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. The Set Partitioning model provides a natural representation of scheduling and rostering problems. In this talk, we will outline some practical applications of the set partitioning model and then discuss various mathematical properties of the model, which explain why some set partitioning problems are relatively easy to solve, and others are particularly difficult to solve. We will also outline some computational techniques based on these mathematical properties, which have been developed specifically to provide solutions to practical scheduling problems.
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