SWAPPING THE ORDER OF SCHEDULED SERVICES TO MINIMIZE EXPECTED COSTS OF DELAYS

In a variety of contexts particularly in public transportation, activities are timetabled in advance. However, when the timetable is in operation, there are usually random variations in activity times, so that some activities are not ready to start at their scheduled times. To reduce the knock-on effects and costs from this, operators may swap the order of such activities and start on the next activity while waiting for a delayed activity to become ready to start . The authors investigate the question of how long the operator should wait before swapping activities or whether to swap at all. How long to wait before swapping (the optimal swap time s) depends on the probabilities of delays and on the various costs of delays. For specificity, and because it is a particularly interesting general case, the authors use the example of a scheduled train service to illustrate the discussion throughout