Modelling the Hop Constrained Connected Facility Location Problem on Layered Graphs

Gouveia et al. [Gouveia, L., L. Simonetti and E. Uchoa, Modelling hop-constrained and diameter-constrained minimum spanning tree problems as Steiner tree problems over layered graphs, Mathematical Programming (2010). URL http://dx.doi.org/10.1007/s10107-009-0297-2] show how to model the Hop Constrained Minimum Spanning tree problem as Steiner tree problem on a layered graph. Following their ideas, we provide three possibilities to model the Hop Constrained (HC) Connected Facility Location problem (ConFL) as ConFL on layered graphs. We show that on all three layered graphs the respective LP relaxations of two cut based models are of the same quality. In our computational study we compare a compact hop-indexed tree model against the two cut based models on the simplest layered graph. We provide results for instances with up to 1300 nodes and 115000 arcs.