Journal
INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH
Volume 25, Issue 5, Pages 1659-1676Publisher
WILEY
DOI: 10.1111/itor.12216
Keywords
multiple objective programming; linear programming; interval programming; uncertainty modeling
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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.
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