Cost-Accounting Inventory-Management Economic Order Quantity EOQ Formula Safety Stock Reorder Point

? What this actually is

Economic Order Quantity (EOQ) is a formula used to determine the optimal quantity of inventory to order that minimizes total inventory costs, including ordering costs and holding costs. It's crucial for inventory management because it helps businesses balance the costs of ordering too much (high holding costs) versus ordering too little (frequent ordering costs). The EOQ formula is:

[ EOQ = \sqrt{\frac{2DS}{H}} ]

where: - ( D ) = Demand rate (units per period) - ( S ) = Ordering cost per order - ( H ) = Holding cost per unit per period

? The core logic (or formula)

1. EOQ Formula:
   [ EOQ = \sqrt{\frac{2DS}{H}} ]
2. ( D ): Demand rate (units per period)
3. ( S ): Ordering cost per order

4. ( H ): Holding cost per unit per period

5. Safety Stock: Extra inventory held to mitigate the risk of stockouts caused by uncertainties in supply and demand.
   [ \text{Safety Stock} = z \times \sigma \times \sqrt{L} ]

6. ( z ): Z-value (number of standard deviations)
7. ( \sigma ): Standard deviation of demand

8. ( L ): Lead time

9. Reorder Point (ROP): The inventory level that triggers a new order.
   [ \text{ROP} = \text{Safety Stock} + (\text{Average Daily Usage} \times \text{Lead Time}) ]

10. Total Inventory Costs: The sum of ordering costs and holding costs.
    [ \text{Total Inventory Costs} = \left(\frac{D}{Q}\right)S + \left(\frac{Q}{2}\right)H ]

11. Optimal Order Quantity: The EOQ minimizes the total inventory costs.

? Hidden rule nobody explains

In practice, the holding cost (( H )) is often estimated as a percentage of the item cost, typically around 25%. This simplifies the calculation and makes it more practical for real-world applications.

? Practical example / breakdown

Let's say a company has the following data: - Demand rate (( D )) = 10,000 units per year - Ordering cost per order (( S )) = $50 - Holding cost per unit per year (( H )) = $2

Using the EOQ formula: [ EOQ = \sqrt{\frac{2 \times 10,000 \times 50}{2}} = \sqrt{\frac{1,000,000}{2}} = \sqrt{500,000} \approx 707 \text{ units} ]

Now, let's calculate the safety stock and reorder point: - Standard deviation of demand (( \sigma )) = 10 units - Lead time (( L )) = 5 days - Z-value (( z )) = 1.645 (for 95% confidence level)

[ \text{Safety Stock} = 1.645 \times 10 \times \sqrt{5} \approx 36.7 \text{ units} ]

Assuming average daily usage is 27.4 units (10,000 units / 365 days): [ \text{ROP} = 36.7 + (27.4 \times 5) = 36.7 + 137 = 173.7 \text{ units} ]

? Your move today

Goal: Calculate the EOQ, safety stock, and reorder point for a hypothetical product.

Step-by-step:
1. Choose a product with the following data:
- Demand rate (( D )) = 15,000 units per year
- Ordering cost per order (( S )) = $75
- Holding cost per unit per year (( H )) = $3
- Standard deviation of demand (( \sigma )) = 15 units
- Lead time (( L )) = 7 days
- Z-value (( z )) = 1.645 (for 95% confidence level)

1. Calculate the EOQ using the formula.
2. Calculate the safety stock using the formula.
3. Calculate the reorder point using the formula.

What to save: A completed calculation sheet with the EOQ, safety stock, and reorder point for your hypothetical product.

? Quick reference asset

EOQ Formula Card

[ EOQ = \sqrt{\frac{2DS}{H}} ]

Example:
- ( D = 10,000 ) units per year - ( S = $50 ) - ( H = $2 )

[ EOQ = \sqrt{\frac{2 \times 10,000 \times 50}{2}} \approx 707 \text{ units} ]

Safety Stock Formula Card

[ \text{Safety Stock} = z \times \sigma \times \sqrt{L} ]

Example:
- ( z = 1.645 ) - ( \sigma = 10 ) units - ( L = 5 ) days

[ \text{Safety Stock} = 1.645 \times 10 \times \sqrt{5} \approx 36.7 \text{ units} ]

Reorder Point Formula Card

[ \text{ROP} = \text{Safety Stock} + (\text{Average Daily Usage} \times \text{Lead Time}) ]

Example:
- Safety Stock = 36.7 units - Average Daily Usage = 27.4 units - Lead Time = 5 days

[ \text{ROP} = 36.7 + (27.4 \times 5) = 173.7 \text{ units} ]

⚠️ Common mistakes & recovery

• Common Error 1: Forgetting to convert annual demand to daily usage for the reorder point calculation.

• Common Error 2: Using incorrect units for holding costs (e.g., using monthly holding costs instead of annual).

• Quick Check: Verify that your EOQ calculation results in a lower total inventory cost compared to other order quantities.

• Exam Tip: Practice the EOQ formula with different sets of numbers to build speed and accuracy.

✅ Completion check

"I can calculate the Economic Order Quantity (EOQ), safety stock, and reorder point for a product and explain how these values help in inventory management."