Columbia Pizza has one oven that can make a whole pie in about 10 minutes. Their late-night business among hungry college students is booming, and from 9 pm – 11 pm, they average 5 pie orders per hour. However, from 5 pm – 9 pm, they average only 3 pie orders per hour. Both order rates can be assumed arrive according to a Poisson distribution.

The owner of Columbia Pizza has discovered that if people have to wait for more than 20 minutes from when they get in the door to when they receive their pie, they are likely to simply go next door to University Falafel, meaning that Columbia Pizza would lose out on their $20 sale.

The owner is thinking of buying a second pizza oven and register (e.g. a second channel) that he thinks would cost $75 per night to operate (for the sake of our example, that is both the amortized cost of the oven and the pay of the person who is taking orders for the six hours that the pizza shop is open).

Details
Answer each of the questions below. You must show all work. Be sure to highlight your final answer and when asked, please be sure to justify your response.

Calculate the following for the 5-9 shift and the 9-11 shift (20 points)
Average # of orders in the system
Average time order spends in the system (minutes)
Average # of orders in the queue
Average waiting time in the queue (minutes)
Utilization
Assuming all customers are able to be served, what is the total maximum revenue opportunity for Columbia Pizza? (5 points)
In order to achieve the 20 minute total time from door to when they receive their pie, assuming one oven is available, what is the total revenue opportunity? (5 points)
Calculate the average daily loss of sales to University Falafel. (5 points)
If Columbia Pizza buys a second oven, calculate the following for the 5-9 shift and the 9-11 shift (20 points)
Average # of orders in the system
Average time order spends in the system (minutes)
Average # of orders in the queue
Average waiting time in the queue (minutes)
Assuming all customers are able to be served, what is the total maximum revenue opportunity for Columbia Pizza? (5 points)
In order to achieve the 20 minute total time from door to when they receive their pie, assuming two ovens are available, what is the total revenue opportunity? (5 points)
Calculate the average daily loss of sales to University Falafel. (5 points)
Based on your calculations, should Columbia Pizza buy the second oven? Why? What is the net financial impact? (15 points)
Assume now that an improvement in the pizza making process results in the time to make pizzas being reduced to 8 minutes/pizza. How does this change your recommendation in #9 (note: no change in order demand)? Please describe. (15 points).
Assessment
You will be assessed based on the following criteria:

The accuracy of your queuing theory calculations
Your explanation of queuing theory as it relates to the case organization’s decisions
Your use of the organization’s finances as one lens for analytical decision-making