GATE 2022 ME (ME2) – Question 33
The demand of a certain part is 1000 parts/year and its cost is ₹1000/part. The orders are placed based on the economic order quantity (EOQ). The cost of ordering is ₹100/order and the lead time for receiving the orders is 5 days. If the holding cost is ₹20/part/year, the inventory level for placing the orders is ______ parts (round off to the nearest integer).
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Correct answer: 13 to 15
Explanation
The question asks for the **reorder point** (the inventory level at which an order is placed), so the order quantity is not needed.
**Step 1: demand per day.** With 365 days a year,
$$d=\frac{1000}{365}=2.74\text{ parts/day}.$$
**Step 2: demand during the lead time.** The lead time is 5 days:
$$ROP=d\times L=2.74\times5=13.7\approx\mathbf{14}\text{ parts}.$$
(EOQ $=\sqrt{2DC_o/C_h}=\sqrt{2\cdot1000\cdot100/20}=100$ parts. It fixes how much is ordered, not when.)
Official GATE 2022 answer key: https://gate2026.iitg.ac.in/doc/download/Answer_keys2022/me-merged_2022.pdf