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.
Multiobjective linear program, bounded variables, $\epsilon$-optimality criterion, adaptive method, efficiency, weak efficiency, $\epsilon$-efficiency
DELHOUM, ZOHRA SABRINA; RADJEF, SONIA; and BOUDAOUD, FATIMA
"Generation of efficient and $\epsilon$-efficient solutionsin multiple objective linear programming,"
Turkish Journal of Mathematics: Vol. 42:
3, Article 24.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/24