Coordinated optimization of equipment operations in a container terminal

Abstract Increasing international maritime transport drives the need for efficient container terminals. The speed at which containers can be processed through a terminal is an important performance indicator. In particular, the productivity of the quay cranes (QCs) determines the performance of a container terminal; hence QC scheduling has received considerable attention. This article develops a comprehensive model to represent the waterside operations of a container terminal. Waterside operations comprise single and twinlift handling of containers by QCs, automated guided vehicles and yard cranes. In common practice, an uncoordinated scheduling heuristic is used to dispatch the equipment operating on a terminal. Here, uncoordinated means that the different machines that operate in the container terminal seek optimal productivity solely considering their own respective stage. By contrast, our model provides a coordinated schedule in which operations of all terminal equipment can be considered at once to achieve productivity closer to the QC optimal. The model takes the form of a hybrid flow shop (HFS) with novel features for bi-directional flows and job pairing. The former enables jobs to move freely through the HFS in both directions; the latter constrains certain jobs to be performed simultaneously by a single machine. We solve the coordinated model by means of a tailored simulated annealing (SA) algorithm that balances solution quality and computational time. We empirically study time-bounded variants of SA and compare them with a branch-and-bound algorithm. We show that our approach can produce coordinated schedules for a terminal with up to eight QCs in near real time.