The concept of r-efficiency and decomposed location problem

Abstract

In this paper, we introduce the new concept of r-efficiency and classify the weakly efficient solutions by this concept, where r = 1, 2, . . . , m and m is the number of objective functions. Afterward, we decompose the multi-objective optimization problem into the collection of subproblems with cardinality r, for two reasons. First, we apply the scalarization techniques for these subproblems to generate r-efficient solutions. Second, in order to present the new mean-equity models for solving the location problem, we employ the mean and inequality measures on these subproblems. Moreover, by introducing the consistency property for the inequality measures and stating the sufficient conditions to maintain this property, we investigate the relationship between r-efficient solutions of the new mean-equity models and efficient solutions of the location problem.