Inventory Management: ABC Analysis and EOQ Frameworks

Effective inventory management balances the cost of carrying stock against the risk of stock-outs. Practitioners use two foundational frameworks to optimize this balance: **ABC Analysis** (prioritization) and **Economic Order Quantity** (replenishment math).

1. ABC Analysis (Pareto Principle)

Not all SKUs are created equal. ABC analysis categorizes inventory based on its annual consumption value (Unit Cost $\times$Annual Demand).

- **Class A (80/20 Rule):** ~20% of SKUs accounting for ~80% of value. Requires tight control, frequent audits, and accurate forecasting.

- **Class B:** ~30% of SKUs accounting for ~15% of value. Moderate control.

- **Class C:** ~50% of SKUs accounting for ~5% of value. Low control; prioritize avoiding stock-out of low-cost items (e.g., bin-stock).

2. Economic Order Quantity (EOQ) Math

The EOQ formula determines the optimal order size that minimizes the sum of **Ordering Costs** (S) and **Holding Costs** (H).$$\text{EOQ} = \sqrt{\frac{2DS}{H}}$$Where:

-$D$= Annual Demand (units).

-$S$= Setup or Ordering Cost per order ($).

-$H$= Holding or Carrying Cost per unit per year ($).

Concrete Example: Industrial Component Replenishment

Consider a high-value sensor (Class A):

- **Demand (D):** 10,000 units/year.

- **Order Cost (S):**$50 (Admin + Shipping).

- **Holding Cost (H):** $4/unit/year (Capital cost + insurance).

**Calculation:**$$\text{EOQ} = \sqrt{\frac{2 \times 10,000 \times 50}{4}} = \sqrt{\frac{1,000,000}{4}} = 500 \text{ units.}$$**Insight:** Ordering 500 units at a time ensures the warehouse isn't overstocked with expensive sensors while minimizing the number of purchase orders issued (20 orders/year).

3. Safety Stock and Service Levels

Safety Stock ($SS$) is the buffer against demand variability during lead time:$$SS = Z \times \sigma_d \times \sqrt{L}$$-$Z$= Service level factor (e.g., 1.645 for 95% service).

-$\sigma_d$= Std Dev of demand.

-$L$ = Lead time.

4. Inventory Performance Metrics

| Metric | Definition | Target |

| :--- | :--- | :--- |

| **Inventory Turnover** | COGS / Average Inventory | High (indicates efficiency) |

| **Days Sales of Inv (DSI)** | (Inventory / COGS) * 365 | Low (minimizes capital tie-up) |

| **Fill Rate** | % of orders fulfilled from stock | >98% for Class A |

| **Stock-Out Rate** | % of lost sales due to no stock | <1% for critical items |