Journal of Mechanical Working Technology, 20 (1989) 441-450 441 Elsevier Science Publishers B N., Amsterdam - Printed in The Netherlands

SIMtKATION MODKW,I-NG OF BATCH JOB SHOP TYPE FLEXIBLE MANUFACTURING SYST~24S

P.K.MISHRA 1 and P.C.PANDEY 2

1Mechanical Engineering Department, M.N.R. Engg. College, Allahabad 211 004 INDIA

2Mechanical & Industrial Engineering Department, University of Roorkee, Roorkee-247 667 INDIA

SL~MARY In this paper, a simulation based scheduling algorithm for the performance

evaluation of Batch Job Shop Flexible Manufacturing Systems ( BJSFMS ) has been developed. The simulation experiments have been conducted for a system with six machines processing six different type of jobs whereas the system performance has been evaluated on the basis of Maximum Makespan and Average Machine Utilization.

Models for the system performance indices have been developed by the use of multiple regression analysis technique. It has been concluded that processing time of jobs and their transportation times are interdependent operating parameters and the average machine utilization becomes virtually constant when the transportation time exceeds the processing time.

INTRODUCTION

The concept of Flexible Manufacturing System (FMS) combines the technique

of highly automated computer controlled machines, automated material handling

and computer hardware and software in order to bring the economics of scale

of batch work, and is a major step towards unmanned batch production.

In view of heavy economic investment in the installation and operation

of the flexible manufacturing system "(ref.1)" one must visualize the effect

of various operating parameters on its efficiency. The FMS performance is

normally derived from models because experimentation on the actual system

is not feasible. All such models can be classified under the following two

catogaries ;

generative models; and evaluative models.

An excellent review of generative models is given by Buzacott and Yao

"(ref.2)". These models however, are useful for systems with relatively few

operating parameters and the effects of machine failures, demand uncertainties,

etc., are difficult to account for. On the otherhand, evaluative models

"(refs.3-5)" are more of a tool to help the decision maker provide an insight

into the working of the system but do not lead to optimality. The computer

simulation is one of the most widely used evaluative tool for the

manufacturing system performance study. In FMS modelling, perturbation analysis

(PA) "(ref.6)" has also been used in a limited way. This has been found to

0378-3804/89/$03.50 © 1989 EIsevierScience PublishersB.V.

442

be more efficient computationally but recommended for systems with few

operating variables only.

In this paper, a simulation model for the batch job shop type FMS (BJS~S)

has been presented with a view to study the influence of various operating

parameters on its performance. The batch job shop type FMS in this case has

been defined as the one where batches of different types of jobs keep on

arriving for processing in a random/regular fashion. However, the number

of parts and their types to be processed are fixed. It should be noted that

in this type of system the planning horizon and the due date have no relevance.

SYST~MODELYNG

The flexible manufacturing system considered in this paper, has been

assumed to process Pi(i=l,2,...P) kind of parts. Each part of type Pi requires

K. number of operations before completion. Processing of the parts is completed 1

on a number of identical general purpose machine tools Mm(m=l,2,...M) each

provided with a buffer of capacity Bm(m=l,2,...M). As soon as the parts

are received at the loading/unloading station they are loaded into a number

of pallets Hh(h=l,2,...P) and thereafter despatched for processing. The part

along with the pallet is stored in the empty buffer space of the concerned

machine otherwise returned back to the L/U station.

The system operates under the following constraints:

- Alternate routing for the jobs is not available.

- The jobs do not recycle.

- One machine processes one part at a time.

- Operations once started cannot be interrupted before completion.

- Machine waiting time due to non-availability of tools, jigs, fixttu-es~ etc., is negligible.

- The processing time is inclusive of the setup times and are independent of the sequence followed.

- The parts are processed as per pre-determined sequence.

- The velocity of pallet travel between the work stations is constant.

- The inter-arrival and processing times of the parts vary randomly.

- The machine tools can not fail before completing the processing of all the jobs.

SCHEDULIRGMETHODOLOGY

For obtaining an efficient schedule for the processing of work pieces,

arrivals to L/U station have been assumed to follow poisson distribution

whereas, intertravel time of pallets between the work stations and processing

times of parts have been assumed to be exponentially distributed "(refs.7,8)".

Total number of operations to be performed on each part and operation sequence

443

have been generated randomly.

Priority of machining of the parts is determined on the basis of their

earliest start times (EST) as follows:

New Arrivals:

EST(Pi) =MAX [Fm,ART i + HT(mi_l,mi)] (i)

Partially Finished Parts:

EST(Pi) =MAX [Fm,Foi_l + HT(mi_l,mi)] (2)

For parts having equal ESTs, the tie is resolved by using the following

heuristic scheduling in that order:

- MWKR (most Work Remaining): Select the operation associated with the job having most work remaining.

- SPT (Shortest Processing Time): Select the job having operation with the minimum processing time.

- MWTT (Most Waiting Time): Select the operation associated with the job having largest waiting time.

The scheduling algorithm (Fig. i) generates a list of workpieces competing

for each machine.

For assignment of buffers and pallets, partially finished parts are given

highest priority. Whereas, the job waiting in buffer with highest priority

(as assigned by heuristic) is selected first for processing.

SIMULATION MOD~.rNG

Based on the next event time flow mechanism pilot simulation, runs were

made assuming the system to be initially "empty and idle". However, allowance

must he made for the system to reach the steady state "(ref.9)". From

preliminary runs it was found that after 20 simulations (each sample of size

i0), the system virtually acquires steady state and hence, the statistics

of the initial 20 runs have been ignored in all the experiments "(ref.10)".

From the simulated data the

evaluated:

Maxirr~ Makespan (MK)

This is given by :

MK = MAX [S i (Pi 1] - MIN [S m (Pi )] l~i~ p l~i ~p

Average Machine Utilization (U)

This is defined as :

U = T xlO0/S m

following system performance indices have been

(3)

(4)

444

L I CALCULATE ES~

l ~ O L ~ ~,~ ~ONO I ..~OB~ OY ~W,~.~P~.~WT~

L I ~ , ~ N P~LL~. B U ~ I

~0 ~ ,~LLY ~,N,~.~O JO~

ASSIGN PALLETS AND BUFFERS 7 TO JOBS FOR THE FIRST OPERATION I

TO COM/¢IENCE J

I SCHEDULE JOBS IN BUFFERS HAVING HIGJ-IEST PRIORITY

CALCULE MAKE SPAN, I MACHINE UTILIZATION I &

Fig.l: Flow chart for obtaining schedules

445

EFFECT OF DISPATCHING RULES ON FM~ PERFORMANCE

The adequacy of the proposed heuristic based on EST, for scheduling of

jobs, was examined. Table 3 gives a performance comparision of the following

dispatching rules for the range of operating parameters given in Table 2.

SPT/TOP - Shortest processing time for the operation divided processing time for that job.

SPT - The operations are ordered according to the shortest time first.

FCFS

MWKR

According to Stecke et al.,"(ref.ll)" the rule based on SPT/TOT should

yield best result. However, it can be noticed that the proposed heuristic

performs better than SPT/TOT in respect of makespan as well as average machine

utilization (Table 3).

by the total

operation

- The job with largest waiting time is given priority over the other.

- Select operation for the job that has the most work remaining.

SYST]~4PERFORMANCE EVALUATION

Maximum makespan (MK) and average machine utilization (U) are the two

important practical measures of FMS performance and these are governed by

a number of interacting parameters. In this study, an effort has been made

to derive empirical predictive equations, for the maximum makespan and average

machine utilization. To get a good number of data points simulation run was

made for different combinations of Np,Nb,Nj,No,Na,Nm, 'a', 's', and pt and

for the levels indicated in Table 1. The predictive equations(5-8) have been

derived by maintaining a few of the operating parameters (given in Table

2) at a constant value.

Equations for MK and 'U' have been obtained by the use of multiple

regression analysis. To make the analysis simple the variables have been

grouped as follows:

Continuous variables ('a', 's', pt), and

Discrete variables (Nj,Na,No,Nm)

Np and Nb have not been included inthe above classification because their

effect on the performance has been found to be insignificant over the range

of experimentation.

System Parameters Influencing the MaximumMakespan

Regression analysis of the simulated data, for various combinations of

the operating parameters, has yielded the equations 5 & 6.

MK1 = 16.6-15.0pt+2.3s+5.3a+2.37pt2+3.8s2+l.44a2+13.4pt.s_l.56pt.a_l.6s.a

• . (5)

446

Table i

Range of Simulation Parameters

Parameters

i. interarrival time of Jobs (a)

2. Mean Processing Times of Jobs (s)

3. Pallet Travel Time (pt)

4. Number of Pallets (Np)

5. Number of Buffers (Nb)

6. Number of Types of Jobs (Nj)

7. Number of Operations on each Job (No)

8. Number of Jobs of each type (Na)

9. Number of Machines Employed (Nm)

Ran6e Min Max

o. 25 [ . 5o

0.25 1.50

<. ~5 i . 5o ] 6

i o

6 £ []

I h

Increment

O. :~5

). 25

o. 5 ]

]

i

Table 2

Selection of Simulation Parameters

Parameters

1. Mean interarrival time between two consecutive parts (a)

2. Mean Processing Time (s)

3. Mean Pallet travel time between ~muchines (pt)

h. Number of Pallets (Np)

5. Number of buffers (Nb)

6. Number of machines (Nm)

7. Number of type of parts (Nj)

8. Number each type of part (Na)

9. Minimum and Maximum Number of Operations on parts (No)

Value

~i time unit

0.'} time ~S

0.25 time tmi<

k/type of' l~.rt

2/Machine £

] and 4 respect ively

Table 3

Comparision of Dispatching Rules

Performance Proposed SPT SPT/TOT FCFS indices Heuristic

MK 22.44 30.02 29.06 32.±5

U 54.8 4o.5 41.4 ~4. i

MK 19.65 26.48 26.25 27.'(0

U 48.1 35.5 36.3 34.

MK 29.16 42.05 41.48 42.99

U 62.16 43.3 43.53 42.13

MK 29.68 44.21 4)4.7 h6.07

U 57.4 39.2 39.3 37.00

V a r i e d ~ e t e r

29. ~3

41.0

26.23

35.8

39.37 44.1

39.51

42.6

Hm=5

N j=5

NO=f%

40

30

~ 10

0

35

30

pt 25

~ a I 2 0

- v 15 :E

10 . . . . . . R e g r e s s i o n

i I I ] I I 5 0.25 0.50 0.75 1.00 1.25 1,50 0

pt, s,a =

447

x No o Nj ,~

~ . ~ Na //2

/ "

#/ Regression I I I I L I 1 2 3 4 5 6 No, Nj, Nc,Nm - - - " -

Fig.2 Fig.3

MK2 = -286.9+48.2No+I0.0Nj+24.9Na+81.65Nm+0.06No2-0.06Nj2-0.003Na 2

+I.05Nm2+I.SNo.Nj+2.7No.Na-21.08No.Nm-4.SNj.Na+I.9Nj.Nm-3.SNa.Nm (6)

With the coefficient of correlation for equations 5 & 6 as equal to 0.9855

and 0.9917 respectively.

Equations 5 & 6 have been employed to study the effects of various FMS

operating parameters on MK and the results shown in Figs.2-3.

It can be observed from Fig.2 that the effect of 's' on MK is more marked

than pt and 'a' in that order and MK varies almost linearly with 's', pt

and 'a'. It can also be noticed from equation 5 that 's' and pt are

interdependent as far as their effect on MK is concerned. From Fig. 3 it

can be noticed that the factors that influence MK are: No,Nj,Na and MK

increases almost linearly with these parameters.

1 36~. x Np o Nb

~Z" 3 4 ~

32 1 2 3 4

Np,N b

O

5 6

Fig. 4

448

60

I 5o 4O

3

x pt o S

. . . . . . Regress ion I I I I I I

0.25 0-50 0-75 1.00 1.25 1-50 pt, s, a - - - - - - -

100

90

80

70 l°° ~ 50

4O

30

2O 0

Simulation ~ - Regression

~ × No ~ o Nj

~, ~ N o

1 2 3 4 5 6 No,N j , N c~, N m ---------'--

Fig.5 Fig.6

MACHINE UTILIZATION

The effect of system parameters on '! ' have been evaluated an~ the :~::, :.

given in Figs. 5-7. Average machine utilization ill this case l~as been o b t , ' ~:

by averaging the utilization o5' all the considered n~rlbers of machixe

the system for the range of operating parameters ~,~' i:[sted in !'abl~ .

Predictive empirical equations ( ,-~ i~ were next derived by the ~n !

simulated data and multiple regression analysis. ?he resultiny equa .,,,

are :

Ul = 43.46-9.Spt+33.15s-6.$a-2.Tpt ~-]7.3s2-;' 3a~+{i.36pt.s+2.,~[ipt.a- , . ~

U2 = - h~l. 78+J i. 6No-6.12N j+[~l. 611a+ff 6. i5Nm-0. 741Jo ~-0. (~Nj 2-0. ,~!3hs ~

+2.7Nm2+12.0No.N j-7.6No.Na-(). 9No. Nm-7.09~I j .Ns-0. 3511 j .]qm-~. 7]i{~ .IL~;

(The coe~'ficients of correlation for equations 7 < ~, respectively wer~, . - ~

and 0.9896). The effect of various FMS operating parameters on ' ' ~ L

equations 7 & ,5 h~ve been studied and the results given ~t Figs.~-l.

The operating parameter ' s' can be sen to have a i'avou~-able el lk'{

'U' (Fig.5). The rate of improvement in 'U' however, diminishes ~t h~,mer

value of' 's'. On the other hand, 'U' tends to diminish for large v~} ~e:,

'a' and pt.

Fig.6 shows that 'U' increases ai~nost linearly with l~o,Na and Nj. ]~Jiqer,:~ ,

increasing the number of machines leads to a reduction in 'U' . t :~

noticed from Fig.7 that 'U' increases slightly with [(b and beyond ~ iu<:

of 2 becomes a constant.

449

7 ~ - x Np o N b

~ 60 " ~ - ' 4 a ~ - ~ - . . - - ®

D 4 t t t I 2 3 4 5 6

N p , N b " - - ' "

Fig.7

CONCLUSIONS

Based on the present work the following conclusions can be drawn:

i. The heuristic based on EST for loading the jobs to machines in batch

job shop type FMS has been found to be superior to some of the well known

dispatching rules proposed by others.

2. For optimum machine utilization the pallet travel time must be kept

as small as possible (Fig.5). In case if this can not be achieved the

operations be scheduled in such a manner that a large number of successive

operations, on a job, are performed at the same work station.

3. The optimum number of buffers to be provided in majority of cases

in two (Fig.7).

4. Based on the simualation results, empirical models for MK and 'U',

has been developed, which can very efficiently be employed to determine maximum

makespan and average machine utilization over a range of operation parameters.

5. The 's' and pt in an FMS are interdependent operating parameters. The

machine utilization becomes virtually constant if pt exceeds 's'(Fig.5).

NOMENCLATLPRE

ART i Arrival time of a part i; a Interarrival time of jobs. Fo~_l~ Finish time of (Oi-l)th operation on part i.

HT(mi-l,m i) Transportation time of the parts. S m Finish time of previously assigned part. Na No. of jobs of each type; Nb No. of buffers. Nj No. of types of jobs; No No. of operations. Np No. of pallets.

REFERENCES

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450

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i~.Buzacott, J.A. and Shanthikumar, J.A. Models for understanding .<'_,>,,.bL( manufacturing systems, AIIE Trans. 12, 1980, ~. Z39.

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