Optimal Overbooking Limits for a 3-Room Type Hotel with Upgrade and Downgrade Constraints

Abstract

The paper develops a mathematical model for optimal overbooking limits for a 3-room type hotel. We assume that the hotel has low, medium and high priced rooms and upgrades and downgrades are possible but with one step only, i.e. low priced rooms can be upgraded only to medium priced ones, high priced rooms can be downgraded to medium priced only, while medium priced room can be both downgraded to low priced and upgraded to high priced rooms. The optimal level of overbookings for each room type is calculated with the help of the expected marginal revenue technique (Ivanov, 2006; Netessine & Shumsky, 2002). In the paper we identify 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 formulate the costs of the overbookings in each of these combinations.

Keywords: overbooking, hotel, upgrade constraints, downgrade constraints, expected marginal revenue