## Inventory Control
CIMA Definition: The function responsible for ensuring that an adequate quantity of goods is retained in stock to meet all requirements, without holding unnecessarily large stocks.
The core challenge is a two-sided trade-off:
- Hold too little → stock-out costs (lost production, lost sales, reputation damage)
- Hold too much → carrying/holding costs (interest, warehousing, obsolescence)
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### Economic Order Quantity (EOQ)
EOQ is the order quantity that minimises total inventory cost (sum of ordering cost + carrying cost).
$$EOQ = \sqrt{\frac{2 \times A \times O}{C}}$$
Where:
- A = Annual demand (units)
- O = Ordering cost per order (₹)
- C = Carrying/holding cost per unit per annum (₹)
#### Assumptions Underlying EOQ
1. Ordering cost per order is known and fixed.
2. Carrying cost per unit per annum is known and fixed.
3. Annual demand is known and constant.
4. Cost per unit is constant (no quantity discounts affecting per-unit cost).
5. Lead time is zero (instantaneous replenishment).
> Note: These assumptions are simplifications. In practice, lead time is non-zero, which is why safety stock and re-order levels exist.
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### Stock-Out and Its Costs
- Stock-out = inability to supply an item due to insufficient inventory.
- Financial costs: idle overhead, lost profit, emergency procurement premium.
- Non-financial costs: damaged reputation, loss of customer goodwill, missed commitments.
- Safety stock (buffer stock) is held to guard against demand fluctuations and supply delays.
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### Key Stock Levels
| Level | Formula / Concept |
|---|---|
| Re-order Level | Maximum consumption × Maximum lead time |
| Minimum Level | Re-order Level − (Normal consumption × Normal lead time) |
| Maximum Level | Re-order Level + EOQ − (Minimum consumption × Minimum lead time) |
| Average Stock Level | Minimum Level + ½ × EOQ |
| Danger Level | Average consumption × Maximum lead time for emergency purchases |