Robust Optimization for Empty Container Allocation Problems Under Uncertainties

Owing to trade imbalance, the challenge faced by liners is how to effectively manage their empty containers. In this paper, we develop a two-stage robust optimization model with a recourse function for solving the dynamic empty container allocation problems under net demand uncertainties. The level of conservatism is taken into account through a budget of uncertainty (Gamma), which is determined by the risk preference of decision-makers. We analyze the recourse function under the worst-case scenarios within the uncertainty budget set, transform the robust optimization model into a linear programming problem with a large number of constraints, and design an efficient solution method based on the properties of the model. Numerical experiments show that the price of robust in our model is low, and the CPU time is acceptable for industrial applications.