Mr. Beautiful, an organization that sells weight training sets, has an ordering

Question

Mr. Beautiful, an organization that sells weight training sets, has an ordering cost of $40 for the BB-1 set (BB-1 stands for Body Beautiful Number 1). The carrying cost for BB-1 is $19 per set per year. To meet demand, Mr. Beautiful orders large quantities of BB-1 7 times a year. The stockout cost for BB-1 is estimated to be $45 per set. Over the past several years, Mr. Beautiful has observed the following demand during the lead time for BB-1 Demand During Lead Time 41) 50 60 70 80 90 Probability 0.1 0.2 0.2 0.2 0.2 0.1 The reorder point for BB-1 is 60 sets. What level of safety stock should be maintained for BB-1? The optimal quantity of safety stock which minimizes expected total cost is sets(enter your response as a whole number)

Explanation / Answer

Safety stock = Z-score x lead time x standard deviation of demand

Generally, a Z-score = 1.65, implying 95% confidence level of NOT running out of stock is used for inventory calculations.

Lead time = 365/7 = 52 days

Average demand = (40+50+60+70+80+90) / 6 = (390/6) =65 units per year

Data points are: 40, 50, 60, 70, 80, 90

Squares of Differences; (65-40)^2 , (65-50)^2, (65-60)^2, (70-65)^2, (80-65)^2, (90-65)^2

Average of squares of differences = [(25)^2 + (15)^2 + (15)^2 +  (15)^2 + (25)^2 + (35)^2 ] / 6 = 525

Sqrt. of above avg = sqrt (525) = 22.9 = 23 approx = standard deviation of demand

so, using our formula, Safety stock = Z-score x lead time x standard deviation of demand

we get , safety stock = 1.65* 52 * 23 = 272.99 = 273

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