Green reverse logistics: Exploring the vehicle routing problem with deliveries and pickups

The Vehicle Routing Problem with Divisible Deliveries and Pickups (VRPDDP) is under-explored in the literature, yet it has a wide application in practice in a reverse logistics context, where the collection of returnable items must also be ensured along with the traditional delivery of products to customers. The problem considers that each customer has both delivery and pickup demands and may be visited twice in the same or different routes (i.e., splitting customers’ visits). In several reverse logistics problems, free capacity restrictions are required to either allow the movement of the driver inside the vehicle to rearrange the loads or to avoid cross-contamination between delivery and pickup loads. In this work, we explore the economic and the environmental impacts of the VRPDDP, with and without restrictions on the free capacity, and compare it with the traditional Vehicle Routing Problem with Simultaneous Deliveries and Pickups (VRPSDP), on savings achieved by splitting customers visits. An exact method, solved through Gurobi, and an ALNS metaheuristic are coded in Python and used to test well-known and newly generated instances. A multi-objective approach based on the augmented ϵ-constraint method is applied to obtain and compare solutions minimizing costs and CO2 emissions. The results demonstrate that splitting customer visits reduces the CO2 emissions for load-constrained distribution problems. Moreover, the savings percentage of the VRPDDP when compared to the VRPSDP is higher for instances with a random network than when a clustered network of customers is considered.