João Almeida

Abstract
Seaport cranes operate continuously and consume large amounts of energy while aiming to minimise containerships’ berthing time. Although previous studies have contributed to addressing the crane scheduling problem, most have focused exclusively on loading time, often overlooking the aspect of energy consumption. Furthermore, crane activity is typically modelled in a simplified manner—commonly assuming a fixed cycle duration or constant energy usage when handling a container—without accounting for the impact of variable container masses. In this study, an energy-aware quay crane scheduling formulation for container terminals is proposed, highlighting the importance of integrating an energy model into the scheduling problem. The optimisation problem is formulated as a Mixed Integer Linear Programming (MILP) model. The objective is to minimise total energy costs by reordering the sequence in which containers are handled, while respecting precedence constraints defined by the ship’s stowage plan. Two solution methods—a MILP approach solved using CPLEX and a genetic algorithm (GA)—are compared. The results indicate that, for larger containerships, the genetic algorithm provides a more efficient solution method. Moreover, incorporating detailed energy consumption models for electric cranes may significantly reduce energy costs during containership handling operations. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.