The capacitated p-center problem is concerned with how to select p locations for facility centers and assign demand points to them such that the maximum distance between a demand point and its nearest center is minimized. This paper focuses on the capacitated p-center problem in an uncertain environment, in which demands and distances are regarded as uncertain variables. Consequently, two minimax models with uncertain parameters are formulated, and their crisp equivalences are investigated. Additionally, a hybrid algorithm based on the 99-method, a genetic algorithm and a tabu search algorithm is designed to solve the models. Finally, some numerical examples are presented to unveil the applications of the models and algorithm.

容量限制的p中心问题与如何为设施中心选择p个位置并为它们分配需求点有关，以使需求点与其最近的中心之间的最大距离最小。本文着重研究不确定环境中的能力p中心问题，其中需求和距离被视为不确定变量。因此，建立了两个具有不确定参数的极大极小模型，并研究了它们的等价性。另外，设计了一种基于99-方法的混合算法，遗传算法和禁忌搜索算法来求解模型。最后，给出了一些数值示例来揭示模型和算法的应用。