Bi-Level Optimization for the Effective Utilization of Resources in a Maritime Container Terminal in Case of Unusual Disruptions

Kurzfassung

Managing the flow of containers efficiently is a key challenge in modern multi-modal terminals, especially when considering disruptions and unusual scenarios with highly irregular arrival patterns. This paper investigates a bi-level optimization approach for controlling container flows in case of scenarios with large amounts of containers arriving at the terminal within a shorter period of time. Precisely, the upper-level problem aims to determine suitable weighting parameters that influence an efficient handling of disruptions, while the lower-level problem models the resulting container dynamics in a regular setting without any disruptions. The bi-level optimization problem is reformulated via Karush--Kuhn--Tucker conditions and solved numerically as a mathematical program with complementarity constraints. To improve numerical performance, a regularization method and the so called Fischer--Burmeister relaxation technique is investigated. The results indicate that the Fischer--Burmeister relaxation shows a more robust behaviour with respect to changes in the corresponding parameters, compared to the regularization scheme. Thus, it is necessary to choose the parameters carefully to balance solution quality and efficiency. From a practical perspective, the optimized parameters enable a stable container flow management and prevent congestion by effectively utilizing the yard as a buffer, the results show that using bi-level optimization, more than twice as many containers can be stored in the yard. This highlights the potential of bi-level optimization for real-world terminal operations.