This paper proposes a bi-level linear programming problem with linear constraints, in which the linear objective functions are to be maximized with different rough goals, the suggested approach in this paper is mainly based on the iterative goal programming method of Dauer and Krueger to develop the optimal solution of the bi-level decisionmaker, then we uses the concepts of tolerance membershi...

______________________ Abstract: Bi-level programming, a tool for modeling decentralized decisions, consists of the objective(s) of the leader at its first level and that is of the follower at the second level. Three level programming results when second level is itself a bi-level programming. By extending this idea it is possible to define multi-level programs with any number of levels. Supply...

vendor managed inventory is a continuous replenishment program that is designed to provide major cost saving benefits for both vendors and retailers. previous research on this area mainly included single objective optimization models where the objective is to minimize the total supply chain costs or to maximize the total supply chain benefits. this paper presents a bi-objective mathematical mod...

one of important problems in supply chains management is supplier selection. in a company, there are massive data from various departments so that extracting knowledge from the company’s data is too complicated. many researchers have solved this problem by some methods like fuzzy set theory, goal programming, multi objective programming, the liner programming, mixed integer programming, analyti...

This paper presents a fuzzy goal programming (FGP) methodology for solving bi-level quadratic programming (BLQP) problems. In the FGP model formulation, firstly the objectives are transformed into fuzzy goals (membership functions) by means of assigning an aspiration level to each of them, and suitable membership function is defined for each objectives, and also the membership functions for vec...

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...