Question

A company has an annual demand of 1000 units, ordering cost of Rs. 100/- order and carrying cost of Rs. 100/unit-year. If the stock-out costs are estimated to be nearly Rs. 400 each time the company runs out-of-stock, the safety stock justified by the carrying cost will be

• A. 100
• B. 4
• C. 40
• D. 20

Answer 1

The correct option is C 40

$\text{Method I:}$

We need to find stock justified by carrying cost

i.e., M*

$\text{M* = Q* - S*}$

$Q^{\ast }=\sqrt{\frac{2D{C}_0}{C_h}}\times \sqrt{\frac{C_h+C_b}{C_b}}$

$=\sqrt{\frac{2\times 100\times 1000}{100}}\times \sqrt{\frac{500}{400}}$

$\text{= 50 units}$

$S^{\ast }=\frac{C_h}{C_b+C_h}\times Q\ast$

$=\frac{100}{100+400}\times 50$

$\text{S* = 10 units}$

$\text{and M* = 50 - 10 = 40 units}$

$\text{Method II:}$

$\text{Given: Demand, D = 1000 units/year,}$

$\text{Ordering cost,}{C}_o=\text{Rs. 100/unit-year}$

$\text{Stock out cost,}{C}_b=\text{Rs. 400}$

Optimum level for stock out condition,

$M\ast =Q\ast \left(\frac{C_b}{C_b+C_n}\right)$

$=\sqrt{\frac{2D{C}_o}{C_h}\times \left(\frac{C_o+C_h}{C_b}\right)}\left(\frac{C_b}{C_b+C_h}\right)$

$=50\times \frac{400}{500}=40\text{units}$