What to do about no-shows

What is the best policy for an organization to follow regarding people who make reservations but then never show up? I was reading about this in the context of restaurants, some of which, as a result of the costliness of broken reservations (which result in empty tables that could have been filled by latecomers), have simply ended the practice of taking reservations at all.

Tom Sietsema, in the Washington Post, is not amused:

Eager to explore the Thai fireworks at Little Serow in Dupont Circle at prime time? Prepare to wait up to three hours on weekends for one of fewer than 30 seats. Meanwhile, ramen slurpers know it’s easier to access Toki Underground on H Street NE on weekdays, when the wait might be a mere hour, versus the weekend, when the drill can take three times as long.

Now, it might be that some restaurants *want* the line-ups, as it is a way of advertising the restaurant as a popular place. But at the same time it might be losing a loyal customer base that would have been valuable once the trendiness of the eatery has dissipated.

But cancelled reservations are a costly problem. At Slate, L.V. Anderson writes:

… a policy of fining no-shows doesn’t scare off all untrustworthy diners—nor does it always help restaurants recoup the lost revenue associated with no-shows. No-shows have been known to cancel their credit cards or dispute the charges on their statement in order to evade cancellation fees. The only way to legally ensure that a restaurant will be able to collect cancellation fees is to make patrons sign a contract when they make their reservation, or to force customers to put down a deposit instead of just threatening to charge their card in the event that they don’t show up. Even then, “Restaurant managers run the risk of coming off as jerks and losing future business if they don’t waive the fee when someone has a good excuse, whether it’s real or not,” as Jessica Sidman wrote in Washington City Paper recently.

There seem to be bad feelings all around. What if the cancellation had a very good excuse – an illness, a delayed flight?

Let me suggest a solution from the economics of contracts. Have people place a deposit when making a reservation, non-refundable, where the amount of the deposit is equal to the amount by which the profit of the restaurant is increased by the reserving party actually showing up, rather than being a no-show. This would involve a calculation (admittedly imprecise) of the revenue minus costs (of preparing the food, serving and cleaning the table) if the party shows up, and of the probability of filling the table anyway even if they don’t. For example, suppose the *profit* from a table for two showing up at the Peach Garden restaurant is about $40, and suppose that if they don’t show, there is a 50:50 chance of some other couple taking the table. Then the expected loss to Peach Garden from a no-show is $20 (a 50% chance of losing $40). Then the deposit for the reservation should be $20.

Economists call such a policy efficient breach. What’s so efficient about it? We want a level of deposit such that the customer will honor the reservation when the sum of benefits to them and to the restaurant if they show up is greater than the sum of benefits if they breach the reservation. And it makes sense for the reservation to be cancelled if in fact that would lead to greater total benefits than with the customer honoring the reservation.

So, suppose, as above, the cost to Peach Garden from a broken reservation is $20 for a table for two. Consider two scenarios.

In the first, for whatever reason, the customer at the last moment thinks that going to Sunny Palace would be better than honoring his reservation at Peach Garden. Indeed, in the absence of any penalties for defaulting on a reservation, he would be willing to pay $30 more to go to Sunny Palace than to Peach Garden. If the deposit at Peach Garden is $20, he will forget the reservation (and regret having made it) and go to Sunny Palace, and be better off having done so. Peach Garden is no worse off (it gets its deposit to compensate for expected losses) and so the outcome is for the best. But suppose the deposit at Peach Garden had been $40. Then the customer will stick with the Peach Garden restaurant – Sunny Palace is not worth giving up $40. But that is inefficient – the customer is forgoing a choice that would have been (in his mind) $30 better, just to save Peach Garden $20 loss from a cancelled reservation. If Sunny Palace is so preferred, then it is better the Peach Garden reservation be broken. But a deposit set too high will prevent this.

Second scenario: now suppose a different customer has made a $20 deposit to Peach Garden, and is considering going to Siam House instead. All things considered, she now values going to Siam House by $10 more than going to Peach Garden. If there is no penalty for breaking a reservation, she will just go to Siam House. But that’s a bad result – she gains $10 by going to Siam House instead of Peach Garden, but Peach Garden suffers a $20 loss from the cancelled reservation. But if there is a $20 deposit at Peach Garden, she will not break the reservation – Siam House is preferred, but not by enough to make it worth it to walk away from a $20 deposit.

Summing up: a deposit equal to the expected profit from the customer honoring the reservation instead of being a no-show is the optimal amount. It will be bigger than zero, but less than the full cost of the meal. Set that way, customers will only cancel when it is genuinely for the best, all parties’ interests considered, that there be a no-show.

Let’s leave food and turn to the arts. Consider a painting class with a limited number of seats. The optimal initial deposit to collect from applicants is equal to the expected loss in profit if in the end the student making the reservation doesn’t show. This would depend on what was lost from turning late applicants away because all seats are booked. If the class is not close to capacity, the deposit should be correspondingly small. If the class is at capacity, then the loss from a no-show is the whole price of a seat in the class if impossible to sell at the last minute, and somewhat less than that according to the possibility of being able to sell the seat at the last minute to someone else. Make the deposit too high, and you scare away potential students unsure about whether they will truly be able to attend. Make it too low, and your class is filled with applicants who in the end may feel no particular urge to follow through.