Calculating Economic Order Quantity (EOQ)

The problem asks us to determine the Economic Order Quantity (EOQ) for a specific item based on its demand rate, ordering cost, and holding cost. The EOQ is the optimal order quantity that minimizes the total inventory cost, which includes ordering cost and holding cost, under certain assumptions.

Understanding the Given Data

We are provided with the following information:

• Demand Rate (D): 12000 units per year
• Ordering Cost (S): Rs. 100 per order
• Holding Cost: Rs. 0.80 per item per month

We are also told that shortages are not allowed and replacement is instantaneous. This indicates that we should use the basic EOQ model formula.

Ensuring Consistent Units for Calculation

The demand rate is given in units per year, but the holding cost is given in rupees per item per month. To use the EOQ formula correctly, all costs and demand must be in the same time units (usually annual).

Let's convert the monthly holding cost to an annual holding cost:

Annual Holding Cost (H) = Monthly Holding Cost per item $\times$ 12 months/year

Annual Holding Cost (H) = Rs. 0.80/item/month $\times$ 12 months/year = Rs. 9.60 per item per year.

Applying the Economic Order Quantity (EOQ) Formula

The formula for the Economic Order Quantity under the basic inventory model (no shortages, instantaneous replenishment) is:

\(\text{EOQ} = \sqrt{\frac{2DS}{H}}\)

Where:

• D = Annual Demand Rate
• S = Ordering Cost per order
• H = Annual Holding Cost per unit

Step-by-Step Calculation

Now we substitute the values into the EOQ formula:

• D = 12000 units/year
• S = Rs. 100/order
• H = Rs. 9.60/item/year

\(\text{EOQ} = \sqrt{\frac{2 \times 12000 \times 100}{9.60}}\)

\(\text{EOQ} = \sqrt{\frac{2400000}{9.60}}\)

\(\text{EOQ} = \sqrt{250000}\)

\(\text{EOQ} = 500\)

So, the economic order quantity is 500 units.

Result and Option Matching

The calculated EOQ is 500 units. Let's check the given options:

Our calculated value of 500 units matches Option 3.

Revision Table: Economic Order Quantity (EOQ) Calculation

Additional Information: Basic EOQ Model

The basic EOQ model is a fundamental concept in inventory management. It operates under several assumptions:

• Demand is known and constant over time.
• Ordering cost is constant per order.
• Holding cost is constant per unit per year.
• Lead time (time between placing an order and receiving it) is zero or constant.
• The entire order quantity is received at once (instantaneous replenishment).
• No shortages or stockouts are allowed.

The goal of the EOQ model is to find the order quantity that minimizes the sum of annual ordering cost and annual holding cost.

Annual Ordering Cost = \(\frac{D}{Q} \times S\), where Q is the order quantity.

Annual Holding Cost = \(\frac{Q}{2} \times H\).

Total Inventory Cost = Annual Ordering Cost + Annual Holding Cost = \(\frac{D}{Q}S + \frac{Q}{2}H\).

The EOQ is the value of Q that minimizes this total cost equation, which is derived using calculus, resulting in the formula \(\text{EOQ} = \sqrt{\frac{2DS}{H}}\).