An adaptive method to solve multilevel multiobjective linear programming problems

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...

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Bibliographic Details
Published in:Operations research and decisions Vol. 33; no. 3; pp. 29 - 44
Main Authors: Kaci, Mustapha, Radjef, Sonia
Format: Journal Article
Language:English
Published: Wroclaw University of Science and Technology 2023
Wrocław University of Science and Technology
Subjects:
Computer Science
Mathematics
Operations Research
Optimization and Control
adaptive method
multilevel programming
multiobjective linear programming
sub-optimality estimate
non-dominated solutions
non-dominated facets
ISSN:2081-8858, 2391-6060
Online Access:Get full text
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Summary: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.
ISSN:2081-8858
2391-6060
DOI:10.37190/ord230302