Improved models for a single vehicle continuous-time inventory routing problem with pickups and deliveries

We consider an inventory routing problem in which a single vehicle is responsible for the transport of a commodity from a set of supply locations to a set of demand locations. At each location the inventory must be kept within predefined bounds, and the location specific supply and demand rates are constant throughout the time horizon. Each location can be visited several times during the time horizon, and the vehicle can visit the locations in any order as long as the capacity of the vehicle is not exceeded. Two models are presented, each defined on a different extended network. In a location-event model, the nodes are indexed by the location and the number of visits made so far to that location, while in a vehicle-event model the nodes are indexed by the location and the number of visits so far on the vehicle route. Both models are based on continuous time formulations. They are tightened with valid inequalities, and a new branching algorithm is designed to speed up the solution time of the models. Computational tests based on a set of maritime transportation instances are reported to compare both models and the corresponding tightened variants.