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The stratified $$p$$-center problem. (English) Zbl 1458.90407
Summary: This work presents an extension of the discrete $$p$$-center problem. In this new model, called stratified $$p$$-center problem (S$$p$$CP), the demand is concentrated in a set of sites and the population of these sites is divided into different strata depending on the kind of service that they require. The aim is to locate $$p$$ centers to cover the different types of services demanded minimizing the weighted average of the largest distances associated with each of the different strata. In addition, it is considered that more than one stratum can be present at each site. Different formulations, valid inequalities and preprocessings are developed and compared for this problem. An application of this model is presented in order to implement a heuristic approach based on the sample average approximation method (SAA) for solving the probabilistic $$p$$-center problem in an efficient way.

##### MSC:
 90B80 Discrete location and assignment 90C59 Approximation methods and heuristics in mathematical programming