority rules in scheduling jobs for the dynamic job shop. The adaptability of priority rules to different types of shop situations, job characteristics and criteria is apparent since many different conditions have been considered. Many priority rules are remarkably simple and can be easily applied with a minimum amount of computation and comparison. In fact, most rules can be applied by a scan of job characteristics. Some rules involve a combination of two or more simple rules or shop parameters extending beyond the machine at which the decision on job selection is being made; these rules likely will require a computer and perhaps an information system. In practice, priority rule job selection is made only when a machine is needing its next job. Each study included in this survey utilized computer simulation in evaluation of priority rule performance. This reliance upon simulation has resulted in the modeling of shop operation with application of the rule for job selection occurring only when each machine is idle; this is identical to the procedure followed in actual practice. REFERENCES I. S. C. Aggarwal & B. A. McCarl, The development and evaluation of a cost-based composite scheduling rule. Naval Res. Logistics Quart. 12(I), 155-169 (1974). 2. S. Ashour, Sequencing Theor.v, Lecture Notes in Economics and Mathematical Systems. Springer-Verlag (1972). 3. K. R. Baker. Introduction to Sequencing Scheduling. Wiley, New York (1974).

A. S. KmAN and M. L. SMitH

98

4. W. L. Berry, Priority scheduling and inventory control in job lot manufacturing systems. AIlE Trans. 4(4), 267-276 (1972). 5. E S. Buffa & J. A. Miller, Production and Inventor), Systems. Irwin, Illinois (1979). 6. D. C! Carroll, Heuristic sequencing of single and multiple component jobs. Ph.D. Thesis, MIT (June 1965). 7. R. W. Conway, An experimental investigation of priority assignment in a job shop. RAND Corp. Memo. RM-3789-PR, (Feb. 1964). 8. R. W. Conway, Priority dispatching and job lateness in a job shop. J. Indus. Engng 16(4) (1965). 9. R. W. Conway, Priority dispatching and work-in-process inventory in a job shop. J. Indus. Engng 16(2) (1965). 10. R. W. Conway, W. L. Maxwell & L W. Miller, Theory of Scheduling. Addison-Wesley, Reading, Mass. (1967). I 1. J. E. Day & M. P. Hottenstein, The impact of advancing due-dates in a pure job shop. lnt..I. Prod. Res. 13(6), 603-613 (1975). 12. R. H. Dearie & C. L. Moodie, A dispatching methodology for balancing workload assignments in a job shop production facility. AIIE Trans. 4, 227-281 (1972). 13. R. A. Dudek, M. L. Smith, S. S. Panwalkar & A. G. Tilak, Scheduling work centers with multiple jobs. Res. Rep., Texas Tech University (1976). 14. S. Eilon & I. J. Chowdhury, Due dates in job shop sequencing. Int. J. Prod. Res. 14(2), 223-237 (1976). 15. S. Eilon & D. J. Cotterill, A modified SI rule in job shop scheduling. Int. J. Prod. Res., 7, 135--145 (1968). 16. S. Eilon & R. M. Hodgson, Job shop scheduling with due dates. Int. J. Prod. Res. 6(1), 1-13 (1967). 17. D. A. Elvers, Job shop dispatching rules using various delivery due date setting criteria. J. Amer. Prod. Inventory Control Soc. 14(4), 62-70 (1973). 18. D. A. Elvers, The sensitivity of the relative effectiveness of job shop dispatching rules with respect to various arrival distributions. AIIE Trans. 6, 41-49 (1974). 19. W. S. Gere, Jr., Heuristics in job shop scheduling. Management Sci. 13(3) (1966). 20. R. H. Hollier, A simulation study of sequencing in batch production. Op. Res. Quart. 19, 389--407 (1968). 21. C. A. Holloway & R. T. Nelson, Job shop scheduling with due dates and variable processing times. Management Sci. 20(9), 1264-1275 (1974). 22. M. P, Hottenstein, Expediting in job-order-control systems: a simulation study. AIIE Trans. 2, 46-54 (1970). 23. J. C. Irastorza & R. H. Deane, A loading and balancing methodology for job shop control. AIIE Trans. 6, 302-307 (1974). 24. C. H. Jones, An economic evaluation of job shop dispatching rules. Management Sci. 20(3), 293-307 (1973). 25. A. S. Kiran & M. L, Smith, Simulation studies in job shop scheduling: Part I. Comput. & Indus. Engng 8(2), 95-105 (1984). 26. R. T. Nelson, C. A. Holloway & R-. M. L. Wong, Centralized scheduling and priority implementation heuristics for a dynamic job shop model. AIIE Trans. 9(1) (1977). 27. M. Oral & J. L. Malouin, Evaluation of the shortest processing time scheduling rule with truncation process. AIIE Trans. 5(4), 357-365 (1973). 28. J. W. Oldziey, Dispatching rules and job tardiness in a simulated job shop. Master's Thesis, Cornell University (Feb. 1966). 29. S. S. Panwalkar, R. A. Dudek & M. L. Smith, Sequencing research and the industrial scheduling problem. In Symposium on the Theory of Scheduling and Its Applications. pp. 29-38. Springer-Verlag, Berlin (1973). 30. S. S. Panwalkar, M. L. Smith & R. A. Dudek, Scheduling with periodic release of orders for production. Presented at O RSA / T I M S Special Interest Conf. on Theory and Application o f Scheduling, Orlando, Florida (1976). 31. L. Shue & M. L. Smith, Sequential approach in job shop scheduling. J. Chinese lnstit. Engrs 1, 75--80 (1978). 32. O. Ulgen, Application of system methodologies to scheduling. Unpublished Ph.D. Dissertation, Texas Tech. University (1979).

APPENDIX: INFORMATION

ON S U R V E Y E D A R T I C L E S

In this appendix we will present information on surveyed articles except reviews. The numbers in the brackets correspond to the reference numbers of the articles in Part I and Part II, respectively. Other information includes: (a) (b) (c) (d)

Arrival pattern, processing and setup time distributions. Number of machines, type of shop, due dates. Performance criteria considered. Type of investigation. [i],

-, Adam and Surkis (1980) a.

Truncated exponential

interarrival

and processing times.

b.

6 work c e n t e r s , job shop.

c.

Average flow time, percent of tardy j o b s , average t a r d i n e s s ,

average e a r l i n e s s . d.

I n v e s t i g a t e s e f f e c t s of p r i o r i t y

intervals for SIOPN rule.

updating procedures and

99

Simulation studiesin job shop ~heduling--II [2], [ I ] ,

Aggarwal and McCall (1974)

a.

Poisson a r r i v a l s , exponential setup and processing times.

b.

6 machine groups, pure job shop, RND due dates,

c.

Number of jobs in queues, percentage of late jobs waiting in

queues, fraction of tardy jobs, machine idle times, total cost function of in-process inventory, idle times, lateness and setups. d. [4],

Compares SPT, SST, S/OPN and a composite cost based rule.

- , Ashour and Vaswani (1972) a.

Poisson and Erlang a r r i v a l s ,

e x p o n e n t i a l and Erlang p r o -

c e s s i n g tilnes.

b.

9 machine pure job shop. NOP due dates.

c.

Average flow time, average number of jobs in the shop,

average lateness, number of tardy lobs, shop u t i l i z a t i o n . d.

Compares FCFS, SPT, SLACK, Enn, S/OPN. Investigates effects

of changing due dates and variation of processing times. [ 6 ] , -, Baker and Ozielinski (Ig60) a.

Exponential interarrival and expected processing times.

b.

9-30 machines; pure job shops.

c,

Average flow time, variation of flow time d i s t r i b u t i o n .

d.

Compares FCFS, RANDOM, LWKR, MWKR, MOPNR, FOPNR, SPT, and

LPT. [/],[4], a.

B e r r y , W.L. Job-lot

(I9/2)

type a r r i v a l s

generated by an i n v e n t o r y c o n t r o l

system, e x p o n e n t i a l p r o c e s s i n g and setup times. b.

IO machines job shop.

c.

Cost of p l a c i n g o r d e r s , cost o f c a r r y i n g work i n - p r o c e s s and

finished d. [8],[7], a.

product

inventories,

shortage cost.

Compares SPT, FISFS, S/RPT, CR, 2 - c l a s s SPT r u l e s . Conway (1964) Exponential

int#rarrival

times, exponential,

uniform,

and

c o n s t a n t due d a t e s . b.

3 , 4 , 5 , 9 machines pure j o b shop; RND, SLK, NQP and TWK due

dates. c.

Mean and v a r i a n c e f)f l a t e n e s s , number o f t a r d y j o b s , mean and

v a r i a n c e of low time, number of j o b s in shop, number of j o b s in queues, t o t a l

work c o n t e n t ,

total

work r e m a i n i n g ,

imminent o p e r a t i o n

work c o n t e n t . d.

D e f i n e s and comDares 92 d i f f e r e n t

f e r e n t shop parameters.

priority

r u l e s unde r d i f -

I00

A S KIRAN and M [9],[;~],

L SMITH

(onway (1965)

This work based on r e f e r e n c e ~14]. based on j o b comp]etion t i m e , [i{I],[9],

on c r l t e r i a

i n - p r o c e s s .lobs, and p r o c e s s o r data.

Conway (1965)

This work based on r e f e r e n c e [ 1 4 ] . based on due d a t e s , e f f e c t s [Ii],-,

Concludes r e s u l t s

Conway, et a l . a.

of different

Concludes r e s u l t s

on c r i t e r i a

due d a t e s e l e c t i o n

rules.

(1960)

Adjusted a r r i v a l s

to m a i n t a i n c o n s t a n t load l e v e l

in the

shop, Poisson p r o c e s s i n g t i m e s . b.

5 machines j o b shop, RND ( n o r m a l l y d i s t r i b u t e d )

due d a t e s ,

lognormal j o b v a l u e s . c.

,Job c o m p l e t i o n time d i s t r i b u t i o n ,

lization

o f machines, d o l l a r

d.

lateness distribution,

uti-

v a l u e o f work i n - p r o c e s s .

Compares RANDOM, FCFS, 2 - c l a s s FCFS, EDD, SLACK, SPT, LPT,

FOPNR, MOPNR, JV, NINO, WINQ. of a r r i v a l s ,

I n v e s t i g a t e s the r e l a t i o n s

job completion times,

between type

l a t e n e s s , number of j o b s

in the

shop. [14],[11],

Day and H o t t e n s t e i n

(1975)

a.

ExponentiaT i n t e r a r r i v a l

b.

5 machines pure j o b shop, TWK du~ d a t e s , customer requested

earlier

and p r o c e s s i n g times.

due d a t e s .

c.

F r a c t i o n o f t a r d y j o b s , mean l a t e n e s s , mean e a r l i n e s s ,

f l o w t i m e , mean w a i t i n g t i m e , mean u t i l i z a t i o n d.

mean

o f shop.

I n v e s t i g a t e s shop p e r f o r m a n c e and due d a t e performance of

S/OPN w i t h d i f f e r e n t

arrival

r a t e s and customer requested due date

changes.

[15],[12],

Deanie and Moodie (1972)

a,

Exponential

b.

No i n f o r m a t i o n

Co

Variance of l a t e n e s s ,

interarrival

and p r o c e s s i n g times.

is given. work-in-process,

workload balance

index. d.

Compares S/OPN, SPT, AWINQ, FCFS, RANDOM, LPT r u l e s with Flow

Controlled

Search A l g o r i t h m .

[16],[13],

Dudek, et a l .

(1976)

a.

Actual

b.

10-20 work c e n t e r s ,

(actual)

shop d a t a ,

due d a t e s .

external

priority

alternative

levels

routings

for jobs.

for jobs,

TWK

I01

Simulation studiesin job shop ~heduling--II c.

Tardiness, tardiness of high p r i o r i t y

jobs, number of tardy

jobs, work center u t i l i z a t i o n . d.

Compares FCFS, SPT, LWKR, EDD, S/OPN, NINQ, SLACK, 2-class

FCFS, 2-class SLACK rules.

[17],[14],

Eilon and Chowdhury (1976)

a.

Constant i n t e r a r r i v a l

b.

5 machines j o b shop, TWK and VTWK due dates.

c.

Mean and variance of lateness, e a r l i n e s s and tardiness

distributions,

times, normal processing times.

cost of e a r l i e r and t a r d i n e s s , f r a c t i o n of tardy jobs,

number of jobs in queues. d.

Compares FCFS, SPT and 2-class SPT rules.

e f f e c t of d i f f e r e n t

due date selection rules.

[ 1 8 ] , [ 1 5 ] , Eilon and C o t t e r i l l a.

Investigates

Poisson a r r i v a l s ,

(1968)

exponential expected processing times nor-

mal work rate f a c t o r . b.

4 machines job shop, TWK due dates with d i f f e r e n t

cofficients. c.

Job w a i t i n g time, queue lengthS, delay f a c t o r , mean and

variance of l a t e n e s s , mean flow time, Parliness and tardiness costs. d.

Compares FCFS, SPT, LPT, SRPT, truncated SPT, 2-class SPT,

and 3-class SPT r u l e s .

[19],[16], a.

Eilon and Hodgson (1967)

Exponential i n t e r a r r i v a l

and px~ected processing times, nor-

mal work rate f a c t o r . b.

2 i d e n t i c a l machines, single oppration jobs, TWK due dates.

c.

Mean flow time, mean lateness, delay f a c t o r , job waiting

time, queue length, machine i d l e times, n,~mbpr of tardy jobs, t a r diness penalty. d.

Compares RANDOM, FCFS, EOD, %pT and LPT rules.

[ 2 1 ] , [ 1 7 ] Elvers (1973) a.

Uniform number of a r r i v a l s ,

periodic release, uniform

expected processing times, t r i a n g u l a r wor~: ~ate f a c t o r . b.

8 machines job shop, TWK due da~os, 5 d i f f e r e n t

levels.

c.

Mean t a r d i n e s s , number of tardy ~'bs.

d.

Compares FCFS, FLSFS, SPT, LPT, ~RPT, S/{)PTI, S/RPT and SLACK

rules i n v e s t i g a t e s e f f e c t of t i g h t due d a ~ e s nn shop performance and r e l a t i v e performance of p r i o r i t y

rules.

A % KlaaN and M. L. SM~T}~

102

[22],[18], a.

flyers

(19Z4)

Periodic

release, t)inomlal,

skewed and Poisson a r r i v a l s , triangular

biiIloda],

Ipft

skewed, r l q n t

u n i f o r m expected p r o c e s s i n g times,

work r a t e f a c t o r .

b.

8 machines j o b shop, TWK due d a t e s .

c.

Tardiness.

d.

Investigates effect

of arrival

distributions

and compares

FCFS, FISFS, SPT, LPT, MWKR, I_WKR, EOD, SLACK, S/~PN, and S/RPT r u l e s .

[23],-,

Gavett (1965)

a°

S t a t i c problems, hatch type j o b s ,

sequence dependent setup

times. b.

One machine problems.

(,

Setup time.

d.

investigates

[24],[19],

travelling

salesman type of h e u r ~ s t l c s .

Gere (1966)

a.

Poisson a r r i v a l s ,

b.

4-6 machines j o b shops, TWK due d a t e s .

c.

Mean t a r d i n e s s and t a r d i n e s s c o s t .

d.

Compares s i m p l e ,

[25],[20], a.

Hollier

u n i f o r m p r o c e s s i n g times.

composite and h e u r i s t i c

schedules ruleS.

(1968)

Poisson a r r i v a l s ,

normal p r o c p s s i n g times,

normally distri-

buted sequence dependent setup times. b.

6 amchines f l o w shop and job shop, NOP and SLK due d a t e s .

c.

Mean f l o w time,

l a t e n e s s , mean machine i d l e

time,

total

pro~

c e s s i n g times o f j o b s in queue. d.

Compares FIFS, RANDOM, EnD, SPT, SST, NINQ, MOPNR, and

earliest

start

-, [21],

Holloway and Nelson (1974)

a,

Static

rules.

problems, u n i f o r m p r o c e s s i n g times, u n i f o r m and b i n o -

mial work r a t e f a c t o r . b.

5-7 machines j o b shops.

c.

Mean and v a r i a n c e of t a r d i n e s s ,

fraction

of t a r d y j o b s , ma~i-

mum t a r d i n e s s . d. [26],[22],

Compares EOD, SPT, SLACK, and a h e u r i s t i c Hottenstein

scheduling r u l e .

(1970)

a.

Exponential

interarrival

b.

6 machines pure f l o w shop and lob shop.

customer requested e a r l i e r

times and p r o c e s s i n g times.

due dateS, e x p e d i t i n g .

TWK due d a t e s ,

103

S i m u l a t i o n s t u d i e s in j o b s h o p ~ h e d u l i n g - - l l

c.

Number of j o b s in the shop, f r a c t i o n

o f t a r d y j o b s , mean t a r -

d i n e s s , mean f l o w time. d.

Investigates 2-class

SPT and 2 - c l a s s FCFS and e f f e c t s

of

e x p e d i t i n g in the shop. [27],[23],

I r a s t o r z a and Dearie (1974)

a.

Exponential

b.

I0 M/C pure j o b shop, TWK due d a t e s .

c.

Total work i n - p r o c e s s ,

variation

interarrival

and p r o c e s s i n g t i m e s ,

total

job pooling.

work completed, mean t a r d i n e s s

o f l a t e n e s s , machine work balance i n d e x , shop work halance

i n d e x , machine queue balance i n d e x . d.

Investigates effects

o f j o b pool and l o a d i n g procedures on

shop performance. [2H],

- , Jackson ( I q 5 7 ) a.

S t a t i c problems, c o n s t a n t and e m p i r i c a l

processing tl~e

distributions. b.

8 machines j o b shop.

c.

Mean l a t e n e s s ,

d.

Examines a h e u r i s t i c

[29],[24],

lateness distribution. priority

rule.

Jones (1073)

a.

Adjusted a r r i v a l

nential

processing times.

times f o r c o n s t a n t shop u t i l i z a t i o n ,

expo-

b.

4 machines j o b shop, MOP due d a t e s .

c.

Cost o f i d l e machines, c o s t o f c a r r y i n g w o r k - i n - p r o c e s s

i n v e n t o r y cost of long p r o m i s e s , c o s t o f missed due d a t e s . d. priority [30],-,

I n v e s t i g a t e s the r e l a t i o n s h i p s r u l e s and c o s t components. Kiran

(1983)

a.

Constant i n t e r a r r i v a l

b.

9 machine g r o u p s , j o b shop.

c.

Mean f l o w t i m e ,

d.

Investigates effects

s i z e s and t r a n s i e n t

[31],-,

between shop u t i l i z a t i o n ,

times,

t r u n c a t e d - B p r o c e s s i n g times.

shop u t i l i z a t i o n . of alternative

conditions

routing,

limited

queue

in j o b shops.

Kuratani and Nelson (1960)

a.

Exponential

interarrival

b.

4 machines j o b shop.

c.

Job f l o w t i m e s ,

and p r o c e s s i n g t i m e s .

queue l e n g t h d i s t r i b u t i o n ,

lateness

distribution. d.

Discusses modeling a s p e c t s o f j o b shops, compares FCF~, ~ ' ,

SLACK, and some slack based h e u r i s t i c (Alt~ Vol ~ ~

2 B

~riority

rules.

104

A S KIRAN and M L SMITH [32],-,

LeGrande (1%3) from actual j o b shop.

a.

Data

b.

115 machine groups.

c.

Number of jobs completed, mean and v a r i a n c e o f f l o w t i m e ,

number o f t a r d y j o b s , mean number of jobs in the shop, machine u t i l l zation. d.

Discusses and compares shop performance under d i f f e r e n t

priority [34],-,

rules. Nanot (I963)

Clo

Poisson a r r i v a l s ,

e x p o n e n t i a l s e r v i c e times.

b.

4-6 machines pure f l o w shops, pure job shops and h y b r i d

shops. c.

Mean and v a r i a n c e o f f l o w time, mean i d l e t i m e .

d.

I n v e s t i g a t e s the e f f e c t s

o f system c o n f i g u r a t i o n

and p r i o r i t y

r u l e s on shop performance. [35],[26], a.

Nelson, e t a ] . Poisson a r r i v a l s ,

(1977) u n i f o r m expected p r o c e s s i n g t i m e s ,

bi nomi al

work r a t e f a c t o r . b.

6 M/C pure flow shop.

TWK due d a t e s .

c.

Percent of jobs t a r d y ,

total

d.

Compares SLACK and two h e u r i s t i c

[36],[27],

t a r d i n e s s , maximum t a r d i n e s s . procedures.

0ra] and Maulin (1973)

a.

Poisson a r r i v a l s ,

b.

5 M/C pure job shop, TWK due d a t e s .

c.

Mean t a r d i n e s s ,

tion,

exponential processing times.

fraction

of tardy job, tardiness

distribu-

maximum t a r d i n e s s . d.

Compares SPT, S/OPN and a combined p r i o r i t y

rule

based n SPT

and S/OPN. [37],[28],

Oldziey (1966)

a.

Poisson a r r i v a l s ,

geometric p r o c e s s i n g t i m e s .

b.

8 machines j o b shop.

c.

Mean and v a r i a n c e of f l o w time, mean and v a r i a n c e o f ] a t e -

TWK due d a t e s .

hess, mean and v a r i a n c e o f t a r d i n e s s , d.

fraction

of tardy jobs.

Compares SPY, S/OPN, EDD, FISFS with composite s c h e d u l i n g

rules. [39],[30], a.

Panwalkar, et a l .

(]9/6)

Constant and e x p o n e n t i a l

interarrlval

r e l e a s e , exponenLia] p r o c e s s i n g tlmes.

times,

periodic

105

Simulation studies in job shop scheduling--ll b.

9 M/C pure job shop.

TWK due dates.

c.

Number of jobs in the shop, mean e a r l i n e s s , mean tardinesS,

shop u t i l i z a t i o n . d.

Investigates effects of p e r i o d i c release on shop performance

and on r e l a t i v e effectiveness of SPT and S/OPN. [40],-,

Rowe (1958)

a.

A r r i v a l s and processing times based on actual shop data.

b.

17 machines job shop based on an actual shop.

c.

Mean wait time, shop u t i l i z a t i o n ,

carrying cost, cost r a t i o ,

f r a c t i o n of tardy jobs. d.

Compares FCFS, SPT, LPT and 2 h e u r i s t i c procedures.

[41],[31], a.

Shue and ~ , i t h (1978)

Constant and exponential i n t e r a r r i v a l

times, sequence depen-

dent setup times. b.

15 machines pure job shop, TWK due dates.

c.

Total cost; a linear function of in-process inventory, setup

and tardifiess costs. d.

Compares FCFS, EOD, SPT, LWKR, SLACK, S/OPN, S/RPT, SST, IV,

and i n v e s t i g a t e s sequential application of p r i o r i t y [43],-,

rules.

Smith and Seidmann (1982)

Investigate effects of due date s e l e c t i o n procedures in job shops. [ 4 4 ] , [ 3 2 ] , Ulgen (1979) a.

Exponential i n t e r a r r i v a l and expected processing times,

t r i a n g u l a r work rate factors, sequence dependent processing times. b.

g M/C pure job shop, TWK due dates.

c.

Mean and variance of flow time, mean and variance of l a t e -

ness, mean tardiness, fraction of tardy j o b s , cost of carrying i n process inventory and product inventory, tardiness cost, setup cost. d.

Compares SPT, SST, S/OPN, IV, FCFS, and EDD. Investigates

e f f e c t s of p e r i o d i c release, job pooling, setup times, and customer requested e a r l i e r due dates. [ 4 5 ] , - , Wilbrecht (1969) a.

Uniform number of arrivals, periodic release, exponential

processing times, sequence dependent setup times. b.

q M/C pure job shop, TWk due dates.

c.

Value of work in-process, number of operations completed,

number of jobs completed, number of late operations, shop u t i l i z a t r o n , Job waiting time, variance of lateness. d.

Compares RANDOM, EDn, SST, SPT, LPT p r i o r i t y

~:~-~.