Problem? What Problem?

A mathematical problem should be difficult to entice us, yet not completely inaccessible. It should be a guidepost on the mazy paths to hidden truths. – David Hilbert

In a space-limited outdoor diner we visited a while ago, we observed the seating arrangement in A. They had two tables for two and ten for four. Seven of the four-place tables had parties of two. So, I wondered – is the setup they had the best for the crowd they faced?

A report I found (see below) noted that restaurant parties of two outnumber four-person parties by over two to one. On average, there should be more tables set up for couples than for larger groups.

But the average condition may not be the usual one. Or the one they faced.

What to do?

Suppose the four left-most tables were modular. The establishment could separate them into eight two-place setups. Then they could seat all seven of their two-person parties and put a two-top in storage. Their capacity would go down by two (at least temporarily), but, in the case shown, occupancy could go up by 30%, as we see in B.

Restaurants make money through occupancy, not capacity. It’s important to know what problem you need to solve.

#sales #demand #restaurants #business #success #management #problemsolving

Restaurant Math – Thin Odds

You spend your life waiting for a moment that just don’t come/Well, don’t waste your time waiting – Bruce Springsteen, Badlands

You know the feeling you get when you walk up to a roulette wheel in a casino, place a $100 on 00, it comes up, you win $3,500, and then you let it ride on 00, hit it again, and walk out with $122,500? No? Me either.

The reason I don’t is that while it’s possible to come up with that combination, the chance of that happening on a 38-pocket wheel is 1/38 * 1/38 = 1/1,444 = 0.00069, about 7 times in 10,000 tries.

But that is more than twice as likely as the probability of a restaurant result I recently witnessed.

As we left a brewery, it had four open tables; each sat eight, B. Four parties waited, C, held in place by their policy not to seat parties of four or fewer in tables for eight. But, the chance of filling them up according to their plan and the data, A, is 0.13^4 = 0.00028, less than half that of our roulette gambit.

Meanwhile, those people stayed hungry. They and the restaurant both suffered.

We are, all of us, always playing games of chance. It pays to know the odds. Anybody up for blackjack?

#business #success #management #probability #sales #restaurant

Restaurant Math

“I was at this restaurant. The sign said ‘Breakfast Anytime.’ So I ordered French Toast in the Renaissance.”
Steven Wright

Forget about ordering off the menu; first, you have to get a seat. That’s not a given anymore.

It was never a slam dunk to get into our preferred local eatery. Once COVID-19 forced all patrons outside with social distancing, it was harder still. As we sat waiting for some seats for the third weekend in a row, we began to fidget. What to do? In an era where restrictions abound, sometimes it’s hard to see the options.

Happily, we knew the owner and every boss in the place. I pulled our most-beloved manager aside and asked her if she would be willing to rearrange the furniture and make more money. I explained to her that smaller parties were crowding out larger ones. Why not go from the arrangement you have (which was A) to one with several smaller tables (which became B), I asked? If you track the revenue changes, you’ll be pleasantly surprised.

As shown below, she did just that. Revenue went up by over 25%. Unlike A, Setup B recognizes they face a Demand Curve, with more parties of one or two people than groups of five or more.

#demand #demandanalysis #restaurant #restaurantmath #profits #revenue