Charlie\'s Pizza orders all of its pepperoni, olives, anchovies, and mozzarella
ID: 367203 • Letter: C
Question
Charlie's Pizza orders all of its pepperoni, olives, anchovies, and mozzarella cheese to be shipped directly from Italy. An American distributor stops by every six weeks to take orders. Because the orders are shipped directly from Italy, they take five weeks to arrive.
Charlie's Pizza uses an average of 160 pounds of pepperoni each week, with a standard deviation of 26 pounds. Charlie's prides itself on offering only the best-quality ingredients and a high level of service, so it wants to ensure a 99 percent probability of not stocking out on pepperoni.
Assume that the sales representative just walked in the door and there are currently 500 pounds of pepperoni in the walk-in cooler. How many pounds of pepperoni would you order? (Round your answer to the nearest whole number.)
Explanation / Answer
Average = 160 pounds
Standard Deviation = 26 pounds
Allowed Stockout probability level = 1% = 0.01
Travel Time = 6
Lead Time = 5
Z value for probability of 0.01 = 2.33
Total Quantity of pepperoni required = Mean * (Travel Time + Lead Time) + Z*Standard Deviation*SquareRoot(Travel Time + Lead Tiime)
= 160*(6+5) + 2.33*26*SqRt(6+5)
= 160*11 + 2.33*26*3.32
= 1760 + 200.92
= 1960.92
rounded up to 1961.
So a total of 1961 pounds of pepperoni is required.
Since the available stock is of only 500 pounds, the additional amount to the ordered = 1961-500 = 1461 pounds.
Hence Charlie's Pizza should place an order for 1461 pounds of pepperoni with the sales representative.