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

Abstract

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 [Formula: see text]-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.