A Multivariate Adaptive Regression Splines Cutting Plane Approach for Solving a Two-Stage Stochastic Programming Fleet Assignment Model. COSMOS Technical Report 10-06. The University of Texas at Arlington. Arlington, TX. VENKATA L. PILLA, JAY M. ROSENBERGER, VICTORIA C.P. CHEN, NARAKORN ENGSUWAN, SHEELA SIDDAPPA Abstract The fleet assignment model assigns a fleet of aircraft types to the scheduled flight legs in an air- line timetable published six to twelve weeks prior to the departure of the aircraft. The objective is to maximize profit. While costs associated with assigning a particular fleet type to a leg are easy to estimate, the revenues are based upon demand, which is realized close to departure. The uncertainty in demand makes it challenging to assign the right type of aircraft to each flight leg based on forecasts taken six to twelve weeks prior to departure. Therefore, in this paper, a two- stage stochastic programming framework has been developed to model the uncertainty in demand, along with the Boeing concept of demand driven dispatch to reallocate aircraft closer to the de- parture of the aircraft. Traditionally, two-stage stochastic programming problems are solved using the L-shaped method. Due to the slow convergence of the L-shaped method, a novel multivari- ate adaptive regression splines cutting plane method has been developed. The results obtained from our approach are compared to that of the L-shaped method, and the value of demand-driven dispatch is estimated. Keywords: Stochastic Programming, Airline Fleet Assignment model, L-shaped method 1. Introduction In the airline industry, many airlines are confronted with increased competition from other car- riers while they continue to address labor costs. Furthermore, high fuel costs have impacted the entire industry. Therefore, airlines try to find ways to reduce costs, increase profits, and improve load factors. One interesting option to reduce cost and increase revenues is to balance supply (seats) and demand (passengers). If an airline assigns an aircraft with too much capacity, flights will depart with empty seats. If an airline assigns an aircraft with insufficient capacity, this may cause lost (spilled) customers because of seat shortage. Consequently, airlines use a Fleet As- signment Model (FAM) in order to balance supply and demand. The objective of this model is to maximize profit (revenue minus operating costs). FAM has been credited for saving costs and improving airline operations. At American Airlines, improvement in operating margins increased 1.4% (Abara 1989). FAM has saved about $15M of operating costs at US Airways (Rushmeier and Kontogiorgis 1997) and $100M at Delta (Subramanian et al. 1994). The accuracy of cost and profit estimates is an important factor for the quality of a FAM solution. Cost estimates are relatively stable and known whereas revenue estimates depend on demand predictions. There are several Preprint submitted to Elsevier July 31, 2010