Some new clique inequalities in four-index hub location models

Hub location problems can be modeled in several ways, one of which is the path-based family of models that make use of four-index variables. Clique inequalities are frequently used to describe solution characteristics for optimization problems with binary variables. In this study, new valid inequalities of the clique type are introduced for the path-based family of hub location models. Some of their properties and corresponding lifting are discussed, and a separation heuristic algorithm is proposed. We also report a set of computational experiments to evaluate the usefulness of the proposals when embedded in a commercial solver.