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 $35 for the BB-1 set (BB-1 stands for Body Beautiful Number 1). The carrying cost for BB-1 is $15 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 $40 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 100 120 140 160 180 200 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 number)

Explanation / Answer

Given:

S = Ordering Cost = $35

H = carrying cost per set per year = $ 15

n = number of orders per year = 4 times

B = Stock-out cost per set = $40

R = Current Reorder point = 140 sets

SS = Safety stock

The objective is to determine the safety stock level that minimizes the sum of the additional inventory holding costs and Stock-out costs.

Additional Holding cost = carrying charge x safety stock = H x SS

Annual stockout costs = [sum of (units short for each demand level) x (probability of that demand level)] x (stockout cost/unit) x (number of orders per year)]

Annual stockout costs = [sum of (units short for each demand level) x (probability of that demand level)] x [B x n]

Demand during Lead Time (DDLT) Probability

100 0.1

120 0.2

140 0.2

160 0.2

180 0.2

200 0.1

Let’s begin with zero safety stock, as the reorder level is 140 units, there will be 0 units short for 140 demand, 20 units short for the 160 demand, 40 units short for the 180 demand, and 60 units short for the 200 demand.

Annual stockout cost for SS= 0 is calculated as follows:

Annual Stockout cost for SS0 = [(0*0.2)+(20*0.2)+(40*0.2)+(60*0.1)] x ($40)(4) = $2,880

Additional Holding cost = (0)($15) = $0

Total Additional Cost = $0 + $2880 = $2,880

Similarly total additional cost for various Safety stock level is calculated as follows:

Safety Stock Additional Holding Cost Stockout Cost Total Additional Cost

0 $0 $2,880 $2,880

20 (20)($15) = $300 [(0)(0.2)+(20)(0.2)+(40)(0.1)]

X [$40)(4)] = $1,280 $300 + $1,280

= $1,580

40 (40)($15) = $600 [(0)(0.2)+ (20)(0.1)]

X [$40)(4)] = $320 $600+$320

= $920

60 (60)($15) = $900 [(0)(0.1)]

X [$40)(4)] = $0 $900+$0

= $900

  

Lowest total additional cost is for safety stock level of 60 sets, so as to minimize the additional total cost.

The optimal quantity of safety stock which minimizes expected total cost is 60 sets

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