Generation of efficient and ϵ-efficient solutions in multiple objective linear programming

Abstract

We develop an algorithm to solve a multiple objective linear programming problem with bounded variables.It is based on the scalarization theorem of optimal solutions of multiobjective linear programs and the single objectiveadaptive method. We suggest a process for the search for the first efficient solution without having to calculate a feasiblesolution, and we elaborate a method to generate efficient solutions, weakly efficient solutions, and ϵ -efficient solutions.Supporting theoretical results are established and the method is demonstrated on a numerical example.