This paper develops a mathematical model for optimal overbooking limits for a three-room-type hotel. It is assumed that the hotel has low-, medium- and high-price rooms, and that upgrades and downgrades are possible but in one step only; that is, low-price rooms can be upgraded only to medium-price ones, high-price rooms can be downgraded to medium-price only, while medium-price rooms can be both downgraded to low-priced and upgraded to high-price. The optimal level of overbookings for each room type is calculated with the help of the expected marginal revenue technique. The paper identifies all possible combinations between the overbooking levels of each room type and the actual number of cancellations, no shows and early departures the hotel can face, and formulates the costs of the overbookings in each of these combinations.
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