p-facility Huff location problem on networks

The p-facility Hu location problem aims at locating facilities on a competitive environment so as to maximize the market share. While it has been deeply studied in the eld of continuous location, in this paper we study the p-facility Hu location problem on networks formulated as a Mixed Integer Nonlinear Programming problem that can be solved by a branch and bound algorithm. We propose two approaches for the initialization and division of subproblems, the rst one based on the straightforward idea of enumerating every possible combination of p edges of the network as possible locations, and the second one de ning sophisticated data structures that exploit the structure of the combinatorial and continuous part of the problem. Bounding rules are designed using DC (di erence of convex) and Interval Analysis tools. In our computational study we compare the two approaches on a battery of 21 networks and show that both of them can handle problems for p ≤ 4 in reasonable computing time.