A Fuzzy Algorithm for Solving a Class of Bi-Level Linear Programming Problem

A Fuzzy Algorithm for Solving a Class of Bi-Level Linear Programming Problem

This paper proposes a kind of bi-level linear programming problem, in which there are two decision makers in a hierarchy and they have a common variable. To deal with this bi-level problem, we introduce a virtual decision maker, who controls the common variable to maximize the sum of the objective functions of the upper and lower level decision maker (the leader and follower). To illustrate the...

An Algorithm for Solving Bi-Level Integer Linear Fractional Programming Problem based on Fuzzy Approach

This paper presents a fuzzy approach for solving the bi-level integer linear fractional programming problem (BILFPP). At the first phase of the solution algorithm and to avoid the complexity of non convexity of this problem, we begin by finding the convex hull of its original set of constraints using the cutting-plane algorithm, and then the Charnes & Cooper transformation is used to convert th...

Fuzzy Compromise Approach for Solving Bi-level Linear Programming Problem with Fuzzy Parameters

In this paper, we have proposed an algorithm to solve bi-level linear programming problems with fuzzy parameters without converting it to crisp equivalent problem and obtained a fuzzy compromise solution. Since the decision variables and objective functions are represented as fuzzy membership functions, the proposed fuzzy compromise solution will be more practical and reasonable. A numerical ex...

A Branch and Bound Algorithm for Solving the Binary Bi-level Linear Programming Problem

A bi-level linear programming problem for computing the nadir point in MOLP

Computing the exact ideal and nadir criterion values is a very ‎important subject in ‎multi-‎objective linear programming (MOLP) ‎problems‎‎. In fact‎, ‎these values define the ideal and nadir points as lower and ‎upper bounds on the nondominated points‎. ‎Whereas determining the ‎ideal point is an easy work‎, ‎because it is equivalent to optimize a ‎convex function (linear function) over a con...