A single vehicle routing problem with fixed delivery and optional collections

The Single-Vehicle Routing Problem with Fixed Delivery and Optional Collections considers a set of delivery customers receiving goods from a depot and a set of collection customers sending goods to the same depot. All delivery customers must be visited by the vehicle, while a collection customer is visited only if the capacity of the vehicle is large enough to fit the collected load and the visit reduces collection costs that would be otherwise incurred. The goal is to minimize the transportation and collection costs. A model is proposed and solved utilizing a branch-and-cut method. Efficient new cuts are proposed. Computational experience is offered on two sets of test problems. It is proved possible to solve instances that previous methods were unable to solve. The method was tested on larger instances.