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 model. The exact dynamic program may have a high-dimensional state space because of the 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 approximated 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 dynamic program, we numerically show that the control policies generated from our approximate model are close to optimal when transit times span multiple periods.