Question C: Your firm is planning to introduce a new product line. Your task is
ID: 329156 • Letter: Q
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Question C: Your firm is planning to introduce a new product line. Your task is to determine the inventory implications of the new product. The typical product will ship an average of 20 units per day from the firm's central DC. Historical sales patterns indicate that the standard deviation of daily sales should be approximately 3. The typical performance cycle for comparable products has been a mean of 7 days and a standard deviation of 2. a. Assuming a replenishment quantity from the plant of 200 units, what are the safety stock and resulting average inventory for a 95 percent case fill rate? b. What are the inventory implications (safety stock and average inventory) of increas- ing the case fill rate objective to 99 percent? Note: Performance cycle represents elements of work necessary to complete various logistics related activities (Similar to Lead time)Explanation / Answer
Given are following data :
Daily demand = d = 20 units/ day
Standard deviation of daily sales demand = Sd = 3
Lead time ( i.e. performance cycle ) = L = 7 days
Standard deviation of lead time ( performance cycle ) = Sdl = 2 days
Therefore , standard deviation of demand during lead time
= Square root ( Sd^2 x L + d^2 x Sdl^2)
= Square root ( 3^2 x 7 + 20^2 x 2^2)
= Square root ( 63 + 1600 )
= Square root ( 1663 )
= 40.78
Answer to question a :
Z value for 95 percent fill rate = NORMSINV ( 0.95 ) = 1.6448
Safety stock = Z value x Standard deviation of demand during lead time = 1.6448 x 40.78 = 67.07 ( 67 rounded to nearest whole number )
Average inventory = Replenishment quantity /2 + Safety stock = 200 /2 + 67 = 167
Answer to question b :
Z value for fill rate of 99 percent = NORMSINV ( 0.99) = 2.326
Safety stock = Z value x Standard deviation of demand during lead time = 2.326x 40.78 = 94.85 ( 95 rounded to nearest whole number )
Average inventory = Replenishment quantity /2 + Safety stock = 200 /2 + 95 = 195
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