The purchasing manager for Alpa Enterprises requested the following data from th

Question

The purchasing manager for Alpa Enterprises requested the following data from the accounting department: Annual demand = 15,500; Cost of placing an order = £180; Annual inventory holding costs = 20 percent; Unit cost = £78
Assume Alpha’s demand for an item during the lead time is normally distributed with a mean of 5,000 and a standard deviation of 50. What reorder point should be used in order to average no more than one stock out every 20 re-order cycles? If safety stock is 70, how often will a stock out occur during a re-order cycle? The purchasing manager for Alpa Enterprises requested the following data from the accounting department: Annual demand = 15,500; Cost of placing an order = £180; Annual inventory holding costs = 20 percent; Unit cost = £78
Assume Alpha’s demand for an item during the lead time is normally distributed with a mean of 5,000 and a standard deviation of 50. What reorder point should be used in order to average no more than one stock out every 20 re-order cycles? If safety stock is 70, how often will a stock out occur during a re-order cycle? The purchasing manager for Alpa Enterprises requested the following data from the accounting department: Annual demand = 15,500; Cost of placing an order = £180; Annual inventory holding costs = 20 percent; Unit cost = £78
Assume Alpha’s demand for an item during the lead time is normally distributed with a mean of 5,000 and a standard deviation of 50. What reorder point should be used in order to average no more than one stock out every 20 re-order cycles? If safety stock is 70, how often will a stock out occur during a re-order cycle?

Explanation / Answer

Target stockout is one stock out in 20 reorder cycles

Thus, probability of stockout = 1/ 20 = 00.05

Thus, in stock probability = 1 – 0.05 = 0.95

Corresponding Z value for in stock probability of 0.95 = NORMSINV ( 0.95) = 1.6448

Therefore, safety stock = Z value x Standard deviation of demand during lead time = 1.6448 x 50 = 82.24 ( 82 rounding to nearest whole number)

Thus, reorder point = Demand during lead time + safety stock = 5000 + 82 = 5082

REQUIRED REORDER POINT = 5082

If safety stock = 70 , Standard deviation of demand during lead time = 50 and corresponding Z value = Z1

Then

Safety stock = Z value x Standard deviation of demand during lead time

Or, 70 = Z1 x 50

Or, Z1 = 70/50 = 1.4

Corresponding value of probability for Z1 = 1.4 as derived from standard normal distribution table 0.91924

Thus in stock probability = 0.91924

Thus probability of stock out during reorder cycle = 1 – 0.91924 = 0.08076 or 8.076 % times

STOCKOUT WILL OCCUR APPROX 8.076% PERCENTAGE OF TIME DURING A REORDER CYCLE

REQUIRED REORDER POINT = 5082

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