In global container liner networks, the costly operations of empty container repositioning are necessitated by the imbalance of cargo flows across regions. Up to 40 and 60 % of containers shipped from Europe and North America to Asia are empty, respectively. Repositioning costs are sizable, often amounting up to 5-6 % of a shipping lines revenue. Therefore, identifying an optimal repositioning schedule to rebalance empty containers with minimal cost is one of the most critical planning problems in liner shipping. This is often complicated by the stochastic nature of demand and long transportation lead times. In this paper, we formulate a multiple-stage stochastic programming problem for the optimal repositioning of containers for a liner shipping network. As the problem is highly complex, the stochastic programming formulation is not computationally tractable. Therefore, we utilize emerging techniques in robust optimization to provide a tight approximation (bond) on the stochastic version of the problem. The resulting formulation is a second-order cone program (SOCP) and is computationally tractable. With this approximation, we perform computational experiments to evaluate the effectiveness of different repositioning policies.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.