Scheduling and rostering problems involving valuable resources such as vehicles, machines or personnel occur in many organizations. Efficient utilization of these resources is obviously an important management consideration. From a mathematical point of view, scheduling applications give rise to many very challenging problems in combinatorial and computational optimization.

In this talk we discuss the development of a single optimisation model which schedules both trains and their associated train drivers. The train scheduling (or timetabling) problem seeks to construct a legal timetable for a specified number of trains that minimises train delays. The driver scheduling problem constructs minimal cost driver shifts for a given train timetable. These two problems are usually considered in sequence and their obvious interaction is ignored. The combined model includes a continuous linear component and a set partitioning like zero-one integer component which are related through a set of linking constraints. These constraints are dynamically generated as required during the solution process. Further constraints associated with train crossings are implemented during the branch and bound procedure used to generate integer solutions.

The model is applied to a specific train scheduling problem in New Zealand and results are presented to demonstrate that the simultaneous optimisation approach provides better solutions than those obtained from the standard sequential approach.