This paper introduces a class of problems which integrate pickup and delivery vehicle routing problems (PDPs) and inventory management, and we call them inventory routing problems with pickups and deliveries (IRP-PD). We consider a specific problem of this class, where a commodity is made available at several origins and demanded by several destinations. Time is discretized and transportation is performed by a single vehicle. A mathematical programming model is proposed together with several classes of valid inequalities. The models are solved with a branch-and-cut method. Computational tests are performed to show the effectiveness of the valid inequalities on instances generated from benchmark instances for the inventory routing problem. Results show that the branch-and-cut algorithm is able to solve to optimality 345 over 400 instances with up to 50 customers over 3 periods of time, and 142 over 240 instances with up to 30 customers and 6 periods. From a management perspective, results show that the average cost of a non integrated policy is more than 35% higher than the cost of an integrated policy. Link to the article
ARCHETTI, C., CHRISTIANSEN, M. and GRAZIA SPERANZA, M. (2018). Inventory routing with pickups and deliveries. European Journal of Operational Research, 268(1), pp. 314-324.