Optimal algorithms for the a‐neighbor p‐center problem

Assigning multiple service facilities to demand points is important when demand points are required to withstand service facility failures. Such failures may result from a multitude of causes, ranging from technical difficulties to natural disasters. The a‐neighbor p‐center problem deals with locating p service facilities. Each demand point is assigned to its nearest a service facilities, thus it is able to withstand up to a ‐1 service facility failures. The objective is to minimize the maximum distance between a demand point and its ath nearest service facility. We present two optimal algorithms for both the continuous and discrete a‐neighbor p‐center problem. We present experimental results comparing the performance of the two optimal algorithms for a =2. We also present experimental results showing the performance of the relaxation algorithm for a =1, 2, 3.