a study of three classes of sequencing rules simulated€¦ · area of sequencing in job shops. the...
TRANSCRIPT
A STUDY OF THREE CLASSES
OF SEQUENCING RULES
IN A SiMULATED JOB SHOP
by
V!nod Chachra
Thesis submitted to the Graduate Faculty of the
Vi~gfnla Polytechnic Institute
in partial fulfillment for the degree of
APPROVED:
P. M. Gh;::re
fvlASTER OF SCI ENeE
in
INDUSTRIAL ENGINEERING
/t' ! f
Chairman, W. J. Fab~ycky'
Paul E. Torgersen
Augu 1968
Blacksburg, Virginia
TABLE OF CONTENTS
Chapter
! NTRODU CT I ON
I I DESCRIPTION OF THE SIMULATOR ••••••••••••••••••••••••••••••• 4
The Ma in Pr.ogram •••••••••••••••••••••••••••••••••••••• 4
Sub rou tin e Ra n d ............................................. 6
Subroutine Subjob
Subroutine Decide
First Come First Serve ••..•.•.•..•••••...••••.•.•
Shortest Process i ng Time ........................... ..
Probab iii ty uencing .. * __ •••••••••••••••••••••••
Subroutine Prob .................................... .. ' .
6
7
7
8
8
9
I I I OPERAT! ON AND OUTPUT OF THE SIMULATOR ......................... ! 0
I nit i a liz at ion I n t e rva I ................................... I 0
Simulation Interval ................................... 12
Test Conditions ••.•••••.•.•••••.•••••••..••.••••••••••. 12
Ou tp ut s .......................................................... I 3
, V OBSERVAT IONS AN 0 0 I SCUSS ! ON ........................................... 30
V RECOMMENDAT IONS FOR FURTHER STUDY .............................. 36
SELECTED REFERENCES ••••••••••••••••••••••••••••••••••••••••••••• 38
VITA •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 39
APPE~~D I X ••• s ••• ~ •••••••• co ••• It ........ •• '. • • • • • • • • • • • • • • • • • • • • • • • • • 40
j i
LIST OF TABLES
Table
TABLE OF TEST CONDITIONS 14
I I QUEUE PROBAB I Lf TIES FOR TEST COND IT! ONS OF SET I, RUN I,
< SEQUENC! NG RU LE FCFS •••••••••••••••••••••••••••••••• e'. • • • • 15
I I I QUEUE PROBABILITIES FOR TEST CONDITIONS OF SET I, RUN 2,
SEQUENC I NG RULE SPT ........................................ 16
IV QUEUE PROBABILITLES FOR TEST CONDITIONS OF SET I, RUN 3,
SEQUENCING RULE PS •••••••••••••••••••••••••••••••••••••••• 17
V QUEUE PROBABILITIES FOR TEST CONDITIONS OF SET 2 & 3,
RUNS 4 & 7, SEQUENCING RULE FCFS ••••••.•••••.••••••••••••• 18
VI QUEUE PROBABILITIES FOR TEST CONDITIONS OF SET 2 & 3,
RUNS 5 & 8, SEQUENC I NG RULE SPT ••••••••••••••••••••••••••• 19
VII QUEUE PROBABI LlTIES FOR TEST CONDITIONS OF SET 2, RUN 6,
SEQUENCING RULE PS •••••••••••••••••••••••••••••••••••••••• 20
VIII QUEUE PROBABI LITI ES FOR TEST CONDITIONS OF SET 3, RUN 9,
SEQUENCING RULE PS ......................................... 21
I X SUMMARY OF RESULTS OF TEST CONDI T IONS OF SET ! ............. 28
X SUMMARY OF RESULTS OF TEST CONDITIONS OF SETS 2 & 3 ••••••• 29
iii
LIST OF F! GU RES
Figure Page
MACH I NE UT I L I ZAT /ONS FOR S I X MACH I t~E CENTERS ••••••• 0 • • '0 • • • I I
2 DUE DATE PERFORMANCE FOR TEST CONDITION OF SET 2, RUN 4,
SEQUENCING RULE FCFS •••• 0 ........... 0 ......... 0............ 22
3 DUE DATE PERFORMANCE FOR TEST CONDITION OF SET 2, RUN 5,
SEQUENCING RULE SPT •••••••••••••••••••••••••••••••••••••••• 23
4 DUE DATE PERFORMANCE FOR TEST CONDI T ION 0 F SET 2, RUN 6,
SEQUENC I NG RULE PS ••••••••••••••••••••••••••••••••••••••••• 24
5 DUE DATE PERFORMANCE FOR TEST CONDITION OF SET 3, RUN 7,
SEQUENCING RULE FCFS ••••••••••••••••••••••••••••••••••••••• 25
6 DUE DATE PERFORMAI\lCE FOR TEST COND I T I ON OF SET 3, RUN 8,.
SEQUENCING RULE SPT •••••••••••••••••••••••••••••••••••••••• 26
7 DUE DATE PERFORMANCE FOR TEST CON 0 I T I ON OF SET 3, RUN 9,
SEQUENCING RULE PS ••••••••••••••••••••• •••••••••••••• ~ •• ••• 27
iv
ACKNOWLEDGEMENTS
The author is grateful for this opportunity to express appreciation
for the fol lowing IndIviduals for their aid in this study:
Dr. W. J. Fabrycky, the author's major advisor, for providing
va I uab Ie gu i dance and constant encou ragement th ro,u ghout the ent ire
graduate program.
The members of his graduate committee, Dr. P. E. Torgersen and
Dr. P. 1\1). Ghare for their constructive criticisms.
Dr. D. C. Montgomery for his invaluable aid during the development
of the computer program for the simulator.
Miss Carol Kirk for her excel lent typing.
v
Chapter I
INTRODUCTION
In its most general form, the Job Shop is a production system
consisting of numerous processing faci lities assigned to various tasks.
Each task has a required set of operations which fol low some pre
assigned logical order. The processing faci lity is normally referred
to as the machine center, the logical order of the operations form the
routing and the task on which the operations are performed constitutes
the job.. Thus, the phrase Job Shop denotes a "general class of
problems" and not merely a "gener'al purpose machine shop" (2).
Experimentation with Job Shops through simulation started as
early as 1952. Among the earlier investigators were Jackson (8) and
Rowe at UCLA and Baker and Dzielinski (I) at IBM. J. R. Jackson (8)
and R. W. Conway (2,3,4,5) have been the chief investigators in the
area of sequencing in Job Shops. The results of Conway are extensive
and many of his experimental results are presented in "his book (6).
Many Job Shop sequencing rules have been formulated and some of
them have been tested through simulation. These .sequencing rules
can be broadly divided into three classes. : Rules In the first class
would be those thai- are completely independent of any characi-er-is-i-ics
of the job and the shop. In the second class would be those rules
whlch depend upon the characteristics of the job but are independent
of the character; Ics of the s!lop Sequencing rules that depend on
charactsl-istics fall in the third class.
-!-
-2-
Sequencing is a smal) but important part of avera I r Job Shop
operations. This investIgation uses simulation to study some aspects
of seq uenc i ng in the Job Shop ,ut iii zing one seq uenc i ng ru lese I ected
from each class. These sequencing rules are:
a. First Come First Serve (FCFS).
b. Shortest Processing Time (SPT).
c. Probabi I ity Sequencing (PS).
Thus far no single measure of effectiveness has been formulated
to measure overal I performance of the Job Shop. Measures of effec
tiveness currently in use are mean flow time, flow time variance,
mean lateness, in~process inventory level, machine uti lization and
due date performa~ce. The measures of effectiveness chosen for this
Investigation are:
a. Due Date Performance ..
b. Number of jobs processed in a simulated interval
of time.
c. Number of jobs late.
d. Mean lateness.
e. I n-p rocess inventory I eve I .
There are two major differences in this investigation and those
reported in literature. The first is that a compari son is made of
the performance of a Job Shop operating under a selected sequencing
rule from each class of rules. The second difference is the basis
for comparison itself. In this study the simulated interval used and
the number of jobs generated are kept constant with the number of jobs
completed al lowed to vary. In other investigations comparisons were
made for the same number of jobs processed. It is recognized that
in the approach of this investigation steady state is a necessary
condition for valid comparisons.
I
Chapter II
DESCRIPTION OF THE SIMULATOR
The Job Shop Simulator was developed to provide an experimental
base from which the" behavior of a complex job shop system could be
observed. The simulation rmits indirect experimentation in a
situation where direct experimentation is difficult and certainly
economi ca I I Y i nfeas i b I e. The computer program for the s i mu I ator is
written for the IBM 7040 digital computer in the FORTRAN IV language.
It consists of a main program with four subroutines. A complete
listing of the main program and the subroutines is given in the
Appendix.
The Main Program
The simulator is of the variable time increment type in which
clock time is advanced by an amount necessary to cause the next event
to take place. The basic time unit used in the simulator is con
tinuous and is expressed in hours. A period of eight hours has been
desIgnated as a day. There Is no discontinuity of operations between
days.
The simulator represents a manufacturing system with a number of
mach i ne centers ltd th queues beh i nd them. A job that enters the system
joins the queue behind the first machine center on i routing. As
soon as the machine center is free, a job is selected from the queue
and is al lowed to occupy the machine center for a time ual to its
process i ng time at th center. A machine center can handle only one
-4-
-5-
operation on a job at a time. When the operation is complete, the
job moves to t~e queue behind the next machine center on its routing
and the machine center selects another job from its queue. When the
job has no more machine centers on its routing it is complete. If
the machine center finds no job in its queue it remains idle unti I
the next job arrives.
Each time an event occurs in the simulator, performance statistics
are updated. Thus, data are collected continuously through the entire
period of simulation. The data collected are as follows:
a. Cumulative time that the queue is of a given length
behind each machine center. This is used in caf
culating queue probabi lities.
b. Cumulative time for which each machine center is in
service. This gives the values for machine uti lizations.
c. Due date performance of each job processed.
"d. Total number of job processed.
e. Waiting time history for the last 15 jobs processed
at each machine center. This is for internal use in
connection with the Probabi lity Sequencing rule.
The simulator is general in that it can handle variable shop size
and different durations of simulation under a multitude of operating
conditions. The operating conditions may be varied by suitably modify
ing the four subroutines to be described next.
-6-
Subrouti ne Rand
Subroutine,Rand is used to generate Inter-arrival times. It
determines the time of arrival of the next job in relation to the
time of arrival of the previous job. Any inter-arrival time distri
bution'may be used. As printed in the Appendix, Subroutine Rand
exhibits a negative exponential distribution for inter-arrival times.
Subroutine SubJob
Every job gets its routing (ITECH), its processing times at the
various machine centers (PRT) and its due date (D) from Subroutine
Subjob. Routings, process time distributions and due date settings
may be changed as desired. In its present form, the routing is
random and a II jobs are made to pass through an approximate number of
machine centers equal to the shop size minus one. This is accomplished
by generating 12 numbers (for shop size of 12) from a distribution
which has,equal probabi lity of generating numbers from zeu through
twelve. Thus, if the generated numbers are 2,0,4,6,6,7,3,9, 11,12,3,10
then the first mach i ne center in the routi ng is mach i ne center 2, the
next would be 4 (zeros are skipped) fol lowed by machine center 6 and
then back to 6 and so on.
For the routing obtained above, processing times are generated
by drawing values from a processing time distribution. A rectangular
distribution for processing times is exhibited in the subroutine
listing.
The due dates are establ ishe,d by summing the processing times and
multiplying the sum by a factor. Changing the due date multiplier
would change the amount of slack in the total al lowed flow time.
-7- .
Therefore" the allowed f lov" time for the incoming jobs depends upon
the mu It i P lie r .
Subroutine Decide
Subroutine Decide is used to determine which job is to be pro-
cessed next on a machine center. Thus" this subroutine provides the
sequencing rule under which the shop operates. The subroutine is
called into operation each time an operation is completed at a machine
center. It first exami nes the queue beh i nd the mach i ne center. If
there are no jobs in queue the machine center is al lowed to remain
idle unti I a job arrives. If there is only one job in queue it is
automatically processed next. When the queue contains more than one
job, the priorities of these jobs are examined and the job with the
highest priority is processed next. Once the job to be processed is
selected, it is put on the machine and the other jobs are moved up
in queue.
The actual assignment of priorities for the jobs is done
differently by the three sequencing rules. Thus, Subroutine Decide
has three forms, one for each rule and only one of these three is
used at any time. The sequencing rules chosen for this study are
discussed next.
This sequencing rule assigns the
highest priority to a job that joins the queue first. The assignment
of priority, therefore, is in no way dependent on either job or shop
characteristics. Symbol ica! ly, if Prj be the p.riority of the ith job
behind the jth machine center and Sj is the set of integers denoting
-8- .
the jobs in queue behind machine center j? in arrival order~ then for
this rule,
max p". = S. J IJ J
where Sj' Is the first number of the set Sj;
Shortest Prpcessing Tfme (SPT) The highest priority is assigned
by th,is rule to that job in queue having the smallest processing time
at the machine center in question. Such pl~iorities are assigned by a
job characteristic, In this case processing time. 1ft·· is the p roIJ
. t" f th .th . b t th .th h' t th' cesslng Ime 0 e 1- JO a e J- mac Ine cen er en,
Probabi Iity Sequencing CPS) The highest priority under Probabi lity
Sequenc ing is ass i gned to that job hav ing the. greatest urgency. Urgency
factors are computed as:
z. = I
n (OJ-C) - L: llj
j = k
Where, Z i is urgency factor of job i.
O. is the due date for job j. I
C is the current date.
v. 2 is the mean flow time through machine center j. J
Oj2 is the flow time variance at machine center j.
k is a machine center number on a route numbered from I to n.
Th "I f Z . I h f i f th . th . b . t h . us, .. IS Tl. e urgency ac 'or 0 Ie 1- JO I.n queue a mac I ne IJ
cente r j} then
max p .. IJ
-9-
Inspection of the urgency factor formula indicates that jobs
wi I I assume priorities that depend upon job and shop characteristics.
A more complete description of Probabi I fty Sequencing is given in (7).
In this investigation a modified method was used for calculating
the value of Z. The L~j term was broken up into two parts, Ltj and
EWj. Etj represents the sum of actual downstream processing times
for the job and LWj is the sum of the mean wa i ti.ng ti mes at the down
stream machine centers. LO'j2 is the sum of the variances of Wj. Thus,
(OJ -C) . - Lt· - LWj Z· = J
I
J LO'-2
J
Su brou tine Prob
Subroutine Prob calculates new Z-values for al I jobs at the end
of each eight hour (I day) period. As stated earlier, the main program
gathers waiting time history for the last 15 jobs processed at each
machine center. This data is used to calculate the mean and variance
of waIting time at each machine center. From the due date, current
date and the processing times this subroutine calculates the Z-values
using the modified urgency factor formula.
Chapter III
OPERAT ION AND OUTPUT OF THE SIMULATOR
This chapter presents the necessary detai led preparation for
simulation and also ~numerates the parameters used in the experimental
runs. The output from the simulation is summarized and extensions from
this output resulting from further computation is presented.
Inftiallzati6n Interval
Before data can be, gathered regarding shop performance, it is
important to make sure that the shop is operating at steady state or
near steady state condItion. The values for machine uti I izations
were used as indicators of steady state. A test run was made with
a shop size of 12 machine centers operating under the FeFS sequencing
rule. Machine uti I ization values were printed at intervals of 6 days
starting at day 8. Uti llzation figures for six machine centers
picked at random are plotted in Figure I.
Inspection of the curves in Figure I indicates that 50 days is
a sufficient interval for initializing the shop. In order to be
consistent between runs, the shop was initialized for a period of
50 days under the FeFS sequencing rule for all experimental runs. If
the sequencing rule being tested was not FeFS,. a switchover took
place after 50 days from FeFS to the sequencing rule in question.
This switchover is effected by the control variable LMN.
-10-
80
70
60
50 PERCENTAGE UT III ZATI ON
40 I --I
30
20
10
0 0 10 20 30 40 50 60 70
DAYS
Figure I. Machine Uti lizations for Six Machine Centers
-12-
S i mu I at i on I n te rva I
The total jnterval of simulation was 300 days of which 50 days
constituted the initialization period. Performance data was gathered
for the last 250 days only. In other studies (3,5) the number of
jobs processed was kept constant and the simulation interval required
to process these jobs was al lowed to vary. Since Figure I indicates
that this simulator was operating near steady state, it was decided
to keep the simulatIon interval constant. The number of jobs pro-
cessed In this interval was used as a performance measure.
Several test runs were made to determine the computer time re-
qui red for various simulation intervals. It was from these runs that
the 300 day interval was chosen ~s being feasible for this study.
Test Conditions
In this experiment, the inter-arrival times were generated from
a negativE? exponential distribution and the processing times were
generated from a rectangular distribution. The means of these distri-
butions were manipulated to give the required traffic densities. Due
to the manner in which the routing is determined, the traffic density
is estimated by:
T.D. (Mean processing time) x (shop size -I) Shop size x Mean time between arrivals
In al I, 9 experimental runs were made under three sets of operating
conditions. Set I was at low traffic density chosen to be 0.6. Sets
2 and 3 were at a high traffic density chosen to be 0.9. In Set 2 the
allowable flow time was smal I and represents the tight due date condi-
tion~ Set 3 had a larger allowable flow time representing a normal due
-13-
date condition. The actual numerical values used for- the three sets
of test conditions are presented in Table I.
Outputs
The actua I outp.uts f rom the comp ute r run s we re mach i ne ut iii za
tions, queue probabi lities and histograms of due date performance.
Tables II through VIII exhibit queue probabilities obtained from the 9
experimenta I runs. Tables of queue probabi I ities for FCFS and SPT
were identical between test conditions of Set 2 and Set 3. Thus
runs 4 and 7 gave identical queue probabi I ities and as did runs 5
and 8 giving seven different tables for 9 runs.
The due date performance histograms for the test conditions of
Set 2 and Set 3 are presented in Figures 2 thr~ugh 8. In these
histograms the abscissa is given as days with negative values repre
senting days early and positive values representing days late. The
dotted portion of the histogram indicates that values beyond that point
have been lumped.
Further calculations were made util izing these results to obtain
measures of in-process inventory, number of jobs late and mean lateness."
These are summarized in Table IX for test conditions of Set I and in
Table X for test conditions of Sets 2 and 3.
ter ing Experimenta I Traffic Due Run Rule Set Densit:t Mu !ti~1 fer
FCFS
2 SPT Set I 0.6 2.0
3 PS
4 FCFS
5 SPT Set 2 0.9 2.5
6 PS
7 FCFS
8 SPT Set 3 0.9 5.0
9 PS
Table 1. Table of Test Conditions
A rr i val Time Mean Yare
3.0 9.0
2.04 4. 16
2.04 4. 16
Process i ng Time Mean Var.
2.0 0.33
2.0 0.33
2.0 0.33
I
~ ,
QUEUE LENGTH
0 0.751 1 O. 15 I 2 0.062 3 0.025 4 0.008 5 0.002 6 0.001 7 0.000 8 0.000 9 0.000
10 0.000
" 0.000 12 0.000
1.000
MACH I N E CENTE RS-
2 3 4 5 6 7 8 9
0.705 0.703 0.774 0.767 0.739 0.724 0.741 0.759 0.132 0.133 0.153 0.127 0.122 0.122 0.155 0.148 0.056 0.065 0.052 0.056 0.050 0.063 0.064 0.057 0.034 0.034 0.017 0.031 0.034 0.025 0.029 0.018 0.023 0.017 0.004 0.015 0.017 0.013 0.010 0.010 O.O! I 0.017 0.000 0.004 0.016 ) 0.010 0.006 0.005 0.010 0.020 0.000 0.000 0.006 0.005 0.002 0.001 0.006 0.010 0.000 0.000 0.008 0.002 0.000 0.000 0.004 0.001 0.000 0.000 0.003 0.002 0.000 0.000 0.004 0.000 0.000 0.000 0.003 0.001 0.000 0.000 0.005 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.006 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.004 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
Table I I. Queue Probabi lities fur Test Conditions of Set I, Run I, Sequencing Rule FCFS
10
0.782 0.146 0.057 I
0.012 -Ul
0.003 I
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1.000
QUEUE LENGTH
0 0.756 I 0.164 2 0.056 3 0.015 4 0.008 5 0.002 6 0.000 7 0.000 8 0.000
1.000
MACH 1 NE CENTERS
0.726 0.712 0.788 0.802 0.745 0.738 0.739 0.780 0.144 O. 114 0.142 0.123 O. 131 o. 151 0.158 0.144 0.073 0.062 0.041 0.046 0.067 0.053 0.070 0.050 0.038 0.041 0.017 0.023 0.036 0.028 0.024 0.017 0.016 0.028 0.01 I 0.005 0.019 0.012 0.007 0.007 0.003 0.024 0.001 0.001 0.002 0.008 0.002 0.002 0.000 0.013 0.000 0.000 0.000 0.006 0.000 0.000 0.000 0.005 0.000 0.000 0.000 0.003 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.001 0.000 0.000
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
Table 1 I I. Queue Probabi lities for Test Conditions of Set I, Run 2, Sequencing Rule SPT
0.799 0.133 0.052
I 0.014 -
0'1 0.002 I
0.000 0.000 0.000 0.000
1.000
2
0 0.753 0.748 I 0.148 0.123 2 0.061 0.059 3 0.019 0.033 4 0.009 0.015 5 0.006 0.006 6 0.004 0.005 7 0.000 0.005 8 0.000 0.005 9 0.000 0.001
1.000 1.000
I NE CENTERS
0.706 0.788 0.790 0.744 0.744 0.746 0.773 0.127 o. 132 O. 135 0.129 O. 141 O. 152 0.150 0.062 0.051 0.046 0.057 0.052 0.066 0.052 0.034 0.020 0.022 0.032 0.026 0.023 0.014 0.031 0.006 0.006 0.016 0.016 0.008 0.010 0.023 0.003 0.001 0.007 0.011 0.001 0.001 0.013 0.000 0.000 0.005 0.006 0.001 0.000 0.004 0.000 0.000 0.007 0.003 0.002 0.000 0.000 0.000 0.000 0.003 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1.000 1.000 1.000 1.000 1.000 1.000 1.000
Table IV. Queue Probabi lities for Test Conditions of Set I, Run 3, Sequencing Rule PS
0.812 O. 118 0.045 0.013 I
0.004 -.....J
0.004 t
0.003 0.001 0.000 0.000
1.000
LENGTH
0 0.268 I 0.139 2 0.088 3 0.099 4 0.082 5 0.071 6 0.058 7 0.054 8 0.038 9 0.019
10 O.Oi 1 II 0.028 12 0.029 13 0.010 14 0.004 15 0.002 16 0.000 17 0.000 i8 0.000 !9 0.000 20 0.000 21 0.000 22 0.000
1.000
MACHINE CENTERS
2 3 4 5 6 7 8 9 10 II
0.253 0.284 0.379 0.269 0.362 0.321 0.283 0.355 0.260 0.370 0.149 0.164 O. 171 0.138 0.169 0.171 o. 132 0.140 0.130 o. 181 O. I I 1 O. I 12 0.139 0.092 0.136 O. I 17 0.150 o. 107 0.082 0.134 0.096 0.084 0.111 0.067 0.096 0.096 0.128 0.102 0.060 0.082 0.089 0.086 0.083 0.065 0.067 0.073 0.085 0.08/ 0.052 0.043 0.078 0.076 0.053 0.038 0.052 0.039 0.078 0.057 0.047 0.042 0.063 0.067 0.036 0.020 0.031 0.034 0.050 0.041 0.053 0.047 0.038 0.049 0.014 0.016 0.022 0.037 0.025 0.034 0.047 0.044 0.031 0.034 0.006 0.0 II 0.020 0.034 0.013 0.015 0.038 0.029 0.019 0.025 0.002 0.010 0.020 0.024 0.012 0.013 0.039 0.018 0.018 0.009 0.004 0.013 0.010 0.010 0.01 1 0.012 0.039 0.007 0.0 II 0.007 0.002 0.018 0.004 0.008 0.007 0.008 0.028 0.003 0.010 0.002 0.000 0.027 0.005 0.0 II 0.010 0.0 II 0.0!7 0.000 0.010 0.001 0.000 0.030 0.005 0.012 0.011 0.009 0.016 0.000 0.0!2 0.000 0.000 0.033 0.001 0.007 0.004 0.005 0.019 0.000 0.009 0.000 0.000 0.040 0.000 0.005 0.001· 0.006 0.018 0.000 0.003 0.000 0.000 0.034 0.000 0.001 0.000 0.003 0.012 0.000 0.000 0.000 0.000 0.029 0.000 0.000 0.000 0.001 0.010 0.000 0.000 0.000 0.000 0.021 0.000 0.000 0.000 0.000 0.016 0.000 0.000 0.000 0.000 0.015 0.000 0.000 0.000 0.000 0.013 0.000 0.000 0.000 0.000 0.009 0.000 0.000 0.000 0.000 0.003 0.000 0.000 0.000 0.000 0.004 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000
1.000 1.000 1.000 1.000 I. 000 1.000 1.000 1.000 1.000 1.000
Table V. Queue Probabi lities for Test Conditions of Set 2 & 3, Runs 4 & 7, Sequencing Rule FCFS
12
0.283 0.154 O. 152 O. 148 0.097 0.072 0.045 0.025 0.015 0.008
I 0.001 -
0:> 0.000 , 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1.000
QUEUE LENGTH
0 0.289 1 O. !51 2 O. I 10 3 0.088 4 0.068 5 0.071 6 0.060 7 0.051 8 0.053 9 0.038
10 0.0!6 II 0.004 12 0.001 13 0.000 14 0.000 1.5 0.000 16 0.000 17 0.000 18 0.000 9 0.000
20 0.000
1.000
MACH I NE CENTERS
2 3 4 5 6 7 8 9 10 I I
0.203 0.279 0.435 0.242 0.410 0.341 0.269 0.359 0.270 0.364 0.138 O. 186 0.219 0.137 O. 191 0.185 _ 0.170 0.174 0.128 0.216 0.145 O. 151 0.158 O. 118 0.142 O. 145 0.157 O. I '9 O. 113 0.170 0.127 0.115 0.089 0.085 0.104 0.113 0.123 0.-083 O. 1 14 0.103 O. 123 0.088 0.057 0.060 0.065 0.069 0.081 0.072 0.093 0.060 0.099 0.065 0.024 0.043 0.034 0.036 0.066 0.057 0.071 0.033 0.065 0.045 0.012 0.031 0.024 0.033 0.047 0.040 0.067 0.017 0.035 0.030 0.005 0.024 0.016 0.031 0.033 0.029 0.045 0.013 0.021 0.020 0.001 0.018 0.0 II 0.021 0.024 0.015 0.034 0.015 0.019 0.015 0.000 0.022 0.002 0.013 0.015 0.010 0.018 0.004 0.014 0.005 0.000 0.021 0.001 0.007 0.007 0.006 0.023 0.004 0.006 0.000 0.000 0.027 0.000 0.002 0.003 0.004 0.014 0.001 0.004 0.000 0.000 0.035 0.000 0.002 0.004 0.009 0.007 0.000 0.001 0.000 0.000 0.045 0.000 0.001 0.001 0.008 0.003 0.000 0.000 0.000 0.000 0.029 0.000 0.001 0.000 0.005 0.000 ·0.000 0.000 0.000 0.000 0.024 0.000 0.000 0.000 0.006 0.000 0.000 0.000 0.000 0.000 0.014 0.000 0.000 0.000 0.003 0.000 0.000 0.000 0.000 0.000 0.011 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.008 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.004 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 . 0.002 0.000 0.000 0.000 0.000 0.000 0.000
1.000 1.000 1.000 1.000 J .000 1.000 1.000 1.000 1.000 1.000
Table VI. Queue Probabi I'ties for Test Conditions of Set 2 & 3, Runs 5 & 8, Sequencing Rule SPT
12
. 0.353 0.214 0.169 O. 113 0.057 0.029 0.024 0.016 0.013 , 0.007 -
\.0 0.004 I
0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1.000
UE MACHINE CENTERS LENGTH
0 II 12
0 0.259 0.213 0.279 0.423 0.278 0.361 o. I 0.320 0.361 0.286 0.394 0.305 O. I 15 0.073 O. ! 31 0.180 0.146 0.138 0.140 O. 151 0.136 0.152 0.184 0.158
2 0.095 0.061 O. 1 13 O. 108 O. I 16 O. 105 O. 118 0.136 O. O. 114 0.126 0.147 3 0.101 0.074 0.085 0.075 0.10 I 0.077' 0.089 0.091 0.073 0.080 0.083 0.134 4 0.078 0.080 0.090 0.052 0.083 0.066 0.064 0.062 0.065 0.059 0.086 0.081 5 0.073 0.059 0.075 0.035 0.068 0.052 0.042 0.047 0.055 0.047 0.084 0.048 6 0.076 0.054 0.060 0.023 0.052 0.038 0.038 0.052 0.049 0.039 0.034 0.040 7 O. 0.049 0.046 0.030 0.034 0.041 0.043 0.051 0.038 0.029 0.016 0.035 8 0.036 0.049 0.042 0.016 0.029 0.035 0.044 0.036 0.030 0.021 0.010 . 0.016 9 0.031 0.042 0.033 0.013 0.022 0.025 0.035 . 0.020 0.035 0.020 0.002 0.015
10 0.024 0.032 0.022 0.010 0.012 0.022 0.021 0.006 0.020 0.015 0.001 0.013 II 0.019 0.031 0.0 II 0.007 0.012 0.019 0.012 . 0.009 0.008 0.018 0.000 0.003 r
N 12 0.014 0.029 0.002 0.004 0.017 0.0 II 0.006 0.008 0.010 0.016 0.000 0.003 0
I 13 0.016 0.022 0.003 0.005 0.0 I! 0.006 0.008 0.001 0.008 0.018 0.000 0.002 14 0.007 0.012 0.005 0.003 0.009 0.003 0.005 0.001 0.005 0.016 0.000 0.000 15 0.002 0.016 0.003 0.004 0.007 0.001 0.003 0.003 0.007 0.014 0.000 0.000 !6 0.000 0.018 0.000 O. 0.003 0.000 0.001 0.002 0.003 0.016 0.000 0.000 7 0.000 0.012 0.000 0.000 0.000 0.000 0.000 0.001 0.001 0.009 0.000 O.
18 0.000 0.018 0.000 0.000 0.000 . 0.000 0.000 0.002 0.000 0.011 0.000 0.000 19 0.000 0.018 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.010 0.000 0.000 20 0.000 0.014 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.006 0.000 0.000 21 0.000 O. a II 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.003 0.000 0.000 22 0.000 0.009 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 O. 23 0.000 0.002 0.000 0.000 , 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 24 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
>24 0.000 0.001 0.000 0.000 0.000 0.000 '0.000 0.000 0.000 0.000 0.000 0.000
1.000 1.000 1.000 i .000 1.000 1.000 1.000 1.000 1.000 1.000 ! .000 I •
Table VII. Queue Probabi lities for Test Conditions of Set 2, Run 6, ~equencing Rule PS
QUEUE MACHINE CENTERS LENGTH
2 3 4 5 6 7 8 9 10 II 12
0 0.298 0.229 0.287 0.411 0.240 0.386 0.333 0.292 0.369 0.276 0.362 0.343 0.156 o. 110 Q 158 O. ! 85 O. I L8 0.144' 0.149 0.159 O. 174 O. 124 0.189 O. 191
2 O. ! II 0.098 O. 121 0.124 0.104 O. 121 0.128 0.146 O. 119 0.097 O. 141 O. 142 3 0.087 0.085 0.103 0.073 0.081 o. 105 0.104 O. 115 O. I 19 0.OT7 0.097 O. J 16 4 0.059 0.061 0.090 0.056 0.063 0.061 0.062 0.067 0.071 0.063 0.077 O. 5 0.054 0.049 0.085 0.034 0.074 0.049 0.032 0.056 0.040 0.059 0.055 0.055 6 0.053 0.052 0.060 0.031 0.077 0.046 0.023 0.044 0.025 0.055 0.030 0.028 7 0.044 0.047 0.046 0.029 0.065 0.035 0.021 0.026 0.020 0.057 0.023 0.014 8 0.039 0.049 0.021 0.027 0.053 0.022 0.018 0.019 0.012 0.051 0.014 0.006 9 0.021 0.036 0.014 0.019 0.042 0.015 0.015 0.021 0.005 0.043 0.007 0.005 I
N 0 0.023 0.033 0.009 0.009 0.032 0.011 0.017 0.008 0.008 0.031 0.004 0.006 -
, I
II 0.016 0.022 0.004 0.002 0.020 0.003 0.021 0.009 0.005 0.021 0.001 0.008 2 0.01 J 0.022 0.001 0.000 0.012 0.002 0.018 0.009 0.009 0.017 0.000 0.005
13 0.009 0.027 0.001 0.000 0.006 0.000 0.018 0.013 0.008 0.015 0.000 0.001 14 0.008 0.024 0.000 0.000 0.003 0.000 0.019 0.007 0.005 0.01! 0.000 0.000 5 0.009 0.015 0.000 0.000 0.000 0.000 0.012 0.002 0.006 0.003 0.000 0.000
16 0.002 0.009 0.000 0.000 0.000 0.000 0.006 0.001 0.004 0.000 0.000 0.000 17 0.000 0.013 0.000 0.000 0.000 0.000 0.003 0.002 0.001 0.000 0.000 0.000 18 0.000 0.009 0.000 0.000 0.000 0.000 0.001 0.004 0.000 0.000 0.000 0.000 19 0.000 0.007 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 20 0.000 0.003 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
Table VI I!. Queue Probabi lities for Test Conditions of Set 3, Run 9,
120
100
80
60
40
20
0 -2 0 2 4 6 8 10 12 14 16 18
DAYS
Figure 2. Due Date Performance for Test Condition of Set 2, Run 4, Sequencing Rule FCFS
20
I N N I
140
120
100
60
40
20
-4 -2 o 2 4 6 8 10 12 14 16 18 20
DAYS
Figure 3. Due Date Performance for Test Condition of Set 2, Run 5, Sequencing 'Rule SPT
I N LN I
100
80
60
40
20
DAYS
Figure 4. Due Date Performance for Test Condition of Set 2, Run 6, Sequencing Rule PS
I N .J:::;. I
120
100
80 1:1' Iii' •• 1
60
40
-12 -10 -8 -6 -4 -2 o 2 4 6 8 10 12
DAYS
Figure 5. Due Date Perf6rmancef6r Test Condition of Set 3, Run 7, Sequencing Rule FCFS
14
I N U1 I
o N
,t"
., +
. ,
+= +-l.
'1
o o
ri-
H-'
;'+
o CO
-26-
t-'
+ R=.
: , f ,
L i +-
+j-'f- --I--
0 I,.Q
,
i
, ,
,
,
i
i-++
, ,
,iTT +H
-+-1 k
+
+++-i- ,+' ::=;:::
F·-+J:-R. ++++ H;-
-:-+IF . ,
1..0
~
N
o
. + ri- f-!- -t co
; :J..L~- c-L ~4f±1 ~
,:
L: I
0 ~
0 N
I,.Q I
o
CJ)
>c::( o
1'1\
+Q)
CJ)
YO
U)
C o +--0 e '0 U
+U)
~ L o Y-
Q) U fe 0... ro CJ) E L Q) o
Y- :J L n::: Q)
0...
Q) +ro o Q) :J Q) o CJ)
1..0
Q) L :J CJ)
LL'
120
100
80
60
40
20
-12 -10 -8 -6 -4 -2 o 2 4 6 8 10 12
Figure 7. Due Date Performance for Test Condition of Set 3, Run 9, Sequencing Rule PS
14 16
I N ......r I
Tota! Jobs Processed
FCFS SPT PS
in 250 Days 604 604 605
In-Process , Mean Lateness 13.75 18.80 16.53
Mach i ne Uti Ii zati on 55.44 55.46 55.47
Table IX. §ummaryof Results of Test Conditions of Set!
I N 0:> I
~ ~
SET 2 ~ SET 3 ~ ~
FCFS SPT PS ~ FCFS SPT PS
Tota 1 Jobs Processed I
N
924 932 921 924 932 931 \0 f
In-Process I nventor1: 48.70 38.18 50. 13 48.70 38.18 46.50
Mean Lateness 48.15 55.85 67.03 30.50 74.54 71.90
Tota I Jobs Late 844 453 627 254 142 208
Table X. Summar1: of Results of Test Conditions of Sets 2 & 3
Chapter I V
OBSERVATIONS AND DISCUSSION
This chapter presents six observations that may be drawn from
the s imu I ation resu I summarized in Chapter I I I. Each observation
is presented sepa
discussion.
I Y as a "conc I us ion" fo II owed by an exp I anatory
Observation Number I
At low traffic densities there is no appreciable
difference among the measures of performance for
the three sequencing rules.
It is seen from Table IX that the number of jobs processed by .
the three sequencing rules is almost identical. The in-process in
ventory levels are also very nearly the same. There is a smal I
difference in the mean lateness but machine uti I i ion values are
almost identical.
The reason for the lack of difference evident from a
study of the queue probabi lity tables for the low traffic density
runs, given in Tables I I, I I I and IV. As seen from the tables, the
probabi I ity for zero jobs in the queue is 74% on the average. The
probabi I ity of one job in the queue is an ave of 14%. Thus 88%
of the time the ing rule selects only job in queue thereby
giving no opportunity for the effect of the
felt on shop rformance. Therefore the op
rule to have an sf exists only 12% of
-30-
ing rule to be
nity for the sequencing
time. This fact resut
-31-
in I ittle or no difference in the various per'formance measures for
the three sequ~ncing rules.
Observation Number 2
Operation of the shop under SPT leads to lowest in
process inventory levels.
Table X shows that the in-process inventory level for SPT is
38.18 compared t6 48.70 for FCFS and 50.13 in Set 2 and 46.50 in
Set 3 for PS. The in-process inventory level depends upon queue
lengths and the durations for which the queue is of different lengths.
The SPT sequencing rule assigns the highest priority to the job that
has the sma! lest processing time at the machine center whereas FCFS
and PS do not. Since jobs with smal I processing times are processed
first, in any given interval of time SPT would process the largest
number of jobs. This keeps the queue behind each machine center at
a minimum. As a result, the in-process inventory level for the
system is a minimum.
Observation Number 3
The mean lateness in the case of SPT sequencing
is greeter than that for FCFS sequencing even
though the number of jobs late is greater in
FCFS than in SPT.
The values for mean lateness and the number of jobs processed are
given in Table X. No direct comparison is being made for the PS rule
as its resul depend both on the extra a [ Iowa b Ie f low time ava i I ab Ie
between Set 2 and Set 3 and the resulting change in priority assignment.
-32-
Under FCFS and SPT sequenc i.ng the change between Set 2 and Set 3
results only from the change in allowable flow time, since the
assignment of priorities remains unaltered. The change in allowable
flow time has the effect of measuring jobs that are late from a new
reference po i nt.
The SPT sequencing rule has the inherent tendency of reducing
queues to a minimum. Hence, the number of jobs in the shop is rela
tively small and so are the number of jobs late. However, the jobs
that tend to be late in SPT are the jobs with large processing times
as these jobs stay in queue while jobs with shorter processing times
keep arriving. Thus the fewer jobs that are late in SPT are very late.
This explains the fact that even though the number of jobs late is
smal I, the mean lateness is larger than FCFS.
Observation Number 4
The difference in mean lateness between SPT and
FCFS is less under tight due date committments
than under normal due date committments.
The difference in mean lateness is 7.7 for the tight case and 44.0
in the normal case. This can be explained by comparing the number of
jobs late. In the case of tight committments the effect of jobs that
are very late for SPT is distributed over a larger number of jobs giving
a smal fer difference between SPT and FCFS. In the normal case since
fewer jobs are late, the effect of very late jobs in SPT is more pre
dominant causing the larger difference between FCFS and SPT.
-33-
Observation Number 5
The in-process inventory level for the PS rule
increases with decreasing allowable flow time,
whereas the inventory level for FCFS and SPT
does not change with changes in allowable flow
time.
Table IV shows that the inventory level for both the FCFS and
the SPT sequencing rules remain unchanged between the conditions
of Set 2 and Set 3, 'where the allowable flow time has been doubled.
In the case of PS the inventory level increases from 46.5 in 3 to
50. 13 inSet 2.
As stated earl ier, in-process inventory level is a function
of queue lengths and queue durations. When the allowable flow time Is
changed, the priority assignment for the FCFS and SPT uencing ru I es
Is in no way fected, since these rules are independent of due
Thus, the queue lengths and durations are unchanged between 2 and
Set 3. Identical queue probabilities are ined between the two
sets for and SPT. The in-process inventory level, therefore,
remains unchanged.
In the case of PS the priority assIgnment depends upon the due
date and hence the inventory level is expected to change with
~n allowable flow time. The reason for the increase in inventory
level with decreasing a! lowable flow time becomes clear on studying
the urgency fact~r formula: n n
Z· = (D·-C) - Lt. - LW' I I J J
-34-
If N be the number of rema i n i.ng mach i ne centers on the rout i ng
and if t, wand (J are average values such that Etj = Nxt, EWj = Nxw
and rcr.2 = Nxcr2 then J ' ,
_ (Oi-C) - NCt+w) Zi -~ x cr
= IN" {( 0 '1 -C) IN - (t+W)] or, Zi cr
Thus Zi is proportional to rN (Average allowable f low time per machine
center - Average time spent per machine
center)
Where the expression in the parenthesis is positive, larger values
of N wi I I give large Z-values and therefore establish lower priorities.
If the expression is negative then largervalues of N wi II give lower
Z-values and therefore establish higher priorities. This indicates that
as long as the average allowable flow time is less than the average
actual flow time, the jobs with larger routings wi I I be processed first.
This causes the jobs to stay in the shop longer resulting in a high
in-process inventory level. Inspection of Figure 4 indicates that
this condition does in fact exist for the tight allowable flow time
causing the higher in-process inventory level.
Observation Number 6
The number of jobs processed under PS is a function
of the allowable flow time and decreases with
decreasIng al lowed flow time whereas this is not the
case for FCFS and SPT.
-35-'
The tota I number of jobs processed is i dentica lin Set 2 and
Set 3 for the FCFS and the SPT sequencing rules as shown in Table X.
This results from the fact that these rules operate independent of
al lowed flow time.
I n the case of PS, Observat i on Number 5 i .11 ustrates that jobs
with larger routings are processed first for a tight flow time
condition. Thus, in any given interval of time, a smaller number of
jobs wi II be processed when compared with the normal allowable flow
time condition.
Chapter V
RECOMMENDATIONS FOR FURTHER STUDY
Relevant conclusions from this research were stated in the
previous chapter. The purpose of this chapter is to recommend four
topics for further study which were suggested by this investigation.
Since only one sequencing rule was tested from each class of
sequencing rules, no general conclusions about the comparative per
formance of Job Shops operating under the three classes were offered.
Other sequencing rules from each class could be tested for the
pu rpose of rmining the general behavior of the Job Shop operating
under each class of rules.
AI I tests in this study were made without replications. If
sufficient replications could be made, formal hypotheses about com
parati ve performance measlJ res COIJ I d be tested. Th is wi /I requ i re
much more computer time than was available for this research.
Once rules with desirable characteri cs are found, it might
be fruitful to design a hybrid rule which combines the best attributes
of each. One promising possibi Iity which resulted from this study
was the potentia! for combining the SPT rule and the PS rule to
secure the benefit of a shop clearing attribute and the it of
a relative urgency measure.
No attempt was made in this study to select a rule which would
be best for a given management goal. Further study could be directed
to the deve loprnent of preference procedu res based on the uti i lty
function management for a ific obj ive. For example,
-36-
-37-
normally on time or early order completions are to be preferred.
However, one may envision a situation in which early completions
could not be tolerated due to lack of sufficient storage for finished
goods.
Selected References
I. c. T. Baker and B. P. Dzielinski, "Simulation of a Simplified
Job Shop, n I BM Bus i ness Systems Memorand um,
August I, 1958.
2. R. W. Conway, "An Experimental of Priority Assignrrrant in a Job Shop," Rand Corporation, Memorandum RM-3789-PR, February 1964.
3. R. W. Conway, "Priority Dispatching and Job Lateness in a Job Shop," J. Ind. Eng. 16, No.4, July 1965.
4. R. ~v. Comvay, "Priority Dispatching and Work-in-Process-Inventory in a Job Shop," J. Ind. Eng. 16, No.2, March 1965.
5. R. W. Conway, W. L. Maxwell and B. M. Johnson, "An rimental InvestIgation of Priority Dispatchi II J. Ind. Eng. II, No.3, May 1960.
6. R. W. Conway, W. L. Maxwe II and L. W. Mi Iler, "Theory of Scheduling," r II, Addison Wesley Publishing Company, 1967.
7. W. J.Fabrycky and J. E. Shamblin, "A Probability Sequencing Algorithm," J. of Ind. Eng. 17, No.6, June 1966.
8. J. R. Jackson, H
UCLA Management Science Research Report, No. 49, March 1956.
-38-
VITA
Vinod Chachra, son of Mr. and Mrs. N. L. Chachra, was born on
August 27, 1945, in Calcutta, India. He graduated from St. Xavier's
School in Calcutta in 1962.
He enrol led at The Indian Institute of Technology, Kharagpur,
in July 1962 and worked for a Bachelor of Technology degree in
Mechanical Engineering which he received in June 1967. He came to
the United States in September 1967 and entered Graduate School at
Virginia Iytechnic Institute. He completed his requirements for his
Master of Science degree in Industrial Engineering in August 1968.
The author is a recepient of the B. C. Roy Gold Medal awarded
at The Indian Institute of Technology. In the United States he is
affi liated with Phi Khappa Phi, Alpha Phi Mu and the American Institute
of Industrial 9 i neers.
il (flaC/U C{' i/ .
-39-
APPENDIX
-40-
$RUN INPUT SIEFTC MAIN C
10 090268
C C C C
c c c
SIMULATION Cf J SHDP OPERATI - MAIN PROGRAM
INITIALIZE
DIMENSION SP(13),lOUTI300), IT(300},KK{25),SSV(13),I (13), *LQUE(13),TDPART(13l,GTIME{3001,ID(401),CQUE(13, ),SERVCE(13), *KG(13}, {13}
DIMENSICN F (13,26) COMMON/ElOCKAJIORDER(12,300) COMMON I lOCKB/ITECH(300~12),O(3CC),PRTI3CO,12),lSIZE
COMMON (12,15), AlUE(3CO} DATA 10TAt,SU~,S CALL CHKPT READ(5,50CO} lZE,I
50eo FCRNA1(lCI3) SU~JOE=O.
lMN=O KKK=l DO 7 IX=1,401
7eo IDCIX)=C DO 99 I=lJ3CC CALL SU 8(1) ClIME'I} = 0.0 L (I) = C
99 CONTINUE DO 20C I=l,LSIIE TDPART(I)=1.OE+3 SERVCE{I)=O.O CHANGE(I) 040 KK{I}=O
2CO IfAC[I)=C DO 206 I=l,LSIZE DO 206 J=1,26 FOUE(l,J)=O.O
206 (I,J)=C.C DO 202 I=l,lSIZE DO 202 J=1,3 C
202 lORD (I,Jl= 0 DC 804 I=l,LSIZ
DO 8(4 J=1,15 804 T(I,J)=C.O
llDAY=l IMI~Ul=
,MAXA
LotD SEep ITH FI T JOB
-41-
c C C C C C
c c c
CALL RAND(T) JX==l JPA=l Nl=l K= 1 LGUT(t():l
-42-
1C2 N=ITECH{K,Nl) PRJ IME= PRT (K ~ 1\)) IF(PRTIME.NE.G.O)GO Te 101 ITECHtK,Nl)=O Nl==N11"1 GO TO 102
101 Tlt"1E= T
1111
IT E C H 0< , Nl ) == (I CH/\NGE(N)=TI E CQUEtN,l)=TIHf WJ\IT{ 1)=Tlt4E DTI (1)=11 E + D(l) IFAC{N}= 1 I ERIN,1)= 1 TOPART(N)=TIME + PRTI~E SERVCE(N)=SERVCElN)+PRTIME CAll r\1J(T) TARIVE == TIME + 1
TIffl G HOUTINE
PART!I)= DEP~RT TI TARIVE = ARRIVAL II
GO Te 333 c.
333 DO 11 I=l,LSIZE 11 KG(I)=l
DO 10 I==l,LSIZE IF(T IVE~GT$TDPART(I})KG{I)=O
10 CDNT Ir-:U E DC 6e LA=l,lSlZE IF{KG(lAl.EC.C) TO 20
608 CONTll\UE
e1\ C[- THE
.I E ! JOB
IfCFL T{LlDAV*I INUTloLEeTARIVE1GO TO lOCO
JCB ARRIVAL R(UTl E - ARRI l IS
1'\1=1 34 JX=JX-tl
JPA=,JFA--J: 1 IF(JPt~lE.3CO) GO TO 38
l EVENT
c c c
Il=JPt-{JPA/3CC)*300 IF(IL.lE.C)GO Te 34 IF(LCUT{Il).EQ.l)GO Te 34 JX=IL CALL SUBJOB{JX)
38 IF(lOVTeJX). C.l)fO Te 34 lOUT(JX)=l
31 N=ITECH(JX,Nl). PRTIME=P (JX,N)
-43-
IF{PRTIME .Gl.e.D) TO. 30 ITECH(JX,Nl)=C Nl=Nl~l IF{Nl.LE¥lSIZE)GG TD 31 WRITE(6,6C031
6CG3 FCRMAT(lHC,I5,5X,12H=N AT STM 30) FILE t
STCP 30 LEN=lCUE{N}+l
IF(lE~.GTa26)L
ITECH(JX,Nl)=O CQUE{~,LEN)=CQLE(N,lE~}+TARIVE-CHANGE(N)
TIME=lARIVE WAIT(JX}=Tl~E
CHANGf(N)=T E DTI E{JX1=TIME (JX) IF (IfAC (N) .EQ~ 0) TG 32 LQUE{N}= L E IN) + 1 l= LOLE {N} 10 R (Nfl)= JX GO TO 33
32 IFAC(N) = JX TDPART(NJ= Tl E + PRJI E SERVCE( )=SERVC {~)+PRTI E
33 C Li tTl TARIVE = lIME + 1 GO TO 333
JCB ARRIVAL RCUTI~E- LEPARTURE IS NEXT E ENT
20 XMIN = lCPART (1) N= 1 DC 12 I=2 t lSIZE IF (X~IN eLE~TCPART{I»GO TO 12 XMI = ART(I) N= I
12 CONTI~UE IFlFlCA1[LlDAV*IMINUT).lE. MIN)GO T8 lCOO L CUE(~}+l
C C C C C C C
-44-
IF(lEN.GT.26)LfN=26 CQUEtNyLEN1=CCUE{N,LEN)+TDPART{N)-CHANGE(N) TI~E :. XMIN CHANGE(i\}=TI E KK (N) =KK { t-:}+ 1 IF(KK(Nl.GT.lS)KK(N)=l KIK=KK(N) WT(N 7 KIK)=TI E- AIT(JCB}-PRT(JOB,N)
JOB DEPARTURE ROUTINE
JOE = JOE NO.DEPARTING N =~ACHINE NO. JDB IS EI MOVED FROM ~ =MACHI E NO Joe IS BEING MOVED TO
JOB == IF (N) 802 00 799 IX == 1,LSI1E
IF(ITECH(JOB,IX)aNE~C) TO 801 7t:;9 CONTII\UE
GO TO 800 801 lL==IT H(JOBtIXl
IF(PHT{ E,LL1.NE.C.G)GO 'TO }303 IT (JCB.,IX )=C GO TO 8e2
BC3 IF(Ll.NE.h) TO aoo (JfJE,IXJ=C
{N)+l IORDER(N,ll)=JC3 WAIT' l=TI F ll=l iN) CALL CECI[EtK,N,Ll,LMN)
PRTI E=Pt1TU<jf\:) TDPART{N)=TI E+PRTI E Sf:: eEC }=5ERVC {j\)+PPTI E GO TO 333
8CO 1F{ (N). ",G}GC TG 5
5
LQU E {N):::: L E ( ) - 1 ll::: L ':U U'i) CALL CECI[E{K,~,Ll,lM~}
Ift!C(t\) K PH TIM f= P :{,1 ( K, ) TDP T(N}= TIKE +FR1I E SERVeE( )=SERVCE(~)+PR11 E
TDPi.i.Rl( }=l"C +3E 6 DC 24 IX=l,LS ZE
c c c c c c
c c c
-45-
IF(ITECH(JOB,IX}.NE.01GO 10 25 24 CONTINUE
GO TO 8 25 L=ITECHtJCB,IX}
IF{PRT(JOB,l).NE.G.O)GO TO 301 ITECH(JDB,IX)::C GO TO 6
30 1 f'~=L ITECHtJOE,IX)=C PRTIME=PR1( ,Ml ilA I T ( JO B ) :: TIE
JOB ADVANCE ROUTI
JOB :: J NO. BEING ADVANCED M AND N AS C INfD ABOVE
IF(IFACIM). .e} 3 lEN=L'-UEU~)+l IF(lEN.GT .. 26)L 6 CQUE (f"', LEN )::C CHANGE (r{) =1 I E lQUE(R) =lQUE( 41 L=lQU!:(lV} IORDER( f.~, l)= JeE GO TO 333
3 IFAC(1VJ= JOB CQUE(V,l}=CQUE{ ,l}+TIME-CHANGE{ C H ~,N G E ( fi. ) = TIE TDPAR1{M)= TIME + P TIME SERVCE(M)=SERVC )+P TIXE GO TO 333
F
a A = D1IME[JCB) - II E LCUT(JOE1=O
OF JOB -
151 T AL=TCTAL+l.C DAYTOT=CAY10T+IRC IF{LLfAY.lEGI TCAY) GO TO 333 SUMJGE=SC~JCE+l.
SUltC, =- SUI" -} A .. SUf/t2= SUM2 + A;:~~;:2
SUM3= S 3. **3 S SLM4 + A**4 I i<.J1.f{=J}
IF ( I !(t.R ) 850 ,.H 51, :::2 850 IKAR=ft-C~5+202o
IF ( I KJ] R f> l1 41> 1 ) "r .1 =1
Dt,[ STATISTICS
c
ID(IKAR}=ID{I R)~l GO TO 333
851 ID(201)=ID(201)+1 GO Te 333
852 IKAR=.A.+2Glo5 IF{IKAR.Gl.401) IKAR=401 IDCIKAR1=IDIIKAR}+1 GO TO 333
-46-'
C ADVlNCE TO NEXT DAY C C OU1PUT ROUTINES C
lOGO TIME=LLCAY*IMINUT ll=Ll[AY LlDAY=-LLCilY+l IF{lL-INl )333,1111, 33
3333 IF({Ll-INTDAY). (30*KKK» GO TO 9'10
T 34·34
3434 DO 180 I=l,lSIZE 780 SSV{I)=S E{I}/ TIME
KKK=Kl<K+l WRITE{6~6fC0}lL,TIME
66(0 (lHl,4[X,4hCAY=,I4,5X,5H1I =~FIC.2)
WRITE(6,6fCl)DAYTCT,TOTAl 6601 FORMAT(lHG,25HJ03S PRCC ED THIS MDNTH,FIO.O,5X,11H TAL JOBS=, F
.$10.0) OA.YI01=O.C WRITE{6,6<;O)
690 FORMATIJ/IHC,7 I ,5X,11HUTILIZ lIeN} co 631 I=l,LSIZE
631 ITE{6,6321I,S (Il 632 FORMAT(lH ,3X,I2 , 1X,FIOe6)
940 IF(lL.LE.I TDAYJ TD 50 LRN=l CALL FReE (L fj,0,Y)
5C CONTII\UE IF{LL.N[.~AXA) GC TO 333 SET=3.0 \-.JRITE{6'j1112lS T
1112 FORM TIIH ,jJ/~CX,lOE?ESULT SET,F6e3) 1r.~R I T i 6 , l{ L 21 )
9 2 L 1· F i:J R fq AT ( I j ;: 5 X 't 1 S H 5 :::: N C I I': G ~::.~ U L E - 'I
~~3PT 'j2X,J.25X, 21 HCP SIZE lC,125X, FFIC , 311HD III e .. )
co l~lCO 1=1,12 L,·lCO J=ly26
4100 (I,J)= U (I,J)
DO SBE I = 1,LSIZE LEN = LeUEII) ~ 1 IF{LEN.GT.26)lEN = 26
-47-'
8S8 FGUE{I,LENJ = C (I,lENl + TIME - CHANGE{I) DO 85~ I = 1,lSIZE DO 859 J = 1,26
859 FQUE(I,J}=FQUE(I,J)/TIME 00 611 I=l,LSIZE SP(Il=O.C DO 611 J=1,26
611 SP(I)=SP(I) + FQUE(I,J) WRITE(6,616)
616 FORMAT(lHC,50X,2SHTABLE OF EUE PROBABILITIES/) WRITE(6 , 620}
620 FORMAT! ,2X, NGTH/MACHI, tlHl, 17X,IH2,lX,lH3,7X,lH4,7X,lE5,7X 7 ,
27X,lH7,7X,lH8,7X,lH9,7X,2EIO,6X, 32Hll,6X,2H12)
DO 613 IY=l,25 Il=IY-l
613 WRITE(6,614)Il,(FGUECIX,IY),IX=1,12) 614 FORMAT{lH ,5X,I2,1X,12F8.4)
WRITE(6,621J (FGUE(IX,2~),IX=1,12)
621 FORMAT(lH, 18HDVE FlDW,4X,12F8.4} WRITE(6, - } (SP(IX),IX=1,12J
622 FORMAT(lHC,14X,12FBe4) WRITE(6,6t03)
66C3 FORMA1{lHl,5CX,2ChDUE DATE PERFC MANCE) DO 853 1=1,401 IF(ID(I).f:Q.O}GG TO 853 IlCW=I WRITE(6,4CC21ILC
4002 FORMAT(lCX,5HILCW=,I4) GO 854
653 CONTINUE 854 DO 85~ I 1,401
J=402-I IF(ID(J} •• OlGO TO 8~5
IUP=J WRITE(6,4CC3)IU
4003 FCRMA1{lOX, IlP =,I4} GO TO 856
855·· I~U
856 DC 851 I=IL[W,IUP IF(IeLT~2Cl)J=I-2Cl If(Ift ~2Gl)J=C
IF(I.GT.2Cl}J=I-2Cl WRllE(6, 5B)J,I (1)
58 FORMA1(lHC,lCX,I5,5X,IE)
-48-'
ITE(6,933)SU~JCE 933 FORMA1(5X~lSHCATA COLLECT
DMEW=SU~/SUMJCE
DVAR=(SUM2-(SU~**2ISUMJCB»)/{SUMJOB-l.) WRITEf6,931}DME ,CVAR,SUM3,SUM4
931 FORMA1(115X,14~KE~N E DATE=,FIO.3//5X,9HVARIANCE=7E14.7115X~1 *UM OF CUBES=,E14.1//5X,20HSUM GF fOURTH pew E14.7)
STOP END
$IBFTC RAND SUBROUTINE RAND (T)
1 Q=RDt4 (X) IF(Q.EQ.O.C) TC 1 T=(-2.04){ALGG(Q) RETURN
-END
-49-
-50-
$IBFTC SUBJ[B SUBROUTINE SUEJCB(!) COMMO~ IBLCCKB/ITECHI300,12),D(300),PRT(3CO,12},lSIIE SX=O.C
2 DO 1 J=l~LSIZE PRT{I,J)=1.C+2.C (X)
1 SX=SX+PRT{I,J} IF(SX~EQ.C.C) TO 2 DO 3 J=l,LSIZE A=lSI il MMM=A*RDM(X)
3 ITECHII,Jl=MMM D{I)=5.C*SX RETURN
-51-
$IEFTC DECIDE
c c c
SUBROUTINE DECIDE(K,N,ll,LMN} COMMON/BLCCKA/IORDER(12,3CO) COMMON IELOCKB/IT H(300,12),D{3CO)~PRT{300,12)tlSI E COMMON WT(12,15),ZVAlUE{3CO) DIMENSIDN IHOlD(3Cl}
THI~ SUBRCUTI
1=1 K=IORCER(N,l} ICRDER(N,lJ=O IF(LI. EQ. 0) 00 1 J=2,301
SEQUENC
10 70
M=J-l IORDER(N,~}=IORDER( ,J)
1 CONTI~UE 70 R URN
JOBS ACCORDING TO
-52-
$IBFTC DECIDE
'c
SUBROUTINE DECIDE(K,N,Ll,LMN) COMMON/BlOCKAJIORnER(12 CO) COMMON IBlOCKE/I1ECH(3CD,12),DC3CO},PRT(3DO,12),LSIZE COMMON WT(12,15),ZVA E{3CO} DI leN IBOlD(301)
C THIS SUERCUTINE S ES JOBS Ace ING FCFS C WHEN LMN=C AND ACCORDING TO SPT WHEN LMN=l C
1=1 IF{LMN.EC.l) GO TO 11 K=IORDER{i\,l) IORDER(N,l}=O IF(L19 e 0) TO 7C DO 1 J=2 7 301 M=J-l IORDER(N,M)=IORDER{N,J}
1 CONTI ~·;U E TO 70
11 IN=IORDE (N,I) JlHIN=PRT (IN; N) I I K=JN IF(ll.EQ.C) GO TO 60 DO 20 I=2,300 M ~1= I 0 HOE , N , I ) 1Ft .E(; .. C) GC TC 20 PRTN=pg'l {riM 1 }
IF( lH .. GE.J.~r~!N) AMI N=PHTf-l I G[],:= I K=MF!
20 CCNTINUE 21 HI:::: I GC-l
1'f;2=IGC+ 1
Te 20
IF{Ml.EC. 1) GO TC 60 DO 30 1=1,301
30 IHCLDII)=ICRDERIN,I) DO 50 1=1(:[,3C( J~-: 1+1
50 IORDER(N,IJ=IHCLD(J) TD 70
60 lORD {N,IGC1=C 7C RET
-53-
$IBFTC DECIDE
c c c c
SUBRUUTINE DECIDEtK,N,Ll,LMNl COrJ\MONI ELCCKAI I CReER (12,300) COMMO~ IBLOCK8/ITECH(300,12),D{3CC),PRT(3CO,121..,lSIZE COMMON WT{12,lS),ZVALUE(3Cb> DIMENSION IHOLD(3Cl)
THIS SUBRCUTINE SEQUENCES WHEN lr-'N=O AND ACCORD I NG TO
1=1 IF(LMN. 41) 10 11 K=1 ReNtl) IfJRDER( N, 1)=0 IF{Ll. • 0) GC TO 70 DO 1 J=2'1301 tvt=J-l lORD (N,~)=IORDER(N,J)
1 CONTINUE GO TO 70
11 IN=IORDER(N,I) At::I IV () IGC=I K=JN IF(llqEQ.C) GO TO 60 DO 12 I=2,3CG MM=IDRDERO\i, I} IF{MM.EC.C) GO TO 12 XYZ=Z\i:\LUE: (rJf'<l IF{XYZ_GE. MIN) GC TO 12 AMIN=;<YZ IGO=I
12. CCi\TII\tj 21 1I:l=I 1
(",,2;= I GC+ 1 IF(Ml~EQ.LlJ GO Te 60 DO 30 1=1,301
3C IHCLD(I)=ICRCER(N,I) DO 50 I=IGC,3CO
50 ICRD R(N 7 I}=IHClC{J) Te 7C
60 IORDEF(~,I )=c 70 R
END
I L
TO FCFS 1
-54-
$IBFTC PROB SUBROUTINE PRCE[llDAY} COMMO~/ELCCKA/IORrER(12,3CC)
COMMON IBlOCKB/ITECH(300,12),D(300),PRT(3CO,12)~lSIZE COMMON ~T(12,15),ZVAlVE(3CO) SUt"lA=O. SU;'U3=C. DIMENSION WMEAN(25), WVAR(25} X=LLDAY DO 2 I=l,lSIZE DO I J= It 15 Y=t~T (1, J) SU:\j~A=SutU\+Y
1 SUMB=5U B~Y**2 WME (1)= /15. Y=WNE11N ( I ) WVARIIJ=( S/15.}-Y
DO 6 1=1,300 . DO 5 J=l,lSIZE KK=ITECF{I,Jl If(KK.E .0) TO 5
SUKA~ A~{KK)+PRT[I,KK)
SUM8=SUM8+WV (KKJ h ceNT I f\'U
ZVALUE(I}=(C(I)-X-SUMAJJS zuz=-:;.c If(ZVALLE{Il.Ll.ZLZ) ZVALlE(I)=ZUZ
RETURf\
A STUDY OF THREE CLASSES
OF SEQUENCING RULES
IN A SIMULATED JOB SHOP
by
Vinod Chachra
ABSTRACT
The purpose of this investigation was to study three classes of
sequencing rules in a simulated Job Shop" A compu r program simulating
the Job Shop was developed to provide an experimental base from which
the behavIor of the Shop could be observed. [n the simulated Job Shop,
three sequencing rules, one from each class, were tested. The sequenc
ing rules used were First Come First Serve (FCFS), Shortest Processing
Ti me (SPT), and Probab iii ty Seq uenc ing (PS)" Due date performance,
number' of jobs processed in a simulated interval, number of jobs late,
mean lateness and in-process inventory level were the measures of
performance used.
The resu Its i nd j cated tha t at low traf f i c dens i ty the re was no
appreciable difference among the measures of perfor-mance for the three
sequencing rules. At high traffic density SPT had the lowest inventory
level but its mean lateness was lat-ger than that of FCFS even though
Its number of jobs was sma] fer. The rformance of FCFS and SPT
did not change with changes in al lowed flow time but for PS the
i n-p rocess inventory I eve I j ncreased wi til decreas r ng a I lowed f low ti me
and the number of jobs processed decreased with decreas i nga 11 owed f j ow
time.