A company faces an annual demand of 10,000 units, a fixed ordering cost of ₹200 per order, and a holding cost of ₹4 per unit per year. What is the EOQ for this company?
The EOQ is 1000 units
This is a standard application of the Economic Order Quantity (EOQ) model, which finds the order size that minimises the total of annual ordering cost and annual inventory-holding cost. As order size increases, fewer orders are placed (ordering cost falls) but average inventory rises (holding cost climbs); the EOQ is the balance point where these two costs are equal and their sum is least.
The Wilson EOQ formula is:
EOQ = √(2 × D × Co / Ch)
where D is annual demand, Co is the fixed cost per order, and Ch is the holding cost per unit per year.
Substituting the given data:
- D = 10,000 units per year
- Co = ₹200 per order
- Ch = ₹4 per unit per year
- EOQ = √(2 × 10,000 × 200 / 4)
- Numerator = 2 × 10,000 × 200 = 4,000,000
- 4,000,000 ÷ 4 = 1,000,000
- EOQ = √1,000,000 = 1,000 units
So the correct answer is 1,000 units. The other figures do not satisfy the formula: 4000, 5000 and 2240 units would each require a different combination of demand, ordering cost or holding cost. In particular, note the square-root behaviour of EOQ — halving the holding cost or doubling the demand does not double the order size, it multiplies it only by √2 — which is why intuitive but un-computed guesses like 2240 or 5000 are incorrect here.
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