Issue: 2023/Vol.33/No.3, Pages 29-44
AN ADAPTIVE METHOD TO SOLVE MULTILEVEL MULTIOBJECTIVE LINEAR PROGRAMMING PROBLEMS
Cite as: M. Kaci, S. Radjef. An adaptive method to solve multilevel multiobjective linear programming problems. Operations Research and Decisions 2023: 33(3), 29-44. DOI 10.37190/ord230302
This paper is a follow-up to a previous work where we defined and generated the set of all possible compromises of multilevel multiobjective linear programming problems (ML-MOLPP). We introduce a new algorithm to solve ML-MOLPP in which the adaptive method of linear programming is nested. First, we start by generating the set of all possible compromises (set of all non-dominated solutions). After that, an algorithm based on the adaptive method of linear programming is developed to select the best compromise among all the possible settlements achieved. This method will allow us to transform the initial multilevel problem into an ML-MOLPP with bonded variables. Then, apply the adaptive method which is the most efficient to solve all the multiobjective linear programming problems involved in the resolution process instead of the simplex method. Finally, all the construction stages are carefully checked and illustrated with a numerical example.
Keywords: multilevel programming, multiobjective linear programming, adaptive method, sub-optimality estimate, non-dominated solutions, non-dominated facets
Received: 26 August 2022 Accepted: 1 June 2023
Published online: 21 September 2023