In this paper, we consider the classical multifare, single-resource (leg) problem in revenue management for the case where demand information is limited. Our approach employs a competitive analysis, which guarantees a certain performance level under all possible demand scenarios. The only information required about the demand for each fare class is lower and upper bounds. We consider both competitive ratio and absolute regret performance criteria. For both performance criteria, we derive the best possible static policies, which employ booking limits that remain constant throughout the booking horizon. The optimal policies have the form of nested booking limits. Dynamic policies, which employ booking limits that may be adjusted at any time based on the history of bookings, are also obtained. We provide extensive computational experiments and compare our methods to existing ones. The results of the experiments demonstrate the effectiveness of these new robust methods.revenue management, robust optimization, competitive analysis

For various parameter combinations, the logistic-exponential survival distribution belongs to four common classes of survival distributions: increasing failure rate, decreasing failure rate, bathtub-shaped failure rate, and upside-down bathtub-shaped failure rate. Graphical comparison of this new distribution with other common survival distributions is seen in a plot of the skewness versus the coefficient of variation. The distribution can be used as a survival model or as a device to determine the distribution class from which a particular data set is drawn. As the three-parameter version is less mathematically tractable, our major results concern the two-parameter version. Boundaries for the maximum likelihood estimators of the parameters are derived in this article. Also, a fixed-point method to find the maximum likelihood estimators for complete and censored data sets has been developed. The two-parameter and the three-parameter versions of the logistic-exponential distribution are applied to two real-life data sets.

Focusing on a seller's regret in not acting optimally, we develop a model of overbooking and fare-class allocation in the multifare, single-resource problem in revenue management. We derive optimal static overbooking levels and booking limits, in closed form, that minimize the maximum relative regret (i.e., maximize competitive ratio). We prove that the optimal booking limits are nested. Our work addresses a number of important issues. (i) We use partial information, which is critical because of the difficulty in forecasting fare-class demand. Demand and no-shows are characterized using interval uncertainty in our model. (ii) We make joint overbooking and fare-class allocation decisions. (iii) We obtain conservative but practical overbooking levels that improve the service quality without sacrificing profits. Using computational experiments, we benchmark our methods to existing ones and show that our model leads to effective, consistent, and robust decisions.revenue management, worst-case analysis, regret, overbooking, fare-class allocation

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