Weighted sum of maximum regrets in an interval MOLP problem

This paper presents a multiobjective linear programming problem with interval objective function coefficients. Considering the concept of maximum regret, the weighted sum problem of maximum regrets is introduced and its properties are investigated. It is proved that an optimal solution of the weighted sum problem of maximum regrets is at least possibly weakly efficient. Further, the circumstances under which the optimal solution is necessarily efficient (necessarily weakly efficient or possibly efficient) are discussed. Moreover, using a relaxation procedure, an algorithm is proposed, which for a given set of weights finds one feasible solution that minimizes the weighted sum of maximum regrets. A numerical example is provided to illustrate the proposed algorithm.