Table Of ContentLecture Notes in Economics
and Mathematical Systems 546
Founding Editors:
M. Beckmann
H. P. Ktinzi
Managing Editors:
Prof. Dr. G. Fandel
Fachbereich Wirtschaftswissenschaften
Fernuniversitat Hagen
Feithstr. 140/AVZ II, 58084 Hagen, Germany
Prof. Dr. W. Trockel
Institut fur Mathematische Wirtschaftsforschung (IMW)
Universitat Bielefeld
Universitatsstr. 25, 33615 Bielefeld, Germany
Editorial Board:
A. Basile, A. Drexl, H. Dawid, K. Inderfurth, W. Ktirsten, U. Schittko
Daniel Quadt
Lot-Sizing and Scheduling
for Flexible Flow Lines
~Springer
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ISBN 978-3-540-22325-2 ISBN 978-3-642-17101-7 (eBook)
DOI 10.1007/978-3-642-17101-7
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To whom it may concern
Preface
Das schonste GlUck des denkenden M ens chen ist, das
Erforschliche erforscht zu haben und das Unerforschliche
ruhig zu verehren
JOHANN WOLFGANG VON Gm~THE
In the sense of Goethe, I hope this book helps to shift the fine line between the
inaccessible and the explorable a little bit in the direction of the latter. It has
been accepted as a doctoral dissertation at the Faculty of Business Admin
istration and Economics of the Catholic University of Eichstatt-Ingolstadt,
Germany, and has been a great pleasure to write~at least most of the time.
At the other times, the following people helped me to get around the moun
tains that seemed too high to climb:
First of all, these were my parents, whom I thank for their continuing
support. This 'thank you' is extended to my brothers Marcel and Dominik
and of course to Angelika, who has strengthened me with love through the
sometimes arduous campaign. Further, I thank my academic advisor Prof. Dr.
Heinrich Kuhn and my colleagues Dr. Georg N. Krieg and Florian Defregger
for many fruitful discussions and helpful thoughts. I also thank Prof. Dr. Klaus
D. Wilde for refereeing the thesis.
Many people have contributed indirectly to this book, mostly by simply
making my life worth living: In this sense, a big thank you to [email protected]
and friends, the Gospel Disco, the PennState class of '98, the 'KCilner Karne
val', and alle Vogelfreien dieser Welt. Further, I thank my 'new' friends from
Ingolstadt, wherever their life has led them in the meantime. I also thank
Alex for some guiding light and David, Eric, Fran, John and Rob from the
'Hooters' for some great music and even better concerts! Finally, a credit to
Pat Lawlor and everybody else involved in designing the pinball 'Twilight
Zone'. The quotes throughout this book are taken from this pinball.
I wish the reader an exciting and interesting time with this book~don't
be scared by science!
Ingolstadt, May 2004 Daniel Quadt
This preface contains quotes by the Hooters, the Rod Rockers, Soulsister, BHick 1"0088 and John Wutts/Fischcr-Z.
Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Lot-Sizing and Scheduling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2
1.2 Flexible Flow Lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4
1.3 Characteristics of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Scope and Outline of the Study .... . . . . . . . . . . . . . . . . . . . . . . . 9
2 Lack of Solution Procedures in the Literature ............. 11
2.1 Lot-Sizing Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12
2.2 Scheduling Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13
2.2.1 Branch&Bound Procedures. . . . . . . . . . . . . . . . . . . . . . . .. 13
2.2.2 Local Search and Metaheuristics .................... 15
2.2.3 Stage Decomposition Approaches .................... 16
2.2.4 Job-Oriented Procedures. . . . . . . . . . . . . . . . . . . . . . . . . .. 20
2.2.5 (Sequential) Loading and Sequencing Algorithms. . . . .. 21
2.3 Summary and Conclusion ................................ 22
3 An Integrative Solution Approach . . . . . . . . . . . . . . . . . . . . . . . .. 23
4 Phase I: Bottleneck Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29
4.1 Lot-sizing and Scheduling on Parallel Machines. . . . . . . . . . . . .. 30
4.2 Literature Review .............. . . . . . . . . . . . . . . . . . . . . . . . .. 35
4.2.1 Back-Order Literature .. . . . . . . . . . . . . . . . . . . . . . . . . . .. 36
4.2.2 Setup Carry-Over Literature. . . . . . . . . . . . . . . . . . . . . . .. 37
4.2.3 Parallel Machines Literature. . . . . . . . . . . . . . . . . . . . . . .. 41
4.3 Standard Models with Extensions ......................... 44
4.3.1 Capacitated Lot-Sizing Problem with Linked Lot-Sizes
(CLSPL) ......................................... 44
4.3.2 CLSPL with Back-Orders and Parallel Machines
(CLSPL-BOPM) .................................. 45
X Contents
4.3.3 Capacitated Lot-Sizing Problem with Sequence
Dependent Setups, Back-Orders and Parallel Machines
(CLSD-BOPM) ................................... 47
4.4 Solution Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 49
4.4.1 A Novel Heuristic Model ........................... 50
4.4.2 Solution Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61
4.4.3 Rolling Planning Horizon. . . . . . . . . . . . . . . . . . . . . . . . . .. 75
4.5 Computational Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 77
4.5.1 Effect of Problem Characteristics. . . . . . . . . . . . . . . . . . .. 77
4.5.2 Effect of Capacity Adjustment and Time Limit ........ 102
4.5.3 Effect of Problem Size ............................. 110
4.6 Summary ............................................... 122
5 Phase II: Schedule Roll-Out ............................... 125
5.1 Premises and Scope ...................................... 125
5.2 Scheduling Non-Bottleneck Production Stages ............... 127
5.2.1 Step 1: Batching and Machine-Assignment ............ 127
5.2.2 Step 2: Generation of Machine/Time Slots ............ 132
5.3 Two Remarks on the Resulting Schedule ................... 134
5.4 Summary ............................................... 136
6 Phase III: Product-to-Slot Assignment .................... 137
6.1 Goal Trade-Off .......................................... 138
6.2 Genetic Algorithms ...................................... 139
6.3 Solution Procedure: Two Nested Genetic Algorithms ......... 141
6.3.1 Setting Target Values .............................. 142
6.3.2 The Inner Genetic Algorithm: Creating a Product
Schedule Using the Target Values ................... 145
6.3.3 The Outer Genetic Algorithm: Calculating New
Target Values ..................................... 165
6.4 Computational Results ................................... 167
6.4.1 Parameter Optimization ............................ 167
6.4.2 Effect of Problem Characteristics .................... 177
6.5 Summary ............................................... 186
7 An Illustrative Example ................................... 187
7.1 Data of the Example ..................................... 187
7.2 Solution after Phase I .................................... 189
7.3 Solution after Phase II ................................... 189
7.4 Solution after Phase III .................................. 190
8 An Application in the Semiconductor Industry .. .......... 195
8.1 Semiconductor Process Flow .............................. 195
8.2 Problem Specifics and Dimensions ......................... 197
8.3 Modeling Assumptions ................................... 198
Contents XI
8.4 Short-Term Production Planning .......................... 199
8.5 Medium-Term Capacity Planning .......................... 199
9 Summary and Conclusions ................................. 203
List of Abbreviations .......................................... 209
List of Symbols ................................................ 211
References ..................................................... 217
List of Figures
1.1 Lot-sizing and scheduling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4
1.2 Schematic view of a flexible flow line. . . . . . . . . . . . . . . . . . . . . . .. 5
1.3 Relationship between products and product families .... . . . . . . 7
1.4 Entity-Relationship Model of the problem. . . . . . . . . . . . . . . . . . . 8
3.1 Lotsizing and scheduling approach for flexible flow lines. . . . . .. 24
3.2 Decomposition of the problem into three planning phases at
different aggregation levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 25
4.1 Inventory holding and back-ordering of products ............. 33
4.2 Setup carry-over ......................................... 33
4.3 Parallel machines and setup carry-over constitute a different
lot-sizing problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 34
4.4 Capacity over- and underestimation in the heuristic model. . . .. 51
4.5 Solution not satisfying premises l' and 2' . . . . . . . . . . . . . . . . . . .. 57
4.6 'Ifansformed solution .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 57
4.7 Initial and transformed solution with leftover capacity ........ 57
4.8 Lot-sizing procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 62
4.9 A run of the lot-sizing procedure without period backtracking.. 63
4.10 Scheduling procedure overview. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 64
4.11 Scheduling procedure (Step 1): Machines using setup carry-over 65
4.12 Scheduling procedure (Step 2): Full machines with setup ...... 65
4.13 Lot-sizing procedure with period backtracking ............... 72
4.14 Example of the period backtracking algorithm ............... 73
4.15 Lot-sizing procedure with period backtracking and capacity
adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 74
4.16 Effect of time limit on cost ratio for large test problems ....... 105
4.17 Effect of time limit on computation time for large test
problems, non-CA procedures .............................. 107
4.18 Effect of time limit on computation time for large test
problems, CA procedures .................................. 107
XIV List of Figures
4.19 Effect of capacity adjustment on cost ratio for large test
problems ................................................ 108
4.20 Effect of capacity adjustment on computation time for large
test problems ............................................ 108
4.21 Effect of varying the number of products on cost ratio ........ 113
4.22 Effect of varying the number of products on computation
time, non-CA procedures and CLSPL 10 min ................. 114
4.23 Effect of varying the number of products on computation
time, CA procedures and CLSPL 300 min ................... 114
4.24 Effect of varying the number of periods on cost ratio .......... 115
4.25 Effect of varying the number of periods on computation time,
non-CA procedures and CLSPL ............................ 116
4.26 Effect of varying the number of periods on computation time,
CA procedures and CLSPL ................................ 116
4.27 Effect of varying the number of machines on cost ratio ........ 119
4.28 Effect of varying the number of machines on computation time. 119
5.1 Schedule for all production stages stretched over several
original period boundaries ................................. 126
5.2 Schedule roll-out: Equal throughputs on all stages ............ 127
5.3 Scheduling stages other than the bottleneck stage ............ 130
5.4 Cyclic production ........................................ 130
5.5 Sub-procedure to load machines with cyclic production ........ 133
5.6 Generation of product family machine/time slots for all
production stages ........................................ 134
5.7 Connection between the number of parallel machines and the
throughput .............................................. 135
5.8 Waiting times of jobs and idle times of machines ............. 135
6.1 Trade-off between number of setups and flow time ............ 138
6.2 General structure of a Genetic Algorithm .................... 140
6.3 Overview of the product scheduling procedure ............... 142
6.4 Overview of the target value calculation ..................... 144
6.5 Algorithm to calculate the target number of setups for each
product ................................................. 144
6.6 Scheduling products on stage S resembles a two-dimensional
packing problem ......................................... 147
6.7 Example of the inner Genetic Algorithm's deterministic
loading procedure for stage S: Loading fewer than the target
number of machines ...................................... 149
6.8 Example of the inner Genetic Algorithm's deterministic
loading procedure for stage S: Loading less than the target
batch-size ............................................... 150
6.9 Inner Genetic Algorithm: Deterministic loading procedure for
the stage with the largest number of parallel machines (stage S) 151
