Variable neighborhood search based approaches to a vehicle scheduling problem in agriculture

A vehicle scheduling problem (VSP) that arises from sugar beet transportation within minimum working time under the set of constraints reflecting a real-life situation is considered. A mixed integer quadratically constrained programming (MIQCP) model of the considered VSP and reformulation to a mixed integer linear program (MILP) are proposed and used within the framework of Lingo 17 solver, producing optimal solutions only for small-sized problem instances. Two variants of the variable neighborhood search (VNS) metaheuristic-basic VNS (BVNS) and skewed VNS (SVNS) are designed to efficiently deal with large-sized problem instances. The proposed VNS approaches are evaluated and compared against Lingo 17 and each other on the set of real-life and generated problem instances. Computational results show that both BVNS and SVNS reach all known optimal solutions on small-sized instances and are comparable on medium- and large-sized instances. In general, SVNS significantly outperforms BVNS in terms of running times.