Using Voronoi diagrams to solve a hybrid facility location problem with attentive facilities

In this paper, we introduce a novel class of facility location problems, and propose solutions based on Voronoi diagrams. Our solutions locate a set of facilities on a two dimensional space, with respect to a set of dynamic demand. The information about these demand is gathered through modifications of the overall system, into a central decision unit. This influences our objective of minimizing the total loss function. Considering a continuous space and discrete time, facilities are assigned to meet demands in each time cycle. Two distinct approaches are proposed and thoroughly studied, followed by a case study. We call our main algorithm Reactive Agent Dynamic Voronoi Diagram Facility Spread. We also test our solutions empirically through a set of experiments. Considering n and p to be the number of demand points, and the number of facilities in hand, respectively, the time complexity of the algorithm is Oðcðn2 þ pÞlognÞ for a complete run of c cycles.