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Risk-sensitive capacity control in revenue management. (English) Zbl 1139.91014
Consider a single-leg flight of an airplane, where each customer requests a single seat, and neither cancellation nor no-shows are considered. The problem is to determine which exogenously arriving requests to accept or reject assuming that customer demand is independent between booking classes and of the controls being applied. The corresponding model is called the static capacity control model if demand for each booking class arrives in non-overlapping periods. The dynamic capacity control model allows passengers to arrive in any order.
In the paper, the authors extend both the static and the dynamic capacity control model in revenue management using the concept of a risk-sensitive Markov decision model in the spirit of R. A. Howard and J. E. Matheson [Manage. Sci., Theory 18, 356–369 (1972; Zbl 0238.90007)] for a decision-maker with an exponential utility function. They show that all well-known structural results of the expected revenue maximizing policy hold for the resulting risk-sensitive optimal policy as well. In particular, it is shown that an optimal booking policy can be characterized by protection levels, depending on the actual booking class and the remaining time. Moreover, monotonicity of the protection levels with respect to the booking class and the remaining time are proven.

MSC:
91B06 Decision theory
91B30 Risk theory, insurance (MSC2010)
91B16 Utility theory
90C40 Markov and semi-Markov decision processes
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