中文摘要：

本文研究了一类故障率低但重要性较高设备的应急抢修点选址问题。设备的故障发生过程和从应急抢修点到故障设备的通行时间是随机的，每个设备被分配给一个应急抢修点进行抢修，并且整个应急抢修系统的服务水平要大于给定标准。本文以应急抢修点总开设成本最小作为目标，同时考虑了设备覆盖约束、抢修分配关系约束和抢修系统服务水平约束，在合理的假设下证明设备发生故障且应急抢修小组迟到的总次数服从泊松分布，最终将应急抢修点选址问题描述为一个0-1整数规划模型。通过对模型中的覆盖约束和抢修系统服务水平约束进行松弛，设计了相应的拉格朗日启发式算法。最后通过对大量随机算例进行计算，证明了该模型和算法的有效性。

英文摘要：

The problem of emergency repair station location for a kind of valuable equipments with low fail- ure rate is investigated in this paper. Considering this problem, equipment failure frequencies and the travel time from emergency station to equipment are stochastic, and each equipment should be assigned to an e- mergency repair station, and the service level of entire emergency repair system should be above some standard level. The distribution of the total times of emergency repair teams be late when equipment be failed has been derived under several assumptions. The problem of emergency repair station location is characterized as O--1 integer programming model, with minimization the whole setup cost of emergency re- pair stations as objective function, and equipments been covered, emergency repair assignment relation, entire system＇s service level as constraints. A lagrangian relaxation heuristic algorithm is proposed to solve the model by relaxing several constraints. The effective of the model and algorithm has been proved by calculating a large number of random examples.