Advances in Sensitivity Analysis and Parametric Programming

The standard view of Operations Research/Management Science (OR/MS) dichotomizes the field into deterministic and probabilistic (nondeterministic, stochastic) subfields. This division can be seen by reading the contents page of just about any OR/MS textbook. The mathematical models that help to define OR/MS are usually presented in terms of one subfield or the other. This separation comes about somewhat artificially: academic courses are conveniently subdivided with respect to prerequisites; an initial overview of OR/MS can be presented without requiring knowledge of probability and statistics; text books are conveniently divided into two related semester courses, with deterministic models coming first; academics tend to specialize in one subfield or the other; and practitioners also tend to be expert in a single subfield. But, no matter who is involved in an OR/MS modeling situation (deterministic or probabilistic - academic or practitioner), it is clear that a proper and correct treatment of any problem situation is accomplished only when the analysis cuts across this dichotomy.

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The numerous advances in mathematical programming have opened up new insights about sensitivity analysis. The paradigm What if...?' question is no longer the only question of interest. Often, we want to knowWhy...?' and Why not...?' Such questions were not analyzed in the early years of mathematical programming to the same extent that they are now, and we have not only expanded our thinking aboutpost-optimal analysis', but also about `solution analysis', even if the solution obtained is not optimal. Therefore, it is now time to examine all the recent advances on sensitivity analysis and parametric programming. This book combines the origins of sensitivity analysis with the state of the art. It covers much of the traditional approaches with a modern perspective, and shows recent results using the optimal partition approach, stemming from interior methods, for both linear and quadratic programming. It examines the special case of network models. It presents a neglected topic, qualitative sensitivity analysis, as well as elements of mixed integer programming and gives a modern perspective of nonlinear programming. It provides recent advances in multi-criteria mathematical programming and also describes the state-of-the-art in stochastic programming. It covers recent advances in understanding redundancy in quadratic programs, considers an approach to diagnosing infeasibility in linear and nonlinear programs, and gives an overview of sensitivity analysis for fuzzy mathematical programming.

Résumé
`... well-organized book can be highly recommended to all who are engaged in operations research and decision making with incomplete information and/or multiple criteria. I do not hesitate to congratulate the two editors on their excellent work.'
OR Spektrum, 22 (2000)

Contenu

1. A Historical Sketch on Sensitivity Analysis and Parametric Programming.- 2. A Systems Perspective: Entity Set Graphs.- 3. Linear Programming 1: Basic Principles.- 4. Linear Programming 2: Degeneracy Graphs.- 5. Linear Programming 3: The Tolerance Approach.- 6. The Optimal Set and Optimal Partition Approach.- 7. Network Models.- 8. Qualitative Sensitivity Analysis.- 9. Integer and Mixed-Integer Programming.- 10. Nonlinear Programming.- 11. Multi-Criteria and Goal Programming.- 12. Stochastic Programming and Robust Optimization.- 13. Redundancy.- 14. Feasibility and Viability.- 15. Fuzzy Mathematical Programming.