Markov decision processes for inland empty container inventory management

Container logistics companies store empty containers at depots, from where they are delivered to export customers satisfying demand for shipping freight, or to where they are returned from import customers receiving freight. Imbalances between demand and supply require frequent repositioning of empty containers. We formulate the inland single-depot empty container reposition problem as a capacitated multiple supplier periodic review inventory management problem. Our development of a discrete-time Markov decision process extends existing inventory models by explicitly accounting for varying lead-times and costs of different transportation modes for receiving empty containers from other depots. Furthermore, we suggest a detailed statistical model for the underlying process of exogenous demands and returns of containers. Extensive computational results illustrate the importance of accurately accounting for the dynamics in modeling empty container repositioning. Our test instances reveal that failure to capture varying lead times and costs may significantly inflate operating costs. We likewise quantify the impact of ignoring serial and cross-sectional dependencies in the exogenous process. Using real-world data for empty container demands and returns, we find costs to be inflated by 7-9%. Further tests, however, show that undetected serial dependencies may have much greater effects on costs under extreme conditions of further undetected and unfavorable cross-sectional dependencies.