A branch and price approach for the Split Pickup and Split Delivery VRP

In this paper we address a Pickup and Delivery Vehicle Routing Problem where the demands of both pickup and delivery nodes can be split between several vehicles. We investigate a new formulation where the route of each vehicle is decomposed into a sequence of simpler substructures called clusters, mitigating the combinatorial explosion of feasible solutions. We implement a branch-and-price algorithm exploiting column generation procedures that dynamically generates clusters to obtain improved dual bounds, and ad hoc branching strategies to achieve integrality