A Stochastic Programming Approach to the Airline Crew Scheduling Problem

Traditional methods model the billion-dollar airline crew scheduling problem as deterministic and do not explicitly include information on potential disruptions. Unfortunately, the effort used to optimize crew schedules and reduce crew costs is often wasted as flight schedules are often disrupted. Consequently, airlines spend a great deal of time and money optimizing crew schedules in the planning phase only to change and readjust the crew schedules in the operational phase in response to disruptions. Disruptions are expensive and lead to loss of time, money, and customer goodwill. Instead of modeling the crew scheduling problem as deterministic, we consider a stochastic crew scheduling model and devise a solution methodology for integrating disruptions in the evaluation of crew schedules. The goal is to use that information to find robust solutions that better withstand disruptions. Such an approach is important because we can proactively consider the effects of certain scheduling decisions. By identifying more robust schedules, cascading delay effects will be minimized. In this paper we describe our stochastic integer programming model for the airline crew scheduling problem and offer a branching algorithm to identify expensive flight connections and find alternative solutions. The branching algorithm uses the structure of the problem to branch simultaneously on multiple variables without invalidating the optimality of the algorithm. We present computational results demonstrating the effectiveness of our branching algorithm.