Skipped out on your restaurant reservation? That will be $200, please

Making restaurant reservations is a way of life -- but, for many consumers, so is breaking them. For every reservation that is made in some large cities, around 20% result in an empty table that the business must hope to fill with walk-in consumers. In an industry that, according to a Wall Street Journal article, often has margins as low as 3% to 5%, those are odds that some restaurants can't afford to bet on.

Why do consumers find it so easy to break their commitment to dine in a particular establishment at a particular time? According to Wharton PhD student Jaelynn Oh, it all comes down to perceived value. When someone makes a reservation, as far as the restaurant is concerned, the meal or meals have already been sold and managers will adjust their staffing and supply levels accordingly. It's a different story, however, for consumers.

"Reservations give convenience to customers and can sometimes attract more customers to a restaurant because they take away the wait time. But they are also a risk for restaurants," Oh says, noting that a reservation is a sign that, at the time of making the commitment, a consumer valued the chance to eat a particular establishment's food more than they valued spending that block of time a different way. But, in most cases, a reservation is a no-strings attached situation for consumers. If they decide at some point before the scheduled meal that they would rather eat somewhere else, or do something else, they can simply fail to show up.

Oh explores the problem of broken reservations in a new working paper, "Pricing Restaurant Reservations: Dealing with No-Shows," co-written with Wharton operations and information management professor Xuanming Su. Using a game theoretic model that took into account businesses' meal prices, diner capacities and other factors, she and Su suggest that many restaurants could maximize profits by employing a solution that involves both punishing customers who break their reservations and rewarding those who keep them. In addition, they note that some restaurants would be better off not taking any reservations at all.

Some restaurants have already started to fight back against no-shows. Le Bernadin, a three-Michelin-star seafood restaurant in New York, charges a $50 penalty to people who fail to show up or cancel their reservations less than 48 hours in advance. Oh notes that other establishments have implemented more public shaming by posting the names of diners who break their reservations on Twitter or Facebook. While most consumers don't think it's fair that they be charged for food they didn't eat, the researchers point out that "restaurant owners have a consensus that the industry is about space" as well as food.

"They consider the open space at dining tables to be the same as a manufacturing machine in a factory," Oh and Su write. "When the machine is not producing, they are losing money." Some restaurants, Oh adds, keep track of customers who don't show up and deny them the chance to make future reservations. Last year, another New York restaurant, Eleven Madison Park, began charging $75 per customer for parties that failed to show up or cancel in a timely manner, the WSJ reported.

"Other restaurants with similarly priced meals charge less -- $50, or even $20," Oh says. "We wanted to answer what is the correct profit-maximizing level that restaurants should charge. On the other hand, some restaurants are using incentive schemes to encourage more people to show up. These restaurants are trying to give discounts to customers who show up and are even giving different levels of discounts depending on the demand or popularity of a particular time slot."

Using their model, the researchers found that charging $50 or $20 isn't enough to make up for the cost of a no-show to a restaurant. They suggest that businesses should impose a fee on no-shows that is equivalent to the cost of eating there: For example, if a reservation was made for a party of four at an establishment where meals cost $50, the optimal fee for not showing up would be $200, or the equivalent of food and beverages for each member of the group. "That was quite shocking because most restaurants are not charging such a high no-show policy," Oh notes. But she says some establishments are, in effect, following such a model by selling tickets for their prix fixe tasting menus. "If customers don't show up, they lose the face value of the ticket," she states. "This is a smart way of framing a no-show fee. Although customers would pay the same price for not showing up either way, the psychology behind [a ticket policy] is different."

But Oh and Su write that restaurants will not get the most bang for their buck by only punishing those who fail to show up for reservations -- they must also reward those who do. "If a restaurant is going to price discriminate, it needs to give a discount to customers who ... bear the risk of paying a no-show penalty," they note. "Because walking in [without a reservation] is an outside option to making a reservation, there is pressure [on] the restaurant to make the inside option more attractive by charging a lower price."

They also point out that having a reservation policy isn't the best option for all restaurants. As the potential market for the business increases, accepting walk-in customers only or implementing a hybrid system of reservations and walk-ins brings in higher profits than relying purely on reservations, Oh says.

Oh cautions that the results detailed in the paper only show what is mathematically optimal. "When it comes to implementing a policy in reality, restaurants should consider that some customers go to very high-end restaurants because they may want to show that they are very sophisticated and that they are not going to wait," she notes. "In those cases where customers have a very, very high aversion to waiting, the restaurant may benefit by taking reservations as opposed to being purely walk-in even though its market size is large."

Carrots and Sticks

Oh and Su also applied their model to the circumstances of some real-life restaurants, including an Asian restaurant in Philadelphia that has about 100 seats at 40 tables. About 60% of the seats are filled through reservations and the rest through walk-ins. Meals cost about $50 a person and last around two hours. In calculating the optimal reservation policy for the establishment, the researchers noted that its main bottleneck had to do with table turnover, and also estimated a dollar value for customers' enjoyment of the meal based on the observation that 20% of reservation holders do not show up when the restaurant does not charge any no-show fee.

Taking all of those factors into consideration, Oh and Su say that the restaurant owners could increase profits by 7.4% by giving a 5% discount on less busy nights to customers who make a reservation and show up. Imposing a fee for no-shows didn't make much of a financial impact on nights with light traffic because the potential pool of customers is smaller. On the other hand, on busy nights -- when, the researchers write, the potential market for the restaurant is twice its total capacity -- they suggest that the owners could earn 14.5% more profit by charging a no-show fee equal to the price of a meal. "Therefore, [the restaurant] should consider giving discounts to reservation customers in slower time slots, such as Monday at 5 p.m., and charging a no-show penalty on busy weekends." Oh adds that the online reservation platform Savored.com uses a similar approach, offering discounts to users who make reservations for less popular nights and timeslots at participating restaurants.

While the model can point restaurants toward what is mathematically the best policy, Oh notes that businesses trying to pinpoint the right reservation policy also have to remember that customers' feelings can't necessarily be plugged into a statistical modeling framework. "I had one restaurant manager tell me that he thinks of what they're selling as real estate rather than food, because if someone has reserved a table, it means they have already purchased that capacity, so it makes sense to charge a no-show fee as high as the price of a meal. Although the customer hasn't consumed the food, when they make a reservation, they have already consumed the table," she says. "But when it comes to really implementing that kind of policy, the restaurateur should be careful. If they consider the chances of a customer making a repeat visit and customer goodwill, they may not want to upset [him or her] by charging such a high no-show fee."

On the other hand, "there is an opportunity for the customer, if they're smart enough to take advantage of potential discounts for keeping their reservations," Oh adds. "It could also turn them into repeat customers if this discount is given in the form of a loyalty program, as it is in OpenTable, where you can redeem a certain amount of points to get a gift certificate."