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: Match up the time units first.
$C_h$ is monthly (Rs. 0.50 per unit per month) but $D$ is yearly, so scale $C_h$ to Rs. 6 per unit per year.

Step 2: Recall why the EOQ formula balances two costs.
It finds the lot size where annual ordering cost equals annual holding cost, giving the least total cost.

Step 3: Plug the numbers into $EOQ = \sqrt{2DC_o/C_h}$.
$EOQ = \sqrt{(2)(10000)(550)/6} = \sqrt{1833333.3} \approx 1354$.

Final Answer:
The stockist should order about 1354 units each time to keep total cost lowest. \[ \boxed{EOQ \approx 1354} \]