The influence of alternate process planning in job shop scheduling

Complaers and Industrial Engineeri.g Vol. 25, Nos 1-4, pp. 263-266, 1993 Printed in Great Britain. All rights reserved

THE INFLUENCE

OF ALTERNATE

0360-8352/9356.00+0.00 Copyright © 1993 Pergamon Press Ltd

PROCESS

PLANNING

IN JOB SHOP BCHEDULING

Juichin Jiang and Ming-ying Chen The Department of Industrial Engineering Chung Yuan Christian University Chung-Li, 320, Taiwan R. O. C. (TEL) 886-3-456-3171 Ext. 4404 (FAX) 886-3-456-3171 Ext. 4499

ABSTRACT

The purpose of this research is to investigate the relationships between the alternate process planning and the scheduling performance regarding to three different criteria; they are mean tardiness, mean work-in-process, and mean machine utilization. In this paper, three factors which are the percentage of alternate process planning, the scheduling algorithm, and dispatching rule are considered relative to those three criteria. The result of this research will show how the percentage of alternate process planning influences those criteria and what the percentage of alternate process planning should be done efficiently and economically. I. I N T R O D U C T I O N

Production control is to apply the principles and philosophies of scientific management such that the manufacturing resources will be used efficiently. In general, it consists of five basic procedures; they are production planning, process planning, production scheduling, job dispatching, and job monitoring. Production scheduling is an intermediate step to connect the process planning and job dispatching. Process planning is the input of production scheduling, and the production schedule is the output of production scheduling and a basis of the job dispatching. In the previous studies, the process planning and scheduling were studied separately or sequentially. Since the process planning is one of major inputs of scheduling system and a schedule is the implement of process planning, the relationship of process planning and scheduling should be studied carefully. The quality of the schedule is dependent on not only how the schedule is generated but also how the process planning is accomplished. Can they be considered together rather than individually, it will result in a better performance such as the reduction of inventory, the elimination of order delay, the decrease of the scheduling complexity, the increase of the resource utilization, and so on. Since the process planning affects the results of the production scheduling, this paper investigates the impact of the process planning on the production scheduling. The influence of alternate process planning on the production scheduling is studied relative to three different measures of performance which are mean tardiness, mean work-in-process, and mean utilization. They are commonly used to evaluate the performance of manufacturing systems by both practitioners and researchers. Ii. N O M E N C L A T U R E

The following variables are used in this paper: t

i

j k

oii

:

ili uk(t) Q(t)

:

the present scheduling time epoch. job index; i = 1, 2, ..., N. operation index; j = i, 2, .... machine index; k = i, 2, ..., M. the j-th operation of job i. the completion time epoch of the operation Oij. the operation O H be processed on machine k. the processing time of Oi.. the processing tlme of Oi.k the avallable time epoch of machine k. a set of unscheduled operations at time epoch t. a set of available operations at time epoch t; Oij e Q(t) if C1(j.D ~ t, for all i. •

.

,

J

J

•

263

264

Proceedings of the 15th Annual Conference on Computers and Industrial Engineering

s(t)

:

di dU ri Si

: : : : : : : :

W|j i Cmx Ti

a set of s c h e d u l a b l e o p e r a t i o n s at time epoch t; O|jk e S ( t ) , t, and A k < t. the due d a t e of job i the due d a t e • of0 o p e r a t i o n 0° iJ ° a set of u n f l n l s h e d o p e r a t i o n s of job i. the s l a c k time of job i. the w a i t i n g time of o p e r a t i o n O... the c o m p l e t i o n time epoch of jo~ i. the m a x i m u m c o m p l e t i o n time, C~x = max(Ci). the t a r d i n e s s of job i; T i -- max(0, C i - d|).

if Ci(j.1> <

The p r i o r i t y r u l e s used in this p a p e r are d e f i n e d as follows: MOD

:

COVERT:

SPT : S/RPT:

the m o d i f i e d o p e r a t i o n due date, min[max(di.,j t + Pij) ]" c o n t i n u o u s l y t r u n c a t e d C O V E R T rule, m a x ( C l ~ Pi )" the s h o r t e s t imminent p r o c e s s i n g time, mih(Pij): slack per r e m a i n i n g p r o c e s s i n g time di - t -

[ Pi] jer i

min

P~j j er i The f o l l o w i n g are the m e a s u r e s MT

:

m e a n tardiness,

of performance: Ti

MT = N Ci

WIP

:

mean work-in-process,

WIP = N

UTLN

:

mean utilization,

Pij

UTLN =

N * Crux III.

SCHEDULING

ALGORITHM

The a l t e r n a t e p r o c e s s p l a n n i n g d e f i n e d in this p a p e r is identical to [4]. It m e a n s that the m a n u f a c t u r i n g p r o c e s s e s of job are p l a n n e d operation by operation. For example, a s p e c i f i c job m i g h t c o n s i s t of four m a n u f a c t u r i n g o p e r a t i o n s (processes). For the p r o c e s s p l a n n i n g of single routing, it only g e n e r a t e s four o p e r a t i o n plans. However, it m i g h t g e n e r a t e six, or eight o p e r a t i o n p l a n s w h i l e the a l t e r n a t e p r o c e s s i n g p l a n n i n g is considered. Due to the a p p l i c a t i o n of a l t e r n a t e p r o c e s s planning, here, t h r e e s c h e d u l i n g a l g o r i t h m s are p r o p o s e d to s t u d y the impact. Basically, the only d i f f e r e n t step among these a l g o r i t h m s is step 5 that involves how to select the p r o p e r p r o c e s s routing, e s p e c i a l l y w h e n the a l t e r n a t e p r o c e s s p l a n s are available. The steps of algorithm 1 are listed completely; only step 5 of a l g o r i t h m 2 and a l g o r i t h m 3 is described. They are shown as follows: Aluorithm

1:

Step Step Step Step Step

1: 2: 3: 4: 5:

Step Step Step Step

6: 7: 8: 9:

I n i t i a l i z e all variables. If all o p e r a t i o n s have been scheduled, then stop, or continue. U p d a t e the set of a v a i l a b l e operations, said Q(t). If Q(t) = 4, go to step 9, or continue. U p d a t e the set of s c h e d u l a b l e operations, S(t), and let P U = Pijk if one of the f o l l o w i n g c o n d i t i o n s is met. (a) if only one o p e r a t i o n plan and A k S t. (b) if t h e r e are two o p e r a t i o n p l a n s available, said 0 U k and Oijz, either (i) A k S t and A k > t. or (ii) A k S t, A z S t, and Pijk.~ Pijz" If S(t) = 4, go to step 9 or continue. Use the s e l e c t e d p r i o r i t y rule to s c h e d u l e the p r o p e r operation. U p d a t e the c o r r e s p o n d i n g data and go to step 3. U p d a t e the p r e s e n t s c h e d u l i n g time epoch then go to step 2.

Aluo~thm

~:

All the steps of a l g o r i t h m 2 are identical to t h o s e of a l g o r i t h m 1 except the step 5 w h e r e it a l w a y s c h o o s e s the o p e r a t i o n p l a n w i t h the s m a l l e r p r o c e s s i n g time. A l t h o u g h the a l t e r n a t e p r o c e s s p l a n n i n g is applied, the p r o c e s s plan is

,]IANG and CHEN: Alternate Process Planning

265

selected sequentially like the two-step scheduling method, which determines the process plans, selects the proper routing, then generates the production schedule. Aluorithm 3; The step 5 of algorithm 3 is like look-ahead dispatching. Step 5:

Update the set of schedulable operations, S(t), and let PIj = Pijk if one of the following conditions is met. (a) if only one operation plan and A k S t. (b) if there are two operation plans available, said Oijk and Oijz, either (i) A k S t, A k > t, and t + Pi~k S A z + Pij," (ii) A k ~ t, A z ~ t, and Pijk ~ ~ljz" IV.

EXPERIMENTAL

ANALYSIS

In order to investigate the influence of alternate process planning on the scheduling performances, an example shop with the following specifications is used for the experiment. (1) (2) (3) (4) (5) (6)

The number of jobs is uniformly distributed from 8 to 16. Each job contains 2 to 6 operations. Due date is assigned based on the total work load rule where the constant is ranged from 1.5 to 2.0 randomly. The percentage of alternate process plans is ranged on 6 levels; they are 0%, 20%, 40%, 60%, 80%, and 100%. The shop consists of 6 machines. The initial status of shop is empty.

The Table 1 shows the factors and their selected levels used in the experiment. This experiment applies the ANOVA analysis of the SAS code by running 3600 data sets. In this experiment, the percentage of alternate process planning, the scheduling algorithm, and the priority rule are significant factors regarding those three measures. While the measures of mean tardiness and mean work-inprocess are considered, the scheduling algorithm 3 always presents the best performance. However, the use of scheduling algorithm 2 produces the best performance when the measure of mean utilization is activated. Figure 1 and Figure 2 show the measure of mean tardiness and the measure of mean work-in-process, respectively, regarding to the priority rule and the percentage of alternate process planning by using the scheduling algorithm 3. The measure of mean utilization relative to the priority rule and the percentage of alternate process planning with the scheduling algorithm 2 is shown in Figure 3. No matter which scheduling algorithm and priority rule are used, the alternate process planning improves those measures. In Figure i, the priority rule of MOD with the algorithm 3 shows the best performance. The priority rule of SPT with the scheduling algorithm 3 generates the best schedule in Figure 2. However, in Figure 3, the application of the priority rule and the scheduling algorithm to generate the best performance should be based on the availability of the alternate process planning. V.

CONCLUSION

In this research, the influence of the alternate process planning associated with three different performance measures is studied. While considering the alternate process planning and scheduling simultaneously, the percentage of alternate process planning affects those three performance measures significantly and is highly interacted with priority rules and scheduling algorithm. Since the alternate process planning improves the measures of schedule performance and the flexibility of manufacturing systems, it should be considered and implemented. Also the technology of the computer aided process planning (CAPP) is quite matured and widely applied, the implementation of alternate process planning won't need further investment for the industry.

REFERENCES

[1]

Chang, ¥. L., R. S. Sullivan, U. Bagchi, and J. R. Wilson, 1985, "Experimental Investigation of Real-time Scheduling in Flexible Manufacturing Systems," Annals of OPerations Research, Vol. 3, pp. 355377.

[2]

Chen,

Injazz J. and Chen-Hua Chung, 1991, "Effects of loading and routing decisions on performance of flexible manufacturing systems,"

266

Proceedings of the 15th Annual Conference on Computers and Industrial Engineering

International 2225.

[3]

Journal

of P r o d u c t i o n

Hutchison, J., K. Leong, D. Snyder, approaches for random job shop I n t e r n a t i o n a l J o u r n a l of P r o d u c t i o n 1067.

Research,

Vol.

29, No.

11, pp. 2 2 0 9 -

and P. Ward, 1991, "Scheduling flexible manufacturing systems," R e s e a r c h , Vol. 29, No. 5, pp. 1053-

[43

J i a n g , J u i c h i n , 1991, "IS: A N I N T E L L I G E N T S C H E D U L E R F O R B A T C H M A N U F A C T U R I N G S Y S T E M S , " C o m P u t e r s a n d I n d u s t r i a l E n q i n e e r l ~ g , Vol. 21, Nos. 1-4, pp. 319-323.

[5]

Kim,

[63

Zeestraten, M. J., 1990, "The look ahead dispatching procedure,,' I n t e r n a t i o n a l J o u r n a l of P r o d u c t i o n R e s e a r c h , Vol. 28, No. 2, pp. 369384.

Y. D., 1990, "A c o m p a r i s o n of d i s p a t c h i n g rules for job shops with multiple identical jobs and alternatlve routings," International Journal of P r o d u c t i o n R e s e a r c h , Vol. 28, No. 5, pp. 9 5 3 - 9 6 2 .

Factor

Selected Levels

R : the priority rule

P , percentage o f

alternate prooess plans

i 2 3 4

: NOD : COVERT : S/RPT : SPT

I

: 0% : 20 % : 40 % : 60 % : 80 % : I00 %

2 3 4 5 6

A : scheduling algorithm

I : algorithm 1 2 : algorithm 2

3 : algorlthm 3 Interaotlona of all factors Table

I

: The

suuerv

of

factors

and

their

selected

leve]~

o o~ 2o'~ 4o'~ 5o'o~ 8o% ~oo% % OF ALTERNATEPROCESSPLANNING ['::l-coo

-4.-¢o,~--~

-e.-a,r

J

Figure 1 : The measure of mean tm-d'l~ess

0.725

50-

0.7 45-

0.675 z

,~ 40-

o

o

065

~ 0.625

z

~35-

o.B

~-

0.575.

,,,j:

0.55. 25" 2(3

0.525

o~ 2o'~o 4o'~o Bo'~ 80'% 1 ~ % OF ALTERNATEPROCESS

]"~,,~

-,.- ~ , , , --*- ,,,,, --m-,,,.. .. I

Figure 2:TI~. measure of w o r k ~ p r o c e s s

0.5

0% 2o'~o 4o'~ 6o'~o ~'~ lod ~o % OF ALTERNATEPROCESSPLANS

L' - ' = - ' - ~ ' - * - "

÷="

I

Figure 3:The measure of mean utiliza~o.