Reservations, and in particular, no-shows, have always been a tricky issue for operators. The topic has heated up of late, spurred by high-profile places like Noma, one of the top restaurants in the world, going on the offensive. In March, the Copenhagen restaurant posted, and then deleted, an image on Twitter of its staff giving the middle finger to diners who didn’t show up for their reserved table. A month later, Red Medicine in Beverly Hills made headlines by naming (and shaming) its no-shows on Twitter.

Now, new analysis from The Wharton School of the University of Pennsylvania suggests restaurants that take reservations would be more profitable penalizing no-shows with hefty charges, and even offering slight discounts to those who do actually show up. It’s the work of Wharton PhD student Jaelynn Oh and Wharton operations and information management professor Xuanming Su.

Taking into account the restaurants’ meal prices, diner capacities and other factors, the two suggest in a paper titled, “Pricing Restaurant Reservations: Dealing with No-Shows,” that just taking credit card information or levying small fines isn’t enough. Penalties should equal the average price of a meal for each person in the party that doesn’t show up.

The restaurant industry is as much about space as it is food, write Oh and Su, who compare open tables to machines in a factory not producing. Both are losing money, and in an industry with approximately a 20-percent rate for no-shows, at least in major cities, that can mean plenty of lost revenue.

Applying math to an industry predicated on food, as only Ivy Leaguers could, the duo found the mathematically optimal approach would be penalizing a no-show party of four $200 if the restaurant’s average meal costs $50.

“That was quite shocking, because most restaurants aren’t charging such a high no-show policy,” Oh says in a story on Knowledge@Wharton, the school’s biweekly business news and analysis Web site. Not many restaurants are fining no-shows, but those that do, typically charge in the $50 to $75 range. Oh does note that some restaurants are in essence charging higher penalties when they sell tickets for a prix fixe tasting menu, but the “psychology behind it is different.”

Just as penalizing no-shows is important, Oh and Su write that restaurants should also reward those who do show up. Those customers should get a discount because they “bear the risk of paying a no-show penalty.” And, since walking in without a reservation is an option, there is “pressure on the restaurant to make [reservations] more attractive by charging a lower price.”