Crowdshipping: An open VRP variant with stochastic destinations

E-commerce continues to grow throughout the world due to people’s preference to stay at home rather than going to a brick-and-mortar retail store. COVID-19 has exacerbated this trend. Concurrently, crowd-shipping has been gaining in popularity due to both the increase in e-commerce and the current pressures due to COVID-19. We consider a setting where a crowd-shipping platform can fulfill heterogeneous delivery requests from a central depot with a fleet of professionally driven vehicles and a pool of capacitated occasional drivers. We divide delivery requests into sectors to represent different neighborhoods in a city. Occasional drivers have unknown destinations that can be anywhere inside the sectors. Route duration constraints are modeled to motivate participation and increase the probability of route-acceptance by keeping routes short. We assume that occasional drivers will choose routes that are better compensated and that the probability of route-acceptance is dependent on other routes being offered. We propose a two-stage stochastic model to formulate the problem. We use a branch-and-price algorithm capable of solving 50-customer instances, and develop a heuristic that can solve larger 100-customer instances quickly. An upper bound for the total number of occasional drivers is used to reduce the number of constraints in the master problem and reduce the complexity of the pricing problems. We show that occasional drivers with destinations far from the depot reduce the cost by over 30%, while occasional drivers with destinations that are near the depot reduce the cost by 20%. We show that route duration constraints and capacity constraints can restrict the occasional driver routes and both need to simultaneously increase in order to have cost reductions. This setting of crowd-shipping is a viable option for last-mile deliveries.