A manufacturing company has an expected usage of 50,000 units of a certain product during next year. The cost of processing an order is Rs. 20 and the carrying cost per unit is Rs. 0.50 for one year. What will be the Economic Ordering Quantity ?
2000 units
Calculating Economic Ordering Quantity (EOQ)
The Economic Ordering Quantity (EOQ) is a fundamental concept in inventory management. It represents the optimal order quantity that minimizes the total inventory costs, which include ordering costs and carrying costs.
The question provides the following information:
- Expected annual usage (Demand, D) = 50,000 units
- Cost of processing an order (Ordering Cost, S) = Rs. 20 per order
- Carrying cost per unit per year (Holding Cost, H) = Rs. 0.50 per unit per year
We need to find the Economic Ordering Quantity (EOQ) using the standard formula.
Economic Ordering Quantity Formula
The formula for calculating the Economic Ordering Quantity (EOQ) is:
\( EOQ = \sqrt{\frac{2DS}{H}} \)
Where:
- \( D \) = Annual Demand or Usage
- \( S \) = Ordering Cost per order
- \( H \) = Carrying (Holding) Cost per unit per year
Step-by-Step EOQ Calculation
Now, let's substitute the given values into the EOQ formula:
\( EOQ = \sqrt{\frac{2 \times 50,000 \times 20}{0.50}} \)
First, calculate the numerator:
\( 2 \times 50,000 \times 20 = 100,000 \times 20 = 2,000,000 \)
So the formula becomes:
\( EOQ = \sqrt{\frac{2,000,000}{0.50}} \)
Now, divide the numerator by the carrying cost:
\( \frac{2,000,000}{0.50} = 4,000,000 \)
Finally, take the square root:
\( EOQ = \sqrt{4,000,000} \)
\( EOQ = 2000 \)
Thus, the Economic Ordering Quantity is 2000 units.
Ordering 2000 units at a time is expected to minimize the total cost of ordering and holding inventory for this product, given the specified usage, ordering cost, and carrying cost.
| Parameter | Symbol | Value |
|---|---|---|
| Annual Usage | D | 50,000 units |
| Ordering Cost | S | Rs. 20 |
| Carrying Cost | H | Rs. 0.50 |
| Economic Ordering Quantity (EOQ) | EOQ | 2000 units |
Understanding EOQ Components
Let's quickly define the components used in the EOQ calculation:
- Annual Usage (D): This is the total number of units of the product the company expects to use or sell over one year. In this case, it's 50,000 units.
- Ordering Cost (S): This is the fixed cost incurred each time an order is placed, regardless of the number of units ordered. It includes costs like processing the purchase order, transportation costs, inspection, etc. Here, it's Rs. 20 per order.
- Carrying Cost (H): This is the cost of holding one unit of inventory for one year. It includes costs like storage space, insurance, taxes, obsolescence, and opportunity cost of the money tied up in inventory. Here, it's Rs. 0.50 per unit per year.
The EOQ model balances the trade-off between ordering costs (which decrease as order size increases) and carrying costs (which increase as order size increases) to find the minimum total cost point.
Revision Table: Key Inventory Formulas
| Formula | Purpose |
|---|---|
| \( EOQ = \sqrt{\frac{2DS}{H}} \) | Calculates the optimal order quantity to minimize total inventory cost. |
| Number of Orders per Year = \( \frac{D}{EOQ} \) | Calculates how many times an order is placed annually. |
| Time Between Orders = \( \frac{365 \text{ days}}{\text{Number of Orders per Year}} \) (or \( \frac{\text{Working Days}}{\text{Number of Orders per Year}} \)) | Calculates the frequency of placing orders. |
| Total Ordering Cost = \( \frac{D}{EOQ} \times S \) | Calculates the total annual cost of placing orders. |
| Total Carrying Cost = \( \frac{EOQ}{2} \times H \) | Calculates the total annual cost of holding inventory (assuming average inventory is EOQ/2). |
| Total Inventory Cost = Total Ordering Cost + Total Carrying Cost | Calculates the sum of ordering and carrying costs. At EOQ, Total Ordering Cost = Total Carrying Cost. |
Additional Information on Economic Ordering Quantity
The EOQ model is a simple yet powerful tool in inventory control. It operates based on several key assumptions:
- Demand is constant and known throughout the year.
- Ordering cost is constant per order.
- Carrying cost is constant per unit per year.
- The lead time (time between placing an order and receiving it) is known and constant.
- Inventory is received in a single batch.
- There are no quantity discounts.
While these assumptions may not hold perfectly in real-world scenarios, the EOQ model often provides a good starting point for inventory decisions. Variations of the EOQ model exist to account for factors like quantity discounts or variable demand.
Calculating the correct Economic Ordering Quantity helps companies manage their inventory efficiently, reducing excess stock (and associated carrying costs) while avoiding frequent small orders (and associated high ordering costs). This leads to lower total inventory costs and improved operational efficiency.
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