Analysis of Distribution-Free Methods for Revenue Management

Revenue management (RM) is one area of research and practice that has gained significant attention in the past decade. The practice originated in the airline industry, where the idea was to maximize revenues obtained from a fixed amount of resources through differentiation/segmentation and strategic use of pricing and capacity. While many of the research models take into account uncertainty, the uncertainty is modeled using random variables and known probability distributions, which is often difficult to estimate and prone to error for a variety of reasons. For instance, demand patterns can fluctuate substantially from the past, and characterizing demand from censored data is challenging. This dissertation focuses on the multifare single resource (leg) problem in RM. We consider the "limited information" case where the demand information available consists of lower and upper bounds rather than a characterization of a particular probability distribution or stochastic process. We first investigate the value of the amount and type of information used in solving the single-leg RM problem. This is done via extensive computational experiments. Our results indicate that new robust methods using limited information perform comparably to other well-known procedures. These robust policies are very effective and provide consistent results, even though they use no probabilistic information. Further, robust policies are less prone to errors in modeling demand. Results of our preliminary computations justify the use of robust methods in the multi-fare single-leg problem. We next apply this distribution-free approach to a setting where progression of demand is available through time-dependent bounds. We do not make any further assumptions about the demand or the arrival process beyond these bounds and also do not impose a risk neutrality assumption. Our analytical approach relies on competitive analysis of online algorithms, which guarantee a certain performance level under all possible realizations within the given lower and upper bounds. We extend the robust model from a problem using static information into a dynamic setting, in which time-dependent information is utilized effectively. We develop heuristic solution procedures for the dynamic problem. Extensive computational experiments show that the proposed heuristics are very effective and provide gains over static ones. The models and computations described above assume a single airline, disregarding competition. As an extension of robust decision-making, in the third part of this dissertation, we analyze a model with two airlines and two fare classes where the airlines engage in competition. The model does not use any probabilistic information and only the range of demand in each fare-class is known. We develop a game-theoretic model and use competitive analysis of online algorithms to study the model properties. We derive the booking control policies for both centralized and decentralized models and provide additional numerical results.