## Economic Order Quantity (EOQ)
Meaning: The order quantity at which the Total Raw-Material Inventory Maintenance Cost is minimum.
### Assumptions (all constant & known)
1. Annual Consumption (A)
2. Purchase Price per unit
3. Ordering Cost per order (O)
4. Carrying Cost per unit p.a. (C)
5. No closing stock
6. No lead time
### Total RM Inventory Cost = three parts
| Component | Formula |
|---|---|
| Purchase Cost (PC) | A × Purchase Price per unit |
| Total Ordering Cost (TOC) | (A ÷ Q) × O |
| Total Carrying Cost (TCC) | (Q ÷ 2) × C |
(Q = order quantity; average inventory = Q/2.)
### EOQ Formula
$$EOQ = \sqrt{\dfrac{2AO}{C}}$$
### Total Relevant Cost
At EOQ, TOC = TCC, so:
$$\text{Total Relevant Cost} = TOC + TCC = \sqrt{2AOC}$$
### Supporting computations
- Number of orders = A ÷ EOQ
- Time gap between two orders = (365 / 12 / 52 / 360) ÷ Number of orders (use days / months / weeks as required)
### EOQ with different price levels (quantity discounts)
When suppliers offer price breaks by quantity range, EOQ formula alone won't decide. Instead: pick an arbitrary representative quantity from each price range, compute total RM inventory cost (Purchase + Ordering + Carrying) at each, and select the range with the minimum total cost.