This paper describes a study of the dispatch planning/scheduling process for inbound containers handled with a reach stacker. Client container pickup is scheduled at least one day in advance for one of six two-hour time windows (six five-container-high stacks per time window) on a given day. A buffer area is available for the containers to be moved in when clients are being served. The aim of this study was to determine the conditions required to ensure that all the containers are dispatched within the scheduled time window and so meet the clients’ requirements. To this end, the performance indicators were identified and compared using simulations as an analytical tool. The results indicate that the shortest-processing-time (SPT) queueing discipline is preferable to the first-come-first-served (FCFS) discipline and that client arrivals can usefully be restricted to periods shorter than two hours in order to meet container-dispatch and service-quality objectives.