The Fleet Size and Mix Vehicle Routing Problem with Backhauls: Formulation and Set Partitioning-based Heuristics

In this paper we present a new variant of the classical Vehicle Routing Problem – the Fleet Size and Mix Vehicle Routing Problem with Backhauls (FSMVRPB). An ILP formulation of the FSMVRPB is presented. Optimal solutions for small size instances are produced and upper and lower bounds are generated for larger ones. In this paper we also propose a Set Partitioning Problem (SPP) based heuristic. Three frameworks are developed and tested on a set of new FSMVRPB data instances which we generated. Computational results are presented which can be used for future benchmarking.