Abstract
An algorithm is proposed in this paper for solving two-dimensional bi-level linear programming problems without making a graph. Based on the classification of constraints, algorithm removes all redundant constraints, which eliminate the possibility of cycling and the solution of the problem is reached in a finite number of steps. Example to illustrate the method is also included in the paper.
Highlights
Multilevel programming is developed to solve the decentralized planning problem in which decision makers are often arranged within a hierarchical administrative structure
The bi-level programming problem is a hierarchical optimization problem in which a subset of the variables are constrained to be solution of a given optimization problem parameterized by the remaining variables
The linear bi-level programming problem, which is a specific case of the Multilevel programming problem with a two levels structure is a set of nested linear optimization over a single polyhedral region
Summary
Multilevel programming is developed to solve the decentralized planning problem in which decision makers are often arranged within a hierarchical administrative structure. Norton [2] that first used the designation bi-level or multilevel programming It was not until the early eighties that these problems started receiving the attention they deserve [3] [4] [5] [6]. One class of techniques inherent of extreme point algorithms and has been largely applied to the linear bi-level programming problems because for this problem, if there is a solution, there is at least one global minimizer that is an extreme point [12]. An attempt has been made to develop a method in which constraints are analyzed, and used for solving two-dimensional linear bi-level programming problems. Constraints have been classified broadly in two categories; we have named them as concave constraints and convex constraints
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