A distance-limited continuous location-allocation problem for spatial planning of decentralized systems

We introduce a new continuous location-allocation problem where the facilities have both a fixed opening cost and a coverage distance limitation. The problem might have wide applications especially in the spatial planning of water and/or energy access networks where the coverage distance might be associated with the physical loss constraints. We formulate a mixed integer quadratically constrained problem (MIQCP) under the Euclidean distance setting and present a three-stage heuristic algorithm for its solution: In the first stage, we solve a planar set covering problem (PSCP) under the distance limitation. In the second stage, we solve a discrete version of the proposed problem where the set of candidate locations for the facilities is formed by the union of the set of demand points and the set of locations in the PSCP solution. Finally, in the third stage, we apply a modified Weiszfeld’s algorithm with projections, which we propose to incorporate the coverage distance component of our problem, for fine-tuning the discrete space solutions in the continuous space. We perform numerical experiments on three example data sets from the literature to demonstrate the performance of the suggested heuristic method. Keywords— continuous location-allocation; planar set covering; multi-source Weber problem; decentralized systems