Perspectives on Operations Research (eBook)

Dr. Martin Morlock ist Professor am Fachbereich für Wirtschaftswissenschaften der Universität Gießen. Dr. Christoph Schwindt ist Professor am Institut für Wirtschaftswissenschaft der Technischen Universität Clausthal. Dr. Norbert Trautmann ist Assistenzprofessor am Departement für Betriebswirtschaftslehre der Universität Bern. Dr. Jürgen Zimmermann ist Professor am Institut für Wirtschaftswissenschaft der Technischen Universität Clausthal.

Preface 7
Contents 10
Overview of Klaus Neumann's Research 13
1 Introduction 13
2 Control Theory and Dynamic Programming 13
3 GERT Networks 15
4 Resource-Constrained Project Scheduling 17
5 Selected Applications 19
References 21
Part I Optimization 27
Matrices in Shop Scheduling Problems 29
1 Introduction 29
2 Basic Notations 30
3 Graphs and Matrices for Shop Problems 31
4 On Sequences in Shop Problems 41
5 Generalization of the Model 44
6 LiSA: A Library of Scheduling Algorithms 47
References 51
Saddle Points from the Geometric Point of View 55
Nachbarschaftssuche bei mehrkriteriellen Flow Shop Problemen 59
1 Einleitung 59
2 Nachbarschaftssuche im Alternativenraum 64
3 Nachbarschaftssuche im Ergebnisraum 69
4 Ausblick 77
Literatur 78
The Solution of a Generalization of a Bayesian Stopping Problem of MacKinnon 81
1 Introduction 81
2 The Model for a Binary Bayesian Problem 83
3 Solution of the Generalization of MacKinnon's Problem 91
References 104
A Remark on the Formulation of Dual Programs Based on Generalized Convexity 105
1 Introduction 105
2 Generalized Convexity 107
3 Augmented Lagrangians 109
4 Duality 114
5 The Dual Program 116
References 120
Part II Operations Research in Production and Service Management 123
An Application of Markov Decision Processes to the Seat Inventory Control Problem 125
1 Introduction 125
2 The Decision Model 127
3 Assumptions 131
4 Optimality of a Booking-Limit Rule 132
5 An Application to Standard Models 134
6 Examples of a Random Environment 137
References 139
Immaterielle Input-Output-Systeme 141
1 Input-Output-Systeme 141
2 Immaterielle Input-Output-Systeme 142
3 Dienstleistungen versus immaterielle Input—Output—Systeme 147
Literatur 148
Audit-Staff Scheduling by Column Generation 149
1 Introduction 149
2 Problem Setting 150
3 Set Partitioning Model 154
4 Shortest Path Model 155
5 Test Bed 159
6 Computational Results 161
7 Summary and Conclusions 166
References 166
Appendix A: Project Scheduling-Based Mathematical Program 169
Appendix B: Illustrative Example 171
An MILP Modelling Approach for Shelf Life Integrated Planning and Scheduling in Scalded Sausage Production 175
1 Introduction 175
2 Case Study: Scalded Sausage Production 176
3 Literature Review 178
4 Profile of Scalded Sausage Production Regarding APS Systems 181
5 Numerical Results 193
6 Conclusions 195
References 196
Optimale Anpassung im Gutenberg-Produktionsmodell: Eine analytische Ermittlung der Kostenfunktion aus den Karush-Kuhn-Tucker-Bedingungen 201
1 Einleitung 201
2 Das Produktionsmodell von Gutenberg 203
3 Analytische Ermittlung der Kostenfunktion aus den Karush-Kuhn- Tucker-Bedingungen 207
4 Bestimmung der Kostenfunktion 216
5 Ein Beispiel 217
6 Schlussbetrachtung 219
Literatur 220
Just-in-Time Production of Large Assemblies Using Project Scheduling Models and Methods 223
1 Introduction 223
2 The Assembly Scheduling Problem 223
3 The Resource- Constrained Project Scheduling Problem 227
4 Modeling and Solving the ASP with the RCPSP 230
5 Impact and Conclusions 233
References 234
A Cyclic Approach to Large-Scale Short-Term Planning of Multipurpose Batch Plants 237
1 Introduction 237
2 Cyclic Batching 239
3 Cyclic Batch-Scheduling and Concatenation 241
4 Experimental Performance Analysis 247
5 Conclusions 248
References 248
Models and Methods for Workforce Scheduling: An Application to Casino Operations 251
1 Introduction 251
2 Problem Formulation 252
3 Solution Procedures 259
4 Conclusions 264
References 264
Part III Operations Research in Logistics 267
Pile Problems and Their Mathematical Treatment 269
1 Introduction 269
2 The Special Case of Chain Pile Problems 272
3 Solvability and Complexity of Pile Problems 274
4 Solving Pile Problems 278
5 Non-Unique Pile Problems 282
6 Concluding Remarks 287
References 288
Risk and Safety Stock Management in Production Planning and Inventory Control with Stochastic Demand and Yield 289
Abstract 289
1 Demand and Yield Risk in Production Planning and Control 289
2 Insights from Stochastic Inventory Control 292
3 Yield Risk and Safety Stock Under Uniform Yield and Demand 294
4 General Insights into the Yield Risk Impact 298
5 Yield Risk Management by Linear Control Rules 300
6 Conclusions 303
References 303
Economies of Scale in Hub & : Spoke Network Design Models: We Have It All Wrong
1 Traditional Models for Hub & Spoke Network Design
2 Existing Approaches to Represent Economies of Scale 309
3 Alternative Model Formulations 313
4 Numerical Examples 319
5 Conclusion 325
Acknowledgement 326
References 327
A Stackelberg Equilibrium Model for Supply Chain Inventory Management 331
Abstract 331
1 Introduction 331
2 The Model and Preliminaries 333
3 Main Results 338
4 Conclusions 348
References 348
Das Potenzial von Operations Research in Transport und Verkehr 351
1 Einführung 351
2 OR von Anfang an 351
3 Enge Kontakte zu Hochschulen 352
4 Traffic, Mobility und Logistics: OR als starke Basis 352
5 Neue Chancen gegen Staus 355
6 Integrierte Systeme halten uns mobil 356
7 Verkehrsmeldungen aus dem fließenden Verkehr - damit der Verkehr im FIuss bleibt 358
8 Neue Kartentechnologie teilt die Welt in Kacheln ein 359
9 OR - heute und in Zukunft 360
Part IV Interdisciplinary Dimensions 363
Evolution of Conventions in Populations with Local Interaction Structures 365
1 Introduction 365
2 The Model 369
3 Experiments 376
4 Conclusions 385
References 387
Empirical Examination of Operational Loss Distributions 391
1 Introduction 391
2 Definition of Operational Risk in Finance 392
3 Capital Requirements for Operational Risk 392
4 Aggregated Stochastic Models for Operational Risk 394
5 Pareto aStable Distributions 398
6 Empirical Examination of Operational Loss Data 401
7 Summary 411
8 Acknowledgements 412
References 412
Fuzzy-Nutzwertanalyse und Fuzzy-AHP 415
1 Einleitung 415
2 Bestimmung des Gewichtsvektors aus einer Paarvergleichsmatrix mit Fuzzy-Ausgleichsraten 419
3 Alternativenauswahl mit Fuzzy-Gewichten und scharfen Teilnutzenwerten 424
4 Ein neues Verfahren zur Normierung der Spalten der Paarvergleichsmatrix 426
5 Alternativenauswahl mit Fuzzy-Gewichten und Fuzzy- Teilnutzenwerten 429
6 AHP-Ansatz zur Bewertung der Attribute 431
7 Schlussbemerkungen 433
Literatur 434
Piecewise Linear Bertrand Oligopoly 437
Abstract 437
1 Bertrand Oligopoly 437
2 The DMP Correspondence 445
3 An Existence Theorem 453
References 455
List of Authors 457

Overview of Klaus Neumanns Research (p. 1)

Martin Morlock

Department of Economics

University of Giefien

Christoph Schwindt and Jiirgen Zimmermann

Institute for Management and Economics

Clausthal University of Technology

Norbert Trautmann

Departement fiir Betriebswirtschaftslehre

University of Bern

1 Introduction

In this paper we give a short overview of the research conducted, initiated, and supervised by Klaus Neumann from the early sixties up to present. Of course, we do not claim exhaustiveness of our review. The major themes of research can be clustered into the three main areas sketched in Sections 2 to 4:

• Control Theory and Dynamic Programming (1960s and 1970s)

• GERT Networks (1970s to 1990s)

• Resource-Constrained Project Scheduling (since 1990s)

In any of those fields, Klaus Neumann has significantly influenced the development of OR in Germany and beyond. Prom the very beginning, his research has combined solid mathematical foundation and applicability of theoretical results. The relevance of his achievements to the treatment of real-world problems has been reflected in many applied research and development projects. A selection of the projects that have been carried out in cooperation with different industrial partners is sketched in Section 5.

2 Control Theory and Dynamic Programming

Among the various approaches existing at the beginning of the 1970s in quantitative economic science, only linear programming has been successful on a broad front. For this simply structured class of static optimization problems, a commonly accepted and transparent model as well as efficient solution algorithms could be developed and applied due to the enormous advances in computer technology.

However, a multitude of practical problems in management and economics is not static in nature, but concern the analysis and optimal solution of time-dependent (decision) processes. Such problems are well-known as control problems (particularly in technology). To find an optimal solution to such problems, mainly two different approaches have been investigated: control theory and dynamic programming.

Control theory in continuous time is based substantially on an analytic approach referring to the Pontrjagin maximum principle and transversality conditions. Fundamental to dynamic programming is the so-called Bellman optimality principle^ which was developed in the 1950s by the American mathematician Richard Bellman (cf. Neumann 1969a). In particular Neumann contributed several publications to the spreading of those two optimization techniques and to their application. Together with Bauer (1969), he was one of the first who explained in a very lucid way these two fundamental approaches and their relationship.

For the acceptance and successful use of dynamic models, both their theoretical foundation and the development of numerical methods were essential. Major contributions to the latter topic, as well as descriptions of relevant applications, can be found for example in Neumann (1969a) and (1975a). Initial considerations were concerned with the question whether analog or digital computers should be used for the numerical solution of dynamic optimization problems, especially for dynamic optimization problems in continuous time (cf. Neumann and Neumann 1963). Rapid progress in the digital computer technology soon decided in favor of the digital computers.