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...

Bi-level programming has been used widely to model interactions between hierarchical decision-making problems, and their solution is challenging, especially when the lower-level problem contains discrete decisions. The of such mixed-integer linear bi-level problems typically need decomposition, approximation or heuristic-based strategies which either require high computational effort cannot gua...

Fuzzy linear symmetrical bi-level programming is the most extensive problem in multi-level programming. A new method based on tolerance degree has been introduced in this paper. The method mainly concerns the modeling of complicated Supply Chain with bi-level Stackelberg structure. We analyze the reason lead to uncertainties in supply chain, summarize methods of dealing with uncertainties, and ...

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...

Bi-level programming techniques are developed to handle decentralized problems with two-level decision makers, leaders and followers, who may have more than one objective to achieve. This paper proposes a λ-cut and goal programming based algorithm to solve fuzzy linear multiple objective bi-level (FLMOB) decision problems. First, based on the definition of a distance measure between two fuzzy v...