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Maximal Covering Location Problems on networks with regional demand

Rafael Blanquero(rblanquero***at***us.es)
Emilio Carrizosa(ecarrizosa***at***us.es)
Boglárka G.-Tóth(bog***at***math.bme.hu)

Abstract: Covering problems are well studied in the Operations Research literature under the assumption that both the set of users and the set of potential facilities are finite. In this paper we address the following variant, which leads to a Mixed Integer Nonlinear Program (MINLP): locations of p facilities are sought along the edges of a network so that the expected demand covered is maximized, where demand is continuously distributed along the edges. This MINLP has a combinatorial part (which edges of the network are chosen to contain facilities) and a continuous global optimization part (once the edges are chosen, which are the optimal locations within such edges). A branch and bound algorithm is proposed, which exploits the structure of the problem: specialized data structures are introduced to successfully cope with the combinatorial part, inserted in a geometric branch and bound. Computational results are presented, showing the appropriateness of our procedure to solve covering problems for small (but nontrivial) values of p.

Keywords: Maximal Covering Location Problem, Location on networks, Regional demand, Global optimization, Branch and bound

Category 1: Global Optimization

Category 2: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 3: Applications -- Science and Engineering (Facility Planning and Design )


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Entry Submitted: 09/19/2014
Entry Accepted: 09/22/2014
Entry Last Modified: 09/19/2014

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