Transshipment and rebalancing policies for library books

Library customers can soon order books online and specify a location to collect them from. Libraries exchange books between locations to meet these requests. Two types of exchanges take place: transshipments from library to library to fulfill the requests and rebalancing to redistribute books between libraries. This research determines optimal decisions for transshipments and rebalancing, so that logistic costs in the library system are minimized. In current practice, libraries typically send the book back to the original library after return. We consider a more general policy, in which we rebalance books in anticipation of demand. Moreover, we determine the optimal location from which to transship a book when it is unavailable at the location of demand. By means of stochastic dynamic programming, we derive the optimal policy for small instances. For larger instances we present two heuristics: the cluster and the expected shortage reduction (ESR) heuristic. The ESR heuristic proves to be near-optimal and significantly outperforms current practice.