α-reliable p-minimax regret: A new model for strategic facility location modeling

Facility location problems are inherently strategic in nature. One approach to dealing with the uncertainty associated with future events is to define alternative future scenarios. Planners then attempt to optimize: (1) the expected performance over all future scenarios, (2) the expected regret, or (3) the worst-case regret. Both the expected performance and the expected regret approaches assume that the planner can associate probabilities with the scenarios, while optimizing the worst-case regret obviates the need for these probabilities. Worst-case regret planning can, however, be driven by a scenario with a very small likelihood of occurrence. We present a new model that optimizes the worst-case performance over a set of scenarios that is endogenously selected from a broader exogenously specified set. The selection is based on the scenario probabilities. The new model is formulated and computational results on a moderately sized problem are presented. Model extensions are discussed.