Robust Optimization with Recovery: Application to Shortest Paths and Airline Scheduling

In this exploratory paper we consider a robust approach to decisional problems subject to uncertain data in which we have an additional knowledge on the strategy (algorithm) used to react to an unforeseen event or recover from a disruption. This is a typical situation in scheduling problems where the decision maker has no a priori knowledge on the probabilistic distribution of such events but he only knows rough information on the event, such as its impact on the schedule. We discuss a general framework to address this situation and its links with other existing methods, we present an illustrative example on the Shortest Path problem with Interval Data (SPPID) and we discuss a more general application to airline scheduling with recovery.