Morlock / Schwindt / Zimmermann Perspectives on Operations Research

Essays in Honor of Klaus Neumann
2006
ISBN: 978-3-8350-9064-4
Verlag: Deutscher Universitätsverlag
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 447 Seiten, eBook

This volume presents state-of-the-art models, algorithms, and applications of quantitative methods in management and economics. The papers are clustered into four parts, focusing on optimization issues, applications of Operations Research in production and service management, applications of Operations Research in logistics, and interdisciplinary approaches.

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.

Zielgruppe

Research

Autoren/Hrsg.

Morlock, Martin

Zimmermann, Jürgen

Schwindt, Christoph

Trautmann, Norbert

Inhaltsverzeichnis

1;Preface;7
2;Contents;10
3;Overview of Klaus Neumann's Research;13
3.1;1 Introduction;13
3.2;2 Control Theory and Dynamic Programming;13
3.3;3 GERT Networks;15
3.4;4 Resource-Constrained Project Scheduling;17
3.5;5 Selected Applications;19
3.6;References;21
4;Part I Optimization;27
4.1;Matrices in Shop Scheduling Problems;29
4.1.1;1 Introduction;29
4.1.2;2 Basic Notations;30
4.1.3;3 Graphs and Matrices for Shop Problems;31
4.1.4;4 On Sequences in Shop Problems;41
4.1.5;5 Generalization of the Model;44
4.1.6;6 LiSA: A Library of Scheduling Algorithms;47
4.1.7;References;51
4.2;Saddle Points from the Geometric Point of View;55
4.3;Nachbarschaftssuche bei mehrkriteriellen Flow Shop Problemen;59
4.3.1;1 Einleitung;59
4.3.2;2 Nachbarschaftssuche im Alternativenraum;64
4.3.3;3 Nachbarschaftssuche im Ergebnisraum;69
4.3.4;4 Ausblick;77
4.3.5;Literatur;78
4.4;The Solution of a Generalization of a Bayesian Stopping Problem of MacKinnon;81
4.4.1;1 Introduction;81
4.4.2;2 The Model for a Binary Bayesian Problem;83
4.4.3;3 Solution of the Generalization of MacKinnon's Problem;91
4.4.4;References;104
4.5;A Remark on the Formulation of Dual Programs Based on Generalized Convexity;105
4.5.1;1 Introduction;105
4.5.2;2 Generalized Convexity;107
4.5.3;3 Augmented Lagrangians;109
4.5.4;4 Duality;114
4.5.5;5 The Dual Program;116
4.5.6;References;120
5;Part II Operations Research in Production and Service Management;123
5.1;An Application of Markov Decision Processes to the Seat Inventory Control Problem;125
5.1.1;1 Introduction;125
5.1.2;2 The Decision Model;127
5.1.3;3 Assumptions;131
5.1.4;4 Optimality of a Booking-Limit Rule;132
5.1.5;5 An Application to Standard Models;134
5.1.6;6 Examples of a Random Environment;137
5.1.7;References;139
5.2;Immaterielle Input-Output-Systeme;141
5.2.1;1 Input-Output-Systeme;141
5.2.2;2 Immaterielle Input-Output-Systeme;142
5.2.3;3 Dienstleistungen versus immaterielle Input—Output—Systeme;147
5.2.4;Literatur;148
5.3;Audit-Staff Scheduling by Column Generation;149
5.3.1;1 Introduction;149
5.3.2;2 Problem Setting;150
5.3.3;3 Set Partitioning Model;154
5.3.4;4 Shortest Path Model;155
5.3.5;5 Test Bed;159
5.3.6;6 Computational Results;161
5.3.7;7 Summary and Conclusions;166
5.3.8;References;166
5.3.9;Appendix A: Project Scheduling-Based Mathematical Program;169
5.3.10;Appendix B: Illustrative Example;171
5.4;An MILP Modelling Approach for Shelf Life Integrated Planning and Scheduling in Scalded Sausage Production;175
5.4.1;1 Introduction;175
5.4.2;2 Case Study: Scalded Sausage Production;176
5.4.3;3 Literature Review;178
5.4.4;4 Profile of Scalded Sausage Production Regarding APS Systems;181
5.4.5;5 Numerical Results;193
5.4.6;6 Conclusions;195
5.4.7;References;196
5.5;Optimale Anpassung im Gutenberg-Produktionsmodell: Eine analytische Ermittlung der Kostenfunktion aus den Karush-Kuhn-Tucker-Bedingungen;201
5.5.1;1 Einleitung;201
5.5.2;2 Das Produktionsmodell von Gutenberg;203
5.5.3;3 Analytische Ermittlung der Kostenfunktion aus den Karush-Kuhn- Tucker-Bedingungen;207
5.5.4;4 Bestimmung der Kostenfunktion;216
5.5.5;5 Ein Beispiel;217
5.5.6;6 Schlussbetrachtung;219
5.5.7;Literatur;220
5.6;Just-in-Time Production of Large Assemblies Using Project Scheduling Models and Methods;223
5.6.1;1 Introduction;223
5.6.2;2 The Assembly Scheduling Problem;223
5.6.3;3 The Resource- Constrained Project Scheduling Problem;227
5.6.4;4 Modeling and Solving the ASP with the RCPSP;230
5.6.5;5 Impact and Conclusions;233
5.6.6;References;234
5.7;A Cyclic Approach to Large-Scale Short-Term Planning of Multipurpose Batch Plants;237
5.7.1;1 Introduction;237
5.7.2;2 Cyclic Batching;239
5.7.3;3 Cyclic Batch-Scheduling and Concatenation;241
5.7.4;4 Experimental Performance Analysis;247
5.7.5;5 Conclusions;248
5.7.6;References;248
5.8;Models and Methods for Workforce Scheduling: An Application to Casino Operations;251
5.8.1;1 Introduction;251
5.8.2;2 Problem Formulation;252
5.8.3;3 Solution Procedures;259
5.8.4;4 Conclusions;264
5.8.5;References;264
6;Part III Operations Research in Logistics;267
6.1;Pile Problems and Their Mathematical Treatment;269
6.1.1;1 Introduction;269
6.1.2;2 The Special Case of Chain Pile Problems;272
6.1.3;3 Solvability and Complexity of Pile Problems;274
6.1.4;4 Solving Pile Problems;278
6.1.5;5 Non-Unique Pile Problems;282
6.1.6;6 Concluding Remarks;287
6.1.7;References;288
6.2;Risk and Safety Stock Management in Production Planning and Inventory Control with Stochastic Demand and Yield;289
6.2.1;Abstract;289
6.2.2;1 Demand and Yield Risk in Production Planning and Control;289
6.2.3;2 Insights from Stochastic Inventory Control;292
6.2.4;3 Yield Risk and Safety Stock Under Uniform Yield and Demand;294
6.2.5;4 General Insights into the Yield Risk Impact;298
6.2.6;5 Yield Risk Management by Linear Control Rules;300
6.2.7;6 Conclusions;303
6.2.8;References;303
6.3;Economies of Scale in Hub &: Spoke Network Design Models: We Have It All Wrong;305
6.3.1;1 Traditional Models for Hub & Spoke Network Design;305
6.3.2;2 Existing Approaches to Represent Economies of Scale;309
6.3.3;3 Alternative Model Formulations;313
6.3.4;4 Numerical Examples;319
6.3.5;5 Conclusion;325
6.3.6;Acknowledgement;326
6.3.7;References;327
6.4;A Stackelberg Equilibrium Model for Supply Chain Inventory Management;331
6.4.1;Abstract;331
6.4.2;1 Introduction;331
6.4.3;2 The Model and Preliminaries;333
6.4.4;3 Main Results;338
6.4.5;4 Conclusions;348
6.4.6;References;348
6.5;Das Potenzial von Operations Research in Transport und Verkehr;351
6.5.1;1 Einführung;351
6.5.2;2 OR von Anfang an;351
6.5.3;3 Enge Kontakte zu Hochschulen;352
6.5.4;4 Traffic, Mobility und Logistics: OR als starke Basis;352
6.5.5;5 Neue Chancen gegen Staus;355
6.5.6;6 Integrierte Systeme halten uns mobil;356
6.5.7;7 Verkehrsmeldungen aus dem fließenden Verkehr - damit der Verkehr im FIuss bleibt;358
6.5.8;8 Neue Kartentechnologie teilt die Welt in Kacheln ein;359
6.5.9;9 OR - heute und in Zukunft;360
7;Part IV Interdisciplinary Dimensions;363
7.1;Evolution of Conventions in Populations with Local Interaction Structures;365
7.1.1;1 Introduction;365
7.1.2;2 The Model;369
7.1.3;3 Experiments;376
7.1.4;4 Conclusions;385
7.1.5;References;387
7.2;Empirical Examination of Operational Loss Distributions;391
7.2.1;1 Introduction;391
7.2.2;2 Definition of Operational Risk in Finance;392
7.2.3;3 Capital Requirements for Operational Risk;392
7.2.4;4 Aggregated Stochastic Models for Operational Risk;394
7.2.5;5 Pareto aStable Distributions;398
7.2.6;6 Empirical Examination of Operational Loss Data;401
7.2.7;7 Summary;411
7.2.8;8 Acknowledgements;412
7.2.9;References;412
7.3;Fuzzy-Nutzwertanalyse und Fuzzy-AHP;415
7.3.1;1 Einleitung;415
7.3.2;2 Bestimmung des Gewichtsvektors aus einer Paarvergleichsmatrix mit Fuzzy-Ausgleichsraten;419
7.3.3;3 Alternativenauswahl mit Fuzzy-Gewichten und scharfen Teilnutzenwerten;424
7.3.4;4 Ein neues Verfahren zur Normierung der Spalten der Paarvergleichsmatrix;426
7.3.5;5 Alternativenauswahl mit Fuzzy-Gewichten und Fuzzy- Teilnutzenwerten;429
7.3.6;6 AHP-Ansatz zur Bewertung der Attribute;431
7.3.7;7 Schlussbemerkungen;433
7.3.8;Literatur;434
7.4;Piecewise Linear Bertrand Oligopoly;437
7.4.1;Abstract;437
7.4.2;1 Bertrand Oligopoly;437
7.4.3;2 The DMP Correspondence;445
7.4.4;3 An Existence Theorem;453
7.4.5;References;455
8;List of Authors;457

Overview of Klaus Neumann’s Research.- Overview of Klaus Neumann’s Research.- Optimization.- Matrices in Shop Scheduling Problems.- Saddle Points from the Geometric Point of View.- Nachbarschaftssuche bei mehrkriteriellen Flow Shop Problemen.- The Solution of a Generalization of a Bayesian Stopping Problem of MacKinnon.- A Remark on the Formulation of Dual Programs Based on Generalized Convexity.- Operations Research in Production and Service Management.- An Application of Markov Decision Processes to the Seat Inventory Control Problem.- Immaterielle Input-Output-Systeme.- Audit-Staff Scheduling by Column Generation.- An MILP Modelling Approach for Shelf Life Integrated Planning and Scheduling in Scalded Sausage Production.- Optimale Anpassung im Gutenberg-Produktionsmodell: Eine analytische Ermittlung der Kostenfunktion aus den Karush-Kuhn-Tucker-Bedingungen.- Just-in-Time Production of Large Assemblies Using Project Scheduling Models and Methods.- A Cyclic Approach to Large-Scale Short-Term Planning of Multipurpose Batch Plants.- Models and Methods for Workforce Scheduling: An Application to Casino Operations.- Operations Research in Logistics.- Pile Problems and Their Mathematical Treatment.- Risk and Safety Stock Management in Production Planning and Inventory Control with Stochastic Demand and Yield.- Economies of Scale in Hub & Spoke Network Design Models: We Have It All Wrong.- A Stackelberg Equilibrium Model for Supply Chain Inventory Managemen.- Das Potenzial von Operations Research in Transport und Verkehr.- Interdisciplinary Dimensions.- Evolution of Conventions in Populations with Local Interaction Structures.- Empirical Examination of Operational Loss Distributions.- Fuzzy-Nutzwertanalyse und Fuzzy-AHP.- Piecewise Linear Bertrand Oligopoly.

Leseproben

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.

Über Autor(innen)

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.