Models and algorithms for the delivery and installation routing problem

Abstract

This paper proposes a variant of the vehicle routing problem with time windows (VRPTW) in which one disposes of two heterogeneous fleets to serve the customers; the first fleet is in charge of deliveries with the possibility to install products while the second one only performs installations. Customers receive some furniture, electronics and home appliances, and may require an installation service according to the items received. Installation can be performed by the deliverymen or by a dedicated installation fleet which needs to be synchronized with the delivery one. Each worker (delivery or installer) has different skills, and thus different installation times. We first formulate the problem as a mixed-integer linear programming model and solve it through a branch-and-bound algorithm. Moreover, we propose a formulation for a variant of the problem which allows the installation service at a customer to be done by more than one worker. We also design a tailored adaptive large neighborhood search heuristic to quickly find good solutions. Several computational experiments with new instances generated for this problem are used to assess the performance of both methods. We also prove the performance of both methods on the test instances of the related VRP with multiple synchronization constraints and the VRP with time windows and driver-specific times, yielding high-quality solutions in a short time using the heuristic and providing new lower bounds with the exact method.