ROBUST REVENUE MANAGEMENT WITH LIMITED INFORMATION : THEORY AND EXPERIMENTS

Revenue management (RM) problems with full probabilistic information are well studied. However, as RM practice spreads to new businesses and industries, there are more and more applications where no or only limited information is available. In that respect, it is highly desirable to develop models and methods that rely on less information, and make fewer assumptions about the underlying uncertainty. On the other hand, a decision maker may not only lack data and accurate forecasting in a new application, but he may have objectives (e.g. guarantees on worst-case profits) other than maximizing the average performance of a system. This dissertation focuses on the multi-fare single resource (leg) RM problem with limited information. We only use lower and upper bounds (i.e. a parameter range), instead of any particular probability distribution or random process to characterize an uncertain parameter. We build models that guarantee a certain performance level under all possible realizations within the given bounds. Our methods are based on the regret criterion, where a decision maker compares his performance to a perfect hindsight (offline) performance. We use competitive analysis of online algorithms to derive optimal static booking control policies that either (i) maximize the competitive ratio (equivalent to minimizing the maximum regret) or (ii) minimize the maximum absolute regret. Under either criterion, we obtain closed-form solutions and investigate the properties of optimal policies. We first investigate the basic multi-fare model for booking control, assuming advance reservations are not cancelled and do not become no-shows. The uncertainty in this problem is in the demand for each fare class. We use information on lower and upper bounds of demand for each fare class. We determine optimal static booking policies whose booking limits remain constant throughout the whole booking horizon. We also show how dynamic policies, by adjusting the booking limits at any time based on the bookings already on hand, can be obtained. Then, we integrate overbooking decisions to the basic model. We consider two different models for overbooking. The first one uses limited information on no-shows; again the information being the lower and upper bound on the no-show rate. This is appropriate for situations where there is not enough historical data, e.g. in a new business. The second model differs from the first by assuming the no-show process can be fully characterized with a probabilistic model. If a decision-maker has uncensored historical data, which is often the case in reality, he/she can accurately estimate the probability distribution of no-shows. The overbooking and booking control decisions are made simultaneously in both extended models. We derive static overbooking and booking limits policies in either case. Extensive computational experiments show that the proposed methods that use limited information are very effective and provide consistent and robust results. We also show that the policies produced by our models can be used in combination with traditional ones to enhance the system performance

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