Stochastic integer programming
(LANCS project - Optimisation: Transport)
With Stein W. Wallace
This project is part of a cooperation with Teodor Gabriel Crainic and Walter Rei (University of Québec at Montreal), Michel Gendreau (University of Montreal) and Michal Kaut (Norwegian University of Science and Technology).
Stochastic integer programs are extremely hard to solve, in fact also hard to formulate in many cases. However, most (if not all) real problems are affected by uncertainty. So these problems are important from a practical point of view. Contemporary research goes in many directions. The overall purpose of the research suggested here is to study what stochastics do to the optimal solution of an integer program. We shall only study what are called “two-stage problems”. Examples of these include “Designing a network for future stochastic transportation needs or future stochastic arc failures”, “Locating facilities for future stochastic customer demands” or “Designing a production site for future stochastic production needs”. So the question is: If we replace the random phenomena (demand, prices, arc capacities) with their expected values (standard in deterministic optimization), what will we lose? In what way will the solution to the explicit stochastic optimization problem differ from its deterministic counterpart? In still other words: What is it that produces robustness in a solution?
Certain programming skills will be needed.
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