The double-assignment plant location problem with co-location

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In this paper, a new variant of the Simple Plant Location Problem is proposed. We consider additional conditions in the classic location-allocation problem for clients and facilities. Namely, some pairs have to be served by a common plant. The resulting problem can be addressed with existing models for the case of single assignment. However, to the best of our knowledge, the proposed setting when each client must be assigned to a couple of facilities is still unexplored. We examine the implications of adding such new constraints to standard formulations of the SPLP with double assignment. We compare the resulting formulations from a theoretical point of view. After that, we focus on the study of one of the models, which turned out to be a set packing problem. All the clique facets are identified and a separation algorithm is devised. Although the separation problem is proved to be NP-hard, our computational experience shows that the separation algorithm is effective and efficient, reducing computational times and duality gaps for all the instances tested.