Robust Scheduling at a Large IT Services Delivery Center

We study a project scheduling problem at a large IT services delivery center in which there are unpredictable delays. We apply robust optimization to minimize tardiness while informing the customer of a reasonable worst-case completion time. Due to the impracticality of quantifying joint probability distributions for delay times, we follow the recent practice of using empirically determined uncertainty sets, which to our knowledge have not been applied to service scheduling. To solve instances of a realistic size, we introduce a new solution method based on logic-based Benders decomposition. We show that when the uncertainty set is polyhedral, convexity properties of the problem allow us to simplify the decomposition substantially, leading to a model of tractable size.