A single allocation -hub median problem with general piecewise-linear costs in arcs.

•We formulate and solve a single allocation p-hub median problem.•The cost of the flow on any arc is modeled as a general piecewise-linear function.•A math-heuristic is proposed, and detailed analysis is made of the solutions.•Our solution approach is stable and scalable for large instances, and moderate values of p.•The solutions are strongly dependent on the cost function considered.