Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
The mixed integer linear bilevel programming problem
Operations Research
Tabu Search
An alternating heuristic for medianoid and centroid problems in the plane
Computers and Operations Research
Practical Bilevel Optimization: Algorithms and Applications (Nonconvex Optimization and Its Applications)
Discrete models for competitive location with foresight
Computers and Operations Research
A leader-follower game in competitive facility location
Computers and Operations Research
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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.