Equivalent weights for lexicographic multi-objective programs: Characterizations and computations

Abstract A recent paper [19] demonstrated the existence of a set of equivalent weights for which the optimal solution set of a preemptive priority multi-objective program is precisely equal to the set of optimal solutions to the resulting nonpreemptive program with the objective function given as a linear weighting of the multiple objectives. This paper addresses two further issues. Firstly, for some important special cases or applications, it is demonstrated that not only is the computation of a set of equivalent weights feasible, but it is also highly desirable. Two algorithms are presented to compute a set of equivalent weights. One method is a direct specialization of the approach adopted in [19], whereas the second approach is an alternative technique. The latter method is shown to yield weights of uniformly smaller values than the former method, while being of the same computational complexity, and is hence preferable. Secondly, as opposed to constructing one vector of equivalent weights, a characterization is provided for the entire set of equivalent weights.