The Fleet Size and Mix Vehicle Routing Problem with Backhauls: A Tabu Search-Based Approach

This paper introduces a new variant of the classical Vehicle Routing Problem - the Fleet Size and Mix Vehicle Routing Problem with Backhauls (FSMVRPB). In this variant a fleet of heterogeneous vehicles is used to serve customers with known demands. The customers are divided into two groups namely deliveries (linehauls) and pickups (backhauls). In this backhauling version the delivery customers are served before any pickups are made. The aim is to find the minimum cost heterogeneous fleet set of routes that start and end at a single depot and visit each customer exactly once. An algorithm to solve the FSMVRPB is developed. This involves a new initial solution method and Tabu Search in which we define the tabu tenure explicitly using linear regression. The proposed approach is tested on a set of FSMVRPB data instances which we constructed for this particular prob-lem. New results are presented which can be used for future benchmarking.