Single-facility location problems in two regions with ℓ1- and ℓq-norms separated by a straight line

Abstract

In this paper, Fermat–Weber location problems with demand points located in two regions Ω1 and Ωq separated by a straight line, are addressed. Ω1 and Ωq are, respectively, endowed by different norms ℓ1 and ℓq, with q > 1. In order to compute distances between points in different regions, the concept of Gate point is applied.With the aim of solving the problem, a new algorithm, called Gate(1, q), is designed. This algorithm uses the characterization of the solutions in the regions Ω1 and Ωq, and the straight line.A comparative study with other well-known algorithms is carried out in order to test the performance of the proposed algorithm. The results are promising since they show that the Gate(1, q) algorithm leads to a more accurate solution than those of the other algorithms in a relatively short computing time.