A product has a reorder point of 110 units, and is ordered four times a year. The following table shows the historical distribution of demand values observed during the reorder period.
$100.3110.4120.2130.1\begin{array} { | c | c | } \hline \text { Demand } & \text { Probability } \\\hline 100 & .3 \\\hline 110 & .4 \\\hline 120 & .2 \\\hline 130 & .1 \\\hline\end{array}$ Managers have noted that stockouts occur 30% of the time with this policy, and question whether a change in inventory policy, to include some safety stock, might be an improvement. The managers realize that any safety stock would increase the service level, but are worried about the increased costs of carrying the safety stock. Currently, stockouts are valued at $20 per unit per occurrence, while inventory carrying costs are $10 per unit per year. What is your advice? Do higher levels of safety stock add to total costs, or not? What level of safety stock is best?

Question

A product has a reorder point of 110 units, and is ordered four times a year. The following table shows the historical distribution of demand values observed during the reorder period.

100.3110.4120.2130.1\begin{array} { | c | c | } \hline \text { Demand } & \text { Probability } \\\hline 100 & .3 \\\hline 110 & .4 \\\hline 120 & .2 \\\hline 130 & .1 \\\hline\end{array}

Managers have noted that stockouts occur 30% of the time with this policy, and question whether a change in inventory policy, to include some safety stock, might be an improvement. The managers realize that any safety stock would increase the service level, but are worried about the increased costs of carrying the safety stock. Currently, stockouts are valued at $20 per unit per occurrence, while inventory carrying costs are $10 per unit per year. What is your advice? Do higher levels of safety stock add to total costs, or not? What level of safety stock is best?

Talasila Bharat Chowdary · Accepted Answer

Final Answer :   Action   Safety stock cost   Stockout cost   Total cost  R O P = 110 ( S S = 0 ) 0 = $ 0 2 × 10 × 20 × 4 = $ 160 1 × 20 × 20 × 4 = $ 160 $ 0 $ 320 $ 320 R O P = 120 ( S S = 10 ) 10 × $ 10 = $ 100 1 × 10 × 20 × 4 = $ 80 $ 100 $ 80 $ 180 R O P = 130 ( S S = 20 ) 20 × $ 10 = $ 200 0 = $ 0 $ 200 $ 0 $ 200 \begin{array}{|c|l|l|l|l|l|}\hline	ext { Action }  &  	ext { Safety stock cost }  &   &  	ext { Stockout cost }  &   &  	ext { Total cost } \\hline \mathrm{ROP}=110(\mathrm{SS}=0)  &  0=  &  \$ 0  &  2 	imes 10 	imes 20 	imes 4=  &  \$ 160  &  \\hline & & & 1 	imes 20 	imes 20 	imes 4= & \$ 160\\hline  & & \$ 0 & & \$320 & \$320\\hline \\hline \mathrm{ROP}=120(\mathrm{SS}=10)  &  10 	imes \$ 10= &  \$ 100  &  1 	imes 10 	imes 20 	imes 4= & \$ 80\\hline  & & \$ 100 & & \$80 & \$180\\hline\\hline\mathrm{ROP}=130(\mathrm{SS}=20)  &  20 	imes \$ 10= &  \$ 200  &  0= & \$0\\hline  & & \$200 & & \$0 & \$200\\hline\end{array}  Action  ROP = 110 ( SS = 0 ) ROP = 120 ( SS = 10 ) ROP = 130 ( SS = 20 ) ​  Safety stock cost  0 = 10 × $10 = 20 × $10 = ​ $0 $0 $100 $100 $200 $200 ​  Stockout cost  2 × 10 × 20 × 4 = 1 × 20 × 20 × 4 = 1 × 10 × 20 × 4 = 0 = ​ $160 $160 $320 $80 $80 $0 $0 ​  Total cost  $320 $180 $200 ​ ​

Definitions

Learning Objectives

Learning Objectives

Related questions