Generation of efficient and $\epsilon$-efficient solutions in multiple objective linear programming

Authors : Zohra Sabrina DELHOUM, Sonia RADJEF, Fatima BOUDAOUD

Pages : 1031-1048

View : 15 | Download : 4

Publication Date : 0000-00-00

Article Type : Research Paper

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 objective adaptive method. We suggest a process for the search for the first efficient solution without having to calculate a feasible solution, and we elaborate a method to generate efficient solutions, weakly efficient solutions, and $\epsilon$-efficient solutions. Supporting theoretical results are established and the method is demonstrated on a numerical example.
Keywords : Multiobjective linear program, bounded variables, epsilon optimality criterion, adaptive method, efficiency, weak efficiency, epsilon efficiency