Crowd-shipping with time windows and transshipment nodes

Crowd-shipping is a delivery policy in which, in addition to standard vehicle routing practices, ordinary people accept to deviate from their route to deliver items to other people, for a small compensation. In this paper we consider a variant of the problem by taking into account the presence of intermediate depots in the service network. The occasional drivers can decide to serve some customers by picking up the parcels either from the central depot or from an intermediate one. The objective is to minimize the total cost, that is, the conventional vehicle cost, plus the occasional drivers’ compensation. We formulate the problem and present a variable neighborhood search heuristic. To analyze the benefit of the crowd-shipping transportation system with intermediate depots and to assess the performance of our heuristic, we consider small- and large-size instances generated from the Solomon benchmarks. A computational analysis is carried out with the aim of gaining insights into the behavior of both conventional vehicles and occasional drivers, and of analyzing the performance of our methodology in terms of effectiveness and efficiency. Our computational results show that the proposed heuristic is highly effective and can solve large-size instances within short computational times.