Multi-objective optimisation of a capacitated and dynamic multi-item inventory system using physical (-related) metaheuristics [Elektronische Ressource] / vorgelegt von Markus Albert Zizler

Description

wrIualnat.tRegensit-MOftenbhejysikevAtiausvebruarederOpti.misakultati-ovnvoMfuabidbandSeeD00ynamictorgradesMulti-NaturItemissensInhav(Drenrer.to)rySystemFusinätgIPPhhUniysicalersität(-relatedburg)orgelegtonDissertationazkusrlErerlZazlernSteingungergdmeFs2D8okRainerFWPromotio(Ph)hnskwurdeProf.hh(tüfer:amT1.umNohvIngoem2.bProf.erömm2007.eitererDieseDr.Arb(Pheitdeswurdeoangleitet1v2008onter:Prof.Dr.Dr.MorgensternIngoysik)Morgenstern.Prter:üDr.fuGnelgsaussWirtschaftenhWussPr:Prof.VTiloorsitzender:ettigProf.ysik)Dr.erminJascPromotiohaollRequipps:(Ph9.ysik)ebruar1.DasContentsPreface 51 General Introduction 91.1 History of Operations Research (OR) . . . . . . . . . . . . . . . . 101.2 OR-Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.3 Combinatorial Optimisation . . . . . . . . . . . . . . . . . . . . . 151.3.1 Basic Terms . . . . . . . . . . . . . . . . . . . . . . . . . . 151.3.2 Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . 181.3.3 Multi-Objective Optimisation . . . . . . . . . . . . . . . . 211.4 (Meta-)Heuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . 221.5 Standard Methods and Problems of OR . . . . . . . . . . . . . . . 271.5.1 Simplex Algorithm . . . . . . . . . . . . . . . . . . .

Sujets

• Physik

Informations

• Publié par: universitat_regensburg
• Publié le: 01 janvier 2008
• Nombre de lectures: 13
• Poids de l'ouvrage: 3 Mo

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Contents
Preface 5
1 General Introduction 9
1.1 History of Operations Research (OR) . . . . . . . . . . . . . . . . 10
1.2 OR-Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 Combinatorial Optimisation . . . . . . . . . . . . . . . . . . . . . 15
1.3.1 Basic Terms . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3.2 Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.3.3 Multi-Objective Optimisation . . . . . . . . . . . . . . . . 21
1.4 (Meta-)Heuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.5 Standard Methods and Problems of OR . . . . . . . . . . . . . . . 27
1.5.1 Simplex Algorithm . . . . . . . . . . . . . . . . . . . . . . 27
1.5.2 Branch & Bound - BB . . . . . . . . . . . . . . . . . . . . 28
1.5.3 Traveling Salesman Problem - TSP . . . . . . . . . . . . . 31
1.5.4 Different Problems . . . . . . . . . . . . . . . . . . . . . . 32
1.6 Simulation as Method of Optimisation . . . . . . . . . . . . . . . 34
2 Physical Optimisation 37
2.1 Spin Glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.1.1 Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.1.2 Theoretical / Experimental Results . . . . . . . . . . . . . 39
2.1.3 Mathematical Spin Glass Models . . . . . . . . . . . . . . 44
2.2 Monte-Carlo-Methods . . . . . . . . . . . . . . . . . . . . . . . . 48
2.2.1 Statistical Physics . . . . . . . . . . . . . . . . . . . . . . . 48
2.2.2 Simple Sampling . . . . . . . . . . . . . . . . . . . . . . . 49
2.2.3 Importance Sampling . . . . . . . . . . . . . . . . . . . . . 50
2.3 Optimisation Algorithms . . . . . . . . . . . . . . . . . . . . . . . 53
2.3.1 Simulated Annealing - SA . . . . . . . . . . . . . . . . . . 53
2.3.2 Threshold Accepting -TA . . . . . . . . . . . . . . . . . . 55
2.3.3 Great Deluge Algorithm - GDA . . . . . . . . . . . . . . . 56
2.3.4 Cooling Scheme . . . . . . . . . . . . . . . . . . . . . . . . 56
12 CONTENTS
3 Different Metaheuristics 59
3.1 Genetic Algorithms - GA . . . . . . . . . . . . . . . . . . . . . . . 60
3.1.1 Biological Background . . . . . . . . . . . . . . . . . . . . 60
3.1.2 Algorithmic Realisation . . . . . . . . . . . . . . . . . . . 62
3.1.3 Genetic Operations . . . . . . . . . . . . . . . . . . . . . . 68
3.1.4 Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.2 Ant Colony Algorithms . . . . . . . . . . . . . . . . . . . . . . . . 75
3.3 Tabu Search - TS . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4 Theory of Inventory Control 83
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.2 Single-Item-Models . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.2.1 Deterministic Models . . . . . . . . . . . . . . . . . . . . . 87
4.2.2 Stochastic Models . . . . . . . . . . . . . . . . . . . . . . . 92
4.3 Multi-Item-Inventories . . . . . . . . . . . . . . . . . . . . . . . . 95
4.3.1 Flaccidities of Single-Item-Models . . . . . . . . . . . . . . 95
4.3.2 Multi-Item-Models . . . . . . . . . . . . . . . . . . . . . . 96
4.4 Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.4.1 Different Types of Forecasting Methods . . . . . . . . . . . 100
4.4.2 Monitoring Forecast Systems . . . . . . . . . . . . . . . . . 105
4.4.3 (Auto-)Correlation . . . . . . . . . . . . . . . . . . . . . . 108
5 Physical Optimisation and Forecasting 111
5.1 Short Term Forecast . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.1.1 Model with Simple Deviation . . . . . . . . . . . . . . . . 111
5.1.2 Model with Value at Risk . . . . . . . . . . . . . . . . . . 113
5.1.3 Application to Grades of Soccer Players . . . . . . . . . . 114
5.2 Medium Term Forecast . . . . . . . . . . . . . . . . . . . . . . . . 118
6 Optimisation of an Inventory System 121
6.1 Implementation of an Inventory Problem . . . . . . . . . . . . . . 121
6.1.1 Variables of the Inventory System . . . . . . . . . . . . . . 121
6.1.2 Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.1.3 Standard Parameter Configuration . . . . . . . . . . . . . 124
6.1.4 Standard Configuration + Stochastic Lead Time . . . . . . 125
6.1.5 Standard Configuration + Capacity Restriction . . . . . . 125
6.2 Inventory Optimisation - Part I . . . . . . . . . . . . . . . . . . . 126
6.2.1 (s,Q) - Level Inventory Policy . . . . . . . . . . . . . . . . 126
6.2.2 (t,S) - Cycle Inventory Policy . . . . . . . . . . . . . . . . 131
6.2.3 (s,S) - Level Inventory Policy . . . . . . . . . . . . . . . . 132
6.2.4 Application of the Different Policies to Future Periods. . . 133CONTENTS 3
6.2.5 Sales Figures of a Steel Company . . . . . . . . . . . . . . 134
6.3 Inventory Optimisation - Part II . . . . . . . . . . . . . . . . . . . 136
6.3.1 Implementation of further Parameters . . . . . . . . . . . 136
6.3.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . 139
6.4 Physical Structures in Inventory Control . . . . . . . . . . . . . . 144
6.4.1 Equivalence of the Systems . . . . . . . . . . . . . . . . . . 144
6.4.2 Optimisation Methods . . . . . . . . . . . . . . . . . . . . 145
6.4.3 Equivalence of the System Variables. . . . . . . . . . . . . 145
6.4.4 Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7 Physical Optimisation by Comparison 149
7.1 Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 149
7.1.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . 149
7.1.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . 149
7.1.3 A new Optimisation Algorithm ? . . . . . . . . . . . . . . 152
7.2 Results of the Research Community . . . . . . . . . . . . . . . . . 153
7.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
7.2.2 Different Papers . . . . . . . . . . . . . . . . . . . . . . . . 154
7.2.3 Mathematical Methods . . . . . . . . . . . . . . . . . . . . 159
7.2.4 Delineation . . . . . . . . . . . . . . . . . . . . . . . . . . 160
8 Summary 161
8.1 Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
8.2 Inventory Optimisation . . . . . . . . . . . . . . . . . . . . . . . . 162
8.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
Bibliography 165
Index 173
List of Figures 174
List of Tables 175
Acknowledgements 1774 CONTENTSPreface
There are many optimisations in nature and in the world of physics. Light for
example tries to find the way with the shortest time; in mechanics the body
movement follows the restrictions of extremal principles. In biology those indi-
viduals survive that adapt most efficiently to their environment. Human beings
optimise, too: strategies in production, in the service sector or in personal affairs
are just series of optimisation actions under restrictions. But there is a funda-
mental difference between optimisation in nature and in human society: nature
knows the bestsolution automatically; whereas human beings have tomake some
calculations at first. Optimisations have a great relevance in mathematics, engi-
neering, economy, informatics and a lot of other areas: the optimal workload of
production units, the arrangement of electronic circuits on a chip or the cheap
laying of water pipes are only a few examples to mention in this respect.
The list can easiliy be extended. There is nearly no area in production and
service that is not involved. In a competitive economic system optimisations
are not only important, but even necessary, especially if there is much money
involved. It is the basic rule of a well functioning econo