decentralization allows channel members to make their decisions, independently. in this decentralized channels, members may have different power to make its decisions. hence, decisions of each member may influence on the other members’ decisions. to model such situations, bi-level programming models are useful. in this study, a supply chain including one manufacturer and multiple competitive re...

One of the most complicated decision making problems for managers is the evaluation of bank performance, which involves various criteria. There are many studies about bank efficiency evaluation by network DEA in the literature review. These studies do not focus on multi-level network. Wu (Eur J Oper Res 207:856–864, 2010) proposed a bi-level structure for cost efficiency at the first time. In t...

The aim of this paper is to propose a robust reliable bi-objective supply chain network design (SCND) model that is capable of controlling different kinds of uncertainties, concurrently. In this regard, stochastic bi-level scenario based programming approach which is used to model various scenarios related to strike of disruptions. The well-known method helps to overcome adverse effects of disr...

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 chain planning problem...

  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 chain planning problems are co...

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...

The multi-level programming problems are attractive for many researchers because of their application in several areas such as economic, traffic, finance, management, transportation, information technology, engineering and so on. It has been proven that even the general bi-level programming problem is an NP-hard problem, so the multi-level problems are practical and complicated problems therefo...