A heuristic to minimax absolute regret for linear programs with interval objective function coefficients

Decision makers faced with uncertain information often experience regret upon learning that an alternative action would have been preferable to the one actually selected. Models that minimize the maximum regret can be useful in such situations, especially when decisions are subject to ex post review. Of particular interest are those decision problems that can be modeled as linear programs with interval objective function coefficients. The minimax regret solution for these formulations can be found using an algorithm that, at each iteration, solves first a linear program to obtain a candidate solution and then a mixed integer program (MIP) to maximize the corresponding regret. The exact solution of the MIP is computationally expensive and becomes impractical as the problem size increases. In this paper, we develop a heuristic for the MIP and investigate its performance both alone and in combination with exact procedures. The heuristic is shown to be effective for problems that are significantly larger than those previously reported in the literature.