Robust Optimisation for an Integrated Model of Berth and Quay Crane Assignment at Maritime Container Terminals Respecting Uncertain Numbers of Quay Cranes

Efficient management of berth and quay crane assignment is critical for optimising operations at maritime container terminals. This paper addresses the integration of berth and quay crane assignment, recognising the essential role it plays in terminal efficiency. The deterministic nature of assigning quay cranes is challenged by uncertainties, primarily due to their potential breakdowns but also influenced by factors such as maintenance schedules and workforce availability. To address this complex problem, we formulate it as a mixed integer mathematical model, where the uncertainties appear on the right-hand side (RHS) of a block of constraints. This is a special stochastic formulation, which is much worth investigating. Due to the NP-hardness of the problem, we propose a matheuristic approach that combines variable neighbourhood search (VNS) and fixed set search (FSS) with mathematical optimisation of sub-problems with a standard solver. The approach aims to find robust solutions that account for uncertainties in the number of available quay cranes at each time period based on some possible scenarios. We conduct extensive experiments using two alternative algorithms. One is a method from the literature and the other is our methodology without mathematical optimisation. Results from testing on a set of randomly generated instances of varying sizes demonstrate the effectiveness of our proposed matheuristic. On average, our approach outperforms alternative methods, providing superior results in optimising berth and quay crane assignment at maritime container terminals under uncertain conditions.