Pricing Restaurant Reservations: Dealing with No-Shows

Abstract

Reservation no-shows lead to wasted capacity in restaurants. In this paper we consider two remedies: punishing no-shows by charging fees and encouraging show-ups by giving discounts. We model the restaurant as a service queue and its reservation policy as an advance selling strategy. When customers make reservations in advance, they face uncertainty in the value of (future) consumption. Reservation holders commit to show up and bear the risk of incurring a no-show penalty in return for a no-wait guarantee. We solve for the restaurant’s optimal pricing policy and no-show penalty. Our analysis suggests that restaurants should charge a no-show penalty as high as the price of meal while giving a discount to reservation holders for the meal. These results are consistent with the current practice of some high-end restaurants selling non-refundable tickets for their prix-xe menus where ticket holders lose the face value of the ticket when they fail to show up. Also, there are online reservation systems that give discounts to customers making restaurant reservations through their website. Our results also suggest that as a restaurant faces a larger potential market, it should allocate less capacity for reservation customers. When the market size exceeds a certain threshold, the restaurant is better o if it stops taking reservations.