Bundle generation for the vehicle routing problem with occasional drivers and time windows

In this paper, we address the vehicle routing problem (VRP) with occasional drivers (ODs) and time windows (TWs). The problem (VRP-OD-TW) is an extension of the VRP-OD, where ODs serve customers within given TWs. Differently from the basic version of VRP-OD-TW, we assume that ODs not only accept single requests, but they can also serve bundles of requests. To deal with the bundle-to-driver assignment problem, an auction-based system has been designed; a company offers a set of bundles to the ODs, who bid for all the bundles they consider attractive. There is no limit on the number of bids a driver can place, but at most one bid per OD can be assigned to avoid infeasible workloads. This system could yield a large cost reduction for the company, but its success is strongly related to the bundles offered. Hence, determining bundles which are attractive for ODs and profitable for the company, becomes a crucial issue. We propose two different bundling strategies, which make use of a spatial-temporal representation of customers in a three-dimensional (3D) space. The former is based on the generation of 3D corridors, while the latter relies on 3D clustering techniques. Through extensive computational results, we show that the former technique outperforms the latter in terms of both solution quality and computational times and that both the approaches strongly outperform bundle generation techniques that neglect the temporal dimension and rely only on spatial information.