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.

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