This paper is concerned with an optimal policy for empty container repositions. A single port is considered. The demand is modeled as a two-state Markov chain. The objective is to transport in and out containers so as to minimize the discounted holding, leasing, and repositioning costs. In this paper, the flow of containers is treated as though it is a continuous fluid. Dynamic programming is used to solve the optimal control problem. The associated HJB equations are used to characterize the value functions. The optimal policies are given in terms of threshold levels. Closed-form solutions of these threshold levels are obtained. Sufficient conditions are given in the form of a verification theorem. Numerical examples are reported to demonstrate the results.