Operations Analysis

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.  Assume that each person orders one pizza, and that people 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).  The owner has analyzed that the total cost of operation (the amortized cost of the additional 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.

Calculate the following for the 5-9 shift and the 9-11 shift (20 points)

Average number of customers waiting in line and being served
Average time a customer spends in the store waiting in line and being served  (minutes)
Average number of customers waiting in line
Average time a customer spends waiting in line (minutes)
Percent of time Columbia Pizza is serving customers (utilization)

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)
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)
What is the average daily loss of sales to University Falafel? (5 points)
If Columbia Pizza invests in a second oven, calculate the following for the 5-9 shift and the 9-11 shift (20 points)

Average number of customers waiting in line and being served
Average time a customer spends in the store waiting in line and being served  (minutes)
Average number of customers waiting in line
Average time a customer spends waiting in line (minutes)

What is the total revenue opportunity for Columbia Pizza with two ovens, assuming that it can serve all of their customers from 5-9 and 9-11 PM? (5points)
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)
Calculate the average daily loss of sales to University Falafel. (5 points)
Based on your calculations, should Columbia Pizza buy the second oven? Explain your answer based on the net financial impact. (15 points)
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:

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

Professor Requirement:
I told you to submit Excel file – only as a supporting document. Your main answer should be in the Word/pdf document, and that should be a complete document by itself, with all major steps. If needed, you can paste screenshots from other files (with all the steps) in that Word/pdf document. What we dont want to see is that the Word/pdf document has only the final numbers, and then we have to search for the underlying calculations in the Excel file. You’ll lose points if your Word/pdf document has only the final numbers.
If you do all calculations by hand, or calculator, and show that on your Word/pdf document, then you dont need submit the Excel. We ask for the Excel because if your answer is not perfect, we can go into that file, and tell you what you missed.
Once again, a reminder –read and understand the Qs before answering;please answer all parts of the questions;and submit the complete package on time.