Question

In computing Wilson's economic lot size for an item, by mistake the demand rate estimate used was 40% higher than the true demand rate. Due to this error in the lot size computation, the total cost of setup plus inventory holding per unit time. Would rise above the true optimum by approximately

• A. 18.3%
• B. 1.4%
• C. 3.3%
• D. 8.7%

Answer 1

The correct option is A 18.3%

Method I:

$Q^{\ast }\propto \sqrt{D}$

$Q_1^{\ast }\propto \sqrt{1.4D}$

$\propto \sqrt{1.4}\sqrt{D}\propto \sqrt{1.4}{Q}^{\ast }$

Now initial inventory cost $=\frac{D}{Q^{\ast }}{C}_0+\frac{Q^{\ast }}{2}{C}_n$

Now total inventory cost

$=\frac{1.4D}{\sqrt{1.4}{Q}^{\ast }}{C}_0+\sqrt{1.4}\frac{Q^{\ast }}{2}{C}_n$

$=\sqrt{1.4}(\frac{D}{Q^{\ast }}{C}_0+\frac{Q^{\ast }}{2}{C}_n)$

$=\sqrt{1.4}\text{(initial inventory cost)}$

$\text{= 1.183 (initial inventory cost)}$

$\text{Total rise = 18.3\%}$

Method II:

Economic order quantity,

$EOC=\sqrt{\frac{2D{C}_0}{C_h}}$

Total inventory cost at EOQ,

$(TIC{)}_{\text{actual}}=\sqrt{2D{C}_0{C}_h}$

$(TIC{)}_{\text{estimate}}=\sqrt{2\left(1.4D\right)C_0{C}_h}=1.183\sqrt{2D{C}_0{C}_h}$

Error in estimate,

$=\frac{(TIC{)}_{\text{estimate}}-(TIC{)}_{\text{(}actual)}\times 100}{(TIC{)}_{\text{actual}}}$

$=\left(\frac{1.183-1}{1}\right)\times 100$

$\text{= 18.3\%}$