Columbia Pizza and make a pizza in 10 minutes with the one oven that they have. Their late-night business among hungry college students is booming, and they average 5 pizza orders/hour from 9 PM – 11 PM. Between 5 PM and 9 PM, they average 3 pizza orders/hour. Both order rates can be assumed arrive according to a Poisson distribution.
The owner of Columbia Pizza has discovered that if customers have to wait for more than 20 minutes from when they enter the shop to when they receive their pizza, they are likely to go next door to University Falafel, meaning that Columbia Pizza loses a $20 sale.
The owner is thinking of buying a second oven and register (e.g. a second channel). He has analyzed that it the total cost of operation (the amortized cost of the oven and the salary of the staff) would be $75 per night.
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.
1. Calculate the following for the 5-9 shift and the 9-11 shift (20 points)
a. Average # of orders in the system
b. Average time order spends in the system (minutes)
c. Average # of orders in the queue
d. Average waiting time in the queue (minutes)
e. Utilization
2. What is the total revenue opportunity for Columbia Pizza, assuming that you can serve all of your customers from 5-9 and 9-11 PM? (5 points)
3. What is the total revenue opportunity with one oven, given the 20 minute time constraint from entering the shop to receiving their pizza? (5 points)
4. What is the average daily loss of sales to University Falafel? (5 points)
5. If Columbia Pizza invests in a second oven, calculate the following for the 5-9 shift and the 9-11 shift (20 points)
a. Average # of orders in the system
b. Average time order spends in the system (minutes)
c. Average # of orders in the queue
d. Average waiting time in the queue (minutes)
6. What is the total revenue opportunity for Columbia Pizza, assuming that you can serve all of your customers from 5-9 and 9-11 PM? (5points)
7. What is the total revenue opportunity with two ovens, given the 20 minute time constraint from entering the shop to receiving their pizza? (5 points)
8. Calculate the average daily loss of sales to University Falafel. (5 points)
9. Based on your calculations, should Columbia Pizza buy the second oven? Explain your answer based on the net financial impact. (15 points)
10. You have improved the pizza making process and reduced the time required from 10 minutes to 8 minutes/pizza. Does this change your recommendation about buying a second oven (assume no change in demand)? Explain the rationale for your answer. (15 points).
You will be assessed based on the following criteria:
1. The accuracy of your queuing theory calculations
2. Your explanation of queuing theory as it relates to the case organization’s decisions
3. Your use of the organization’s finances as one lens for analytical decision-making