The single vehicle routing problem with deliveries and selective pickups

The single vehicle routing problem with deliveries and selective pickups (SVRPDSP) is defined on a graph in which pickup and delivery demands are associated with customer vertices. The difference between this problem and the single vehicle routing problem with pickups and deliveries (SVRPPD) lies in the fact that it is no longer necessary to satisfy all pickup demands. In the SVRPDSP a pickup revenue is associated with each vertex, and the pickup demand at that vertex will be collected only if it is profitable to do so. The net cost of a route is equal to the sum of routing costs, minus the total collected revenue. The aim is to design a vehicle route of minimum net cost, visiting each customer, performing all deliveries, and a subset of the pickups. A mixed integer linear programming formulation is proposed for the SVRPDSP. Classical construction and improvement heuristics, as well as a tabu search heuristic (TS), are developed and tested on a number of instances derived from VRPLIB. Computational results show that the solutions produced by the proposed heuristics are near-optimal. There is also some evidence that the best solutions identified by the heuristics are frequently non-Hamiltonian and may contain one or two customers visited twice.