# Economic Order Quantity (EOQ)
## The Problem
As Re-Order Quantity (ROQ) increases:
- Total ordering cost ↓ (fewer orders per year)
- Total carrying cost ↑ (more average inventory held)
Conversely, as ROQ decreases, ordering cost ↑ and carrying cost ↓. There is a trade-off.
## The Solution: EOQ
EOQ is that specific Re-Order Quantity at which Total Ordering Cost + Total Carrying Cost is MINIMUM. It is the best version of ROQ.
Graphically, EOQ is the point where the ordering cost curve and carrying cost curve intersect — at that point total cost is minimised.
```
Annual Cost
↑
│\ / Total Cost (U-shaped curve)
│ \ /
│ \ ____ ____ / Carrying Cost (rising line)
│ \/ \/
│ /\ /\
│ / \______/ \______ Ordering Cost (falling curve)
│ / |
│/ EOQ
└─────────────────────→ Re-order Quantity
```
## EOQ Formula
$$\boxed{EOQ = \sqrt{\frac{2 \times A \times O}{C}}}$$
Where:
- A = Annual Consumption (per year)
- O = Ordering Cost per Order
- C = Carrying Cost per Unit per Annum
## At EOQ — A Key Identity
At EOQ, Total Ordering Cost = Total Carrying Cost. This identity is often used to verify EOQ answers and to solve missing-data problems.
## Types of EOQ Questions in Exam
| Type 1 | Type 2 | Type 3 |
|---|---|---|
| Simply calculate EOQ | EOQ vs Without EOQ — Compare only carrying cost + ordering cost at both levels | EOQ vs Discount offer — Compare purchase price + carrying cost + ordering cost at both levels |
### Type 1 — Plain EOQ
Plug values into the formula and report the answer.
### Type 2 — EOQ vs Some Other Order Size
Compare Total Cost (ordering + carrying) at EOQ vs at the alternative quantity. The lower total cost wins. Purchase price is excluded because it is the same under both options.
### Type 3 — EOQ vs Quantity Discount
When supplier offers a discount on bulk purchase, purchase price differs across alternatives. Hence compare:
Total Cost = Purchase Cost + Ordering Cost + Carrying Cost
at EOQ vs at the discount-eligible higher quantity. Choose the lower total.