Robust Optimization Approach to Empty Container Repositioning, in Handbook of Ocean Container Transport Logistics

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