The Economic Order Quantity (EOQ) is the order quantity that minimizes the total relevant inventory cost, consisting primarily of ordering cost and carrying (holding) cost. In this problem, the engineering firm has an annual demand of 12,000 units, an ordering cost of Rs 600 per order, and a unit purchase price of Rs 100. The carrying cost is 20% of the purchase price per unit per year. We can calculate the EOQ and the minimum variable inventory cost using the standard EOQ model.
Given Data
- Annual demand, D = 12,000 units
- Ordering cost per order, S = Rs 600
- Unit purchase price = Rs 100
- Carrying cost = 20% of unit price
- Therefore, annual holding cost per unit:
H = 20% × Rs 100 = Rs 20 per unit per year
The standard EOQ formula is:
EOQ = √(2DS/H)
Step 1: Calculate EOQ
Substituting the given values:
EOQ = √[(2 × 12,000 × 600) / 20]
First, calculate the numerator:
2 × 12,000 × 600 = 14,400,000
Now divide by the annual carrying cost:
14,400,000 / 20 = 720,000
Therefore:
EOQ = √720,000
EOQ ≈ 848.53 units
Since inventory is normally ordered in whole units, the firm should order approximately:
EOQ ≈ 849 units per order
This means that an order quantity of about 849 units provides the most economical balance between ordering and carrying costs under the assumptions of the EOQ model.
Step 2: Calculate Number of Orders per Year
The approximate number of orders placed annually is:
Number of orders = D / EOQ
= 12,000 / 848.53
≈ 14.14 orders per year
Thus, the firm would place approximately 14 orders per year under the EOQ policy.
Step 3: Calculate Annual Ordering Cost
Annual ordering cost is:
Ordering Cost = (D/Q) × S
Substituting the values:
= (12,000 / 848.53) × Rs 600
≈ 14.142 × Rs 600
≈ Rs 8,485.28
Therefore, annual ordering cost is approximately:
Rs 8,485.28
Step 4: Calculate Annual Carrying Cost
Average inventory under the basic EOQ model is:
Average Inventory = Q/2
= 848.53 / 2
= 424.27 units
Annual carrying cost is:
Carrying Cost = (Q/2) × H
= 424.27 × Rs 20
≈ Rs 8,485.28
Therefore:
Annual carrying cost ≈ Rs 8,485.28
Step 5: Calculate Total Minimum Variable Inventory Cost
The total relevant or variable inventory cost is the sum of ordering and carrying costs:
Total Variable Inventory Cost = Ordering Cost + Carrying Cost
= Rs 8,485.28 + Rs 8,485.28
= Rs 16,970.56 per year
Therefore:
Total Minimum Variable Inventory Cost ≈ Rs 16,971 per year
At the EOQ, ordering cost and carrying cost are equal. This equality confirms the cost-minimizing property of the EOQ under the standard assumptions.
It is important to note that the purchase cost is not included in the minimum variable inventory cost calculated above. Annual purchase expenditure would be 12,000 × Rs 100 = Rs 12,00,000, but because the unit price is constant and does not depend on order quantity, it is not relevant to determining EOQ.
Final Answer
| Particular | Result |
|---|---|
| Annual demand | 12,000 units |
| Ordering cost | Rs 600/order |
| Carrying cost | Rs 20/unit/year |
| EOQ | 848.53 ≈ 849 units |
| Annual ordering cost at EOQ | Rs 8,485.28 |
| Annual carrying cost at EOQ | Rs 8,485.28 |
| Minimum variable inventory cost | Rs 16,970.56/year |
Thus, the firm should order approximately 849 units per order, resulting in a minimum annual variable inventory cost of approximately Rs 16,971.
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