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A two-stage robust model for a reliable $$p$$-center facility location problem. (English) Zbl 1443.90239
Summary: We propose a two-stage robust model for reliable facility location when some facilities can be disrupted, for instance by a natural disaster. A reliable network is designed in a “proactive” planning phase, and when a facility is disrupted, its original clients can be reallocated to another available facility in a “reactive” phase. When demand and cost are uncertain, the initial design is also robust against the realizations (scenarios) of these parameters, which will only be revealed post-disruption. Based on the $$p$$-center location model, which attempts to optimize the worst-case performance of the network, our model is concerned with the reliability for every client. Three solution methods have been implemented and tested to solve the model, namely, a linear reformulation, a Benders dual cutting plane method, and a column-and-constraint generation method. We present an extensive numerical study to compare the performance of these methods. We find that, depending on the size of the instance (as given by the number of client sites and scenarios), either the Benders dual cutting plane method or column-and-constraint generation performs best. The effectiveness of our model is also examined in comparison with alternative facility location models.

##### MSC:
 90B80 Discrete location and assignment 90C35 Programming involving graphs or networks