Question

Problem 11-14 (Algo)

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 eight weeks to take orders. Because the orders are shipped directly from Italy, they take seven weeks to arrive.

Charlie's Pizza uses an average of 240 pounds of pepperoni each week, with a standard deviation of 18 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 440 pounds of pepperoni in the walk-in cooler. How many pounds of pepperoni would you order? (Use Excel's NORM.S.INV() function to find the z value. Do not round intermediate calculations. Round z value to 2 decimal places and final answer to the nearest whole number.)

Answer 1

Given values:

Service level = 99% or 0.99

Weekly demand (d) = 240 pounds

Time between orders (T) = 8 weeks

Lead time (L) = 7 weeks

Standard deviation of demand, Sigma (d) = 18 pounds

Current Inventory (I) = 440 pounds

Solution:

Using NORMSINV function in MS Excel, value of Z can be determined.

Z = NORMSINV (Service level)

Z = NORMSINV (0.99)

Z = 2.33

Order Quantity (Q) is calculated as,

Q = d (T + L) + Z Sigma (T + L) - I

Sigma (T + L) = Sigma (d) x SQRT (T + L)

Sigma (T + L) = 18 x SQRT (8 + 7)

Sigma (T + L) = 69.71

Putting the given values in the above formula, we get,

Q = d (T + L) + Z Sigma (T + L) - I

Q = [240 x (8 + 7)] + [2.33 x 69.71] - 440

Q = 3600 + 162.42 - 440

Q = 3,322.42 or 3,322 (Rounding off to the nearest whole number)

Order Quantity = 3322 pounds