Integrated planning and allocation: A stochastic dynamic programming approach in container transportation

Container transportation has developed rapidly in recent years because of the growth of international trade. However, transportation demands along shipping lanes or in different regions are unbalanced and change over time. This high-growth and uncertain operation environment makes empty container-capacity management important and challenging. Carriers usually face two types of demands from forwarders/shippers with long-term contracts and from the spot market. Empty container-capacity planning and allocation are based on demand information from forwarders and the spot market. In this paper, we focus on the empty container-quantity decision problem over one planning horizon of multiple schedules, each with a random demand. The carrier builds empty container capacity with its own containers and leased containers. We construct a stochastic dynamic program model to maximize the profit of the carrier. The objective function is shown to be concave in empty container quantity. We can also formulate a static model and a myopic model. We run simulations by assuming that demand follow colored and white Gaussian Noise processes, we observe that the optimal empty container quantity using the static model is identical or close to identical to that from the dynamic model, while the optimal empty container quantity from the myopic model is always more than that from the dynamic model. Therefore, a simplified iteration algorithm utilizing the static and myopic models is developed to obtain the optimal dynamic solution efficiently. Numerical experiments show that the proposed algorithm is effective.