Branch-and-cut solution approach for multilevel mixed integer linear programming problems

A multilevel programming problem is an optimization problem that involves multiple decision makers, whose decisions are made in a sequential (or hierarchical) order. If all objective functions and constraints are linear and some decision variables in any level are restricted to take on integral or d...

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Vydáno v:EURO journal on computational optimization Ročník 11; s. 100076
Hlavní autoři: Awraris, Ashenafi, Wordofa, Berhanu Guta, Kassa, Semu Mitiku
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 2023
Elsevier
Témata:
Branch-and-cut
Mixed integer programming
Multilevel optimization
Valid inequalities
Mixed integer programming
Valid inequalities
Multilevel optimization
Branch-and-cut
ISSN:2192-4406, 2192-4414
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Popis
Shrnutí:A multilevel programming problem is an optimization problem that involves multiple decision makers, whose decisions are made in a sequential (or hierarchical) order. If all objective functions and constraints are linear and some decision variables in any level are restricted to take on integral or discrete values, then the problem is called a multilevel mixed integer linear programming problem (ML-MILP). Such problems are known to have disconnected feasible regions (called inducible regions), making the task of constructing an optimal solution challenging. Therefore, existing solution approaches are limited to some strict assumptions in the model formulations and lack universality. This paper presents a branch-and-cut (B&C) algorithm for the global solution of such problems with any finite number of hierarchical levels, and containing both continuous and discrete variables at each level of the decision-making hierarchy. Finite convergence of the proposed algorithm to a global solution is established. Numerical examples are used to illustrate the detailed procedure and to demonstrate the performance of the algorithm. Additionally, the computational performance of the proposed method is studied by comparing it with existing method through some selected numerical examples. •Multilevel mixed-integer linear programming problems are considered.•A new Branch-and-cut algorithm is developed to solve any k-level of such problems with a finite natural number k.•Convergence of the proposed method to the exact solution is established.•Numerical experiments indicate the validity and computational efficiency of the proposed method.
ISSN:2192-4406
2192-4414
DOI:10.1016/j.ejco.2023.100076