A fuzzy approach for bi-level integer non-linear programming problem

Bi-level programming, a tool for modeling decentralized decisions, consists of the objective of the leader at its first level and that is of the follower at the second level. Integer programming deals with the mathematical programming problems in which some or all the variables are to be integer. Th...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 172; no. 1; pp. 62 - 71
Main Author: Emam, O.E.
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 2006
Elsevier
Subjects:
Applied sciences
Bi-level
Calculus of variations and optimal control
Exact sciences and technology
Fuzzy approach
Integer programming
Mathematical analysis
Mathematical programming
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Operational research and scientific management
Operational research. Management science
Sciences and techniques of general use
Stackelberg game
Integer programming
Fuzzy approach
Bi-level
Stackelberg game
Membership function
Optimization method
Non linear programming
Constrained optimization
Optimal decision
Numerical analysis
Bi level
Applied mathematics
Optimal solution
Mathematical programming
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:Bi-level programming, a tool for modeling decentralized decisions, consists of the objective of the leader at its first level and that is of the follower at the second level. Integer programming deals with the mathematical programming problems in which some or all the variables are to be integer. This paper studies a bi-level integer non-linear programming problem with linear or non-linear constraints, and in which the non-linear objective function at each level are to maximized. The bi-level integer non-linear programming (BLI-NLP) problem can be thought as a static version of the Stackelberg strategy, which is used leader-follower game in which a Stackelberg strategy is used by the leader, or the higher-level decision-maker (HLDM), given the rational reaction of the follower, or the lower-level decision-maker (LLDM). This paper proposes a two-planner integer model and a solution method for solving this problem. This method uses the concept of tolerance membership function and the branch and bound technique to develop a fuzzy Max–Min decision model for generating Pareto optimal solution for this problem; an illustrative numerical example is given to demonstrate the obtained results.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2005.01.149