An Evaluation of Integer Programming Models for Restaurant Reservations

Abstract

A notable difference in rooms (hotel) revenue management reservations versus table (restaurant) revenue management (TRM) reservations is the variation that occurs in duration. In the hotel setting, durations are explicit in the reservation itself: a stay of a specified number of nights. In restaurants, by contrast, there is a natural variation in the amount of time parties are at the table. This duration variation presents interesting challenges to TRM. Dealing with these challenges is our goal in the article. Specifically, we introduce and evaluate 10 different models for restaurant capacity and reservations, five each of two different types. In one type of model, tables are pooled and parties are not explicitly matched to tables; in the other parties are matched to specific tables. The objective is to maximize revenue (or contribution) from known reservation demand. Variables are both the mix of tables in the restaurant and the reservations accepted. An important ancillary goal we have is to evaluate the effectiveness of the models from the perspective of customers, specifically examining whether a table is ready for them at the time of the reservation, an issue of high importance to restaurant patrons. Of the 10 models, seven define a pareto frontier between revenue and service; of those seven, five are pooling models. We use this frontier to offer advice to restaurateurs looking to better manage reservations.