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Abstract
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.
Highlights
There are many ways to incorporate demand forecast information into inventory control models (Goltsos et al 2022), we take a common approach of including an exogenous stochastic demand process into the Markov decision process (MDP)
We propose an MDP formulation for the operation of an inland empty container inventory, allowing for multiple transportation modes with varying lead times, and facilitating the stochastic and dynamic nature of the environment
We extend existing empty container allocation models by accounting for varying lead times of transportation modes that are available in inland logistics networks
Summary
Global trade imbalances results in accumulation of empty containers in importdominant regions and shortages in export-dominant regions. This paper formulates a Markov decision process (MDP) for inland empty container inventory management with multiple modes of transportation available. The decision process allows us to capture the dynamic operations of a container depot, accommodating a fine time resolution and a long planning horizon, while accounting for serial and cross-sectional dependencies in uncertain future demand and returns. There are many ways to incorporate demand forecast information into inventory control models (Goltsos et al 2022), we take a common approach of including an exogenous stochastic demand process into the MDP This approach can likewise accommodate serial dependence of empty container returns and dependence between demand and returns, at the expense of expanding the state space. We analyze the existence of serial and cross-sectional dependencies in the empty container demand (by export customers) and returns (from import customers) processes, using real-world data.
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