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.

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.