Ebook: Algorithms and Model Formulations in Mathematical Programming

The NATO Advanced Research Workshop (ARW) "Algorithms and Model Formulations in Mathematical Programming" was held at Chr. Michelsen Institute in Bergen, Norway, from June 15 to June 19, 1987. The ARW was organized on behalf of the Committee on Algorithms (COAL) of the Mathematical Programming Society (MPS). Co-directors were Jan Telgen (Van Dien+Co Organisatie, Utrecht, The Netherlands) and Roger J-B Wets (The University of California at Davis, USA). 43 participants from 11 countries attended the ARW. The workshop was organized such that each day started with a - minute keynote presentation, followed by a 45-minute plenary discussion. The first part of this book contains the contributions of the five keynote speakers. The plenary discussions were taped, and the transcripts given to the keynote speakers. They have treated the transcripts differently, some by working the discussions into their papers, others by adding a section which sums up the discussions. The plenary discussions were very interesting and stimulating due to active participation of the audience. The five keynote speakers were asked to view the topic of the workshop, the interaction between algorithms and model formulations, from different perspectives. On the first day of the workshop Professor Alexander H.G. Rinnooy Kan (Erasmus University, Rotterdam, The Netherlands) put the theme into a larger context by his talk "Mathematical programming as an intellectual activity". This is an article of importance to any mathematical programmer who is interested in his field's history and present state.

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This book treats the problem of formulating models in mathematical programming, and thereafter solving the resulting model. Particular emphasis is placed on the interaction between the two. The topic is viewed from different angles, namely linear programming (Walter Murray), integer programming (Ellis Johnson), network flows (John Mulvey), and stochastic programming (Roger J-B Wets). The book will be very useful for any mathematics programmer or operations researcher who works in the field of real-world modelling. The book is an important part of any university course in modelling, particularly in operations research, economics and business. The book also contains an article on the origins of mathematical programming (Alexander Rinnooy Kan). This is important reading for anyone interested in the history of the field.

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This book treats the problem of formulating models in mathematical programming, and thereafter solving the resulting model. Particular emphasis is placed on the interaction between the two. The topic is viewed from different angles, namely linear programming (Walter Murray), integer programming (Ellis Johnson), network flows (John Mulvey), and stochastic programming (Roger J-B Wets). The book will be very useful for any mathematics programmer or operations researcher who works in the field of real-world modelling. The book is an important part of any university course in modelling, particularly in operations research, economics and business. The book also contains an article on the origins of mathematical programming (Alexander Rinnooy Kan). This is important reading for anyone interested in the history of the field.
Content:
Front Matter....Pages I-IX
Modeling and Strong Linear Programs for Mixed Integer Programming....Pages 1-43
Advances in Nonlinear Network Models and Algorithms....Pages 45-72
Mathematical Programming as an Intellectual Activity....Pages 73-90
The Aggregation Principle in Scenario Analysis and Stochastic Optimization....Pages 91-113
Methods for Large-Scale Linear Programming....Pages 115-137
Front Matter....Pages 139-139
Resource Constrained Assignment Problems....Pages 141-141
The Resource Constrained Spanning Tree Problem: Alternative Modelling and Algorithmic Approaches....Pages 142-143
Constructive Dual Methods for Non-Linear Discrete Programing Problems....Pages 144-144
A Decomposition Based Procedure for Production Scheduling in Job-Shops with Negligible Setup Times....Pages 145-146
An Example of a Declarative Approach to Model Creation....Pages 147-148
Optimal Solution of the Local Delivery Problem Through Minimum K-Trees....Pages 149-149
AMPL: A Mathematical Programing Language....Pages 150-151
Multiperiod Linear Stochastic Programming and a Forestry Application....Pages 152-154
A Multi-Period Network Design Problem: Model and Solution Techniques....Pages 155-156
Finite-Dimensional Variational and Quasivariational Inequalities: Algorithmic Developments and Applications in Socio-Eoonomic Planning....Pages 157-157
Stochastic Equilibrium Programming for Dynamic Oligopolistic Markets....Pages 158-159
A Dynamic Approach to Oligopolistic Market Equilibrium....Pages 160-160
Estimated Parameters in Mathematical Programming: Modelling and Statistical Issues....Pages 161-161
Modelling for Parallel Optimization....Pages 162-162
Long-Term Hydro-Thermal Coordination of Electricity Generation Through Multicommodity Network Flows....Pages 163-164
Front Matter....Pages 139-139
Equilibration Operators for the Solution of Constrained Matrix Problem....Pages 165-166
A General Dynamic Network Spatial Price Equilibrium Model with Gains and Losses....Pages 167-168
Incorporating the Concept of Internal Rate of Return in Linear and Integer Programming Models....Pages 169-169
Procedures for Solving Bottleneck Generalized Assignment Problems....Pages 170-171
Weighted Matching in Chess Tournaments....Pages 172-173
Decentralized Optimization for Structured Linear Programming Models....Pages 174-176
Transport Planning in Airborne Operations....Pages 177-177
A Hierarchical Approach to the Placement Problem....Pages 178-178
Optimisation of Oil Depletion Strategy to Satisfy Long-Term Objectives....Pages 179-179
Approaches to Optimizing Fuel Consumption in Cars....Pages 180-181
Equilibrium Definitions in Simulated Annealing: A Computational Experiment....Pages 182-183
Decomposition in Integer Programming....Pages 184-184
Computational Geometry and Low Dimensional Linear Programs....Pages 185-186
Back Matter....Pages 187-195

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This book treats the problem of formulating models in mathematical programming, and thereafter solving the resulting model. Particular emphasis is placed on the interaction between the two. The topic is viewed from different angles, namely linear programming (Walter Murray), integer programming (Ellis Johnson), network flows (John Mulvey), and stochastic programming (Roger J-B Wets). The book will be very useful for any mathematics programmer or operations researcher who works in the field of real-world modelling. The book is an important part of any university course in modelling, particularly in operations research, economics and business. The book also contains an article on the origins of mathematical programming (Alexander Rinnooy Kan). This is important reading for anyone interested in the history of the field.
Content:
Front Matter....Pages I-IX
Modeling and Strong Linear Programs for Mixed Integer Programming....Pages 1-43
Advances in Nonlinear Network Models and Algorithms....Pages 45-72
Mathematical Programming as an Intellectual Activity....Pages 73-90
The Aggregation Principle in Scenario Analysis and Stochastic Optimization....Pages 91-113
Methods for Large-Scale Linear Programming....Pages 115-137
Front Matter....Pages 139-139
Resource Constrained Assignment Problems....Pages 141-141
The Resource Constrained Spanning Tree Problem: Alternative Modelling and Algorithmic Approaches....Pages 142-143
Constructive Dual Methods for Non-Linear Discrete Programing Problems....Pages 144-144
A Decomposition Based Procedure for Production Scheduling in Job-Shops with Negligible Setup Times....Pages 145-146
An Example of a Declarative Approach to Model Creation....Pages 147-148
Optimal Solution of the Local Delivery Problem Through Minimum K-Trees....Pages 149-149
AMPL: A Mathematical Programing Language....Pages 150-151
Multiperiod Linear Stochastic Programming and a Forestry Application....Pages 152-154
A Multi-Period Network Design Problem: Model and Solution Techniques....Pages 155-156
Finite-Dimensional Variational and Quasivariational Inequalities: Algorithmic Developments and Applications in Socio-Eoonomic Planning....Pages 157-157
Stochastic Equilibrium Programming for Dynamic Oligopolistic Markets....Pages 158-159
A Dynamic Approach to Oligopolistic Market Equilibrium....Pages 160-160
Estimated Parameters in Mathematical Programming: Modelling and Statistical Issues....Pages 161-161
Modelling for Parallel Optimization....Pages 162-162
Long-Term Hydro-Thermal Coordination of Electricity Generation Through Multicommodity Network Flows....Pages 163-164
Front Matter....Pages 139-139
Equilibration Operators for the Solution of Constrained Matrix Problem....Pages 165-166
A General Dynamic Network Spatial Price Equilibrium Model with Gains and Losses....Pages 167-168
Incorporating the Concept of Internal Rate of Return in Linear and Integer Programming Models....Pages 169-169
Procedures for Solving Bottleneck Generalized Assignment Problems....Pages 170-171
Weighted Matching in Chess Tournaments....Pages 172-173
Decentralized Optimization for Structured Linear Programming Models....Pages 174-176
Transport Planning in Airborne Operations....Pages 177-177
A Hierarchical Approach to the Placement Problem....Pages 178-178
Optimisation of Oil Depletion Strategy to Satisfy Long-Term Objectives....Pages 179-179
Approaches to Optimizing Fuel Consumption in Cars....Pages 180-181
Equilibrium Definitions in Simulated Annealing: A Computational Experiment....Pages 182-183
Decomposition in Integer Programming....Pages 184-184
Computational Geometry and Low Dimensional Linear Programs....Pages 185-186
Back Matter....Pages 187-195
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