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

•A new variant (FSMVRPB) of the classical Vehicle Routing Problem is introduced.•A mathematical formulation, optimal solutions, lower/upper bounds are presented.•We have also developed hybrid heuristic based on set partitioning.•New data instances are created; results can be used for future benchmarking.

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.