Abstract
In this paper, considering an efficiency condition in multiobjective linear programming problems, we propose effective efficiency tests, and apply these methods to extended problems with interval coefficients. In the conventional multiobjective programming literature, it is required to solve a linear programming problem in efficiency test procedure. Hence, in the case of our extended problems with interval coefficients, we need excessive computational demand for necessary efficiency tests. Therefore, development of effective efficiency test methods has been desired. In the former part of this paper, we consider the efficiency condition and its dual condition in ordinary multiobjective linear programming problems, and propose effective "efficiency tests" based on the extreme ray generation method. In the latter part of this paper, we apply the proposed efficiency tests to interval multiobjective linear programming problems and propose "necessary efficiency tests". These methods consist of the branch and bound algorithm and the efficiency test methods proposed in the former part of this paper. Numerical examples are shown to explain these proposed methods.
