Applying Queueing Theory in a restaurant operation might be helpful to those who proactively wish to manage revenue. After all, the drivers of revenue in a restaurant is how many guests a restaurant can serve in a given shift, as well as average order value. One must employ all sorts of restaurant improvements and restaurant kaizen to meet the customer need.
So how does one apply Queueing Theory in a restaurant operation? Suppose the following information below for a typical restaurant:
| Time | 7:30 | 8:00 | 8:30 | 9:00 | 9:30 | 10:00 | 10:30 | Total |
| Number of Arrivals | 60 | 25 | 80 | 50 | 20 | 5 | 0 | 240 |
| Number of Departures | 0 | 0 | 30 | 30 | 50 | 85 | 45 | 240 |
| Number in Restaurant | 60 | 85 | 135 | 155 | 125 | 45 | 0 | 605 |
Here are some assumptions:
- The restaurant operates 180 minutes on the evening shift, which starts at 7:30 PM and closes at 10:30 PM.
- This restaurant is unusual because the guests arrive and leave exactly at the half hour mark (this is to make it simpler)
- Read the data above like: The number of guests in the restaurant between 8:00 and 8:30 is 85. The number of arrivals at 8:30 is exactly 25. The number of guests that depart at 8:30 is 30.
So, given our restaurant data, we arrive at the following questions:
- What is the average throughput of customers, using the unit of (customers per minute) of operation?
- What is the average cycle time of a customer in minutes?
Restaurant Operations Management
The questions above are important because:
- The lower the cycle time per restaurant customer, then the restaurant manager can accept more guests and increase the restaurant revenue.
- Knowing the throughput of the restaurant can give the restaurant manager more ability to manage the restaurant to a drum beat. This is typically called Takt Time in the language of lean manufacturing.
1. What is the average throughput of customers, using the unit of (customers per minute) of operation?
Answer: We get 240 / 180, which means 1.33 customers per minute.
2. What is the average cycle time of a customer in minutes?
Answer: To get cycle time, we first calculate total inventory. By inventory in this setting, we’re talking about restaurant guests. This means we sum the number of guests in the restaurant during the evening shift:
(60+85+135+155+125+45) / 6 = 605 / 6 = 100.83 customers.
So, cycle time can be calculated:
100.83 / 1.33 = 75.64 minutes is the average cycle time of a restaurant customer
So, if one’s goal is to increase restaurant revenue, then the restaurant manager can do the following, given the data above:
- lower the average cycle time of the restaurant guests, which allows for other guests to occupy that spot and thereby increase revenue
- do nothing to cycle time, but try to increase the average order value per guests through menu up-sell or cross-sell
- do nothing to cycle time, but investigate menu pricing and increase menu item prices as appropriate, but done with wisdom and care, otherwise customers will leave if prices aren’t in line with their expectations
Additionally, if one is interested in reducing cycle time per restaurant guest, this is also an area in which Queueing Theory and Lean can work together. Perhaps there are process steps that do not add value, which contribute to the current cycle time calculation. Perhaps eliminating wastes in the restaurant operations processes can thereby reduce cycle time per customer.
In business school, we studied Benihana. They do an incredible job of both increasing average order value per guest AND reducing average cycle time — without the customers realizing it.
They increased average order value by making people wait in the bar for precisely 12 minutes (I think): long enough to order a drink, but not too long to make people impatient.
They decreased cycle time by having the chef set the pace of the dinner: you don’t choose when the food comes, the fancy chef flips the shrimp and steak onto your plate when *he* wants. As a result, you’re in and out of there before you know it — and, because it’s “theater,” no one feels rushed or minds the pace.
Dan,
Thanks much for your comment. I love Benihana and, after what you shared above, can see now those principles at play in their restaurant management.
Again, thanks much. Awesome.
Pete
One simple improvement would be to have portable POS and credit card terminals. Instead of asking for the check, getting the check, waiting for the receipt, then signing for it… it can all be done at the table.
Although you may like Benihana, this is precisely why I would not go to certain restaurants. The factor of hospitality and return visit potential is not in the equation.
Food service offers an interesting way to handle an aspect of queuing that is often mishanlded: that is where there are mulitple ‘pace’ streams within the queue. So the restaurant above seems to ‘de-couple’ or create queue buffers: the bar is an example, I would think.
A counter example is at conferences where the tea and coffee is arranged in many instances to create backlogs, where people who just want to fill up on coffee are delayed by the ones who want to carefully titrate their milk add sugar…opps no, just have the raw sugar; no not that stirer, I’ll use..hmm.. that one; and so one.
So, decouple by making a queue for the hot drink, then force people to move away to multiple lanes for the slow activities.
I really like what you said about how restaurants who have lower cycle times per customer can accept more guests and generate more revenue. One would think that lowering cycle times not only require a fast service, but also an efficient queuing system for your regulars. That way, there will be less waiting time and even less time searching for customers with the correct food order.