Question

The inventory holding cost of an item is Rs. \(0.50\) per unit per month and the ordering cost per order is Rs. \(550\). A stockist needs to supply \(10000\) units of the item per year to the customers. Assume demand is fixed and the shortage cost is infinite. Using the classical economic order quantity (EOQ) model, the optimal lot size is ________ units per order (rounded off to the nearest integer).

Hint:

Convert the monthly holding cost to an annual value before using the standard EOQ formula.

Answer 1

Correct Answer: 1354

Step 1: Convert the holding cost to a yearly figure.
Holding cost is given per month, so \(C_h = 0.50 \times 12 = 6\) rupees per unit per year.

Step 2: Write down the other EOQ inputs.
Annual demand \(D = 10000\) units, ordering cost \(C_o = 550\) rupees per order.

Step 3: Apply the EOQ formula.
\(EOQ = \sqrt{\dfrac{2 D C_o}{C_h}} = \sqrt{\dfrac{2 \times 10000 \times 550}{6}} = \sqrt{1833333.3}\).

Step 4: Take the square root and round.
\(EOQ \approx 1354.0\) units, which rounds to the nearest integer as 1354.

Final Answer:
The optimal lot size is close to 1354 units per order. \[ \boxed{EOQ \approx 1354} \]