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 $5 per set per year. To meet demand, Mr. Beautiful orders large quantities of BB-1 4 times a year. The stockout cost for BB-1 is estimated to be $10 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	Probability
40	.1
50	.2
60	.2
70	.2
80	.2
90	.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).

Answer 1

Ordering cost = $40 per set

Carrying cost = $5 per set per year

Stockout cost = $10er set

Number of orders per year = 4times

Formula to calculate Total cost = Stock out cost + Additional cost

Stockout cost = Number of units short*probability*stockout cost*number of request per year

Additional cost = number of units short * carrying cost per set

Reorder point = 60 sets

Here safety stock is zero

so the stockout cost = (10*0.2*10*4) + (20*0.2*10*4) + (30*0.1*10*4) = 80 + 160 + 120 = $360

Additional cost = no shortage units * $5 = $0

So total cost = $360 + $0 = $360

Safety stock at 10 sets short where these safety stock is added to ROP gives = 60+10 = 70 sets

Stockout cost = (10*0.2*10*4) + (20*0.1*10*4) = 80 + 80 = $160

Additional cost = 10 sets * $5 = $50

Total cost = $160 + $50 = $210

Safety stock at 20 sets short where safety stock is added to ROP gives = 60 + 20 = 80 sets

Stockout cost = (10*0.1*10*4) = $40

Additional cost = 20 sets * $5 = $100

Total cost = $40 + $100 = $140

Safety stock at 30 sets short where safety stock is added to ROP gives = 60 + 30 = 90 sets

Stockout cost = No shy of sets = $0

Additional cost = 30 sets * $5 = $150

Total cost = $0 + $150 = $150

From the above analysis the optimal quantity of safety stock which limits expected total cost is 80 sets.