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 190 pounds of pepperoni each week, with a standard deviation of 14 pounds. Charlie's prides itself on offering only the best-quality ingredients and a high level of service, so it wants to ensure a 90 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? (Use Excel's NORMSINV() function to find the correct critical value for the given α-level. Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to the nearest whole number.)

Answer 1

Average weekly demand (d) = 190 pounds

Standard deviation of weekly demand (d) = 14 pounds

Review period (R) = 6 weeks

Lead time (L) = 5 weeks

Service level = 90%

At 90% service level value of Z = 1.28

On hand inventory (I) = 500 pounds

Order quantity = [d(L +R)] + [Z x d x sqrt of(L+R)] - I

= [190(5+6)] + [1.28 x 14 x sqrt of (5+6)] - 500

= (190 x11) + (1.28 x 14 x sqrt of 11) - 500

= 2090 + (1.28 x 14 x 3.32) - 500

= 2090 + 59.49 - 500

= 2149.49 - 500

= 1649.49 or rounded to 1649 pounds