Cross docking for libraries with a depot

Library organizations in the Netherlands show an increasing interest to employ depots for low-cost storage and demand fulfillment of item requests. Typically, all libraries organization have a shared catalog, and, on local unavailability, requests can be shipped from elsewhere organization. The depot used consolidate shipment by making tours along libraries, delivering requested items, but also picking up items that stored at depot, or one library another. Cross docking delayed shipments are two preferred methods fulfilling cannot directly met using on-hand stock depot. In this paper, we compare these inventory control perspective. We model system as Markov Decision process. For one- two-location systems, derive analytical results average-cost optimal policy, showing decision store location satisfies threshold structure depending number rented items. larger instances, effective heuristic is proposed exploiting structure. numerical experiments, important managerial insights obtained comparing cross different situations. shown add most value systems with low total stock, however, may achieve similar costs when high frequently visit locations. Furthermore, decisions based simple formulations memoryless rental time distributions.