d scheduling flexible systems: a study of machine material...
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D ynamic Scheduling of Flexible Manufact uring Systems: A Study of Machine and Material
Handling Control Strategies
Devi G. Sivagnanavelu
A Thesis
in
The Department
of
1 IechanicaI Engineering
Presented in Partial Fulfillment of the Requirements
for the Degree of Master of Applied Science a t
Concordia University
llontreal! Quebec, Canada
February 2000
@) Devi G. Sivagnana~elu~ 2000
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ABSTRACT
Dynamic Scheduling of Flesible llanufacturing Systems: .A Study of llachine and
Material Handling Control Strategies
Devi G . Sivagnanavelu
In recent years there has been an increased interest in autornated and Fles-
ible Slanufacturing S-stems (FSIS). These systems are comprised of a number of
computer-controlled machines and material handling devices integratcd together for
the purpose of producing different parts R-ith little or no setup. Scheduling and
control of al1 manufacturing systems is a n area that receives considerable attention
because of the potencial for significant improvement in shop performance and asso-
ciated cost benefits that can be realized.
Planning and control of FSIS differs considerably from the problems cited in
traditional flon- shop and job shop environments due to a different set of operating
conditions such as the integrated material handling system and the lirnited buffer
capacity. Furthermore. the operating enïironment of an FSIS is dynamic. so static
rules based on having al1 information in advance are not appropriate.
The focus of this research is to det-elop and test on-line scheduling rules for
both machines and material handling sub-systems of a n FAIS. The scheduling rules
use various priority attributes and relevant information concerning the availabiIity
status of resources in the decision making process. These rules are dynamic in nature
because the priority of a job in the system can change continually The scheduling
rules are applied to control a hypothetical FMS consisting of multiple shared re-
sources fm different operating conditions. Simulation is used to mode1 the system
and consequently test the performance of different scheduling rules n-ith respect to
mean flowtime? consistency of output, and efficient operation of the mater id han-
dling system.
Design of esperiments is used to esplore the relative effectil-eness of scheduling
rules on the system performance measures for a variety of esperimental conditions.
Analysis shows that there is a significant difference in the performance of schedul-
ing rules. The performance of machine and material handling scheduling rules can
be dependent, and the choice of mies depends on the operating environment. The
results are summarized to rnake recommendations on rule selection for a $ - e n FAIS
operating condition against each of the important performance measures.
ACKNOWLEDGEMENTS
1 express my utmost gratitude to my research supervisor Dr. Samir Y. Amiou-
for guiding and mentoring me through the various stages of this research. 1 am also
grateful to Dr. S. S. SIerchawi for having originallu proposed the research area. I
also acknowledge the constant support provideci by m i family and friends.
To rny late mother Dr. K. Porkodi.
TABLE OF CONTENTS *
LIST OF FIGCXES LIST OF T.4BLES LIST OF SYMBOLS LIST OF ACRO-WIS
is X
si siii
1 Int roduct ion 1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Background I
. . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 FhIS.Re!atedProbierns 3
. . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Scope of the Research 4
. . . . . . . . . . . . . . . . . . . . . . . . 1 Organization of the Thesis 6
2 Literature Review C i
C . . . . . . . . . . . . . . . . . . 2.1 Classification of Scheduling Problems I
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 .AG \.' Dispatching 8
. . . . . . . . . . . . . . 2.3 Scheduling and Dispatching of Jobs in FMS 11
. . . . . . . . . . . . . . . . . . . . . 2.4 Tool Sharing Strategies in FMS 22
. . . . . . . . . . . . . . . . . . . . . . 2.5 Contributions of this Research 25
3 Scheduling Rules 29
. . . . . . . . . . . . . . . . . . . 3.1 Concepts Used in F4IS Scheduling 29
. . . . . . . . . . . . . . . . . . . . . . . . 3.2 Machine Scheduling RuIes 31
. . . . . . . . . . . . . . . . . . . . . . . . . 3.3 .-\ GV Dispatching Rules 34
. . . . . . . . . . . . . . . . . . . . 3.1 Machine-AGV Rule Combinations 38
4 System Description and Simula t ion 39
4.1 Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 System Description 40
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 AGV Layout 41
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Tool Utiiization 43
vii
4.5 Assumptions . . . . . . . . . . . . . . . . . . . - * . . . . . . . - . - . 44
4.6 Sysïem 3lodeling and Simulation . . . . . . . . . . . . . . . . . . . . 44
4.7 Erperimental Conditions . . . . . . . . . . . . . . . . . . . . . . . . . j o 4.5 Variance Reduction Technique . . . . . . . . . . . . '. . - . . - . - . . 50
4.9 System Blocking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.10 Performance MeasUres . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5 Experimental Design and Analysis 54
5.1 Esperirnental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2 EsperimentaI Anal-sis . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6 Conclusion 75 --
6 Summary of Results . . . . . . . - a . . . . . . . . . . . . . . . . . . i a
6.2 ;\pplicacion of Performance Based Se!eccion of Rules to FSIS Decision
Maker . . . . . . . . . . . . . . . - . . . - . . . . . . . . . . . . . - . 76 --
6.3 Suggestions for Future Research . , . . . . . . . . . . . . . . . . . . . / i
ASOVA Results: Effect of Machine and AGV Dispatching Rules on Performance Measures for the 64 Treatrnent Combinations
95 % Confidence-Interval of Performance Measures
Best Combination of Machine and AGV Dispatching Rutes for the 64 Treatments against Flowtime, Consistency of Output and Efficient Operation of AGVs
viii
LIST OF FIGURES
. . . . . . . . . . . . . . . . . . . . . . . 1.1 Layout for Vought Aerospace 2
. . . . . . . . . . . . . . . . . . . . . . . . 4.1 Layout of hypothetical FLIS 40
. . . . . . . . . . . . . . . . . . . . . 4 . 2 Flon-chart of simulation program 4.5
3.2 Flowchart of simulation program (continued) . . . . . . . . . . . . . . 16
. . . . . . . . . . . . . . 4.2 Flowchart of simulation program (continued) 47
. . . . . . . . . . . . . . 4 -2 F lm-chart of simulation program (cont inued) 48
4.3 Prioritj- routine for machine and AG\- scheduling rules . . . . . . . . . 49
LIST OF TABLES
4.1 Processing sequence of job-types with required resources. . - . . . . . 42
1.2 Distance matris of the hypothetical FAIS. . . . . . . . . . - . . . . . 43
5.1 Flow shop and bot tleneck indices. . . . . . . . . . . . . . . - . . . . . 62
3.2 -ASOl--A Results: Experimental factors affecting performance measures. 6.5
5.3 Surnmary of best combination of XI/C-..iG\- rules based on fion-time.
consistency of output and efficient operation of -AGVs. . . - . . . . . 70
3.1 Performance of rules based on average waiting time and waiting time
variance.. . . . . . . . . . . . . . . . . . . . . . . . . . . . - . . . . . 72 - - 3.3 95% Confidence Intenal for each M/C--AGI- rule averaged over 64
treatments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
LIST OF SYMBOLS
Fiow shop index
Bottleneck index
Number of job arrivais per hour
Total nurnber of machines
Number of job-types
Proportion of job-type j
Processing time of job-type j on machine i
Position in sequence of machine i
Total flow from machine i to machine j
Utilization of machine i
Maximum utilization of ni machines
Averase utilization of rn machines
Total throughput
Average flowtime per job
Average waiting time per job
Vruiance of averagz waiting time of job-types
Average work-in-process
Average AGV utilization
Empty to loaded travel ratio
Mean time between arrivals
AD
SHOP
BKK
TD
AS
&val distribution
Type of shop
Bottleneck machine
TooI duplication
AGV speed
xii
LIST OF ACRONYMS
m s
AGV
CSC
JIT
m o
SPT
S IO
LQM
MRT
3-s
QSSS
>TJ
.&NOVA
FIexible -Vanufacturing System
Automated Guided Vehicle
Computer Numerically Controlled
Just-In-Time
First-In-First-Out
Shortest Processint Time
Shortest imminent Operation
Longest Queue of Machines with tie-breaking
Maximum Request for Tools with tie-breaking
Nearest Station
Queue Size Nearest Station
Nearest L'nassigned Job
Analysis of Variance
Chapter 1
Introduction
1.1 Background
Flexible llanufacturing Systems (FUS) are automated systerns where a number of
different types of resources n-ork together under cornputer control to rransform a
workpiece into a final product or a sub-assernbly. This transformation process is a
sequence of processing steps. -At each processing step. a number of recources are
simultaneously needed to complete the operation. An FAIS processes a number of
different parts simultaneously wit h little or no set up and it combines automation
suitable for mass production with Aesibility suitable for job shop production.
An F'r IS is highly capital-intensive and its users are concerned with achieving
high system utilization. Because of cost. the majority of FlIS are installed in large
rnanufacturing corporations, namely automotive. aerospace? major defense indus-
tries, large. h e a y equiprnent manufacturers. and machine tool builders. i ough t
-1erospace. Dallas. Tesas for esample uses FMS to produce component parts for air-
craft fuselage. -Another example of FZLIS installation is Cincinnati Sfifacron Plastics
llachinery Division ttiat manufactures parts for plastic processing machines.
The resources typicaily used in an FMS include Cornputer Numerically Con-
trolled (CSC) machines: fktures, tools, robots, and material handliog equipment.
AGV STASDBY PARiCiSC
Figure 1.1: Layout for Vought Aerospace.
Figure 1.1 illustrates the la:-out for 1-ought -4crospace consist ing of four CSC hori-
zontal machining centers with automatic tool delivec- and eschange systcm. Three
-4utomated (\vire) Guided Céhicles are employed for material handling purpose.
Other equipments used are pallets: manual inspection station, part cieaning unit,
and automatic chip removal and separation. The system processes 600 part types.
Limited buffer space in an FUS also imposes a constraint similar to having a limited
shared resource n-hich is the number of buffer spaces. Occasionally, there ma? also
be a human operator overseeing the overall operat.ion of one or more cells. Machin-
ing operations require the availability of the machine as well as certain tools, and
possibly a robot or worker to place the n-orkpiece. .A transportation task requires
t.he avai1abilit.y of the material handIing equipment as well as a buffer space at the
destination station. The resources are usually espensive and t.herefore cannot be
dedicated to a certain process, but are rather shared between the vanous processes
in the FUS.
1.2 FMS-Related Problerns
FUS problems can be grouped into two areas: design problems dealing with the
optimal selection of t h e FhIS components; and operational problerns dealing \vit h
the optimal utilization of the F'cIS.
FAIS design problems are related to the decisions thar: must be made before
the installation of an FUS. These decisions include: the selection of parts to be
made. the selection of appropriate machine tools. the selection of material handling
equipment, the cornputer system confi,buration, the process design of each part. and
the cvaluation of different layouts. Of these design issues. the selcctiûn of parts to
be made and its process design determine the level of flesibilit- and may undergo
changes after installation.
FXIS operational problems involve production planning and scheduling. Pro-
duction pIanning in an F'IIS is more difficult than in assernbly lines or job-shops
because each machine is versatile and is capable of performing different operatio~s.
the system can process several different part types simultaneously. the system is
characterized by limited local buffers. and each part may have more than one route
in the system. The limited size of buffers in particular can cause system bIock-
ing. a state in which al1 operations come to stop because of conflicting resource
requirements.
FUS operational control is usually coordinated by a central computer or con-
trol unit. as shon-n in Figure 1.1, that is equipped n i th comprehensive software
modules for scheduling. tool allocation. trafic. production processing. and possibly
çystem simulation. The control unit takes as input information on the state of al1
resources and continuously monitors the activities of the equipment and provides
supervisory and engineering reports. Under cornputer control, parts are prioritized
to use the resources.
The criteria used to evaluate different operational control strategies are based
on performance related mesures such as the production rate (Le., number of pans
processed per period). the mean flowime of parts. ivork-in-process. average u-aiting
time, variance of n-aiting tirnes and resource utilization. Some of the rneasures of
performance can be conflicting. For esample. the scheduling strate= that reduces
average n-ork-in-process mal- not necessarily improve production rate.
1.3 Scope of the Research
The focus of this studj- is on the scheduling of jobs for an FSIS. The performance
and efficiency of an F l l S is highly dependent on the efficient allocation of resources.
Prior studies indicate that FMS performance is sipificantly affected by the choice
of scheduling rules. hlontazeri et al. (1990) evaluated scheduling rulos for an FSIS
and the results indicated t hat the deve-eioped heurist ics significantly reduced average
waiting times and improved machine utilization. Sabuncuoglu et al. (1992) investi-
gated the performance of sereral job shop rules in a hypothetical F M . They found
v-hich scheduhg rule significantly reduced the mean flon-time measure.
Static and deterministic off-line scheduling techniques. commonly used for pro-
duction scheduling in traditional job shops. are not appropriatc for F'rIS control.
Instead. a more dynamic decision making process is generally used to react quickly
to changes in the state of the system as different parts arrive for processing in the
systern at random points in time.
It is important that the scheduling rules CO-ordinate the allocation of al1 types
of resources (CSC machines, tools' material handling equipment, buffer spaces. etc.)
depending on their current status of availability The objective of this research is t 3
derelop and test dynamic scheduling niles for machine and material handling sub-
systems for different FAIS operating conditions against multi-criteria performance
measures.
-1 part undergoing an operation on a machine n-ill have to request al1 the
required machining resources before processing can take place. Machine schedul-
ing rules prioritize jobs on a machine upon the completion of current machining
operation. Priority rules are developed based on the current status of machining
resources required for processing a job. A part that has completed its processing on
the current machine ml1 have to be physically transported to the nest machine in
sequence. This study utilizes -\utomated Guided Léhicles (AGI-) t o transport ran-
materials and i\-ork-in-process for the hypot hetical F M S. Hon-el-er. the dispatching
ruIcs proposed in this study can also be applied to operate FMS which uses robots for
material handling. AGVs are driverless. battery powered' and can be programmed
from a system controller to trai-el along a predetermined path. The control system
dispatches idle vehicles to perform material handling functions in the shop floor. car-
rying materials from one station to the other. Failure to design an efficient on-line
-AG\* dispatching algorithm may lead to poor performance of the FSIS. An - iG\-
dispatching rule assigns an idle AGI* to move a part from one location to another
location in the FAIS. If there is no part n-aiting for pick-up. the =\GI- remains idle
and an-aits for a travel request to emerge. Possible interaction betwen the machine
scheduling and -4GV dispatching rules are also studied.
The F M scheduling literature includes research studies ranging from analyt-
ical techniques (Sawik 1995. Sabuncuoglu and Sule>man 1998) to simulation (Ma-
hadevan and Sarendran 1990. Lee 1996) and artificial intelligence/espert systems
(Seifert et al. 1998). I l l d e research through each technique is necessa- for better
understanding and solving the problems associated wit h FAIS' this study focuses
on simulation-based experimental studies of the FlIS scheduling problem. Discrete-
event simulation models are developed to implement the scheduling rules in an
esample FAIS v i t h an uni-directionaI -1GV track layout. An esample FhIS problem
is special1~- designed to study the effectiveness of machine-scheduling in combination
with AGV dispatching rules under varying conditions. The simulation models were
developed in SIXISCRIPT 11.5 language.
This research investigates the relative effectiveness of machine and AGV schedul-
ing rules against the performance criteria based on the mean flowtime: consistency of
output, and efficient operation of AGVs. The operation of AGVs is judged based on
empc-to-loaded t rave1 time ratio and average .AGV ut ilization. The FSIS scheduling
rules are tested under a variet>- of experimental conditions. -1 factorial esperiment
is conducted to investigate the importance of several sptern operating parameters
related to the performance of the FMS scheduling rules. Statistical analysis \vas
carried out using the ST-JiTISTIC;\ software package.
1.4 Organization of the Thesis
The remainder of this thesis is organizcd as follo~i-s:
Chapter 2 "Literature Reviewy provides a detailed Iiterature survey of FSIS schedul-
mg.
Chapter 3 "Scheduling Rules" esplains the machine schcditling and .AGI- dis-
patching rules that are developed in this research.
Chapter 4 "System Description and Simulation'' discusses the hypothetical FlIS
n-ith the AG\' track layout and system paranieters. ;\lso, the simulation
technique to test the rules and performance mesures is described.
Chapter 5 "Esperimental Design and -4naIysis" discusses the design of the sim-
ulation esperiments to evaluate the performance of the rules. Esperimental
analxsis of the output are aiso presented.
Chapter 6 "Conclusion" lists some recornmendations.
In addition there are three appendices containing detailed results.
Chapter 2
Literat ure Review
This chapter revien-s the work done b?- some researchers in evaluating scheduling
rules against different performance measures in different environments. The litera-
ture on design and operational control of FUS are both estensive: but this chapter
discusses only the scheduling aspect.
2.1 Classification of Scheduling Problems
-1 typical job in an FSIS needs a primary resource and possibly a number of addi-
tional secondan- resources. For instance, if the job is a machining operation: the
primary resource is the machine, and the secondary resources may be tools, fisture:
pallet. hcman operator or a robot. If the job is a transport operation? the primary
resource is the material handling equipment: and the secondan- resource may be the
buffer space at the destination machine, and a robot or human for loading the part.
One of the most important aspect,^ of operational control in an F-VIS is the
allocation of limited resources to waiting jobs. Decisions made in this regard can be
classified into:
0 AGV dispatching - Assigns an idle vehicle to moye a part from one location
to another in the manufacturing system. Decisions such as which -1GV a job
requiring service should select among a set of vehicles available. and which
job a released -AG\- should consider for pick-up assignment frorn one of the
work-stat ions are made.
Scheduling and dispatching of jobs in FIIS - .\Ilocation of prima? resources for
whicli multiple jobs are waiting 11-ith its required additional resources available.
rn Tool sharing strategies in FLIS - ;Ulocation of second= resources to satisf-
the needs of component parts and products.
The foIlowing sections summarize some of the previous papers relevant to each
of the categories.
2.2 AGV Dispatching
The structure of industrial production has drastically changed due to automation
and the material handling system is one of the main areas that has looked to au-
tomation to improve system performance. An -AGIv system is a cornputer-controlled
factory-wide transporter. The fiesibility of an -AGI- system makes the task of con-
trolling the -AGI-s challenging. The issues of controlling -AG\-s ma? include dispatch-
ing. routeing and scheduling. Dispatching involves a decision rule or methodolog?-
for selecting a 1-ehicle or station for pick-up or delivery assignments. The routeing
problem is concerned with finding a route that n-il1 allou- a aehicle to reach a desti-
nation in the shortest possible time without interruption. Scheduling encompasses
the dispatching and routeing issues with the introduction of time.
The follon-ing review addresses the operational control of -AG\.*-based material
handling sustems. -1ccording to Klein and Kim (1996). AGV dispatching rules
can be classified into single-at tribute dispatching and multi-at t ribute dispatching
based on the number of attributes included in the decision making process. Possible
attributes include information with respect to the -1GV track layout, location of
=\GI-s, -lG\.- status, and queue size of pick-up and destination n-orkstations. ln the
literaturc, different AG\- dispatching rules are developed and tested under different
manufacturing envir0nment.s such as FAIS and job-shop involving uni-directional
and bi-directional Iayouts.
2.2.1 Single-Attribute Dispatching
Single-attribute dispatching models are based on just one dispatching criteria in the
decision making process.
llahadevan and Sarendran (1990) studied the design and operation of -\G\-
based material handling systems for an FAIS. They addressed the key issues such
as the traffic fion- pattern along the -lG\,- tracks, decisions regarding provision of
control zones. number and capacity of buffer for the vehicles, the number of vehicles
required. and vehicle dispatching rules. The vehicle dispatching rules tested in the
study are al1 based on single attribute. The discussion on vehicle dispatching rules
is made following the design issues that are addressed in the paper.
-1ccording to the authors. if a single -4Gl- operates in a closed Ioop. the traffic
control problem is simple. and the need for control zones and buffers does not arise.
However. when more vehicles circulate in the system. decisions regarding control
zones, bufTers. traffic flow pattern along the AGV tracks. and vehicle dispatching
have to be made. For resolving traffic problems. the use of control zones and buffers
would help. A control zone will allon- only one vehicle to use a track at a time.
In addition. buffers m a - be provided for the vehicles waiting to use the control
zones. -1nother strate= suggested by the authors to overcome collisions is to design
a single vehicle loop configuration which divides the entire network of -1GV tracks
into fen- small closed loops, each of u-hich allows only one vehicle to circulate. This
design removes the problems of vehicle collision and interference and simplifies traffic
management. Buffers have to be suitably placed in order to facilitate inter-loop
transfer of jobs. As mentioned by the authors. the drawback of this arrangement
would be its inabilit- to tackle vehicle breakdoms which ni11 paralyze the loops.
-idditional problems such as creation of bottleneck loops, requirements of additional
space. guide path and storage points ma>- also arise. To overcome these problems, the
authors suggested an alternate strates- wherein the vehicles are restricted to travel
along selected AG\' tracks only. This scheduling strate=- retains the advantages of
the small closed-loop configuration and also adapts to vehicle breakdon-ns.
Xest. they developed a formula to estimate the minimum number of veliicle
required. This estimate is for an FMS processing jobs in more than one sequence
which allows aIternate routeing of the jobs due to machine failure or work-load
balance considerations.
-4 simulation model for a systern producing five job types with s i s machines. a
load/unload station and a central buffer for work-in-process iras constructed using
GPSS/PC and some of their suggested strategies were tested. They estimated the
number of AGI3 required to be three for a set of processing times at the machines
and cwo for the same systern with Iarger values of processing times.
The? studied the same model u-ith 3 -AGIs based on three vehicle dispatching
rules. namelj-. the l e s t utilized vehicle rule. the farthest idle vehicle rule. and the
sequential dispatch rule. -411 the t hree dispatching rules use the following single
attributes: the least utilized vehicle rule considers the amount of time an AGI- iç
held bus': the farthest idle vehicle rule uses the distance betu-een idle vehicle and
the job. and the sequentiai dispatch rule is based on the arriva1 time of jobs. Besides
dispatching rules. the performance based on the single vehicle loop configuration n-as
also studied. The performance mesures used were the mean flow-time of the jobs:
the utilization of the -AG\-s and the average number of jobs waiting for an -4GV.
In the study, the single vehicle loop configuration and the sequential dispatch
rule is found to fare better than the other rules in the system considered for the study.
This is because: the system under consideration has small number of machines and
fen. inter-loop transfers.
Nore recently Seifert, K a - and Wilson (1998) introduced a dynamic vehicle
routeing s t r a t e s based on hierarchical simulation. When routeing is dynamic. dif-
ferent paths can be taken bj- an -\GI- at different times n-tien moving between two
given nodes. Taking into consideration the current status of the system. the ve-
hicle router selects a path for the AGI* at the time that the vehicle is dispatched
(Hodgson et al. 1987) and if there is a communications link between the router and
the vebicle. then the router modifies the c-ehicle-s path during t r ad .They obsen-ed
that the shortest travel-distance route may not be the shortest travel-time route.
,\long an? given route. the actuaI travel speed of a vehicle depends on the amount
of congestion encountered. This can affect the overall performance of the AGI- s-s-
tem. The research uses single-at tribute. namelj- the travel-time for -4GI- routeing
decision.
In their proposed hierarchical simulation. whenever there is an -AGI* routeing
decision in the main simulation: subordinate simulations are performed to evaluate
a limited set of alternative routes in succession until the current routeing decision
is finalized and the main simulation resumed. -41~0. they used the global vision as
information support to avoid obstacles in the waj- of an ..AGIe. Global-vision-system
refers to the use of cameras (or other types of sensors) placed at fised locations in
a work space to estend the local sensing available on board each vehicle in a free-
ranging -AGI.- system (Kay 1992, Kay and Luo 1993). Information from the cameras
is used to:
1. hlonitor the workspace to detect and track potential obstacles in the immediate
vicinity of each AGV and over its intended path.
2. Track each AGV along its intended path to bound errors in the vehicle's dead-
reckoning sensors.
3. hlonitor the load aboard each -1GV to detect positioning errors
4. Provide video images of the entire n-ork space so that a human operator can
monitor the stat.us of operations throughout the facility
The authors have used item (1) in their study to evaluate the use of a cornputer
simulation mode1 as a short-term decision tool for -AGI' routeing that accounts
for the current systern status and determines the current optimal path with the
minimum travel time to reach a certain destination. -1 case study of a prototype
AG\- systcm consisting of ten P ar?d D stations, se\-en intersection region nodes.
varied number of -AGI-s and pedestrians and operatirig under the control of a global
vision system is used to test the static and dynarnic vehicle routeing strategïes.
To evaluate the performance of the AGI- system. they formulated a specific
performance measure referred to as the -relative dela'-' of an AGI-. which is the
difference betu-een the -4G\,--s actual travel time to its current destination. and the
corresponding theoretica1 minimum travel tirne of the -AG\.- as determined by its
maximum speed and the shortest-travel-distance path between the -AG\."s current
origin and destination nodes.
The results of the case study indicated the superiority of dynamic approach
in cornparison to the deterministic shortest travel-distance path. However. as indi-
cated in the paper, these results cannot be generalized n-ithout rnuch more extensive
esperimentation. 'rloreover. to enjoy the full benefits one can gain from the dynamic
vehicle routeing approach. the authors suggest to account for the capabilities of this
approach during the design phase of the AGV system by including more flesibility in
-AG\' system design. Specifically. the -AG\- system design should provide a sufficient
number of alternative paths that can be chosen so that critical bottlenecks can be
bypassed dj-namicalllv, allon- for dynamic selection of P and D stations correspond-
ing to the same work-center? and allow for varying degrees of sensing capabilities to
provide information concerning the congestion status of the system, ranging from
purely local, vehicle-based sensing to full global vision capabilities.
2.2.2 Multi-Attribute Dispatching
hlulti-at t ribute dispatching models consider several dispatching criteria concurrently
in the decision rnaking process.
Lee (1996) evaluated three composite rules which combine the p r i m a - dis-
patching rules with tie-breaking rules in a job-shop environment. He considercd an
assembl- system with AG\--based rnaterial handling system. Slultiple vehicles were
used on an uni-directional track la!-out. The system consisted of four major assern-
bly lines and each has a pair of drop-off station and pick-up station for material
handling purpose. The possible routes of -AG\-s among the u-orkcenters and the
warehouse can be thought as directed links of a network.
Four types of assernbly jobs arrive at incoming dock. -As incoming jobs are
generated. four -lG\-s are available to carry loads of materiah from the warehouse
co the dropoff stations of the assembly lines. The materials are then assembled
into finished products which can be picked up from the pick-up station a t the end
of the assembly line. Since multiple vehicles are allowed in the system, collisions
are avoided by the zone control capability that allon-s only one -AGI- to access the
junction or a section of the track a t a time.
Four vehicle-initiated dispatching rules namely S t a - in Same Scat ion (SS):
Xearest Station and Stax in Same Station (YS-SS), Xearest Station and High actirity
area (3s-H-A) and High queue and Searest Station (HQ-SS) were evahated in this
s t u d l SS was used as a benchmark for cornparison purpose. Of the rules tested,
SS and SS-SS are single-attribute dispatching rules' and 5s-HA and HQ-KS are
multi-attribute dispatching rules.
Discrete-event simulation models were developed in SIM-IS language to im-
plement the composite dispatching rules. -1 dispatching rule is used when an -AG\'
completes a drop-off task and looks for the nest task. When an AGV approaches a
junction. a FCFS contrai scheme is used to avoid possible collisions.
He used the design of simulation esperiments to evaluate the performance of
the scheduling rules. He identified mean tirne between arrivalsl arriva1 distribation
and ratio of -4GV travel time to the assembly time as the three factors which might
affect the performance of the rules. The factors were tested at 2 by 2 b - 3 levels
resulting a 2 s 2 x 3 factorial design ~ i t h 12 experiments. With 4 rules and 3
replications. the total number of simulation experirnents performed n-as equal to
1-44. Thc performance measures collected from the simulation were t hroughput . average Aon--tirne per job and average in\-ento- level in the s-stem. An analysis
of variance (-ASO\--A) procedure \vas then performed to identify the factors and the
factor interactions t hat m a - affect the performance measures.
The results reveal that the SS-SS and HQ-SS performed equally well in
rhroughput and \VIP: whiIe SS-SS outperformed HQ-YS on flow time. The per-
formance difference between the SS rule and the composite rules 1%-as significantly
affecred by the job inter-arriva1 time (TB-%). the ratio of AGI- travel tirne to assem-
bly rime (RT). and the interaction betn-een the two factors (TBA'RT).
The above study has not shon-ed importance over the performance of machine
schecluling rules in relation to the -AG\' dispatching rules. Further tie-breaking is
required n-hen considering a layout wherein two or more stations are equi-distant to
eachot her.
Klein and Kim (1996) proposed a multi-attribute decision models ('cLAD1I)
x-hich consider several dispatching criteria concurrently in the decision making pro-
cess. They presented four such rules narnely simple additive weighing method
(S.4KN)? Yager's multi-artribute decision malring method (\--\GER): modified ad-
ditive weighinp rnethod (hl-%WM) and mau-max method (SIlIXl). There is no clear
mention of the list of attributes used in the priority calculation of SZ-ADSI.
S-UVM is the widely used method of bI-IDbI. Suppose the decision maker
assigns a set of importance weights to the attributes, Il-{w,: u ; ~ . . . . m,). Then the
most preferred alternative, -4' is selected such that
rv-here xLj is the outcome of the i th alternative about the j t h attribute with a nu-
merical comparable scale. x, can be the values that represent the number of loads
in output buffers, the waiting time of a part, or a travel distance of a vehicle.
Yager (1 9 ï ï , l 9 X . 198 1) developed a fuzzy XI-AD11 model which employs a
fuzzy numeric rating approach. Consider the objectives. G1, G2. . . . . G,: each associ-
ated n-ith a fuzzy subset over the set of alternatives -41, -A2: - . . --lm- Let R,I. Riz: - . - - Rim
be fuzzj- numerical ratings of each alternative assessed by objective i. Each objective
may be represented as
The decision D is denoted as
D = min {Gl. G 2 . . . . . G,) .
In order to normalize attribiite values 'LI-IIV'LI uses membership functions of
the fuzzy sets which represent the objectives. By this, the ' r l -UVl1 is able to take
an expert's opinion or previous esperience of operating a shop into account when
converting an attribute value to a nerv value that ~ i 1 1 represent the situation of each
department more adequately.
, \ I l I l 1 determines the value of an alternative by selecting the maximum value
of the objectives rather than adding up al1 the values of objectives. In other words:
the most urgent or desirable situation of an objective is used to represent the situ-
ation of the alternative. The mosr preferred alternative, -4": is selected such that
where x l j is the outcome of the i th alternative about the j t h attribute (or objective)
which is obtained from a membership function of the attribute.
-4 simulation model n-as det-eloped to test the dispatching mles for an -AG\.'
systern. The four M A D M methods along with three other single at tribute dispatch-
ing rules narnely, shortest travel time/distance rule: maximum queue size rule and
longest waiting time rule were tried for a three-depanment and thirteen-department
laj-oii t configurations. The results of the simulations under different rules xere ana-
lyzed and cornpared according to the performance measures collected such as the job
completion time. total trat-el time of empty vehicles. ma~ imurn and al-erage queue
length and waiting time. -1nalysis shon-ed the multi-at tribut.e dispatching rules out-
performed the single-attribute ones and ' \ I . ~ ~ ~ ' ~ I appeared to be the most robust
rulc overall. Thus the superiority of the multi-attribute dispatching rules for -AG\-s
is obsen-ed in this paper.
-1kturk and Yilmaz (1996) proposed a micro-opportunistic approach to solve
the -AG\- scheduling problem. Automated Slanufacturing Research Facility (-411 RF)
is a n-ell-known factory reference mode1 at the Sational Institute of Standards and
Technolog- in the L7SA. There are five let-els in the -UIRF hierarchy, n-hich are
factor?. shop, cell, workstation and equipment. The paper presents a neu- approâch
to incorporate -AG\- into the overall decision-making hierarchy. To achieve t his. t hey
proposed a hybrid approach in which the control mechanism for the -AGI- module is
designed using a hetererchical structure, so it can interface both shop and ce11 levels
directfy.
In the shop level's scheduling problem, the beginning and ending times of
jobs in cells are deterrnined \vit h approximate transport ation time requirements,
which will be passed to the proposed ,AGI7 module. Furthermore, the ce11 level
is responsible for scheduling the jobs to workstations. R-ith some approximate
time requirements for material movement, each ce11 prepares an initial schedule.
Similar to those of the shop level, a release time and due-date for each move is
determined. The AGV module receives move orders between and within cells in the
form of time windows in which the corrcsponding move request has to be completed.
This forrns a special case of multi-at tribute dispatching since the move requests are
known in advance and an off-line schedule is determined satisfying certain constraints
(attributes) of the problem formulation. Therefore. the proposed method is an off-
line scheduling algorithm for the AGV dispatching problem.
The objective of the AGV module's scheduling problem is to minirnize the
amount of deriation from the @\-en time windows. They considered .Y move requesrs
with gi\-en time n-indon-s and pick-up drop-off points and JI identical vehicles in
a planning horizon. The AGI- track layout is assumed to be uni-directional. The
loads are unit loads. and one vehicle is sufficient for a Ioad request. For the traffic
management problem. the control a t intersection points of the uni-directional guide
path is used to avoid collisions. The aboi-e problern is modeled as a mixed integer
program (MP). where the objective is to minimize the total deviation from the time
windows.
The developed algorithm n-as tried on a 20-job problem with the required
parameters such as release time. due-date. and transportation time of jobs with the
pick-up and drop-off points. The system is sen-ed bu two vehicles operating on an
uni-directional Iayout. The final schedule obtained is feasible: Le. the total deviation
is equal to zero. and also free of collisions.
The esperimental factors that might affect the performance of the proposed
algorithm n-ere the number of jobs to be scheduled. layout. tightness factor and
number of iehicles. Each factor has three levels in the design resulting in 3" full-
factorial design, n-hich corresponds to eighty-one treatment combinations. The num-
ber of replications of each cornbination is taken as fivet that gives 405 different runs.
Finally. a n .-\KO\:X mode1 is perforrned to observe the effects of factors on the
performance measure. Al1 factors n-ere found to be significant on the performance
of the proposed method. For combination of factors, only the layout-time window
tightness interaction is found to be significant.
2.3 Scheduling and Dispatching of Jobs in FMS
Scheduling of machines and vehicles in an FXIS environment are considered under
this catcgory. Job dispatching rules can further be classified based on the informa-
tion required to prioritize the jobs waiting for the resources to process its repuest.
The priority calculations may require information purel'- related to the job or the
resource or both. Job information may include its arriva1 time to the shop. p r e
cessing time on each machine and the number of operations required to complete
processing. Resource information may include the qiieue size of jobs in the input and
output bcffers. -11~0, some research studies use the same information to schedule
bot h machines and vehicles.
)Iontateri and \an \\-assenhove (1990) used modular F l IS simulator to an-
ai>-ze scheduling rules. The modular FXIS simulator is a general-purpose. user-
oriented. discrete-event simulator designed to help the user in design. operation.
and scheduling of manufacturing systems. It provides the user with a n-ide range
of priority rules to choose from and enables the user to define his/her own rules if
required. The software configuration of the simulator includes three subsystems: an
input part to allon- user to input various kinds of data in an interactive mode: a
process part which forms the main body of the simulator consists of four major sec-
tions namely event section, control section: decision-rule section. and a simulation
section: and an output part prirnarily designed to generate statistical reports.
The authors tested fourteen different scheduling rules for a hypothetical system
n-ith the modular FMS simulator. The hypothetical FAIS consists of three machine
families. three load/unload stations, five machines, three carriers. and 11 worbin-
process buffer positions. Al1 machines in the families have their on-n dedicated
shuttle and a worker is assigned to each station to load parts on the pallets and
unload parts frorn the pallets. The scheduling rules tested were:
0 SI0 - Shortest Imminent Operation time
SPT - Shortest Processing Time
SRPT - Shortest Rernaining Processing Time
0 SAIT - Shonest SIO-TP multiplication value
SDT - Shortest SIO/TP ratio
0 L I 0 - Longest Imminent Operation time
LPT - Longest Processing Time
LRPT - Longest Remaining Processing Time
LlIT - Largest LIO-TP multiplication value
LDT - Largest LIO/TP ratio
)IR0 - Largest number of remaining operations
F R 0 - Felvest number of remaining operations
FIFO - First In First Out
F-4SFO - First -\t Shop First Out
Based on the classification, al1 the above tested rules use information related
to job alone.
At each decision point in the system, the authors assign the same priority rule
in every run. The performance measures for evaluating scheduling ruIes were aver-
age waiting time per part, average machine utilizationt average buffer utilization.
average shu t tle/carrier utilization, and makespan. Results indicated that no single
scheduling rule performed well with respect to al1 measures. SPT based rules min-
imized average waiting times and LPT based rules maximized machine utilization.
SPT rule performed well n i t h respect to average buffer and shuttle utilization: and
both LDT and SPT performed well with respect to average carrier utilization. SDT
had the lowest makespan.
This paper clearly showed that dispatching rules ma? have an important im-
pact on system performance. Since in the above stud_v, a part type visits just one
machine, the results cannot be carelessly generalized to other systems involving jobs
thar go through a sequence of machines.
Sabuncuoglu and Hommertzheirn (1992) at tempted to inrest igate the perfor-
mances of machine and .lGV scheduling rules against the rnean flow-tirne criterion.
Since only the machines and materials handling aspects of a FlIS are under study.
they classified scheduling rules into: (1) Sfachine scheduling rules and ( 2 ) AG\'
scheduling rules. The foliowing rules under each c a t c g o - n-ere tested:
1. hfachine scheduling rules:
a Shortest processing time (SPT)
a Sniallest value of operation time multiplied by total operation rime (SI'S-TOT)
a Smallest value of operation time divided b - total operation tirne (SPT/TOT)
a Largest value of operation time multiplied by total operation time (LPT-TOT)
0 Largest value of operation time divided b - total operation time (LPT/TOT)
a Least work remaining (LII-KR)
a Most ~vork remaining (SIWKR)
a Fewest number of operations remaining (FOPSR)
a Most number of operations remaining (MOPNR)
0 First come first served (FCFS)
r First arrived first served (F-IFS)
r RWDOàI (job priority is random)
Based on the ~Iassification, al1 the above tested rules use information related
to job alone.
2. -AGI- scheduling rules:
e First corne first sened (FCFS)
a Lagest output queue size (LOQS)
0 Shonest travelling distance (STD)
a Largest queue size (LQS), including incoming and outgoing parts - Most work remaining (NWKR)
a Fewest number of operations remaining (FOPTR)
FCFS. STD' SlKk'R. and FOPSR rules use job information. LOQS and LQS
rules use resource information.
The above rules were tested on a hypothetical FSIS consisting of eight work-
stations. S k of these workstations are tj-picai machining centers n-hich perform a
wide ~ a r i e t y of operations, such as tumingo milling and drilling. The two remain-
ing stations are used for washing and inspection. Each workcenter bas a limited
input/output buffer queue in nhich parcs can m i t before and after an operation.
In addition. there is an input/outout carousel a-here parts are mounted/demounted
to fistures and palletized for transfer. The arriving parts are held in t he carousel
and allon-ed into the system on FCFS basis as long as both an AGV and one queue
space at the destination workcenter are available. There are also two central buffer
areas at which parts are temporarily stored to prevent system locking or when the
destination station queue is full for a pan travelling to this station. Materials and
parts are transferred by AGVs. The path (material Bon-) is assumed to be unidirec-
tional. The job inter-arriva1 time is exponentially distributed. Each job is processed
by a series of workcenters. The number of operations (number of machines to iisir)
was determined by a discrete uniform distribution between one and sis. Only two
AGYs 11-ere employed in the study.
-An FAIS simulation mode1 n-as constructed to study the scheduling rules. The
scheduling rules were tested under a variety of esperimental conditions such as bu
varying machine and -AG\' load levels! queue capacities and AGY speeds. Mean
flon--timc is the average of the flon--timcs of al1 jobs measured during a simulation
run. They analyed the performance of scheduling rules nith respect to elements
of rnean flotv-time as it is a ver)- critical indicator of the lead-time and it also
provides important information that can be used for setting the due-dates or due-
date allowances (Sabuncuoglu and Hornmertzheim 1990). -4nalysis showed that
SPT and SPT-TOT appeared to be the best rules with any combination of AGI'
rules. In most of the cases, SPT performed better than SPT-TOT. Among the AGI-
rules that they tested, STD and LQS were the best -\G\- rules with any machine
scheduling rule combination. Hon-ever: LQS ah-a!-s dominated the STD rule u-hen
the queue capacities were decreased. They found that with the increase in machine
and -4G\- loads (or utilizations) . the mean flotv-time also increases.
,As no single dispatching rule can dominate al1 other rules in al1 situations.
importance have to be given to other measures of performance also. Sone of the
rules tested in the above two research studies have used information related to both
job and resource. Also, resource information of the downstream machine is not used.
2.4 Tool Sharing Strategies in FMS
-Allocation of required tools to meet the processing needs of component parts and
products is an important element of FMS production planning. The folloming re-
search studies describe heuristics that can be used to allocate tools to an FMS.
Kashyap and Khator (1995) analyzed tool sharing in an FhIS using simulation.
They studied the impact of tool request selection and tool dispatching rules in a
tool sharing environment. Request selection rules are invoked when more than one
request for a tool are pending. Tool selection rules, on the other hand. come into
play when there are more than cne copy of tools in the system. The authors used
a "look ahead-' policy to determine the status and condition of a tool required for
the nest operation when the current operation is in progress. -4 co~tro l rule is then
used for selecting a tool request. -4 tool selection rule is then applied when a tool is
available a t more than one machine.
Reyuest selection niles that were studied are first come first sen-ed (FCFS).
least nurnber of operations rernaining (LOR) and shortest processing time (SPT).
Tool selection niles that were studied are shortest distance traveled by tool trans-
porter (SDT) and high value of tool life (HYTL). The above rules are tested on a
four machine F'clS system. -AGI-s are used for the transportation of n-orkpiece and
tools. Performance measures collected were makespan and tool transporter utiIiza-
tion. Design of esperiments technique \vas used to analyze simulation outputs. The
esperiment al factors considered were tool duplication (single copy. two copies. and
t h e e copies). request selection (FCFS. LOR. SPT) . product mis (four job-types
equal mis. randomly generated job-types) and tool selection (SDT. Hl-TL).
Results from -iXO\--A indicated that tool duplication and product mis signifi-
cantIy affects the performance of the system for both makespan and tool transporter
utilization. Request selection rules do not significantly affect the utilization of the
tool transporter and makespan. Howes-er. both measures are significantly affected
by request selection rules when there is only one copy of tools. Tool selection rules
significantly affect the tool transporter utilization: \\-hile it has no significant effect
on makespan.
-4moako-Gyampah and Sleredit h (1996) evaluated t hree heuristic procedures:
tool and part batching, tool sharing and flesible tooling to allocate the required tools
in order to meet the cutting needs of component parts and
The main purpose behind this research %-as to compare tool
products in an FSIS.
allocation procedures
t hat are aimed at reducing the frequency of tool changes with thosc aimed at bet ter
utilization of tool magazine capacity.
Tool and part batching approach partitions part types for a specified planning
period into separate batches to be machined individually. Assuming there is enough
machine capacity to process al1 parts during a planning period. the need to divide
the parts into batches arises mainly because of limited tooI magazine capacity at
the machines. In this approach, the authors a s s i s parts to batches based on first
selecting part types that require the Iargest number of tool slots which n-ould mean
fen-er tool changes ma>- be required. hlain drawbacks of this approach. as pointed
out bu the authors are excessive tool inventory and greater t o d handling time as it
ignores tool sharing aniong part types.
Tool sharing approach recognizes tool cornmonality among part types. Failure
to recognize this may lead to unnecessa- tool duplication and underutilization of
tool magazine capacity. By this way. more orders can be selected into a batch.
Flexible tooling approach aims at minimizing the bottleneck effects of the
tool magazine capacity a t each machine. This approach is implemented by the
authors as follows: when part types are selected for production. their required tools
are allocated to the machines, and the tool slot consumption at each machine is
updated just as in the tool-part batching procedure. Follon-ing the completion of
the part types requiring those tools; any toois not fully consumed are removed from
the tool magazine n-hile another part is being machined. This frees up space on the
tool magazine to permit the selection of another part type to be processed and the
allocation of the needed tools to the machine. The tools that are removed can be
migrated to other machines or to the central toolcrib. The authors suggest that this
approach has the potential of reducing cutting tool inventory and leads to higher
utilization of the tool magazine capacity.
The authors tested the above heuristics for an FUS processing 10 and 25 part
types. The FbIS consists of five identical machines capable of processing any part
types if allocatcd with the needed tools. The tool magazine at each machine has a
tool slot capacity of 30. AGVs are used to move parts to and from the machines.
In addition to the -kGI-st there is one robot that loads and unloads parts from the
machines. The robot also changes and shuttles the cutt,ing tools.
The performance of heuristics n-ere tested against mean tardiness' percentage
of orders tardy and mean flon- time of orders processed on t hc F U . Results indicated
that for both l o ~ and high part type mis, the flexible tooling approach outperforrns
the tool batching and tool sharing approaches on al1 performance measures.
JIerchan-i et al. (1996) developed dynamic dispatching rules in FAIS n-here
rnultipIe shared resources are needed to complete one task. The study includes mod-
eling of five espensive tool types that are shared among four machines for processing
four part types.
They tested three resource allocation rules, namely Strict Wait for Resources
(%\-FR). Strict -\vailable Resources First (S-ARF)! and -kailable Resources Pre-
ferred (-4RP). SII'FR prioritizes jobs based on arriva1 time. i.e.. on a First In First
Out basis. S-&RF prioritizes jobs based on the smaliest value of difference between
number of required resources and number of available required resourccs. -ARP
prioritizes jobs based on the smaiiest value of the follon-ing calculation,
Current time- Arriva1 t ime Priority = zcl x +
Average flowtirne
Xumber of Required Resources - 'Tumber of Available Resources w2 X
Xumber of Required Resources
The variables u;l and w2 are the weights to be assigned based on whether
n-aiting time or resource availability is more important. The authors assign a larger
weight to resource requirement over the waiting time, Le-! u:l = 0.3 and w2 = 0.7.
The authors used simulation to test the performance of the rules. The dis-
patching rules are applied to control the esample F!dS and their relative performance
was studied. Results indicated that -ARP ruie performed well with respect to mean
flon-t ime follon-ed b - S--\RF. -4SO1.'_1 analysis be tween the different dispatching rules
at various values of the inter-arriva1 tiine shou-ed that the differcnce in performance
of the dispatching rules is significant at a confidence factor of 93% at lower values
of int er-arriva1 t ime.
2.5 Contributions of this Research
Sote that the above review is by no means an exhaustive one. It is havever fairly
representative with respect to priority rules. performance measures and environ-
ments used in previous research.
Though the literature in -1Gt- dispatching rules: job dispatching rules and tool
management rules is vec- rich and extensive, very little research has been attempted
to derive rules to got-ern the allocation of the mixture of resources in a shared
multiple resource environment. In this study. the simultaneous scheduling of both
machines and material handling system is considered. and composite scheduling
rules which can flesib1:- cope trith the change of system configuration are developed
for F'rlS. Thece rules are dynarnic since they incorporate the status of the system
as it evolves over time. One of the machine-scheduling rules uses the information
of don-nstream machine to schedule jobs in the current machine. \-ehicle-initiated
rules are developed for -AG\- dispatching in the study.
In the published research. there is not rnuch importance given to the alloca-
tion of additional resources required for operating a job on each machine. These
additional resources may include pallets, fistures, cutting tools. or even a human op-
erat or. Throughout t his study these addit ional resources are referred to as "tools."
-4 part undergoing an operation on a machine will have to request the required tools
before processing can take place. The requested tools are released after comple-
tion of that operation. The proposed machine-scheduling rules are then applied to
allocate the released tools to n-aiting jobs. In practice- some types of additional re-
sources: such as pallets and fistures. are released after al1 operations on the job are
completed. Though this study does not esplicitly mode1 such additional resources. it
is espected that t hey would show similar effect as the job request for the ot her types
of resources that are needed only for a particular process. In fact every resource in
our study has a separate queue and the jobs in queue d l have to be prioritized
upon t heir availability.
Slost of the scheduling rdes proposed in previous research do not provide in-
formation to break the tie when two or more jobs receive the same prioroty. For
instance. First-Corne-First-Serve (FCFS) is a common rule for a resource to select
a job. Considering a busy manufacturing environment: jobs may arrive at various
workcenters a t the same tirne. This situation calls for a tie-breaking rule to fur-
ther prioritize the jobs. In general. the tie-breaking rule could be another simple
scheduling rule. But n-hether a tie-breaking rule can significantly affect the FSIS
performance has not been fully esplored in the published research. This research
provides practical yet simple composite rules nhich combine the primary scheduling
rules wit h t ie-breaking rules.
The simulation esperiments are carried out in more realistic situations than in
the published research. That is. this study includes lirnited buffer capacity. limited
number of -1GI-s: and simultaneously considers multi-criteria performance measures
~vhich are either not included a t al1 or only partially included in the previous research
studies. -%O: the FSIS scheduling rules are tested under a variety of esperimental
conditions including varying the nature of shop. Factors such as type of shop being
flow shop or job shop. and machine load level tvere found to influence decision making
in static environments. but were not addressed for F M dynamic scheduling. So,
these factors are considered in the study to see if they influence rule selection. The
rules are studied for both flow shop and job shop types mherein for each shop type
the machine load-level is balanced in one case and in the other a bottleneck machine
is introduced. .-\Ise, a new approach is developed here to determine the nature of
shop (Le.: fion- shop or job shop) and presence of a bottleneck machine.
In this research, a comprehensive study of different ruIes in different en\-iron-
ments is conducted and compared with respect to different performance measures
such as flan-time. consistency of output. and efficient operation of AG\-S.
Chapter 3
Scheduling Rules
This chapter describes the details of the FSfS scheduling rules that are developed to
improve system performance. Machine scheduIing rules and AGI' dispatching rules
are dealt in separate sections.
3.1 Concepts Used in FMS Scheduling
The solution procedure of the FSIS scheduling problem can be classified based on
the type of scheme used to generate schedules. Sabuncuoglu and Hommertzheim
(1992) have identified t~vo types of scheduling schemes: off-line and on-Iine. Off-
line scheduling refers to scheduling al1 operations of available jobs for the entire
scheduling period? whereas on-line scheduling attempts to schedule operations one
at a time when they are needed.
Off-line scheduling rnethods are better suited for static environment where the
job arrivals and processing times are deterministic. The on-line scheduling approach
is used for a stochastic system which involves variations in job arrivd time and
processing times. Dynamic scheduling is a short-term decision-making process which
generates and updates the schedule based on the current status of the system and
the overall system requirements and the scheduling decision is made nhen the state
of the system changes, such as job completion. arriva1 of parts, etc.
According to the above classification. the scheduling procedure proposed in t his
research can be considered as an on-line approach that employs d y a m i c scheduling
concepts.
Since scheduling of machines and AGITs are under study. scheduling rules can
be classified into machine scheduling rules and ,AGI- dispatching rules. These rules
prioritize jobs for resources (i-e.. machines or AGIS) upon t heir a\-ailability. And
b:- their nature, these rules are very suitable for on-line scheduIing implementations.
Machine-scheduling rules do not consider the availability of AGI3 n-hen the prior-
ities of jobs are set for any n-orkstation. Sirnilarit-, -AGI- scheduling rules do not
directly take into account availability of machines for jobs to be served. Therefore.
in implementation. these rules form a dispatching mechanism consisting of two in-
dependent sets of rules. one for each type of resource (i-e.. machining and -lG\-
subsystems) .
In a multiple shared-resource environment. an operation can only be started if
al1 the required resources for that task are available. Therefore. the scheduling ruIes
must be developed so that the time spent u-aiting for any resource is minimal. For
instance. a transportation task requires the availability of an -4Gi- as well as a buffer
space at the destination machine. If an ,AGI; \vas dispatched to this job. but no
buffer space was available. the dispatched -AGI' ends up waiting n-hen it could have
been used for another transportation task. AGI' dispatching rules that do not take
into account the need for other resources would be ineficient. The same scenario
applies to machining tasks that require a machine. a certain tool. and possiblv a
robot to be available. FMS scheduling rules should take into account the availability
and the current status of al1 required resources.
Composite scheduling rules are developed in this research to prioritize jobs on
resources. These rules incorporate tie-breaking concepts which is essential when tu-O
or more jobs receive the same priority.
3.2 Machine Scheduling Rules
Machine scheduling rules prioritize jobs on a machine upon the completion of current
machining service. The allocation of additional resources required for opcrating a
job on each machine is considered in this research. These additional resources are
referred to as 'tools' and may include espensive cutting tools: robots or even a
human operator that are needed only for the operation on that machine. -1 part
undergoing an operation on a machine ivill have to request for the reqiiired tools
before processing can take place and are released after processing is completed on
t hat machine.
The request for resources: namely the machine and tools. can be sequential or
simultaneous:
Sequential Request This mode aIlo~t-s a job to grab the required machine first and
then seek to grab the tools as required. If any of those tools is not available.
the machine cannot process any other job waiting at the input.
Sirnultaneous request This mode allow the job to place a simultaneous request
for ail the required resources namely. the machine and tools as required. If the
request is not satisfied then the job joins a n-aiting queue and another loiver
priority job could use that machine in the meantime.
Consider a situation where jobs are airaiting service in front of a machine.
Cnder sequential request mode, the high priority job will seize the machine even
if the required tools are not available. Therefore. the machine n-ould be left idle
when it could have actually been used b - some other low priority job for which tools
are either not required at al1 or are available for use. Unnecessary blocking of the
machine would cause the input queue size to increase. Since an FhIS is characterized
b!- limited buffer capacity, a blocking situation ma)- also arise. To overcome this
problem. simultaneous request mode is recommended which will assign the job to a
machine for which al1 the required resources are arailable. .Usa; preliminary testing
of the request modes showed that sequential request did not perform well as it caused
a lot of blocking situations and so it was dropped.
AI1 machine scheduling rules developed here use simultaneous mode of request
for resources. Based on the classification for machine scheduling rules made in
Chapter '2: the rules developed use information related to both job and resource.
The following machine scheduling rules are tested:
3.2.1 S hortest Imminent Operation (SIO)
This rule works in the following manner: Ilchen a job arrives processing at a station.
it starts immediately if al1 the required resources are alailable. Othenvise. the job
joins a n-aiting queue that is common to the whole system. Then whenever any
resource becomes available. the waiting queue is scanned and. among the jobs that
have al1 their resources available. the one with shortest processing time at the current
station is seIected for processing. Ties are broken by First-In-First-Out (FIFO) to
the waiting queue.
In single machine static scheduling problems. shortest processing time dis-
patching is knon-n to minimizc average flowtime and average lateness measures. S I 0
is a variation of this rule for the d p a m i c environment. In the published research of
llontazeri et al. (1990) and Sabuncuoglu et al. (1992). machine scheduling rules for
an FAIS environment were evaluated and S I0 rule showed better performance with
respect to mean flowtime measure over the other rules that were tested. Therefore.
SI0 is used as a benchmark for comparison of the machine scheduling rules that are
developed in this research.
The S I 0 rule uses only job information for performing priority calculation.
Specifically. the processing time for each job a t the current machine is required for
impiementing the rule.
3 - 2 2 Longest Queue of Machines wit h tie-breaking (LQM)
This rule alloivs the job to place a request for al1 the required resources. If the
request is not satisfied, the job waits at the input buffer. Whenever a resource is
relinquished after completing an operation. this rule permits the available tools to
be used by the machine that has the highest number of jobs on the input side. Ties
are broken by least number of jobs at the input of nest destination machine of the
job. Furrher ties are broken by SIO. then FIFO to the waiting queue.
This rule prevents machines from becoming the bottleneck resources since the
jobs waiting at the machine with the longest queue size arc @en the highest priority
to use the available tools for processing the jobs. Intui t i~ely~ this rule should n-ork
well in terms of preventing system blocking and in terms of reducing long 11-aiting
times for jobs in front of a single machine.
Cornpared to SIO, L Q l I rule uses additional information such as the queue size
of prima^ resource. namely current and succeeding machines for impIementation.
3.2.3 Maximum Request for Tools with t ie-breaking (MRT)
'clRT rule operates in the folloning manner: 11-hen a job arrives for processing at a
station. it starts immediately if al1 the required resources are available. Othenvise.
the job waits at the input buffer. Then whenever a resource becomes available. this
rule checks the queue size of each tool. The tool with maximum pending requests is
found and the corresponding jobs waiting for this tool in the queue are sorted based
on the high queue size of the other tools required for the current operation. If there
is still a tie. then the high queue size of current machine is used. Further ties are
broken by SIO, then FIFO to the waiting queue.
This rule prevents took from becoming the bottleneck resources since the tool
with the highest queue size is always considered and jobs waiting for those tools
are giïen the highest priority. Intuitivelq: this rule should have a similar effect to
LQSI when the utilization of additional resources in the system is higher than that
of prima- resources.
CnIike SI0 and LQM. MRT rule uses information related to additional re-
sources to prioritize the jobs. Information such as queue size of tools. queue size of
the current machine. and processing time of job a t the current machine are used for
implementing the rule.
3.3 AGV Dispatching Rules
An - lGl* dispatching rule prioritizes jobs on an idle -AGI- to mot-e a part from one
location to another location in the rnanufacturing system. If there is no request. the
-1Gl' remains idle and awaits for a transportation task to emerge. -At each station.
a job seizes the input buffer of the nest station before it is physically transported
to the nest station. The proposed rules use important attributes in addition to the
distance betu-een the pick-up station of a job and free -AG\- locations for priority
calculation. The following -AGI- dispatching rules are tested:
3.3.1 Nearest Station (NS)
-4 job in need for -1GV first looks for an idle vehicle. If there are more than one
idle vehicle, then the nearest AGI- is selected. On the otherhand, if al1 -AG\-s are
busy: then the job joins a queue for AGV. When an .-\GI: gets relinquished later
on in the system, the waiting queue is scanned and, the job which is a t the pick-
up workstation nearest to the relinquished AG\- is selected. If there are no load
requests, then the relinquished AGV stays in the same station.
This ruIe is used here as a benchmark for cornparison purposes. Lee (1996)
evaluated AGV dispatching rules for a job shop environment and showed that
vehicle-initiated rules perform better t han the workcenter-initiated rules. Of the
vehicle-initiated rules that were tested, the S S rule showed superior performance.
The distance between the location of idle -AG\- and the pick-up station of jobs
is the only att.ribute uscd in SS rule.
3.3.2 Queue Size and Nearest Station (QSNS)
-4 job in need for ,AGI' looks for an idle vehicle. If there are more than one idle
vehicle. then the nearest -AGI,' is requested. On the otherhand, if al1 -AGI-s are
busy. then the job joins a queue for -AGI-. 11-henever an -AGI' gets relinquished in
the system. i t checks for the output queue size of al1 the stations. If there is a
workstation u-ith output buffer that is nearly full (output buffer capacity less one).
then the -AG\.- moves to this station for pick-up. Ties broken by nearest station
to the relinquished .iGI-. Otheru-ise, it moves to the nearest station n-ith travel
request. Ties broken bu high number of jobs in the output buffer. If there are no
travel requests. then the relinquished -AG\' stays in the same station.
In surnmary. this rule can be n-ritten as:
When a job finishes processing and there is space at destination:
- If there is only one idle vehicle. select that vehicle.
- If tn-O or more idle ~ehicles are available. select the nearest vehicle.
- If al1 -\GIS bus- join a single wairing line and. m i t until a vehiclc is
available.
0 W h e n a n AG V finishes deliuery:
- If n-aiting line is not empty:
r If there is one station with output buffer nearly full. select rhat sta-
tion. Jobs in waiting line at that station are prioritized FIFO.
* If two or more stations have output buffers nearly full, select the
nearest station. Jobs in waiting line at that station are prioritized
FIFO.
* If no station is nearly full, the -lG\* selects the nearest station with
travel request. Ties are broken b - the highest number of jobs in the
output buffer, then by FIFO to n-aiting line.
- If waiting line emptj-z the AGI- stays a t the place n-here it became idle
and n-aits for a pick-up rcquest.
This rule is a modification of HQ-SS rulc that n-as developed by Lee (1996).
-4s esplained in Chapter 2. HQ-XS is a 1-ehicle-initiated rule that operates in the
follon-ing manner: The AGV goes to the pick-up station of the assembly line with
the highest number of in-process jobs. If there are t11-O or more stations having the
highest number of jobs. the AGI- goes to the nearest station. If there is no load
assignment on the list. it waits for the nest assignment to emerge.
The HQ-XS ruie is modified here to suit the FAIS environment n-hich is char-
acterized bu lirnited local buffers. Consider a situation n-here jobs ma!- happen
to be waiting for pick-up a t the current drop-off station of the .-lGI' for XI-hich the
ernpty tral-el tirne is practically zero. Under HQ-XS rule. the idle -AG\- moves to the
pick-up station n-hich has relativelu more number of jobs than the current dropoff
station. If this station happens to be farther away from the current drop-off station.
the empty travel time n-ould be high enough that the station n-here it had left n-il1
start to have equal number of jobs n-aiting for pick-up. Therefore, to improre the
efficiency of ,AGI- operation, the QSSS rule is developed. An idle -\GIS serves a job
waiting at the station nearest t o i t unless the output buffer of some other station is
nearly full.
The QSSS rule uses attributes such as the distance between the location of
idle AGI' and the pick-up station of jobs, and the output queue size of each station.
3 -3.3 Nearest Unassigned Job (NUJ)
A job in need for ,4G\; first Iooks for an idle vehicle. If there are more than one
idle vehicle. then the nearest ,AG\- is selected. On the otherhand, if al1 AGI-s are
bus>-. then the job joins a queue for -4GV. 11-hen an -AG\- gers relinquished later
on in the system. it checks if there are jobs n-aiting at the current dropoff station.
If so. it serves this job. Ties are broken by high difference betn-een number of jobs
n-aiting and number of AGI-s destined at the destination station. If t here are no jobs
\vaiting at the current drop-off station. then the free -\GI- checks the destination of
al1 other vehicles and chooses the nearest pick-up station for which the number of
-AG\-s dispatched is less than the number of jobs n-aiting at the output buffer. Ties
are broken by high difference between nurnber of jobs n-aiting and number of -AGI-s
destined. If there are no load requests, then the relinquished AG\' stays in the same
station. This rule can be witten as:
a Cmen a job finishes processing and there is space at destination:
- If there is only one idle vehicle, select that vehicle.
- If tn-O or more idle vehicles are avaiIable? select the nearest vehicle.
- If al1 -lG\--s bus?, join a single waiting line and. m i t until a vehicle is
available-
- If n-aiting line is not empty
* If only one job in the waiting line is a t the current dropoff station.
select that job.
* If two or more jobs in the waiting line are at the current dropoff
station, select the job which has the highest difference between num-
ber of jobs waiting and number of AGVs destined a t the destination
station.
* If no job wait at the current dropoff station. the ,\GY selects the
nearest station for n-hich the number of ,AGI-s dispatched is less than
the number of jobs waiting at the output buffer. Ties are broken by
the highest difference between number of jobs ~ a i t i n g and number
of -AGI-s destined. then by FEFO to waiting line.
- If waiting line empty! the .AG\' stays at the place where it became idle
and n-aits for a pick-up request.
This rule is developed to avoid unnecessary assignment of an idle -1GI' to a
job waiting a t its pick-up station for n-hich there is an ;\GY alread- assiped for a
drop-off t w k . thereby reducing the empty travel of .AGIS.
The SCJ rule uses atxributes such as the distance between the location of idle
AGI' and the pick-up station of jobs: the output queue size of each station. and
number of AGI-s dispatched to each station.
3.4 Machine- AGV Rule Combinat ions
The three machine scheduling rules are each combined with the three .AG\- dis-
patching rules to study the possible interactions. Each of the nine combinations are
treated as separate rules and applied to control the h-pothetical FAIS described in
the following chapter. The relative performance of the rules are rhen studied.
Chapter 4
System Description and
Simulation
This chapter is del-oted to the description of the hypothetical FUS used to study
the performance of scheduling rules. The system along with various scheduling rules
lias to be sirnulated to collect the relevant performance mesures. This chapter also
esplains how the system n-as modeled and how the simulation esperiments were
carried out.
4.1 Strategy
The objectil-e is to apply the scheduling rules to control a hypothetical FSIS under
different esperimental couditions. Esperimental factors such as time between ar-
rivals' arriva1 distribution: type of shop. bottleneck machine. duplicating tools and
-AG\' speed are considered in t.he study. -A new approach is deveIoped to implement
the type of shop and bottleneck machine factors by wrying the proportion of job-
types. This requires to develop a system for nhich the experimental factors can be
varied independently of one another.
bf 1. M2. CXC ILIachining b13,.LI4 Centers
1 - Inspection Sution
L- Lociding Strition
C- Unloading Station
Figure 4.1: Layout of hypothetical FAIS.
4.2 System Description
The hypothetical FMS under study shon-n in Figure 4.1 consists of four machines
111. 112: 113, 114 and an inspection station 1. ,411 jobs undergo inspection before
leaving the system. Parts are transferred by three ,AG\-s in the system. The number
of ,AG\-s needed in the system was determined based on a preliminary simulation
stud'-- Parts enter and leave the system through the loading/unloading station.
Each machine has a set of input and output buffer space of a limited size with
higher capacity on the input side (9) and a lower on the output side (4). n-hich were
also determined based on a preliminary study.
Four types of jobs are manufactured in this system and their processing se-
quence is given in Table 4.1. These routeings v-ere selected in such a way that
changing the proportion of job-types arriving in the system will resuit in varying
the type of shop esperimental factor. The job-types 53 and J4 involve opposite
routes through machines M l and h12, but job-types J1 and 52 do not. Therefore, by
generating more number of job-types J1 and 52 than job-types 53 and J4. the shop
is more of a Bon shop type. On the other hand. if more number of job-types 53 and
J4 are generated compared to J l and 52: the shop is more of a job shop type.
A11 processing times are assumed log-normallu distributed (Law and Kelton
1991) with mean as given in Table 4.1 and standard deviation equai to one. The
processing times are selected so that proportions do not affect average utilization of
an- machine. Each job has three operations and each assigned operation is asigned
to a different machine. r\t each of the machines. different types of tools are required
by each of the jobs as shown in the table. Tools are dist.ributed among the job-types
in such a ivaJ- that the variations in job-type proportions do not affect the average
utilization of any tool.
Furthermore' the bottleneck machine factor can also be controlled by varring
proportions of job-types. and this can be done independently of the type of shop
variation. By keeping the total proportion of job-types J1 and J2 same' and vax-ying
t heir relative proportion 11-il1 let the shop to be a Aow shop type but the bottleneck
machine factor can be varied. Similar concept is used for job-types 53 and -1-1 in
the job shop case. This variation in proportion of job-types enables to van- the
esperimental factors independently. These are dealt in a detailed manner in the
follo~ving chapter.
The mean inter-arriva1 time is treated as an esperimental factor to study the
FllS for different levels of system congestion.
4.3 AGV Layout
The distance between the two ends of each segment is 6.17 distance units in the
la>.out. ,Usa: the accompanying arrows s h o ~ that the layout considered is uni-
directional. The distance between any two locations of stations is shown in Table
42 .
1 .JOB-TYPE 1 OPER,\TIOS 1 XIACHISE 1 TOOLS i PROCESSITG 1
l 1 t 4 I IXSPECTOR I - i 4 I
I 1 REQL-IRED REQCIRED 1 TNE (min)
1
Table 4.1: Processing sequence of job-types with required resources.
111 $13
J1 - T-4,TC
3 I 3.1 4 I TB-TD
4 1 INSPECTOR 1 - .J 3 1 1 1 112 TB-TC
1 3 - 8
4 4
4 8
4 8 4
1 1 1
3
1 4 IXSPECTOR 113 11 1
J4
- - -
TCtTD A.12
1 2
4 1 ISSPECTOR - 1 4 T-4,TB 4
hl1 hl2 L.13 1 4 IKSPECT LO-AD CSLO-AD hi1 - 24.69 18.52 18.52 1.5 -43 6.79 5-56 112 24.69 - 18.52 15.32 15-43 4.32 3.09 113 30.56 30.56 - 24.69 21.60 33.19 33.95 l14 30.86 30.86 24.69 - 21.6 3.5 -19 33-95
ISSPECT 33.95 9.26 27.78 3.09 - 13.58 1'2.3.5 LOAD 3'2.84 22.84 16.67 16-67 13.38 - 3-70
CSLO-4D 24.01 24-07 17-90 11.90 14-51 1.23 -
Table 1.2: Distance mat rk of the hypothetical FAIS.
-AGI- layout is designed such a way that the total loaded trat-el distance are
the same for al1 job-types and, therefore changing proportion of job-types does not
affect -4Gi- load. The -AGI- load is varied by varying speed.
J i : LOAD + 1 + 3 + 4 + ISSPECTOR + CSLO--ID
= 22-84 - , 18.32 + 24.69 + 21.60 t 12.35 = 100 distance units.
JC: LOAD + 112 -+ LI3 + 114 --+ ISSPECTOR + C-XLO-AD
= 22-84 1 , 18.52 + 24.69 t 21.60 t 12.35 = 100 distance units.
53: LOAD + 112 + M4 -+ 111 + ISSPECTOR + LSLOAD
= 22.84 - 18.52 + 30.86 t 15.43 + 12.35 = 100 distance units.
4 : O -+ 1 3 + 1 1 -+ 1 + ISSPECTOR -+ CXLO-AD
= 16.67 + 30.56 + 24.69 -+ 15-43 + 12.35 = 100 distance units.
This way irrespective of the type of shop (flow shop. job shop) and machine
load level (balanced, bottleneck machine) combination, the average loaded trat-el
time 11-ould be the same.
4.4 Tool Utilization
Tools are distributed among job-types such that the utilization of tools are not
affected by vaqing the proportion of job-types. This implies that the expected
utilization of tools will remain the same irrespective of the nature of shop. Tool
load is varied by vaq-ing the number of tool copies Le., having a duplicate for each
tool type.
4.5 Assumpt ions
The follon-ing assumptions are made in carrying out the simulation studies:
50 job pre-empt.ion is allowed. Thus. an operation once bePn should be
completed before starting the nest operation.
Part routeing for each job as well as the resource requirements are predeter-
mined and there are no alternatives.
Tool availability is immediate.
There are no major disturbances on the shop floor, e.g.? no machine break-
don-ns or tool failures. 1Iinor disturbances are assumed to be accounted for in
the job machining times.
System Modeling and Simulation
Simulation is used to analyze the performance of the rules. One important advantage
of a simulation esperiment is that we can manipulate the different input parameters
such as arriva1 distribution, mean inter-arriva1 time and so on to s t u d ~ - their effects
on the system and to evaluate performance of the scheduling rules.
In order to carry out the simulation esperiment. it is necessac- to mode1 the
system. The s-stem described in Figure 4.1 along with the various scheduling rules
is modeled using SIbISCRIPT 11.5 language. The simulation modeling logic is shown
in Figure 4.2.
For each queue in the system, namely queue for machine and queue for AGV,
there is a corresponding routine which calculates the dynamic priorities of the
Entities Arrive al the Loading Station
Assign Job Types , Seize Input Buffer of 1 Appropriate Machine I
B usy AGVs 7
Select the 'Teclrrst AGV for Pick-up
Release Output BufTer Sprice o f the Previous Machine
1 Unload and Free AGV 1
6 Figure 4.2: Flowchart of simulation program.
Join Queue and Wait until riIl Requircd
Resources arc AvaiIabIe
1 Seize kIachine and Tools 1
Relcase Input Buffer c Begin Proccscing ?l
1 Release Tools 1
< buffer space Cali Priori* Routine-iI
Wriir u n d a space is Available
Seize Output Buffer f
1 Call Prioritv Routine-Il 1
Figure 4.2: Flo~vchart of simulation program (continued).
Seize Input Buffer of inspcctor .
Yes Join Queue and Wait ) until 3 Frre AGV is
AvaiIabie
Select the Xearest AGV for Pick-up
Retease Output Buffer of the Last Machine
1 UnIoad and Free AGV
I Seize Inspecter I
Release Input Buffer
Begin Ins~ection t
Figure 4.2: Flowchart of simulation program (continued) .
Seize Output Buffer of Inspector
I Release Ins~ecror I
Join Queue and Wait until a Free AGV is
Available Select the Nearcst AGV for
Pick-up
- --
Release Output Buffer of Inspector
Station and Frec AGV
Collect Job Statistics a Exit the System s
Figure 4.2: Flowhart of simulation program (continued) .
Example Pnoritv Routine-1: N S Rule
Sort Jobs in Queue for AGV According to the Travel
Distance with the Shonest
Sorted List
I Resume this Job
Examde Prioritv Routine-II: S I 0 Rule
Son Jobs in Queue for Idle Machines According to its Currrnt Proccssing Time
with the Shonsst Processing Time First
Rssurne this Job J
Join Queue and Suspend s Figure 1.3: Priority routine for machine and .\GV scheduling rules.
parts/jobs in the queue. Figure 4.3 esplains the priority routines for SI0 machine
scheduling rule and KS AGIi dispatching rule. The jobs in the queue are then
automatically ordered according to the priority attribute. The priority calculation
routines are called n-henever a resource finishes a job and is ready to start a nen-
job from its queue.
4.7 Experimental Condit ions
The mode1 is initially simulated for 200 hours and 10 replications in order to deter-
mine the n-arm-up period of the system using Welch's procedure. It is found that the
system requires about 60 hours to reach steady state. For the purpose of analysis.
the run length is fised to be for 10 eipht-hoiir shifts and the number of replications
as 20. Initial testing showed that this is enough to get confidence in the results and
drau- stat istically significant conclusions.
4.8 Variance Reduction Technique
Since the objective ivas to measure the relative performance of alternative rules. it
n-as logical to compare them under identical conditions. The use of common ran-
dom numbers variance reduction scheme ensured that each job arrived at the same
time and Kas assigned identical set of processing and inspection times for al1 the
rules analysed. -1ccording to Law and Kelton 1991, this method gives results with
greater st.atistica1 precision, c g . smaller confidence inten-als. The basic idea is that
we should compare the alternative configurations "under similar esperimental condi-
tions" so that ive can be more confident that any obsen-ed differences in performance
are due to differences in the system configurations rather than to fluctuations of the
"esperimental conditions.''
4.9 System Blocking
FUS scheduling problem is associated with limited input and output queue ca-
pacitics. Therefore. there is always a possibility that a particular machine can be
blocked. Blocking occurs when a part cannot be takcn to the destination station
due to unavailable buffer space. These successi~e events can also cause deadlocks,
Le.. the system is totallj- prevented from functioning and no part movement can be
furt her achieved.
The ctudy does not include preventing blocking situations. Hon-ever. blocking
occurs for some replications a t esponentially distributed Ion- inter-arriva1 tirne cases.
The replication that had the blocking situation b vas ignored and simulation Kas
resumed by manually setting the seeds for inter-arriva1 time. job-type generation.
and processing times. This n-ay the rules are tested under identical esperimental
conditions.
The number of blocking situations that occur for a L ~ e d nurnber of replications
is noteci and treated as a measure to evaluate che performance of different rules. ,\
rule that minimizes the queueing time of jobs in front of the resources n-il1 tend to
reduce the number of blocking situations.
4.10 Performance Measures
Performance measures relevant to make scheduling decisions in the areas of pro-
ductivity: inventory-level, consistency of output. and efficient operation of -AG\-s
are collected. Some of the performance measures are redundant. but are never-
theless included in the study for program verification. For each of the ninc rule
combinations the performance measures that are collected from the simulation are:
total throughput (TP)' average flowtime per job (FT), average waiting time per job
(Ivg(WT)) variance of wait ing times (Var(WT)) average work-in-process (FtlP)
input queue (IP.Q), output queue (OP-Q), average empty t o loaded travel ratio (EL),
average AG\* utilization (-IGI,*.L7TZ), and ayerage queue for -1Gi)'s (..AG\-.Q). These
measures are computed as folloivs:
Throughput, Flowtime and WP: Throughput is rneasured as the total number
of jobs completed in eighty hours. Flan-time is the average of the flon-times
of ail jobs measured during a simulation run. IVIP is the average number of
jobs present in the system. In tbis research. flowtime is more relevant since
it denotes maximum possibIe throughput. -As measured. throughput cannot
csceed total job arrivals which is finite.
-4verage waiting time per part: Waiting time is an important cornponent of
floivtime. Since in this stud- the set-up time is included in the processing
time. the only [va>- to minirnize the mean flon-time is to reduce the waiting
times. 11-aiting time is the total time a job spends waiting in the input buffer
and output buffer of each machine in its sequence. This can be espressed as
folio\\-s:
Total M-aiting Time = Flon-time - Total Processing Time -
Total Transportation Time - Load/Unload Time.
Average of total waiting time of al1 jobs completed during a simulation run is
measured from the simulation.
Variance of Waiting times: \:a.riance of waiting times is deterrnined as the vari-
ance of the average waiting times across job-types. This measure of perfor-
mance esplains the consistency of output in a system. -4 scheduling rule that,
discriminates job-types !vil1 perform poorly in terms of this measure.
Input and Output queue: Input queue is the average number of jobs in the input
buffer of al1 machines and output queue is the average number of jobs in
the output buffer of al1 machines. It is espected that machine scheduling
rules would affect the number of jobs n-aiting in the input buffer. and AG\-
dispatching rules would affect the number of jobs n-aiting in the output buffer.
Therefore, 1P.Q and 0P.Q were colIected.
EL ratio: EL ratio is the average total empty travel tirne to total loaded travel
time of al1 the jobs completed in eighty hours. Loaded travel time is constant
for a gît-en -AG\- speed since the total loaded travel distance from loading to
unloading ( = 100 distance unitsj is the same for al1 job-types. The empty
~eiiicle travel time of a load request depends on the location of the vehicles
and the origin and destination of the load request. If a load request arrives at
a station with a t Ieast one vehicle, then there wi11 be no empty-vehicle trax-el
time. However: if a load request arrives at a station with no vehicle, then the
amount of empty travel time will depend on the location of the empty vehicles
and the -4GI- dispatching rule utilized by the system. By minimizing the total
trave1 time of empty vehicles, the transportation of parts n-il1 be accelerated
and the efficiency of the whole manufacturing process n-il1 increase.
Average AGV.UTZ and AGV.Q: -AG\'.L-TZ is the average utilization of al1 the
t hree AGI'S in the system. -4GV.Q is measured as the average number of jobs
waiting for AG\; in the output buffer of al1 stations. AG\-.Q is different from
0P.Q as 0P.Q counts al1 the jobs in the output buffer and --\Gi7.Q counts those
jobs for which an input buffer space is resen-ed a t the destination station.
Chapter 5
Experiment al Design and Analysis
Intuiti~ely. the performance of dispatching rules depends on the environment in
which they are used. This chapter presents the esperimental factors selected for
performance comparison and outlines the design of esperiments approach used to
perform the companson. The main objective of esperimental design is to evaluate
the performance of scheduling rules under al1 possible combinations of the factors
with respect to al1 performance criteria. This chapter also recommends decision
makers to select appropriate rules based on their environment and the relative im-
portance of different performance criteria.
5.1 Experiment al Design
.-\ccording to Ozdemirel et al. (1996): an esperimental design approach is emplo-ed
for three main reasons. First, esperimental design provides a way of deciding which
particular configurations to simulate before any runs are made. so that the desired
information can be obtained with the minimum number of simulation runs. -1 care-
fully designed esperiment is much more efficient than a trial and error sequence of
runs that compares a number of alternative configurations unsystematically. Sec-
ondll; esperimental design provides the analyst with a tool for deterrnining which
factors have the greatest effect on output performance measures (sensitivity analysis)
or n-hich combination of factor levels Iead to the optimal performance. Finally. full
or fractional factorial design esperiments are the on l - statistical meâns of studying
the interaction effects betn-een two or more factors.
The esperimental research design selected here is rnotivated by the need to
determine how the performance of FAIS scheduling rules are affected b5- the system
parameters. This research design has two sets of esperirnental factors: controllable
factors and uncontrollable factors. The controllable or managerial decision factors
are duplicating tools and v a - i n g speed. The uncontrollable or en\-ironmental
factors are mean time between arrivals: arriva1 distribution. type of shop and bot-
tleneck machine. Each of these esperimental factors and their respective settings
are t abulated and discussed belon-.
Esperimental Factors Levels
Alean Time Betn-een arrivals (TB-A) 5 min. 6 min.
Arrival distribution (-AD) Esponent ial Cniform
Type of shop (SHOP) Flow shop Job shop
Bottleneck Machine (BXK) No lés
Tool Duplication (TD) S o Yes
AG\- Speed (AS) 15 20
Esperimental factors such as rnean time between arrivals? arrivai distribution.
tool duplication. and AG\- speed are chosen for the studv in order to be consistent
with the previous FXIS research. Type of shop and bottleneck machine factors were
found to influence the performance of traditional job shops, but were not addressed
for FAIS dynamic scheduling. The shop is of a flow shop type when jobs tend to
have similar routeings through the machines: and i t is of a job shop type when the
jobs tend to have different routeings. The scheduling of a job shop is usually more
difficult than that of a flow shop. The type of shop factor is measured here in terms
of flou- shop indes. Sirnilarlyy the bottleneck machine factor is measured in terrns of
the bottleneck indes. Each of these factors is esplained in detail as belou-.
Time Between Arrivals and Arriva1 Distribution
Lee (2996) used mean time between arrit-als and arriva1 distribution to evaluate the
.AGI- dispatching rules. On the average. a job ma>- arrive to the shop at everj-
5 ~ninutes or every 6 minutes. -At inter-arrivai time equal to five. the resource
utilizations are high. There is not much difference between the Ion- and high levels
of this factor because of the reason that at very high TB-\. say T or 8 minutes the
resource utilization are Ion- t hereby Ion-ering the waiting t imes. This situation may
not be good cnough to test the effectiveness of the diffcrent machine scheduling and
AG\- dispatching rules as an- rule xi11 perform well since there lx-il1 be little waiting
in system. Therefore' the high level of this factor is set to 6 minutes. -4s suggested
by Lee (1996). inter-arriva1 time can be uniforrnly distributed tvith a possible 50%
variation above and belou- t he mean, or esponent iallj- distributed.
Flow Shop Index
Pinedo and Singer (1998) used flow shop index and bottleneck indes to evaluate
their heuristic algorithm for a static job shop problem.
They define flow shop indes O 5 II $ 1 as a measure of the occurence of
similar job routes within a job shop instance. For each pair of machines i and k:
the? identif- the set of jobs that are processed on machine i and then immediateiy
rouced to machine k for subsequent processing, and let n i k denote the number of
such jobs (nik = O if i = k). They define
and
In the estreme case of the flon- shop If = 1. If the jobs have different machine
routes. the values nib tend to be close to 1 so the corresponding II remain close to
O -
The dran-back of flou- shop index as measured above is that it only considers
the immediate successors of operations. and so it can fail to capture the overaH flon.
picture.
Flow shop index is modified in this studt- as a two-level categorical factor.
namely type of shop. In this study? the tvpe of shop factor is implemented by
van-ing the proportion of job-types. Job-type arrivals are such that the type of shop
is either flow shop or job shop. By increasing the proportion of job-types J1 and J2
than job-types 53 and J-1. the shop becomes more of a flow shop type. On the other
hand. by generating more number of job-types 53 and J-1 than job-types .JI and J2.
the shop becomes more of a job shop type. In the esample FUS. if the ratio of total
percentage of job-types JI and 52 to job-types 53 and J4 is TO:30 then the shop is
flow shop and if the ratio is 30:10 then the shop is job &op.
The number of jobs of a particular type that flow through different machines
depend on the proportion of job-types. Therefore. for a given job-type distribution,
it is possible to determine a sequence of machines through u-hich back-tracking of
jobs is minimal, or in other 1%-ords the amount of forward flow of jobs is maximum.
Such a sequence of machines is called "the dominant Bon- sequence." Therefore, the
first step is to determine the dominant flow sequence of rn machines by solving the
following pure integer linear prograrnming (ILP) .
Let
fi, = total flow from machine i to machine j.
JI = a large number
The decision variables are
xi = position in sequence of machine i? i = 1: . . . . m. f
1 if xi < X j Y i j =
O othem-ise
1 5 2, 5 m integer
Yzj = O: 1
The objective is to ma.ximize the forward flon-. The first set of constraints (5.1)
ensure the precedence relation between a pair of machines Le.. either i before j or
j before i. The second set of constraints (5.2) ensure that the positions of a pair of
machines. say x, and Ij satisfy the required precedence relation of those machines.
Y;].
Example: For the job-tj-pe distribution 35:35:15:1.5. and time between arrivak
= 5 rninures the flou- matrk fivj (ref Table 4.1) is as ~~~~~~~~S.
-t A13 + 114. The algorithm was tried for a more compies problem consisting of
five machines and ten jobs and the optimal solution was determined in a reasonable
computation tirne.
1
'VI2
hl3
b14
- 1.8 4.2 - - - 4.7 1.8
1.8 - - 8.4
1.8 - - -
The optimal solution of ILP gave the dominant Bon. sequence to be hl11 +
';est. the flow shop indes is computed as follows:
Let
-\- = number of job arrivals per hour
T = total number of job-types
p = nurnber of operations, and
nu denotes number of jobs of particular type t that are processed on machine
i and then immediately routed to machine k for a particular pair of consecutive
operations j . nu is positive, if the route i + k follows the dominant flow sequence.
Otherwise. nt, is negative. The Bon- shop index O 5 If 5 1 is defined as'
ET=, EJL: ntj rf = : q p - 1)
Ir is equal to 1 for a case where al1 the consecutive pairs of operations involve
machines that obey the dominant flow sequence which irnplies a pure flon- shop. On
the other hand, if the machines in each pair of consecutive operations do not follotv
the dominant Bon- sequence then If is equal to O and the shop is a pure job shop
type.
For the dominant flou- sequence 311 + 112 -+ 113 -F 114: consider the routeings
of consecutive operations of two different jobs to be SI- + 513 and 11-2 -+ SI4 The
fact that both these routeings satisfy the dominant flov- sequence is not captured in
Pinedo and Singer (lW9).
Example: For the same example. the process routeing for each job-type is as
foilo~vs (ref Tabte -1.1):
JI: 1 -+ 3 + hI4 J2: 112 + 113 + hl4
J3: hl2 - 1114 + Ml J4: h13 + Ml + M2
Therefore,
Since II is 0.70, the type of shop is more of a Bon- shop type.
Bottleneck Index
Pinedo and Singer (1998) define bottleneck indes O 5 Ib 5 1 as a measure that
determines the estent to which the utilization of the machines is concentrated. They
developed a formula to determine Ib for a job shop n-ith n 2 2 jobs. The formula
is based on the assumption that each job visits each machine esactly once. Let
rn,k denote the number of jobs of n-hich the k-th operation must be processed on
machine i. They define
and
If the utilization of machines is less et-enly distributed over tirne: then Ib is
closer to 1. On the othcr hand, if the machine utilization is spread out over the
scheduling horizon? the values mi,, tend to be close to 1 so the corresponding Ib
rernains close to O.
The drawback of bottleneck indes as measured above is that it does not in-
volve processing times and inter-arriva1 time of jobs which measure the load on the
machines.
This is modified in t,he study as a two-level categorical factor. namely bottle-
neck machine. Similar to type of shop, bottleneck factor is implemented by varying
the proportion of job-t-ypes, Machine load level is balanced in one level and in the
other there esists a bottleneck machine. The bottleneck machine is introduced by
unbalancinp the relative proportion of job-types J 1 and J 2 in the flon- shop case.
and job-types 53 and 34 in the job shop case. Whether or not a bottleneck machine
esist, the ratio of total percentage of job-types J1 and J2 to job-type 53 and J-l is
the same for a particular type of shop. The bottleneck machine in unbalanced flon-
shop is machine 112 and in unbalanced job shop is machine 113. -4s esplained be-
fore. tool utilization remain unchanged whether or not a bottleneck machine esists
in the system. -AGI- layout is designed such that irrespective of the distribution
of job-types chosen, the a..-erage loaded travel is the same. Therefore, the type of
shop and bottleneck machine factors can be varied independently. The approach
developed to determine the bottleneck index is esplained belov.
First. determine the utilization of each machine for a particular time between
arriral of jobs as follows:
Let
, I f z = utilization of machine i
-\- = number of arrivals per hour
n = number of job-types
r, = proportion of jobtype j
pij = processing tirne of job-type j on machine i in minutes
Example: From Table 4.1: the utilization of machines for time betn-een arrivals
= .5 minutes and job-type distribution 35:35:15:15 are as follo~vs.
1 Typeof iBottleneclc! Job-type Dominant 1 If ! I b 1
Table 5.1: Flow sshop and bottleneck indices.
i Çhop 1 3Iachine 1 Flow shop Ko
From above.
Sest step is to determine the bottleneck index O 5 lb < 1 which is defined as.
Distribution 1 F 10x1- 35:3.5:1.5:15 [ M l + 1 , 1 ' 2 - + 3 E 3 - + 1 4 4
Example: For the same esample,
(1 - 0.80) I b = l - = O
(1 - 0.80)
Since la = O: the shop is balanced. For the same case. if the maximum utiliza-
tion: Mm, is 100%: then 4 is equal to 1 and the shop is severel:- unbalanced.
0.70
The formula For Ib involves processing times of each job-type and the arriva1
frequency of jobs in its calculation. n-hich were not considered by Pinedo and Singer
(1999). Table 3.1 shows the dominant flow, It: and Ib for the different levels of type
O 1
of shop and bottleneck machine factors.
Tool Duplication
Hutchison (1991) showed that duplicating tools improves the performance of an
FlIS. The lon- level of tool duplication factor is to have no duplicate tooling. -At the
high level. there is one duplicate of evey tool type. Tools are distributed among
job-types such that al1 tool types have equal load. This n-a>-. other factors such
as t?-pe of shop and bottleneck machine can be varied independently. For no tool
duplication level: the espected utilization of tools at the low 1ei.el of time between
arrivals is 80% and at the high leveI is 67%.
AGV Speed
Sabuncuoglu and Hommertzheim (1992) suggested that the AG\- load levels are
adjusted by changing the -AG\; speeds. -AGV speed can be 1.5 distance units/rnin
or '20 distance units/min in the simulation.
5.2 Experiment al Analysis
il-ith sis factors set at two levels each, the number of treatment combinations is
z6 = 64. Three machine scheduling rules and three .AG\- dispatching rules n-ere
tested ~vhich gives 9 x 6-4 = 576 euperiments. The number of replications for each
esperiment is set to 20. Schmeiser (1952) suggested that making twenty replications
per treatment combination is an often-used rule of thumb in simulation esperirnents.
Ozdemirel (1996) also suggest that more than t w e q replications are usually useless:
because this would result in an unnecessarily large error degree of freedom in factorial
designs. Preliminary testing showed that making twentv replications of eighty hours
each gave acceptable confidence-interval.
Esperimental analysis is carried out in two parts. In the first part, the main
and interaction effects of experimental factors such as the inter- arrival tirne, arrival
distribution, type of shop, bottleneck machine: tool duplication and -1GV speed
on the performance measures are studied for a specific rule. In the second part
of the analysis. the effect of machine scheduling and AGV dispatching rules on
performance measures for each of the t reat ment combinat ions are discussed in det ail
and recommendations are made based on selection criteria.
5.2.1 Main and Interaction Effects of Experimental Factors
-4 26 full-factorial analysis is performed to determine n-hich of the factors and their
interaction effects are significant. The level of significance used is 0.0-5. The p-values
for this design are tabulated in Table 5.2. The results are shona for LQSI-XS rule.
The discussion vil1 hold for the other rules since similar response is displayed.
Main Effects
The t>-pe of shop and bottleneck machine factors affect the FUS performance. It
can be seen that al1 the main effects are significant for flowtime and \\'IP measures
while throughput is affected only by time between ar r i~a ls and arrival distribution.
-4s shown in Graph 5.1: flowtime is high for job shop compared to Aon- shop. Lnbal-
ancing the load level on machines causes the flowtirne. \\?P and variance of IL-aiting
tirnes to increase.
EL ratio is 10x1- for job shop compared to fiow shop thereby causing -AG\-
ut ilization to increase for the flow shop case. Since EL ratio is Ion- for job shop case.
i t is evident that increase in flowtime is due to increased waiting of jobs in front of
the machines. Increasing the arrival rate increases EL ratio because it is less likely
tha t a part might find an =\GV located at its pick-up point. It is also interesting to
note rhat unbalancing the shop does not affect EL ratio and -1GV utilization.
kactor
(1) TB-1 ( 2 ) AD (3) SHOP (4) BSK ( 5 ) TD (6) -1s 1 b'- 2 1 by 3 1 bJ- 4 1 by 5 1 by 6 2 by 3 2 by 4 2 b - 5 2 by 6 3 by 4 3 bu a 3 by 6 4 by 5 4 by 6 5 by 6
p-values
Table 3.2: -1YOVA Results: E.sperimenta1 factors affecting performance measures.
Significant at 0.05 Ievel.
TBA SHOP BNK
j l : / i I/ .
+"- I d . j
FLOW JOB NO YES ONE TWO LOW HlGH 100.5 loo.s 100.5
EXP UNI FIVE SIX 100.5 100.5- 100.5
Graph 5.1 : Effect of Experimental Factors on Performance ~Measures.
Interaction Effects
It can be readily seen that not al1 two-nia- interactions are significant. In particular.
the interaction of the type of shop (SHOP) and bottleneck machine (BSK) is signif-
icant for flowtirne and WIP indicating that these measures show increase in values
when the shop is unbalanced. The impact of duplicating the tool is significant with
respect to the type of shop (SHOP). bottleneck machine (BSK) and -AGI- speed
(-4s) as far as variance of naiting times is concemed. This shows that irrespective
of the nature of shop. variance of waiting times is reduced bj- duplicating the tool
t'-pes. ll'ith respect to EL ratio and AGV utilization. the interaction effect of -1GI'
spced (-1s) with time between arrivals (TBA) and tool copy (TC) is significant
showing that EL ratio increases with increase in -AG\' speed.
5.2.2 Effect of Dispatching Rules on Treatment Combina-
tions
The machine scheduling rules and -4GI' dispatching rules are considered as factors
and a 3? full-factorial analysis is performed on the s i s - f o u r treatments separately.
Factors Levels
llachine-scheduling rule SI0 LQSI hl RT
AGI' dispatching rule KS QSSS KCJ
A'rOV-A results and recommendations for each of the sist-four treatments are
tabulated in appendices. Each treatment combination in Appendk -1: B and C is
espressed in terms of the ievels set for each of the sis factors. For example,
5/E/F/N/ 1/ 15 implies that the time between arrivals is (5) minutes' arriva1 distri-
bution is (E)sponential, type of shop is (F) lowshop' (N)o bottleneck machine'
no tool duplication (1): and AGV speed is (15) m/rnin.
G/U/J/Y/2/20 implies that the time between amvals is (6) minutes. arriva1 dis-
tribution is (C)niform, type of shop is (.J)obshop, bottleneck machine esists
(Y). tool duplicate esists (2): and AGI- speed is (20) m/min.
The results for the skty-four treatments are sumrnarized b - categorizing them
into eight categories. Categories are formed such that each of them differ in time
berween arrivais. arrivd distribution and type of shop. This is because .ASOL-A
results revealed that for the eight treatments nithin a categor- the performance of
rules n-ere more or less identical. The eight categories are listed as foI1ows.
1. TB;\ = 3: AD = Esponential, ST = Flow shop (5/E/F/s/s/x)
2 . TB;\ = 5 : AD = Esponential, ST = Job shop (5/E/J/s/x/s)
3. TBA = 5 : AD = L-niform. ST = Flow shop (J./C/F/s/s/x)
4. TBA = 5 . AD = Ilniforrn, ST = Job shop (5/C/J/s/s/s)
5 . TB-A = 6' AD = Esponential, ST = Flow shop (6/E/F/x/s/s)
6. TB;\ = 6. AD = Esponential. S T = Job shop (G/E/J/x/s/s)
7. TBA = 6: AD = Eniform. ST = Flow shop (ô/C/F/x/s/x)
8. TBA = 6: AD = Gniform. ST = Job shop (6/C/J/s/s/s)
Selection Criteria
It is important to make scheduling decisions in FAIS. Scheduling decisions for an
F'rlS is concerned with obtaining good performance measures such as the aver-
age flowtimes of al1 jobs: consistency of output of job-types. operation of material-
handling transporters and so on. In this study: performance of scheduling rules are
classified based on following criteria:
0 Flowtime: The rules that perform well in terms of flowtime criteria n-il1 also
show improvement in average waiting time, i\;IP and input queue measures.
Yariance of waiting times: Lariance of waiting times is used to measure the
consistency of output. If the variance of waiting times is small. then it means
that the average waiting times of al1 job-types are more or less the same
which is more appropriate for a JIT environment. -4 scheduling rule that
discriminates among job-types and gives priority to certain job- types over
others will tend to have larger variance of waiting times. A s a result: the
output of job-types per unit time \\-il1 be affected.
0 Efficient operation of AGVs: -4GI- related statistics such as the empty-to-
Ioaded travel time ratio, output queue and average utilization of -AGI'S play
ail important role in the design and control of -AGI-S. These measures are
espected to be affected more by the .AG\.' dispatching rule than by the machine
scheduling rule utilized in the systern.
Based on these factors. machine scheduling and -\GI.- dispatching rules are
recommended for each category in Table 5.3 and for each treatment in -4ppendis-
C. In addition, performance based on the frequency of blocking situations and overall
performance of rules are studied.
Performance of mies based on flowtime
In terms of flowtime performance, NUJ -AG\' dispatching rule significantly per-
forms well at the low level of inter-arriva1 tirne and AGI' speed. and high level
of tool duplication factor (Le. 5/x/s/s/2/15) as seen in Appendk-C. About 10%
improvement in flowtime measure can be seen when NLJ -AG\- dispatching rule is
used. For those combinations MRT-YUJ and SIO-NCJ are recommended. For the
other Ion- inter-arriva1 time combinations SIO-NUJ rule is the best. For esample, in
5/U/J/Y/1/20 treatment combination. there is about 7% improvement in flowtime
Category
Table 5.3: Sumrnac of best combination of N/C--AG\' rules based on flon-rime. consistency of output and efficient operation of AGI'S.
6/E/F/s/s/s G/E/J/s/s/s G/C/F/s/s/s
G/C/J/S/X/S 1
n-hen SIO-SC-J rule is used instead of LQM-SCJ. For al1 esponentially distributed
high inter-arriva1 time combinations (G/E/F/s/s/s. G/E/J/s/s/s) SIO-SCJ fares
well n-hiIe LQN-XC-J rule performs well for uniformly distributed high inter-arriva1
time combinations (G/L/F/s/s/x: G/C/J/x/x/s).
Flowtime
Performance of rules based on consistency of output
Consistency Efficient of Output Operation of X S s
SIO-SC-J SIO-SUJ
LQXI-NCJ
LQSI-NCJ, LQLZ-QSXS
lariance of waiting times is often aEected by the machine scheduling rulc factor.
LQhI and LIRT rules perform well with respect to this measure. LQhI rule is
preferred for the flon- shop combinations
3/E/F/s/s/s 4IRT-SLiJ, 1 SIO-SUJ
(5/E/F/x/x/x. 5/ll/F/s/x/x. G/E/F/s/x/x. 6/C/F/r/x/x).
while MRT rule for the job shop combinations
(5/E/ J/s/s/s, 3/U/ J/x/s/s, 6/E/ J/s/s/x).
70
~/L /F /+ /X/X 1 31RT-\iL.J_ 1 LQbl-YCJ. LQhI-QSNS LQlI-SUJ ZIRT-X.I i SIO-SC- J 1
LQN-SCJ' LQ31-QSSS
l,IRT-SS, ?tIRT-‘lr?j.J, AIRT-QSXS
S/E/ J / s / s / s
'IIRT-QSSS I LQ'cl-YS. LQ'II-St'J 1 LQSI-SCJ. IIRT-XUJ
LQbl-NLJ? IIRT-SCJ
LQLI-SCJ, h[RT-SUJ SIO-XUJ
1 IRT-5s. SIRT-SCJ LQhl-?;S. LQlI-SCJ,
LQS1-3l.J. lIRT-KCC.J LQSI-SL7J, IIRT-NCJ
hIRT-NS. '1IRT-KCJ 1 LQSI-';S. LQU-QSXS LQlI-SLJ
Performance of rules based on efficient operation of AGVs
For al1 the treatment combinations: NLJ AGV dispatching rule performs ive11 in
output queue. EL ratio and -AGI,- utilization. For the Iow-leveI of tool duphcation
case (e.g. .3/E/F/S/1/15) there is about 8% improvemcnt in EL ratio and for
the high level of tool duplication case ( e g . 5/E/F/S/2/15) there is about 13%
improvement in EL ratio when NCJ -AG\- dispatching rule is used instead of SS
and QSSS. It can be seen from -4ppendis-B that with no tool duplication. machine
scheduling rule affects the operation of -AGI-S. LQ'II and LIRT rules are preferred
for those cases. For example' in .5/L/J/\-/1/20 treatment combination. about 6%
improvemcnt in EL ratio can be achieved when either LQL1-W.J or 3IRT-SUJ is
used instead of SIO-SCJ. In general. L Q U - S U J and IIRT-PX-J performed equally
weil in these measures.
Performance of rules based on average waiting time and variance of wait-
ing times
In practice one m a - be interested in a dispatching ru!e which does reasonably well
on both average n-aiting time and variance of waiting times. From the initial analy-
sis discussed in section 1.3.1, it is seen that duplicate tools reduces a\-erage waiting
time and variance of n-aiting times. Therefore, treatments n-hich involve tool dupli-
cates are eliminated and the mean values are shown in Table 5.4 for the machine
scheduling rules combined with XCJ -4GV dispatching rule as Xl l J shows superior
performance over Pis and QSKS ;\GV dispatching rules. MRT-NL-J rule seems to
be doing well for such an application. SI0 rule performed poorly in variance of
waiting times and L Q N rule in average n-aiting time mesure.
Performance of rules based on minimum blocking situations
hlRT-NUJ also tries to minimize the blocking situations that arise for esponentially
distributed low inter-arriva1 time treatments with no tool duplication. Graph 0.2
Table 5.4: Performance of rules based on average waitinp time and waiting tirne variance.
Average waiting 1 1 rime 1 LQbI-XCJ 1 82.30
SIRT-KXJ 81 .Z
Yariance of waiting times
1608.S6 2020.1 T
Table 5.5: 95% Confidence Inten-al for each M/C-AGI- rule averaged over 64 treat-
SIO-YLJ 1 79.56 I 2180.71
Performance Neasures
ments.
FT 14.49~k1.39 T3.84Az1.37 7 . 9 8 1 . 13.81&1.31 T3.'241tl.30 74.33i 1.34
shows the percentage of blocking situations esperienced in seventy replications for
each rule combinat ion. This explains that NRT-ScJ handles job queuing-time
WIP
better than the other d e s . LQM rule performed poorly in this matter.
Overall performance of rules
EL
Sometimes it ma? be necessary to decide on one machine scheduling and -AGI- dis-
,i\Gil*. CTZ
patching rule that rnight perform well irrespective of the arriva1 time and distribu-
87.58I0.46 81.36=0.45 87.8%tO.-l'T 87.66zk0.16 87.35=0.4.5
13.8'2=0.31 ' 0.34=0.003
tion, nature of shop. tool copies and AGV speed. For this purpose a 95% confidence
13.7010.30 14.00~0.31 13.69=0.29 13.5TAz0.29
interval is determined for each machine and AGV scheduling rule averaged over the
0.33zk0.003 0.34zt0.003 0.34~0.003 0.33I0.003
13.7810.30
sisty-four treatment combinations. These values are shown in Table 5.5.
0.34&0.003 1 87.68f 0.46
G n p h 5.2: Percentage of blocking situations for each rule combination
LQM MRT
liachine schcduling rule
I t can be seen that both SIO-SS and SIO-YLJ mies perform n-ell in terms of
flowtirne and l \ lP mesures. Han-ever. SIO-ScJ outperforms SIO-YS in EL ratio
and AGI- utilization. The 95% confidence-inten-al for each treatment and each rule
is shon-n in Appendix-A.
Simultaneous study of machines and material handling systems
Decisions regarding selection of appropriate machine scheduling and AG\- dispatch-
ing rules are important for an F U S user. From -1ppendis-C. it can be seen that
in most cases selection of a scheduling rule for machines and -AG\-s are indepen-
dent. Hoivever. in some cases the selection requires combined evaluation of machine
scheduling and -1GV dispatching rules. For esample. in P/L,/F/'k-/l/'O treatment
combination. independent selection based on flowtime measure shows SIRT and S I 0
rules for machines and S S and XC-J d e s for AG\.- dispatching. However. URT-NL-J
and SIO-YS rule combinations yield best results. If machines and -4GI.- sub-q-stems
were to be studied separately then it might happen that SIRT-SS or SIO-3C.J could
be recommended instead of 1RT-SCJ and SIO-SS. for 3/C/J/S/1/1' 3 treat-
ment under flowtime criteria. both S S and SC3 -4Gi- dispatching rules perfora
equallj- ive11 but SIO-XLJ is alone recommended.
Chapter 6
Conclusion
This study addressed the FMS scheduling problem b - evaluating the performance
of different machine and AGI- scheduling rules using a simulation model. Three
machine scheduling rules and three AGI' dispatching rules giving rise to nine rule
combinations were tested in this study. Tn-O of the three machine scheduling rules
(LQSI. SIRT) are developed based on combinations of simple rules proposed in
previous research, n-hile the SI0 rule is used as a benchmark for cornparison purpose.
Similarly. two new -AGIv dispatching rules (KCJ. QSSS) are proposed and 3's rule
is used as a benchmark.
6.1 Summary of Results
The results indicated that a t high utilization rates, in which most FMS usuallv
operate. the way that machines and AGVs are scheduled can significantly affect
the system performance. Therefore, not only machines but aIso AGVs should be
scheduled in the rnost effective way- -41~0: the choice of rules is found to be dependent
on FSIS operathg condition as well as on the performance criteria chosen. The
results can be surnmarized as follows:
1. The two newly tested factors! namely type of shop and bottleneck machine
are found to have significant effect on FAIS performance.
2. -4rnong the machine scheduling rules tested against the mean flot\-time crit,e-
rion, SI0 appeared to be the best rule n-ith X L J AG\- rule cornbination at
high ut ilization rates. NUJ -AG\* rule significantly minimized the flotnime for
the tool duplication cases. LQII rule performed well for the high inter-arriva1
time treatments.
3. \Vit h respect to variance of waiting times, LQhI and MRT machine scheduling
rules performed better than SIO. AGIT dispatching rule showed no effect on
variance of n-aiting tirnes.
4. MRT-SLJ rule performed well in both average n-aiting time and variance of
n-aiting times measures. AIRS-SCJ rule has also shown to reduce the nurnber
of blockings during a simulation run.
5 . Based on -AG\.- operation, NL.J rule performed better than XS and QSSS
rules in EL ratio: output queue and -IGl-- utilization measures. L Q l I and
IIRT machine scheduling rules in combination n-ith YI.*-J rule showed better
operation of AGI'S for the cases 11-here there tvere no tool duplicates.
6.2 Application of Performance Based Selection
of Rules to FMS Decision Maker
Selection of appropriate scheduling rules improves FSIS performance. Hon-ever:
if an FLIS user is concerned more on a particular performance measure than the
ot hers. then the classification of results based on selection criteria such as flowtime,
consistency of output, and efficient operation of AGVs w-ould be of use in the decision
making process. Assume that the FhIS decision-maker is faced wirh an FAIS as
follows: jobs of different varieties arriving to the shop in an uniform manner at
high frequency: there are no tool duplicates; the AGVs are operated at high speed;
and the load level on machines is slightly unbalanced. This situation is similar to
j/L/J/l-/l/20 treatment combination tested in the study. The ASO\*A results
shon- t hat SIO-SLJ performs ive11 \vit h respect to flon-t ime measure, MRT-SLJ
n-ith respect to consistency of output. and both LQ'cI-SCJ and h[RT-5C.J n-ith
respect to efficient operation of AGI-s. The decision maker can rnake appropriate
rule selection correspondiag to the concerned performance criteria of importance. If
al1 the measures matter to him equally then SIRT-';CJ rule u-ould be a good choice-
6.3 Suggestions for Future Research
Future w-ork based on the initial insights provided in this research are listed belon-.
Since local buffer capacity is limited. there is a possibi1it~- that deadlock sit-
uation occurs. Therefore, deadlock a\.oidance and prevention algorithms can
be incorporated to the resource allocation schemes.
Further development of robust rules that perform well in both congested and
less congest ed environments.
To study the effect of vaq-ing the number of AG\-s and machines on FSIS
performance.
To include routeing flesibility as a factor in the esperimental design and study
the performance of rules with or nithout alternative routeings.
Performance prediction for different FAIS operating conditions by building a
regession model.
Diagnostic technique based on residual analysis can be included as a part in
the experimental design for model adequacy checking.
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Appendix A -Ah-OVA Results: Effect of Machine and AGV Dispatching Rules on
Performance Measures for the 64 Treatment Combinations.
Treatment 1 Rules 1 Performance lleasures
Table 1: ASOV-A Results: Rules affecting performance measures for TBA = 5 min and AD = esponential.
* Significant at 0.05 levei.
Rules
M/C -AG\- M/C -AG\- N/C -AGI- M/C -AGI- 'LI /C -AG 1.' sr/c -AG\- u/c -AG\- M/C AG\- 11 /c -AG\- M/C AGI(- M/C AGI- M/C AGV M/C -AG\' SI/C ,AG\' SI /C -4GV bI/C AG 1,-
Performance Measures
Table 2: ANOV-4 Resu1t.s: Rules affecting performance measures for TB.-\ = 5 min and -AD = Lniform.
Treatment
6/E/F/N/1/15
6/E/F/S/1/20
6/E/F/S/2/13
6/E/F/X/2/20
Performance lleasures
Table 3: AXOV-4 Results: Rules affecting performance rneasures for TB-4 = 6 min and -AD = exponential.
' Significant at 0.05 level.
1 Rules / Performance lleasures
Table 4: AXOVA Results: Rules aEecting performance measures for TBA = 6 min and -ID = Uniform.
' Significant at 0.05 let-el.
Appendix B -95% Confidence-Lnterval of Performance Measures
1 reatment
5/E/F/3/1/15 LQ'c1-SS LQlI-SL'J
LQl 1-QSSS 11 RT-SS
LIRT-SCJ l1RT-QSNS
SIO-3s SIO-XLJ
SIO-QSSS LQ31-SS
LQXI-NEJ
l IRT-Xv.J 'LIRT-QSXS
SIO-YS SIO-XLJ
SIO-qsss LQM-SS
LQlI--TcJ
&IRT-XC'J 'clRT-QSNS
SIO-SS SIO-SL'J
SIO-QSNS LQh.1-XS
LQM-XUJ LQbI-QSNS
3lR.T-YS ILIRT-NLJ
1IRT-QS-SS SIO-KS
SIO-YU J SIO-QSXS
Performance 31 easures \ n P EL
23.64ï1.30 0.21ï0.008 23.15I1.28 0.26Zk0.005 23.65I1.32 0.2Sk0.001 23.2.5-Ll.E : 0.2110.009 22.94=1.29 0.26~0.009 23.67ï1.25 O.SSi0.009 22.63&1.10 0,281k0.010 2 2 4 4 1 1 5 0.27*0.009 33.53I1.29 0.28-CO.008 20.98I1.24 0.33=0.003 20.91=1.0-4 0.32~0.003 21 .09=1.17 0.33Zk0.003 20.45k1-03 0.33&0.003 20.483Z1-00 0.32I0.004 20.63-Cl.13 0.33=0.003 20.383Z0.99 ' 0.34=0.003 '20.35-LO.98 0.33&0.004 2 0 O 0.3-EO.004 14.39ik0.19 0.265~0.009 13.9'7310.4-1 0.24~0.009 15.1-4I0.18 0.26=0.008 14.22zt0.47 0.26k0.009 13.8110.43 0.24-LO.009 15.09I0.73 0.27~0.008 1 5 0 . 8 0.263=0.010 1 3 7 5 0 . 4 4 0.24&0.009 1 5 0 5 0 . 7 1 0.27~0.007 12.22i10.39 0.33I0.004 12.13i10.39 0.31*0.004 12.26I0.40 0.33*0.004 l2.12k0.39 0.33I0.004 12.03I0.39 0.31I0.004 12.lkk0.38 0.33=0.004 12.11k0.40 0.33k0.004 12.03zt0.39 0.311t0.004 12.09I0.39 , 0.33+0.004
Table 1: 95% Confidence Interval for TB-1 = 5 min.; -AD = Exponential; Flowshop; Balanced
Treat ment 1 Rulec 1 Performance Ueasures 1
SIO-QSSS S/E/F/S/1/20 LQSI-NS
AG\'- CTZ 96.93,0.58 96.52k0.56
1 SIO-QSNS 1 106.523.75 1 20.99I1.20 . / / F / / / l 1 LQ'rI-NS 1 73.33~k.2.18 1 14.8-Li0.60
Table 2: 93% Confidence Interval for TB.-\ = 5 min.; AD = Exponential; Flowshop: Unbalanced.
L I - Y u LQM-QSSS
MRT-SS 1.1RT-XC'J
MRT-QSNS SIO-3s
SIO-XUJ SIO-QSSS L M -
LQLI-YCJ LQM-QSSS
MRT-XS &IRT-NCJ
MRT-QSXS SIO-NS
SIO-YLJ SIO-QSNS
0.33k0.004 0-2610.009
87.12+0.88 93.92~k0.69
73.33k2.01 78.58&3.05 74.2(&2.04 71.57k1.99 77.3Tf 2-73 74.2'712.12 71.313~1.91 i8.42f 3-24 64.73k1.58 64.32h1.96 64.83k 1.89 63.93~k1.75 63.66k1.74 63.99f 1.79 63.83k1.82 63.33*1.79 63.83f 1-72
14.40I0.56 1.5.48&0.1/ 14.58*0.58 14.24=0.56 15.17i0.71 l4.58ii0.59 1 4 . 1 9 0 5 l3.39I 0.81 12.71&0.52 12.66k0.54 12.73*0.53 12.54izO.50 12.49zt0.49 12.35k0.50 12.5E0.5 1 12.4TztO.51 L2.Szt 0.49
0.25k0.009 0.263l.009 0.261,0.009
95.38I0.68 96.2E0.69 95.94*0.69
0.25I0.009 95.443~0.68 0.2610.009 1 96.16d~O.66 0.26i0.009 0.25&0.009
, 0.2fi0.009 0.331s0.003 0.32h0.004 0-3350.004 0.33&0.004 0.313~0.004 0.33i~0.004 0.32i50.004 0.31&0.004 O.33f 0.004
/ 95.94I0.68 95.41i~0.69 96.3lf 0.65 86.SOzt1.08 86.334~1.02 S6.86kl.OS 86.76=l .O5 86.34i1.05 86.74-t 1 .O? 86.69&1 .O3 86.29&1.06 86.78=1.01
Performance 1 Ieasures lreatment
5/E/J/S/1/15
MRT-5C.J LIRT-QSXS
SIO-SS SIO-NCJ
SIO-QSXS LQlI-YS
LQhl-SCJ LQlI-QSSS
SIRT-YS -\TRT-XC'J
SIRT-QSSS SIO-NS
SIO-SCJ SIO-QSXS LQ11-SS
LQLI-Nu J LQlf-QSNS
hIRT-SS hIRT-NCJ
LfRT-QSSS SIO-xs
SIO-SCJ SIO-QSXS LQM-SS LQM-YC J
LQLI-QSXS LI RT-KS
MRT-'i'C J MRT-QSNS
SIO-xs SIO-XUJ
SIO-QSXS
Table 3: 95% Confidence Interval for TBA = 5 min.: AD = Exponential; Jobshop: Balanced.
- Rules 1 Performance Measures 1 reat-ment
s/E/.J/I-/l/ 15
Table 4: 95% Confidence Interval for TBA = 5 min.; AD = Exponential: Jobshop; Unbalanced.
LQlI-XS LQ&I-Yt-J
LQU-QSNS 1lRT-KS
1IRT-YCJ IIRT-QSSS
SIO-ss SIO-SCJ
SIO-QSXS
ET 124.42it5.91 123.77it6.10
CVIP 24.4Cd~1.39 24.41=1.43
22.012~1.18 22.03i~1.22 21.84=1.25
LQlI-SS LQ'cI-XCJ
LQAI-QSYS
126.28ï6.39 1 24.87il.51
111.79k4.71 11 l.84d~-l.89 110.83=5.28
122.06k5.37 1 2 0 . 6 5 1 125.55i6.83 ~ i g . s i = ~ o s 116.00rt4.89 l'îO.88f 3-23
SIRT-SS AIRS-XCJ
31RT-QSNS SIO-SS
SIO-SLJ SIO-QSXS LQhI-3s
LQII-SCJ LQAI-QSSS
AlRT-XS AIRI-SC-J
'LIRT-QSSS 1
24.02=1.30 23.141k1.23
, 24.73+137 23..zs&l.-a '21.8451.22 23.8Of 1-27
109.63=-4.76 1 21.60it1.18 1 lO.G=3.36 ll0.53&4.93 107.80k4.69 106.59it4.50 10'7.81&4.69
21.713~1-26 21.78I1.20 21-22=1-15 20.98=1.09 21.2451.12
14.39&0.52 14.17&0.49 1-1.9ako.63 12.46I0.46 12.44&0.43 l2.48f 0.46 12.49I0.44 12.47&0.45 12-53kO.45 12-493ZO.46 12.46k0.45 l2.-lg&O. 45
SIO-SS SIO-SCJ
SIO-QSSS LQhI-NS
LQLI-KL'J LQh1-QSXS +
i-l.SOk1 .C9 il.O9&1.ïO i6.or=2.-11 63.33=1.63 63.27=1.48 63.4251.66
74.99+1.89 1 l-l.XiO.54 72.24=1.78 -- r r -0112.66 74.6-4iI1.89 il.l2*1.69 77.25&2.54
IIRT-YS T -
MRT-QSSS SIO-XS
SIO-XCJ SIO-QSKS
l4.19*0.51 15 . l4f 0.68 14.4SiI0.53 14-lïd~O.49 15.18A0.63
63.49h1.52 63.45~kI -53 63.72itl.57 63.54id.38 63.38&1.53 63.541Sl .57
'lreat ment
5/L- /F/K/ l / l5 LQhI-XS LQ'cI-XCJ
LQN-qsxs 1IRT-XS
hlRT-YL'J 11 RT-QSSS
SIO-SS SIO-NLJ
SIO-QSXS LQ'II-KS
LQ1LI-XUJ LQlI-QSSS
'cIRT-NS XIRT-YU J
h1RT-QSXS SIO-xs
SIO-S'J SIO-QSXS LQLI-SS
LQlI-YUJ LQlI-QSXS
NRT-SS 31RT-SLJ
MRT-QSXS SIO-XS
SIO-YLJ SIO-QSXS LQLI-KS
LQh1-3U.J LQ3I-QSXS
11 RT-xs AIRT-XC'J
MRT-QSXS SIO-KS
SIO-YC'J SIO-QSXS
Performance Measures
Table 5: 95% Confidence Interval for TBA = 5 min.: AD = Uniform; Flowshop: Balanced
LI-. 1 1 1 7 7 9 3 9 2 23.58=0.84 LQ'lI-QSYS 118.95=3.26 23.80I0.65
IIRT-XS 114.03~2.3I 22.86&0.38 hfRT-SLJ 112.15k2.85 22.66=0.64
'CI RT-QSSS 1 1 2 6 23.00I0.63 SIO-SS 1 l4.811k3.13 23.0250.69
1 SIO-ZCJ 1 1O.iiH.OI ' 223930.65
SIO-QSSS 113.89I4.56 22.89k0.95 -5/C/F/Y/1/20 LQSI-NS 105.'21I3.45 21.06I0.74
LQhI-XLJ 10-4.671t2.73 20.98=0.59 LQ'lI-QSNS 105.95Zk3.25 21 .8OI0.68
'CIRT-NS 103.17*2.29 20.663~0.49 LIRT-XCJ 100.19&1.9~ 20.23I0.47
1IRT-QSSS 101.90*2.55 20.42I0.36 SIO-YS 100.53k2.76 20.33k9.63
SIO-XUJ 103.03ï4.29 20.61=0.59 SIO-QSSS 101.6693.04 20.36k0.66
5/C/F/k-/2/15 LQ3f-SS 65.99*0.87 13.21I0.21 LQhf-SUJ 64.14=0.81 12.84f 0.19
LQAI-QSSS 66.33I0.91 13.28k0.22 1IRT-NS 65.03I0.77 13.02f 0.19
AIRS-SC'J 63.5O&O.T2 12.71~k0.17
Treatmenr 1 Rules
SIO-QSXS 65.38&0.89 13.09~k0.21 5/C/F/Y/2/20 LQ4I-SS 56.01f 0.73 11.21k0.17
LQM-XCJ 55.65I0.67 11.1510. 16 LQbI-QSXS 56.02&0.70 1 1.22&0.17
LIRT-XS 55.38f 0.65 11.09*0.16 M T - J 55.19k0.67 11.053~0.16
MRT-QSKS 55.13k0.67 11.09*0. 16 SIO-SS 55.39k0.62 11 .09&0. 15
S I O - 55.09~kO.59 11.03&0.15 SIO-QSXS 55.32k0.73 11.08-tO.lT
Performance Measures
Table 6: 95% Confidence Interval for TB-. = 5 min.: AD = Uniform; Flowshop; Unbalanced.
92
lreat ment
5/Ly/.J/S/1/15 LQ'rl-SCJ
LQSi-QSXS LIRT-XS
blRT-S'J IfRT-QSSS
SIO-SS SIO-SLJ
sro-QSYS LQhI-YS
LQSI-XLJ LQ31-QSSS
,LIRT-SS 11 RT-PX-J
NRT-QSXS SIO-SS
SIO-SCJ SIO-QSSS LQ'LI-SS
LQLI-YCJ LQM-QSSS
1IRT-XS MRT-3UJ
'rIRT-QSSS SIO-5s
SIO-SC'J SIO-QSXS LQII-KS
LQhI-Y'C'J LQILI-QSSS
Performance Measures \VIP EL
24.16-10.79 0.27?~0.004 23.52*0.84 0.2fd~O.OO-l 24.46&0.90 , 0.27f 0.004 23.02&0.67 0.2T50.004 22.60=0..59 0.273~0.004 23.18~t0.65 , 0.21k0.00-4
19.84i0.49 0.36f 0.002 19.19i~0.58 0.35i0.003 19.86*0.44 0.35i0.003 12.8ÏI0.18 0.27FO.005 11.60rtO. 16 0.21I0.004 12.9010.'~1 o . z ~ o . o o a 12.78*0. 18 0.211,0.004 12.34=0.14 0 . X f 0.004 12.81zi0.19 0.275 0.005 12.78rtO. 17 0.2Ï3~0.004 12.5550. 18 0.'21&0.004 12.84=0.22 0.2Ïf 0.005 10.99k0. 15 0.36f 0.002 10.94kO. 16 0.35*0.002 10.98=0.15 0.36f 0.003 10.94~kO. 15 0.36zi0.003 10.9kiO.1-3 0.3510.002 10.96~k0.15 0.36i0.002 10.9610.16 0.36f 0.002 10.92=0. 16 0.3510.003 10.95~k0.16 0.36k0.003
Table 7: 95% Confidence Interval for TBX = 5 min.; -AD = h i f o r m ; Jobshop; Balanced.
Performance Measures 1 reat ment
6 /E/F/X/ l / l5 LQAI-SS LQlf-SUJ
LQ3f-QSXS MRT-XS
1IRT-SCJ 1IRT-QSSS
SIO-XS SIO-XLJ
SIO-QSXS LQlf-XS
LQlI-SLJ LQlf-QSKS
L\IRT-3s 1IRT-XLJ
XIRT-QSXS SIO-SS
SIO-SCJ SIO-QSXS LQl1-SS
LQlI-SUJ LQl1-QSXS
11R.T-SS LIRT-XCJ
hIRT-QSSS SIO-5s
SIO-SUJ SIO-QSXS LQM-SS
LQL\f-SUJ LQ3Z-QSXS
hl RT- S S h1RT-Xu J
MRT-QSXS SIO-XS
SIO-KUJ SIO-QSXS
Table 9: 95% Confidence Interval for TBA = 6 min.: AD = Esponential; Flowshop; Baianced.
Treat ment
6/E/F/Y/l / l5
I Itules ' Performance Measures
LQlI-SS LQ'tI-'IuJ
LQ'c1-QSSS 3IRT-SS
AIRT-NCJ 11 RT-QSSS
SIO-3s SIO-XCJ
SIO-qsss LQ>I-XS
LQ3I-XCJ LQ31-QS'iS
hIRT-YS hIRT-KC J
MRT-QSYS SIO-SS
SIO-SV J SIO-QSKS LQl1-XS
LQM-SUJ LQl1-QSXS
LIRT-XS SIRT-NCJ
NRT-QSXS SIO-NS
SIO-NU J SIO-QSSS LQbI-,US
LQkI-'J'C J LQM-QSYS
hl RT- N S hIRT-KC'J
MRT-QSYS SIO-3s
SIO-SC'J SIO-QSXS
Table 10: 93% Confidence Interval for TB;\ = 6 min.; AD = Esponential; Flowshop; Unbalanced.
Treatment Rules
LQhI-XS LQhI-SL7J LQ'LI-QSNS
URT-SS 'r IRT-SCJ
l f RT-QSXS STO-XS
SIO-YCJ SIO-QSSS LQhl-SS
LQlI-3CJ LQLr-gsxs
IIRT-SS hIRT-SC'J
hIRT-QSXS SIO-3s
SIO-3U.J SIO-QSYS LQlI-SS
LQM-XC J LQU-QSXS
NRT-XS 3IRT-SC J
MRT-QSYS SIO-YS
SIO-SC J SIO-gsxs LQhI-KS
LQbI-YUJ LQs1-QSXS
MRT-KS 1IRT-NU J
RT-QSKS SIO-NS
SIO-Xu-J SIO-QSNS
Performance Measures
Table 11: 95% Confidence Interval for TBA = 6 min.; AD = Exponential: Jobshop; Balanced.
1 Treatment Rules Performance Measures i i
SIO-XLTJ 77.09&1.89 12.74~k0.40 0.36~k0.00-5 SIO-QSYS 76.941k1.93 12.73~k0.33 0.36-C-0.005 LQM-SS 71 1 1 . 3 1 1 7 7 0 . 3 0.34zk0.004
LQhI-'J'C J 70.43Zk1.68 1 1.65IO.36 O-343~0.003 LQII-QSNS Tl.20Zk1.86 11.78I0.39 0.341=0.004
MRT-XS 71.94-1.66 1 1.90=0.37 0.34~0.003 MRT-XC'J 71 -94I1.65 11.90=0.36 0.31~0.003
MRT-QSXS 72.0jI1.75 1 1.91=0.36 0.34&0.002
SIO-XL.J SIO-QSYS LQ'LL-NS
LQA.1-SC J LQhI-QSSS
lIRT-NS ,\.IRT-SC J
'LIRT-QSXS sro-sis
SIO-XLï J SIO-QSNS LQhl-XS
LQM-SUJ LQU-QSSS
LI RT-XS MRT-NL J
MRT-QSNS
SIO-NU J SIO-OSNS
Table 12: 95% Confidence Interval for TBA = 6 min.; AD = Esponential; Jobshop: LTnbalanced.
Treatment - -
Rules 1 Performance Measures
1 - 66.16*0.90 11RT-QSXS 66.65k0.94
SIO-SS 65.7'0I0.87 SIO-SU3 65.56k0.79
SIO-QSXS 63.81&0.86 LQh1-SS 58.60k0.90
LQhI-XCJ 58.39k0.89 LQ'\l-QSXS 58.593~0.90
hIRT-KS 59.63~k0.84 f R U 59.60&0.78
LIRT-QSSS 59.65k0.83 SIO-XS 58.833~0.86
SIO-SLJ 58.933~0.81 SIO-QSSS 58.89k0.86 LQLI-SS 50.283~0.30 L I - J 49.79k0.32
LQ11-QSSS 1 50.3030.29
SIO-NCJ 49.i3i-0.33 1 8.303~0.08 SIO-QSNS 50.04d~0.27 8.35~k0.07
Table 13: 95% Confidence Interval for TB-1 = 6 min.; -4D = Uniform; Flowshop; Balanced.
Treat ment - -
Performance h.1 easures
LQAI-ss LQlI-XCJ
LQN-QSXS MRT-NS
URT-YIIJ URT-QSXS
SIO-SS SIO-MJJ
SIO-QSXS LQLI-';S
LQ3I-XLJ LQU-QSXS
blRT-YLLJ 31RT-QS SS
SIO-3.3 SIO-SL'J
SIO-QSXS
SIO-YUJ 49.83&0.32 SIO-QSKS 50.27k0.35 LQM-KS 44.181k0.26
LQXI-YL'J 44. 14&0.28 LQM-QSKS 4-1- 16~k0.26
MRT-YS 43.97h0.30 3IRT-hTJ 43.92ï0.27
Table 14: 95% Confidence Interval for TBA = 6 min.; AD = ljniform; Flowshop; Unbalanced.
Rules
LQM-3s LQN-3U.J
LQJI-QS'iS JIRT-SS
h,lRT-SC J LlRT-QSNS
SIO-SS SIO-3L.J
SIO-QSSS LQhI-SS
LQII-SCJ LQ'rfI-QSXS
1IRT-SS 'CIRT-XCJ
SIRT-QSYS SIO-YS
SIO-XCJ SIO-QSKS LQ'cl-SS
LQhl-PX J LQS1-QSKS
11RT-YS liRT-XC'J
h1RT-QSXS SIO-3s
SIO-SCJ SIO-QSXS LQM-YS
LQhI-PX J LQh4-QSKS
ILI RT-YS h1RT-SU J
'VIRT-QSNS SIO-YS
SIO-NUJ SIO-QSKS
Performance Measures
Table 15: 95% Confidence Interval for TB-\ = 6 min.; AD = Uniform; Jobshop: Balanced.
Treatment 1 Rules 1 Performance lleasures
AIRT-SCJ
SIO-3K.J SIO-QSXS
lIRT-SCJ AIRT-QSXS
SIO-SCJ
MRT-3C.J LIRT-QSSS
SIO-YS SIO-SUJ
SIO-QSXS 6/L/J/Y/2/20 LQM-NS
LQlI-NUJ LQhI-QSXS 14 RT- N S
1IRT-NU J MRT-QSXS
SIO-I\;S SIO-NCJ
SIO-QSNS C Table 16: 95% Confidence Interval for TB-4 = 6 min.; AD = Uniforml Jobshop: U n balanced.
Appendix C -Best Combination of Machine and AGV Dispatching Rules for the 64
Treatments against Flowtime, Consistency of Output and Efficient Op-
eration of AGVs.
SI0 b-u J SIO-YCJ SI0 SIO-SS, SIO-SCJ
KL.J MRT-X.J. SIO-ScJ
Treatment Combinat ions
5 /E /F /S / l / l 5 j /E/F/S/1/20 5/E/F/S/2/15 5/E/F/S/2/20 5 /E /F / l - / l / l 5 5/E/F/\-/I/?O 5/E/F/k-/2/15 .J,IE/F/Y/2/20 5 /E/ . J /S / l / l j S /E/J /S / l /?O
hIRT, SI0 l,lRT-XLJ1 SIO-SUJ hlRT-YUJ: SIO-XS
1,IRT-XUJ. SIO-SUJ LIRT-YC'J. SIO-YL'J
.5/E/J/S/2/15 1IR.T-SLJ. SIO-NCJ
41/C Scheduling Rule
SI0 SI0
SIO-YS, SIO-SUJ, SIO-QSSS
1,IRT-XL'CiJ, SIO-NUJ
NUJ
AGV Dispatching Rule
?Jl J
NCJ
Table 1: Best combination of rules based on flowtime criteria for TBA = 5 min.
hI/C-..AG\* Rule I 1
1IRT-ScJ, SIO-NCJ
11RT-SLJ: SIO-NCJ
SIO-SS, SIO-XUJ SIO-SUJ
M/C-AG\' Rule Treatmenr Combinat ions
6/E/F/X/l/l5 6/ E/F/S/ 1/20 6/E/F/S/2/15 6/E/F/S/2/20 6/E/F/Y/l / l5 6/E/F/Y j1/20 6/E/F/\-12/15 6/E/F/\-/7/20
BI/C Scheduling Rule
S I0
SIO-SS. SIO-SCJ. SIO-QSSS 6/E/J/S/l/l.5 S I 0 6/E/J/N/1/20 / S I 0 LQSI 6/E/J/N/2/13 6/E/J/'ri/2/20 6/E/J/Y/l / l5
i S I 0
6/E/J/E'/1/20 S I 0 6/E/J/Y/2/15 6/E/J/Y/2/20 6/C/F/N/l / l3 LQM 6/C/F/K/1/?0 L Q l a 1
6/L./J/S/2/15 6/C/J/S/2/20 6/U/J/Y/1/15 6/U/J/Y/1/20
LQSI-YS, LQhI-SL'J:
LQM LQM, SI0
LQM-QSSS LQhI-SS, LQM-SCJ,
LQh.1-QSXS
Table 2: Best combination of rules based on flowtime criteria for TBA = 6 min.
105
L Q ~ I LQ~I-XCJ. LQ~I-QSXS LQM LQILI-YUJ, LQ11-QSSS
A-L- J LQN-SC'J LQM LQ>,l-SL-.J. LQ3.1-QSSS 1IRT bIRT-XS
LQN: SIRT I
LQlI-SS: bIRT-XS
r
Treatment Combinations
L Q l I LQhI-YS, LQhl-QSSS MRT XIRT-'J'L J XIRT hLRT-QSSS
Table 3: Best combination of rules based on consistency of output for TB-\ = 5 min.
hI/C Scheduling Rule
AG\' Dispatching Rule
M/C-.AG\- Rule
Treatment 1 XI/C Scheduling 1 ;\GY Dispatching 1 II/C-AG\- Rule
Table 4: Best combination of rules based on consistency of output for TBA = 6 min.
Rule Combinations 1 Rule 6 / E / F / / l / 6/E/F/-\'/1/20 6/E/F/X/2/15 6/E/F/K/2/20 6/E/F/>-/I/l5 6/E/F/E-/1/2O 6/E/F/Y/2/15 6/E/F/Y/2/20 6/E/J/Y/l/l5 6/E/.J/Y/l/20 6/E/J/K/2/1.5 6/E/J/&'/2/20 6/E/J/\-/ l / l5 6/E/J/Y/1/20 6/E/J/Y/2/15 6/E/J/E'/2/20 6 / / F / l / l 6/L/F/N/1/20 6/C/F/X/2/15 6/U/F/N/2/20 6/C/F/Y/l/l5 6/U/F/Y/1/20 6/L-/F/Y/2/15 6/L/F/U/ZpO 6/G/J/S/ l / l5 6/C/J/N/1/20 6/C/J/N/2/15 6/C/J/N/2/20 6/L/J/\-/1/15 6/C/J/\i/1/20 6/C/J/Iv/2/l5 6/C/J/Y/2/20
1 LQlf, MRS
L Q l l
LQXI. SIRT
MRT
MRT, S I0
LQM. SIRT LQU. SIRT
L Q M
MRT
L Q !VI
LQkI
Combinat ions 5/E/F/Y/l/l5 j /E /F/ N/1/20
Treatment
-, Rule
LQAI? A,IRT
LQM, MRT 1 NUJ
SI/C Scheduling 1 .AG\; Dispatching Rule X C J KCJ KT,. J ?XJ 5 L- .J XLJ 5L-J KLTJ
LQU, 181RT
LQAI, 1,IRT LQlL MRT
LQM. LIRT LQ111, MRT
LQM-NCJ, 'LIRT-NL.J LQXI-5L-J: 5,IRT-KCTJ
LQ'r 1-SLLJ: URT-YCJ, SIO-XCJ LQSI-SUJI 11 RT-NL-J: SIO-Sl-.-.J
LlRT-XU J LQhI-SCJ, X.IRT-SUJ
LQ'r 1-SLJ, XIRT-'J'LTJ'J? SIO-XLJ LQhI-XUJ, AIRT-XCJ. SIO-3L.J
hl /C--AGI- Rule
XLÏ J NL7J YU J NUJ ,ù"L'J XUJ YLLJ NUJ YCJ XLÏJ NUJ
LQM-XLJ, MRT-NCJ. SIO-YLJ MRT-NEJ: SIO-XCJ
LQlI-NUJ, LIRT-NUJ LQhI-NCJ. AIRT-YuJ
LQhI -WJ : 1IRT-SC'J. SIO-XCJ LQ&I-Sli'J? 31RT-SUJ: SIO-YLJ
LQhI-NUJ, 1lRT-YCJ LQhI-NUJ. MRT-XLJ
LQhI-XUJ. A'IRT-KC'J. SIO-YCJ LQhI-KUJ. kIRT-XUJ. SIO-YCJ
LQhI-YUJ: MRT-XC'J LQ'r I-NUJ, hIRT-NC'J
LQM-XuJ. hlRT-NUJ. SIO-NL J LQhI-WJ. hIRT-NUJ. SIO-YC'J
Table 5: Best combination of rules based on efficient operation of AGVs for T B A = 5 min.
Treatment Combinat ions
SLJ KL7.J
M/C Scheduling Rule
AG\' Dispatching / h I / C - - 4 G V ~ u l e Rule
L Q M NUJ J
6/E/J/ \ r - / l /20 6 /E/J /Y/2/13 6/E/J/Y/2/20 6 / / F / / l / l 6 /L/F/K/1/20 6 /C/F/K/3/13 6 /C /F /S /2 /20 6 / / F / / l / l
LQLI-SLJ LQhI-NCJ. I IRT-SCJ ,
SIO-NCJ LIRT-KLÏJ. SIO-SCJ
L Q l I - S u J LQhI-SUJ LQl.1-NCJ
LQ31: MRT NUJ h l RT- X L- J LQM LQl'l-NS, LQSl-NCJI
L Q l l , 5 IRT LQhl , M R T
LQM, SIRT
SC'J LQhI-XUJ, MRT-NUJ, SIO-XUJ
- -- -
Table 6: Best combination of rules based on efficient operation of AGVs for TB.-\ = 6 min.
XC'J ?KJ SCJ
XJ s~r J
X J
LQl,I-XC;Jr MRT-NCJ LQ'LI-XCJ, IIRT-SL'J LQhI-NUJ, LIRT-KLJ LQlI-XUJ. 1IRT-NL.J
LQSI-SKJ LQLI-XE J: !VIRT-XC J LQhI-NLJ? lsIRT-XuJ