The Vehicle Routing Problem with Divisible Deliveries and Pickups

Abstract

T he vehicle routing problem with divisible deliveries and pickups is a new and interesting model within reverse logistics. Each customer may have a pickup and delivery demand that have to be served with capacitated vehicles. The pickup and the delivery quantities may be served, if beneficial, in two separate visits. The model is placed in the context of other delivery and pickup problems and formulated as a mixed-integer linear programming problem. In this paper, we study the savings that can be achieved by allowing the pickup and delivery quantities to be served separately with respect to the case where the quantities have to be served simultaneously. Both exact and heuristic results are analysed in depth for a better understanding of the problem structure and an average estimation of the savings due to the possibility of serving pickup and delivery quantities separately.

Adaptive large neighborhood search for the commodity constrained split delivery VRP

“…In this case, because of the limited quantities available for each commodity at each depot, it is worth considering splitting deliveries to find feasible solutions. Another interesting variant of the problem is the VRP with divisible deliveries and pickup (Gribkovskaia et al (2007), Nagy et al (2015)): in this case, delivery and pickup naturally represent two different commodities, but a pickup operation increases the use of the vehicle capacity, and it could then be optimal to visit twice the same customer in one route.…”

“…Columns nbN earDepot and nbLargeDemand report the number of split customers located near the depot and the number of split customers with a large demand respectively. As Nagy et al (2015), we consider that a customer is located near the depot if he or she is one of the 25% of customers closest to the depot; and we consider that a customer has a large demand if he or she is one of the 25% of customers with the largest demand. Note that the demand of a customer is the sum of the demands for the commodities they need.…”

“…Column nbCluster reports the number of split customers located inside a cluster of customers. As Nagy et al (2015), we consider a customer to be in a cluster if at least five other customers are inside its neighborhood. Two customers are neighbors if the distance between these two customers is less than 30% of the average distance between the depot and all the customers in the instance.…”

Capacitated vehicle routing problem with pick-up and alternative delivery (CVRPPAD): model and implementation using hybrid approach

“…(Nielsen et al 2014b;Nielsen et al 2014a) and implementation in the cloud (Deniziak et al 2013). The model is planned to be enriched with fuzzy logic (Bocewicz et al 2016).…”

“…Most of VRPs and their variants are modeled as integer linear program (ILP) problems with two-index or rarely with three-index decision variables for the commodity flow (Nagy et al 2015). According to the assumptions made, the presented problem (Sect.…”