Improving minimax regret approach of expected recourse Problem with vectors of uncertainty

Abstract

Uncertainty means that more than one realizations can represent an entity of interest. This thesis concerns a special pattern of uncertainty, which is a probability interval that can be represented as a random set. Our linear optimization model min x cT x; AT x b; x ≥ 0 has a special structure of the uncertainty; i.e., the coefficients and the right hand side of each constraint form vector of uncertainty. We transform a linear program with this special uncertainty into an interval expected recourse problem, then find the minimax regret of this issue by a relaxation procedure. The relaxation procedure finally has been improved by using the idea of ordering and the fact that we can reduce the size of the probability set of all possible ordering cases and reduce the calculation time.