Robust Revenue Management with Limited Information : Theory and Experiments

Title of Dissertation: ROBUST REVENUE MANAGEMENT WITH LIMITED INFORMATION: THEORY AND EXPERIMENTS Yingjie Lan, Ph.D. candidate, 2008 Dissertation directed by: Professor Michael O. Ball R.H. Smith School of Business 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.