Split pick-up and delivery vehicle routing problem with cross-docks

Abstract

A novel variant of the pick-up and delivery vehicle routing problem with time windows is proposed addressing an industry requirement to efficiently route less than truck load, time sensitive, orders between multiple collection and delivery locations. We introduce cross-docks, order splitting and consolidation, thereby allowing routes to contain an arbitrary mixture of collection, delivery, and cross-dock locations. There are potentially multiple orders for each collection and delivery point, and orders can transfer between routes at any number of cross-docks. The problem is formally defined, test instances created and a MILP column generation formulation is presented, with heuristics for creating and evaluating columns (routes). The linear relaxation has weak lower bounds, and heuristic methods for identifying im- proving columns are developed. Extensive computational testing is undertaken demon- strating the effectiveness and size limitations of the proposed MILP formulation. Efficient heuristics are introduced to create and improve candidate routes to feed into the MILP. A path relinking algorithm is introduced, including novel solution encoding and definitions of distance between solutions in the solution space. To solve larger instances, a matheuristic algorithm tailors the search of the routes being considered by including available information from the branch-and-bound tree while solving the MILP, such as pseudo-costs. A further method called order group fix-and-release is introduced to heuristically identify high quality routes within large candidate sets. For commercial large instances, driver breaks consistent with EU regulations need to be scheduled, constraints on maximum drive time and maximum shift time are imposed, and variable service times are allowed. A variable neighbourhood search (VNS) heuristic is developed using ruin and repair. The heuristic includes two novel neighbourhoods, and critical paths and induced graphs are used to efficiently verify time-feasibility. For driver breaks, a dynamic program is developed that allows the splitting of breaks, and allows the break to occur within a service time when this is permitted. Extensive computational testing shows that our VRP variant typically results in a lower cost than pickup and delivery routing or previously studied applications of cross-docking. Additionally, computational testing shows the VNS heuristic efficiently creates good- quality solutions for industry instances.

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Identifiers

ORCID for Michael Kevin Flynn: orcid.org/0000-0002-0642-2760

ORCID for Toni Martinez Sykora: orcid.org/0000-0002-2435-3113

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