Abstract 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.

中文翻译：

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协同定位的双分配工厂选址问题

摘要 在本文中，提出了简单工厂定位问题的一种新变体。我们考虑了客户和设施的经典位置分配问题中的附加条件。即，某些对必须由共同的植物提供服务。对于单一分配的情况，可以使用现有模型解决由此产生的问题。然而，据我们所知，必须将每个客户分配到几个设施的建议设置仍未得到探索。我们研究了将此类新约束添加到具有双重分配的 SPLP 标准公式的含义。我们从理论的角度比较得到的公式。之后，我们专注于研究其中一个模型，结果证明这是一个集合包装问题。识别所有集团方面并设计分离算法。