vii
TABLE OF CONTENTS
CHAPTER
1
TITLE
PAGE
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGEMENTS
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
xii
LIST OF FIGURES
xiv
LIST OF SYSMBOLS
xvi
LIST OF APPENDICES
xx
INTRODUCTION
1
1.1
Introduction
1
1.2
Background of the Study
1
1.3
Statement of the Problem
4
1.4
Objectives of the Study
5
1.5
Significance of the Study
5
1.6
Scope of the Study
6
1.7
Outline of the Thesis
7
viii
2
LITERATURE REVIEW
8
2.1
Introduction
8
2.2
Facility Layout Problem (FLP)
8
2.2.1
EFLP and UFLP
10
2.2.2
Basic Type of Layout
11
2.2.3
Classes of Facility Layout Problems
12
2.2.3.1 Objective Functions
12
2.2.3.2 Distance Measures
13
2.2.3.3 Layout Representations and
15
Configurations
2.2.4
2.2.5
2.3
2.4
2.2.3.4 Types of Flow Patterns
17
2.2.3.5 Nature of the Flow Data
20
Facility Layout Problem Formulation
21
2.2.4.1 Quadratic Assignment Problem
22
2.2.4.2 Quadratic Set Covering Problem
24
2.2.4.3 Linear Integer Programming Problem
24
2.2.4.4 Mixed Integer Programming Problem
25
2.2.4.5 Graph Theoretic Approach
25
Previous Work on FLP
26
Solution Methods
36
2.3.1
Exact Methods
36
2.3.2
Heuristic Methods
37
2.3.3
Composite Heuristic
40
2.3.4
Metaheuristics Methods
41
2.3.4.1 Genetic Algorithm
42
2.3.4.2 Tabu Search
45
2.3.4.3 Simulated Annealing
47
2.3.4.5 Other Approaches
57
Summary
60
ix
3
RESEARCH METHODOLOGY
61
3.1
Introduction
61
3.2
The Methodology at a Glance
61
3.2.1
63
Establishment of the Problem Statement
and Objectives (Stage 1)
3.2.2
Formulation of Mathematical Modelling
64
and Validation (Stage 2)
3.2.3
Improvement of Simulated Annealing
64
Algorithm (Stage 3)
3.2.4
Software Development (Stage 4)
65
3.2.5
Performance Measures of the Simulated
66
Annealing (Stage 5)
3.3
4
Summary
MODELLING UNEQUAL FACILITY LAYOUT
67
68
PROBLEM AND IMPROVED SIMULATED
ANNEALING ALGORITHM
4.1
Introduction
68
4.2
Problem Descriptions
68
4.3
Data Collection
76
4.4
Mathematical Modelling of the Problem
80
4.4.1
Assumptions
80
4.4.2
Decision Variables
81
4.4.3
Nomenclatures
82
4.4.4
Objective Function and Constraints
86
4.4.5
Model Validation
91
4.5
4.6
Solution Methods
92
4.5.1
Solution Representation of SUFLP
92
4.5.2
Algorithm Construction for SUFLP
93
4.5.3
Implementation of SA Algorithm
94
Software Development
97
4.6.1
.NET Framework
97
4.6.2
Microsoft Visual Studio 2008
98
x
4.6.3
Coding Style
98
4.6.4
The Software
100
4.6.5
Graphical User Interfaces
101
4.6.6
Classes
106
4.6.6.1 MethodBStuff class
106
4.6.6.2 DataAccessB class
106
4.6.6.3 CompareObjectiveFunction class
108
4.6.6.4 Acceptance class
108
4.6.6.5 RandomNumber class
109
4.6.6.6 GetTwoDept class
109
4.6.6.7 GetColumnCount class
110
4.6.6.8 GetRowCount class
111
4.6.6.9 Other classes
111
Method Implementations
112
4.6.7
4.6.7.1 Objective Function for SUFLP Model 112
4.6.8
4.7
5
4.6.7.2 Simulated Annealing Method
113
Software Validation and Evaluation
117
Summary
IMPROVED TEMPERATURE SETTING
118
119
SCHEMES IN SIMULATED ANNEALING
5.1
Introduction
119
5.2
Simple Scheme (SS)
119
5.2.1
124
Parameters Setting
5.3
Cycle Scheme (CyS)
127
5.4
Cyclic Exponential Scheme (CES)
129
5.5
Composite Scheme (CoS)
133
5.6
Summary
135
xi
6
NEW TEMPERATURE REDUCTION RULES
136
IN SIMULATED ANNEALING
6.1
Introduction
136
6.2
Cooling Factor based on Van Laarhoven
136
and Aarts (αVA)
6.3
Iteration based Van Laarhoven and Aarts (kVA)
140
6.4
Iteration based Theoretically Optimum (kTO)
145
6.5
Cooling Factor based on Theoretically
150
Optimum (αTO)
7
6.6
Parameter-less Theoretically Optimum (pTO)
153
6.7
Restricted Neighbourhood Search for kTO
160
6.8
Summary
161
CONCLUSION AND FUTURE WORKS
163
7.1
Introduction
163
7.2
Summary
163
7.3
Contributions
164
7.4
Future Works
167
REFERENCES
168
Appendices A-K
191 – 256
xii
LIST OF TABLES
TABLE NO.
TITLE
PAGE
2.1
Distance based and adjacency based objectives
13
2.2
Related works on FLP
27
2.3
Graph theoretic, construction, improvement
and hybrid algorithms
38
2.4
Related works of GA on FLP
44
2.5
Reated works of TS on FLP
46
2.6
Temperature reduction rules (Triki et al., 2005
and Boon, 2006)
53
2.7
Related works of SA on FLP
57
2.8
Related works of other approaches on FLPs
58
4.1
Details of Layout_1, Layout_2 and Layout_3 datasets
76
4.2
Layout_1 dataset
77
4.3
Layout_2 dataset
78
4.4
Layout_3 dataset
79
4.5
Blocks in each department for all the datasets
80
5.1
Summary results of various cooling factors for SS_GRR
123
5.2
Combination of parameters setting for SS_GRR
using α = 0.95
125
5.3
Summary results of all SS_GRR cases
126
5.4
Summary statistics of SS_GRR_6 for all the datasets
126
5.5
Summary statistics of SS_GRR_6 and CyS_GRR_6
for all the datasets
5.6
129
Summary statistics of SS_GRR_6, CyS_GRR_6 and
CES_GRR_6 for all the datasets
132
xiii
5.7
Summary statistics of SS _GRR_6, CyS _GRR_6,
CES_GRR_6 and CoS_GRR_6 for all the datasets
6.1
134
Combination of parameters setting for αVA_SS
using α = 0.95
138
6.2
Summary results of all αVA_SS cases
138
6.3
Summary statistics of αVA_SS_3, αVA_CyS_3,
αVA_CES_3 and αVA_CoS_3 for all the datasets
139
6.4
Summary statistics of GRR and αVA
140
6.5
Combination of parameters setting for kVA_SS
141
6.6
Summary results of all kVA_SS cases
142
6.7
Summary statistics of kVA_SS_9, kVA_CyS_9,
kVA_CES_9 and kVA_CoS_9 for all the datasets
143
6.8
Summary statistics of GRR, αVA and kVA
144
6.9
Combination of parameters setting for kTO
146
6.10
Summary results of all kTO_SS cases
147
6.11
Summary statistics of kTO_SS_9, kTO_CyS_9,
kTO_CES_9 and kTO_CoS_9 for all the datasets
148
6.12
Summary statistics of GRR, αVA, kVA and kTO
149
6.13
Summary statistics of αTO_SS_9, αTO_CyS_9,
αTO_CES_9 and αTO_CoS_9 for all the datasets
151
6.14
Summary statistics of GRR, αVA, kVA, kTO and αTO
152
6.15
Combination of parameters setting for pTO_SS
154
6.16
Summary results of all pTO_SS cases
154
6.17
Summary statistics of pTO_SS_9, pTO_CyS_9,
pTO_CES_9 and pTO_CoS_9 for all the datasets
6.18
Summary statistics of GRR, αVA, kVA, kTO,
αTO and pTO
6.19
6.20
155
156
Solution quality (deviation in %) of all the temperature
setting schemes
157
Summary results of the restricted neighbourhood search
161
xiv
LIST OF FIGURES
FIGURE NO.
TITLE
2.1
Distance measures
2.2
Relative positions of Pick-up and Drop-off (P/D)
PAGE
14
points (Welgama and Gibson, 1993)
15
2.3
Layout configurations (Chae and Peters, 2006)
17
2.4
Basic horizontal flow pattern (Francis et al., 1992)
19
2.5
Vertical flow pattern (Francis et al., 1992)
20
2.6
Location site diagram
22
2.7
A block layout constructed based on an UFLP with
grids structure
24
3.1
Overall methodology for the research
62
3.2
Flow chart for the Stage 1 of the research
63
3.3
Flow chart for the Stage 2 of the research
64
3.4
Flow chart for the Stage 3 of the research
65
3.5
Flow chart for the Stage 4 of the research
66
3.6
Flow chart for the Stage 5 of the research
67
4.1
Placement of machines A in a block
71
4.2
Different orientation of machines in blocks
72
4.3
An example of the arrangement of functional tools in
a block
4.4
An example of a department with five non-homogeneous
blocks
4.5
73
74
An example of single row floor layout with four
non-homogeneous departments
75
4.6
Vertical and horizontal orientations
82
4.7
Illustration of parameters for blocks
84
xv
4.8
Illustration of P/D parameters for blocks
4.9
An example of support tools and machines arrangement
in a block
4.10
85
91
Indices representing ten blocks assigned in the layout
follow the S-Shaped flow pattern for single row layout
93
4.11
SA algorithm implementation
96
4.12
Cartesian coordinate and Screen coordinate
99
4.13
Links from user input and output to calculations
100
4.14
Interfaces and forms connections
102
4.15
MDI interface
102
4.16
Data settings form
103
4.17
First division of real estate data
104
4.18
Second division of tools data
104
4.19
Cooling schedule cases interface
105
4.20
Floor layout (AutoLayout) interface
105
4.21
Final results for each iteration
117
5.1
Simple scheme (SS)
120
5.2
Cycle scheme (CyS)
127
5.3
Cycle scheme algorithm
128
5.4
Cyclic exponential scheme (CES)
130
5.5
Cyclic exponential scheme algorithm
131
6.1
The best solution for Layout_1 ( Z  = 28039.85)
159
6.2
The best solution for Layout_2 ( Z  = 15942.50)
159
6.3
The best solution for Layout_3 ( Z  =39452)
160
xvi
LIST OF SYMBOLS
ACO
-
Ant Colony Optimization
Ave
-
Average
CO
-
Combinatorial Optimization
FLP
-
Facility Layout Problem
EFLP
-
Equal-sized FLP
UFLP
-
Unequal-sized FLP
SA
-
Simulated Annealing
TS
-
Tabu Search
GA
-
Genetic Algorithm
QAP
-
Quadratic Assignment Problem
SSA
-
Segmented Simulated Annealing
SBL
-
Shape-based Block Layout
IP
-
Integer Programming
LIP
-
Linear Integer Programming
MIP
-
Mixed Integer Programming
NP
-
Non-polynomial
P/D
-
Pick-up and Drop-off
SFLP
-
Static Facility Layout Problem
DFLP
-
Dynamic Facility Layout Problem
non-QAP
-
non-Quadratic Assignment Problem
M
-
Machinery locations
WIP
-
Work-in-process
Exp
-
Exponential
MDI
-
Multiple Document Interface
FCL
-
Framework Base Class Library
CLR
-
Common Language Runtime
TRR
-
Temperature reduction rule
xvii
TSS
-
Temperature setting scheme
SC
-
Stopping criteria
VRL
-
Vertical Referrence Line
HRL
-
Horizontal Referrence Line
SS
-
Simple Scheme
CyS
-
Cycle Scheme
CES
-
Cyclic Exponential Scheme
CoS
-
Composite Scheme
GRR
-
Geometric Reduction Rule
αVA
-
Cooling factor based Van Laarhoven and Aarts
kVA
-
Iteration based Van Laarhoven and Aarts
kTO
-
Iteration based Theoretically Optimum
αTO
-
Cooling Factor based Theoretically Optimum
pTO
-
Parameter-less Theoretically Optimum
secs
-
Seconds
Dev
-
Deviation
W
-
Floor width
L
-
Floor length
N
-
Number of blocks
Or
-
Orientation of functional tool r  P
Lx
-
Length of the horizontal side of total floor
Ly
-
Length of the vertical side of the total floor
U x (i )
-
Length of the horizontal side of block i  N
U y (i )
-
Length of the vertical side of block i  N
r
-
Width of the functional tool r  P
r
-
Length of the functional tool r  P (where,  r   r )
1
-
Normalized weight for distance measure
2
-
Normalized weight for perimeter measure
H
-
Large value, H  Lx L y
mr
-
Distance between centroid of functional tool r  P and VRL
nr
-
Distance between centroid of functional tool r  P and HRL
xviii
er
-
Length of the horizontal side of functional tool r  P
gr
-
Length of the vertical side of functional tool r  P
pxi
-
Distance between the pick-up point of block i  N and VRL
dxi
-
Distance between the drop-off point of block i  N and VRL
py i
-
Distance between the pick-up point of block i  N and HRL
dy i
-
Distance between the drop-off point of block i  N and HRL
ers
-
Distance between functional tool r and s are to be separated
horizontally
g rs
-
Distance between functional tool r and s are to be separated
vertically
P
-
Number of total tools
Sup i
-
Number of support tools (Sup) for each block i  N
Mac i
-
Number of machines (Mac) for each block i  N
i
Argmt Sup
-
Arrangement of support tools for each block i  N
i
Argmt Mac
-
Arrangement of machines for each block i  N
i
ArgmtWIP
-
Arrangement of work-in-process (WIP) for each block i  N
Col Pri edefined
-
Predefined number of columns for each block i  N
Row i
-
Number of rows for each block i  N
ij
-
Binary variable

-
Initial permutation
k
-
Iteration

-
Cooling factor
x0
-
Initial solution
x
-
Current solution
x'
-
Neighbourhood solution
F ( xo )
-
Cost of initial solution
N (x) , Z (x' ) -
Objective value of neighbourhood solution
Z ( x0 )
-
Objective value of initial solution
Z (x)
-
Objective value of current solution
xix
Z ( x * ), Z *
-
Best objective value out of k  K iterations
Z
-
Objective value
Z b*
-
Best objective value for each b  B run
Z Ave
-
Average solution (objective values)
Z best
-
Overall best solution (objective value)
Z
-
Best objective value out of B runs
T Ave
-
Average computational time in seconds
P 
-
Probability of acceptance
T0
-
Initial temperature
Tf
-
Final Temperature
Tk
-
Temperature update coefficient
Ts
-
Tabu list size
Uk
-
Absolute value of neighbourhood solution minus current
solution
Zk
-
Current objective value
Z k 1
-
Previous objective value
C
-
Depth of the deepest local minimum
U
-
Upper bound
B
-
Number of runs
C max
-
Estimation of the maximum value of the cost function
c
-
Boltzmann’s constant

-
Change in total distance or real number

-
Random number between 0 and 1

-
Small real number
p
-
Integer value
xx
LIST OF APPENDICES
APPENDIX
TITLE
PAGE
A
Publications/Presentations
191
B
Model Validation
193
C
Software Evaluation Form
196
D
GRR Results
198
E
αVA Results
213
F
kVA Results
220
G
kTO Results
227
H
αTO Results
234
I
pTO Results
238
J
Source Code of Simulated Annealing for
245
Temperature Setting Schemes
K
Source Code of Temperature Reduction Rules
254