The efficient management of maritime logistics operations improves the performance of global supply chains. An important issue in container terminal operations is the scheduling of quay cranes (QCs), which is affected by the productivity rate of QCs. This productivity rate depends on the type of tasks to be completed by QCs on any given vessel. In this paper, we propose an artificial neural network (ANN) model with a variable neighbourhood search (VNS) as a training algorithm to build a productivity rate predictive model. This model considers several predictors depending on the type of containers in the vessel and the expected equipment downtime. We also study how QC scheduling is impacted by the productivity rate of QCs. The proposed predictive model and a moving average model are used to estimate the productivity rate, which is then taken as input to the QC scheduling optimisation model. Results show that when the proposed predictive model is used, QC schedules are closer to those generated using real data obtained from our container terminal partner.