Zhongwei Huang, Yahan Zhang

Johanna comes to a coffee shop and wants to buy a cup of coffee. There are some people waiting in a line, so Johanna wants to estimate how long she needs to wait for to get a coffee.

The statistics we are interested in are Johanna's wait time and two baristas’ break time.

1. besides Johanna, the number of people in the line      

   Number 0 1 2 3 4 5 6 7 8

   Pr 0.04 0.08 0.12 0.16 0.2 0.16 0.12 0.08 0.04

2. size of a cup of coffee: tall, grande, venti

   Size Tall Grande Venti

   Pr 0.25 0.5 0.25

3. time of ordering a cup of coffee: Truncated Normal (mean=25, std=5, lower=5, upper=60)

4. time of making a tall cup of coffee: Truncated Normal (mean=25, std=5, lower=5, upper=80)

5. time of making a grande cup of coffee: Truncated Normal (mean=28, std=7, lower=5, upper=80)

6. time of making a venti cup of coffee:Truncated Normal (mean=30, std=8, lower=5, upper=80)

After we generate times from truncated normal distributions, we would round them into integers.

1. The wait time and break time may follow normal distribution.
2. The barista B may have more break time.

We first designed a relatively simple scenario where there was only one barista. Based on the simulation outcomes we found that most of the time the barista eventually cannot catch up with the speed of order, because we set the mean of time of ordering a cup of coffee to be smaller than the mean of time of making a cup of coffee. Then we wrote classes to have two baristas working at the same time, which adds some complexity to the simulation, and is more realistic.

1. The wait time and break time do follow normal distribution.
2. The barista B does have more break time.

1. Run Simulation.py
2. By changing the argument in function simulation, you can change the times of Monte Carlo Simulation.

Miller & Ranum: Problem Solving with Algorithms and Data Structures Using Python, Section 3.4, pages 106-119