A continuous-time supply-driven inventory-constrained routing problem

We address an inventory routing problem (IRP) in which routing and inventory decisions are dictated by supply rather than demand. Moreover, inventory is held in containers that act as both a storage container and a movable transport unit. This problem emanates from logistics related to biogas transportation in which biogas is transported in containers from many suppliers to a single facility. We present a novel and compact formulation for the supply-driven IRP which addresses the routing decisions in continuous-time in which inventory levels within the containers are continuous. Valid inequalities are included and realistic instances are solved to optimality. For all experiments, we found that the total transportation time is minimized when the storage capacity at each supplier is larger than or equal to the vehicle capacity. These routes are characterized by tours in which mostly single suppliers are visited. In 95% of the instances, the average content level of the exchanged containers exceeded 99.6%.