We 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.

中文翻译：

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具有随机需求权重的多设施中心问题

我们研究了具有概率需求权重的网络上的两个p中心模型。第一个问题称为最大概率p中心问题，其目标是最大化需求与开放设施之间的最大需求加权距离不超过给定阈值的概率。第二种，称为β -VaR p-中心问题，目标是在预先选择的置信水平下最小化最大需求加权距离的风险价值。结果表明，这两个模型都是 NP 难的。我们开发了求解这两个模型的算法，并进行了计算实验以比较它们的性能。我们建议使用分支定界算法求解第一个模型，并使用集成优化方法求解第二个模型。提出的解决方法可以很容易地扩展到随机需求权重不独立的情况。