Answer to Question #253990 in Operations Research for Raj

Question

A shopkeeper has a uniform demand of an item at the rate of 600 items per year. He buys from the supplier at a cost of Rs.8 per item. And the cost of ordering Rs. 12 each time. If the stock holding costs are 20% per year of stock value, how frequently should he replenish his stocks and what is the Optimal Order Quantity.

Answer 1

We are given demand rate R=600items/year

Ordering or set up cost C₃=R_s.12

Holding cost C₁or C₁I=R_s.8 per item

I=0.20

Economic ordering quantity (Q) =$\sqrt\frac{2C_3R}{C_1 I}$

$\sqrt\frac{2×12×600}{8×0.20}$ =$\sqrt{9000}$ =94.87units

Cycle time (t) =$\frac{EOQ}{R}$

$\frac{94.87}{600}=0.16years$

0.16×12=1.92months

=1.92months

Therefore the frequency that he should replenish his stocks is 1.92 months

The Optimal Order Quantity is 94.87 units