The capacitated plant location problem with multiple facilities in the same site

In this paper, we introduce the capacitated plant location problem (CPLP) with multiple facilities in the same site (CPLPM), a special case of the classical CPLP where several facilities can be opened in the same site. Applications of the CPLPM arise in a number of contexts, such as the location of polling stations. Although the CPLPM can be modelled and solved as a standard CPLP, this approach usually performs very poorly. In this paper we describe a novel Lagrangean relaxation and a tailored Lagrangean heuristic that overcome the drawbacks of classical procedures. These algorithms were used to solve a polling station location problem in Italy. Computational results show that the average deviation of the heuristic solution over the lower bound is less than 2%.