Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
The mixed integer linear bilevel programming problem
Operations Research
An alternating heuristic for medianoid and centroid problems in the plane
Computers and Operations Research
Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications)
Practical Bilevel Optimization: Algorithms and Applications (Nonconvex Optimization and Its Applications)
Discrete models for competitive location with foresight
Computers and Operations Research
A hybrid tabu search heuristic for a bilevel competitive facility location model
HM'10 Proceedings of the 7th international conference on Hybrid metaheuristics
Solution method for the location planning problem of logistics park with variable capacity
Computers and Operations Research
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We address the problem of locating new facilities of a firm or franchise that enters a market where a competitor operates existing facilities. The goal of the new entrant firm is to decide the location and attractiveness of its new facilities that maximize its profit. The competitor can react by opening new facilities, closing existing ones, and adjusting the attractiveness levels of its existing facilities, with the aim of maximizing its own profit. The demand is assumed to be aggregated at certain points in the plane and the new facilities of both the firm and the competitor can be located at predetermined candidate sites. We employ the gravity-based rule in modeling the behavior of the customers where the probability that a customer visits 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. We propose heuristics that combine tabu search with exact solution methods.