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 $45 for the BB-1 set (BB-1 stands for Body Beautiful Number 1). The carrying cost for BB-1 is $10 per set per year. To meet demand, Mr. Beautiful orders large quantities of BB-1 5 times a year. The stockout cost for BB-1 is estimated to be $15 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 100 120 140 160 180 200 Probability 5.1 0.2 0.2 0.2 0.2 0.1 The reorder point for BB-1 is 140 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 numbern.

Explanation / Answer

Given that,

Ordering cost, S = 45

Carrying cost, H = 10

Stockout cost, B = 15

Number of orders per year = 5

Average demand during lead time = (100*.1+120*.2+140*.2+160*.2+180*.2+200*.1) = 150 sets

Safety stock = ROP - Average demand during lead time.

Average demand during lead time is more than ROP, therefore, safety stock = 0

Expected leftover inventory = (140-100)*.1+(140-120)*.2 = 8

Expected shortage = (160-140)*0.2+(180-140)*.2+(200-140)*.1 = 12

Total cost = Ordering cost + Carrying cost + Stockout cost = (45 + 8*10+12*15)*5 = $ 2425

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