Search

We consider a problem in which a firm or franchise enters a market by locating new facilities where there are existing facilities belonging to a competitor. The firm aims at finding the location and attractiveness of each facility to be opened so as to maximize its profit. The competitor, on the other hand, can react by adjusting the attractiveness of its existing facilities, opening new facilities and/or closing existing ones with the objective of maximizing its own profit. The demand is assumed to be aggregated at certain points in the plane and the facilities of the firm can be located at prespecified candidate sites. We employ Huff΄s gravity-based rule in modeling the behavior of the customers where the fraction of customers at a demand point that visit a certain facility is proportional to the facility attractiveness and inversely proportional to the distance between the facility site and demand point. We formulate a bilevel mixed-integer nonlinear programming model where the firm entering the market is the leader and the competitor is the follower. In order to find a feasible solution of this model, we develop a hybrid tabu search heuristic which makes use of two exact methods as subroutines: a gradient ascent method and a branch-and-bound algorithm with nonlinear programming relaxation. [ABSTRACT FROM AUTHOR]

Filter methods, introduced by Fletcher and Leyffer for nonlinear programming are characterized by the use of the dominance concept of multiobjective optimization, instead of a penalty parameter whose adjustment can be problematic. This paper presents a way to implement a filter based approach to solve a nonlinear bilevel programming problem in a linear approximations framework. The approach presented is based on the trust region idea from nonlinear programming, combined with filter-SQP algorithm, smooth and active sets techniques. The restoration procedure introduced in our algorithm consists in computing a rational solution. [ABSTRACT FROM AUTHOR]

A bilevel decision problem may have multiple followers as the lower decision units and have fuzzy demands simultaneously. This paper focuses on problems of fuzzy linear bilevel decision making with multiple followers who share a common objective but have different constraints (FBOSF). Based on the ranking relationship among fuzzy sets defined by cut set and satisfactory degree, a FBOSF model is presented and a particle swarm optimization based algorithm is developed. [ABSTRACT FROM AUTHOR]

Telecommunications have always been the subject of application for advanced mathematical techniques. In this chapter, we review classical nonlinear programming approaches to modeling and solving certain problems in telecommunications. We emphasize the common aspects of telecommunications and road networks, and indicate that several lessons are to be learned from the field of transportation science, where game theoretic and equilibrium approaches have been studied for more than forty years. Several research directions are also stated. [ABSTRACT FROM AUTHOR]