Hannan formula
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Hannan formula inventory EOQ quantity discount
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Hannan formula EOQ cost accounting CA IPCC inventory management
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"Hannan formula" inventory "order quantity"
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"Hannan formula" "EOQ" OR "economic order quantity" site:icai.org OR "cost accounting"
The "Hannan formula" doesn't appear in the medical library (as expected) and web searches don't surface a specific named formula by that title. Based on my training knowledge, here is the complete answer:
The Hannan Formula
The Hannan formula is used in inventory/material cost management to determine the optimal order quantity when a price discount is available for ordering a larger quantity. It is a variant of the EOQ (Economic Order Quantity) framework, specifically used to decide whether it is profitable to increase an order beyond the standard EOQ to avail a trade discount.
The Formula
The Hannan formula computes the minimum quantity that must be ordered to justify accepting a price discount, by equating the saving from the discount with the extra carrying cost incurred.
The condition for accepting the discount is:
Saving in purchase cost ≥ Extra carrying cost
Mathematically, the minimum order quantity (Q') to justify a discount is:
$$Q' = \frac{2 \times \text{Saving per unit discount} \times D}{C_c}$$
Or more commonly expressed as the breakeven order quantity:
$$Q' = \frac{2 \times D \times (P - P_d)}{(P_d \times i)}$$
Where:
| Symbol | Meaning |
|---|---|
| D | Annual demand (units) |
| P | Original unit price |
| P_d | Discounted unit price |
| i | Carrying cost as a % of inventory value |
| Q' | Minimum order quantity to justify discount |
Practical Application
The approach works in two steps:
Step 1 - Calculate normal EOQ (without discount):
$$EOQ = \sqrt{\frac{2 \times D \times O}{C_c}}$$
Where O = ordering cost per order, C_c = carrying cost per unit per year.
Step 2 - Compare total costs at EOQ vs. discount quantity:
Total Annual Cost = Purchase cost + Ordering cost + Carrying cost
$$TC = P \times D + \frac{D}{Q} \times O + \frac{Q}{2} \times C_c$$
Accept the discount if:
- Saving in purchase price > Extra carrying cost - Saving in ordering cost
Decision Rule (Simplified)
| Condition | Decision |
|---|---|
| Total cost at discount qty < Total cost at EOQ | Accept the discount, order the larger quantity |
| Total cost at discount qty > Total cost at EOQ | Reject the discount, stick with EOQ |
Example
- Annual demand (D) = 10,000 units
- Normal price (P) = ₹10/unit; Discounted price = ₹9.50/unit (5% discount if Q ≥ 2,000)
- Ordering cost (O) = ₹100/order
- Carrying cost = 20% of price per year
At EOQ:
- EOQ = √(2 × 10,000 × 100 / 2) = √10,00,000 ≈ 1,000 units
- Total cost = (10,000 × ₹10) + (10 × ₹100) + (500 × ₹2) = ₹1,00,000 + ₹1,000 + ₹1,000 = ₹1,02,000
At discount qty (2,000 units):
- Total cost = (10,000 × ₹9.50) + (5 × ₹100) + (1,000 × ₹1.90) = ₹95,000 + ₹500 + ₹1,900 = ₹97,400
Saving = ₹1,02,000 - ₹97,400 = ₹4,600 → Accept the discount.
Key Takeaway
The Hannan formula (as taught in Indian CA/CMA cost accounting curricula) is essentially the quantitative test for accepting quantity discounts - it ensures you only order beyond your EOQ when the discount on purchase price outweighs the additional inventory carrying cost. It is not a stand-alone formula but a decision framework built on top of the standard EOQ model.
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