Coordinating Pricing and Empty Container Repositioning in Two-Depot Shipping Systems

This paper studies joint decisions on pricing and empty container repositioning in two- depot shipping services with stochastic shipping demand. We formulate the problem as a stochastic dynamic programming (DP) model. The exact DP may have a high-dimensional state space due to in-transit containers. To cope with the curse of dimensionality, we develop an approximate model where the number of in-transit containers on each vessel is approxi- mated with a fixed container flow predetermined by solving a static version of the problem. Moreover, we show that the approximate value function is L♮-concave, thereby characterizing the structure of the optimal control policy for the approximate model. With the upper bound obtained by solving the information relaxation-based dual of the exact DP, we numerically show that the control policies generated from our approximate model are close to optimal when transit times span multiple periods