91Ó°ÊÓ

Economic order quantity is a computation used by businesses to determine the appropriate order amount to reduce logistical expenses, warehouse space, stockouts, and overstock prices. The EOQ model's purpose is to identify the optimal order quantity you should have.

Given data

Cost per tire = $ 35 each

Holding cost = 20% of tire each

Annual demand = 1000 per order

Ordering cost = $ 20 per order

The standard deviation of daily demand = 3 tires

Delivery lead time = 4 days

Calculation of order quantity

$$\begin{gathered} \mathrm{EOQ}=\sqrt{\frac{2×\mathrm{A}×\mathrm{S}}{\mathrm{H}}} \\ \mathrm{Where}, \\ \mathrm{A}=\mathrm{Annual}\mathrm{Demand} \\ \mathrm{S}=\mathrm{Ordering}\mathrm{cost}\mathrm{per}\mathrm{unit} \\ \mathrm{H}=\mathrm{Carrying}\mathrm{cost}\mathrm{per}\mathrm{unit} \\ \mathrm{EOQ}=\sqrt{\frac{2×\mathrm{A}×\mathrm{S}}{\mathrm{H}}} \\ =\sqrt{\frac{2×1000×20}{8.75}} \\ =67.6\mathrm{or}68\mathrm{tires} \end{gathered}$$

So, the reorder quantity is 68 tires.

Calculation of reorder point

$\mathrm{Reorder}\mathrm{level}=\mathrm{dL}+{\mathrm{³úσ}}_{\mathrm{L}}$

Where,

$$\begin{gathered} \mathrm{Annual}\mathrm{Demand}=\frac{\mathrm{Annual}\mathrm{Demand}}{\mathrm{No}.\mathrm{of}\mathrm{Days}\mathrm{in}\mathrm{one}\mathrm{year}} \\ =\frac{1000}{365} \\ =2.73 \end{gathered}$$

Lead time = 4 days

z- value = 2.05 using Excel function = NORMSINV(0.98)

Standard deviation = 3 tires

Substituting all the values in equation

Reorder point = 2.73 × 4 + 2.05 × 3$\sqrt{4}$

= 11 + 12.3

= 23.3 or 23

Therefore, the required reorder point is 23 tires.