To improve the operational efficiency of container terminals, it is important to consider the coordination of different types of container-handling equipment, which typically include vehicles, yard cranes and quay cranes. This paper addresses the integration of scheduling each constituent of handling equipment in an automated container terminal, in order to minimise the loading element of the ship’s berthing time. A mixed-integer programming (MIP) model was developed to mathematically formulate this challenge. Small-sized problems can be solved optimally using existing solver. In order to obtain approximately optimal solutions for large-sized problems, an adaptive heuristic algorithm was created that can adjust the parameters of a genetic algorithm (GA), according to the observed performance. Experiments were carried out for both small-sized and large-sized problems to analyse the impact of equipment used in the loading process on berthing and computation times, as well as to test the efficiency of our proposed adaptive GA in solving this integrated problem.