Abstract
AbstractWe study two p‐center models on a network with probabilistic demand weights. In the first, which is called the maximum probability p‐center problem, the objective is to maximize the probability that the maximum demand‐weighted distance between the demand and the open facilities does not exceed a given threshold value. In the second, referred to as the β‐VaR p‐center problem, the objective is to minimize the value‐at‐risk of the maximum demand‐weighted distance with a pre‐selected confidence level. It is shown that both models are NP‐hard. We develop algorithms for solving the two models and conduct computational experiments to compare their performance. We recommend that the branch and bound algorithm be applied to solve the first model, and an ensemble optimization method to solve the second model. The solution approaches presented can be easily extended to the case where the random demand weights are not independent.
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