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).

The correct answer is 14.

Step-by-Step Explanation:

To determine the inventory level for placing the orders (also known as the Reorder Point), we need to find the demand during the lead time.

Let's first list the given parameters:
Annual demand, D = 1000 parts/year
Cost of the part, C = ₹1000/part
Cost of ordering, C_o = ₹100/order
Holding cost, C_h = ₹20/part/year
Lead time, LT = 5 days

First, we calculate the Economic Order Quantity (EOQ) to understand the ordering parameters, although the reorder point primarily depends on the daily demand and the lead time:
$$\mathrm{EOQ}=\sqrt{\frac{2\times D\times C_o}{C_h}}$$
Substituting the given values:
$$\mathrm{EOQ}=\sqrt{\frac{2\times 1000\times 100}{20}}=100$$

Next, we calculate the daily demand. Since the annual demand is given per year, we convert it to a daily rate assuming 365 days in a year:
$$\text{Daily demand}=\frac{1000}{365}\approx 2.7397\text{parts/day}$$

The reorder point (inventory level to place a new order) is the quantity of inventory that will be consumed during the lead time. It is calculated as:
$$\text{Reorder point}=\text{Lead time}\times \text{Daily demand}$$
Substituting the lead time of 5 days and the daily demand:
$$\text{Reorder point}=5\times 2.7397=13.698\text{parts}$$

Rounding off to the nearest integer, we get:
$$\text{Reorder point}\approx 14\text{parts}$$