YumPizza, a delivery-only pizza chain, would like to serve the suburban pizza market. Their goal is to offer guaranteed delivery within 30 minutes. Assume a pizza is ready for delivery 15 minutes after receiving a call (this includes the total baking time). There are 49 neighborhoods YumPizza would like to serve in the region. For each neighborhood, you are provided with representative longitude and latitude coordinates and the average weekly demand for pizza. YumPizza has identified 10 possible locations for its pizzerias. For each possible location, you are provided with longitude and latitude coordinates and the monthly rental cost. A distance matrix has been created between neighborhoods and candidate locations measured in minutes. See separate data file for more details.

Part I: 

YumPizza initially started serving all customers without budget restrictions. 

• Solve optimal pizzeria locations using Excel. How many facilities do you need to cover all the neighborhoods? What is the total cost? 

• What are your general observations on your approach? 

• Perform sensitivity analysis, such as marginal coverage of last facility location, second to last facility, etc.

Part II: 

YumPizza agrees that serving all customers may not be a realistic goal. Additionally, YumPizza can spend only $6,000 per month on rent. 

• How would you suggest YumPizza change its supply chain strategy? Specifically, what should they choose as the objective function and why? 

• Solve the optimal locations of the pizzerias using Excel under the strategy and objective function proposed above. How many neighborhoods does YumPizza serve now? What is the total cost? What are your general observations? 

• Compare with the previous solution in Part I where all neighborhoods are covered. Comments.