Reorder Point, Safety Stock, and Economic Order Quantity: A Worked Inventory Example

Safety Stock

Safety stock covers the variation in demand during the lead time. If daily demand has a standard deviation of 12 units, the standard deviation over 7 days is 12 × √7 = 31.7 units. For a 95% service level (a 5% chance of a stockout during a cycle), the z-score is 1.65, so safety stock = 1.65 × 31.7 = 52 units. For 99%, z = 2.33 and safety stock is 74 units. If lead time is also variable, include that variance as well: the combined standard deviation = √(L × σd² + d² × σL²).

Higher service levels require disproportionately more stock: going from 95% to 99% adds 22 units, or 42% more safety stock, to reduce stockout risk from 5% to 1%.

Reorder Point

ROP = demand during lead time + safety stock = 280 + 52 = 332 units. When on-hand plus on-order inventory falls to 332, place an order. This ensures that on average you run out only 5% of the time before the order arrives. The reorder point is reviewed whenever demand or lead time patterns change, such as seasonality or supplier delays. For items with seasonal swings, compute separate reorder points for peak and off-peak periods.

Economic Order Quantity

The EOQ formula balances the cost of placing orders against the cost of holding inventory: EOQ = √(2DS ÷ H), where D is annual demand, S is the cost per order, and H is the annual holding cost per unit. With annual demand of 12,000 units, an order cost of $50, and a holding cost of $2 per unit per year: EOQ = √(2 × 12,000 × 50 ÷ 2) = √600,000 = 775 units. That means about 15.5 orders a year, or one every 3.4 weeks. Total annual cost at the EOQ is ordering ($775) plus holding ($775), balanced, and any deviation increases the total.

Ordering 2,000 units at a time would cost 6 orders × $50 = $300 plus average inventory of 1,000 units × $2 = $2,000, a total of $2,300 versus $1,550 at the EOQ.

Assumptions and Real-World Adjustments

EOQ assumes constant demand, a fixed order cost, and a constant holding cost, and no quantity discounts. Real suppliers offer price breaks, minimum order quantities, and case packs. When discounts exist, compare total cost at each price break. Holding costs include capital, storage, insurance, shrinkage, and obsolescence, commonly 20% to 30% of item cost a year. Perishable or short-life products need smaller orders. Modern systems use forecasts and software to compute dynamic reorder points, but the principles remain the same.

Putting It to Work

Collect data on daily demand and supplier lead times, compute the averages and standard deviations, and decide on service levels based on the cost of a stockout versus the cost of holding. Prioritize high-value (A) items for tight control and use simpler rules for low-value items. Review the results regularly, comparing predicted and actual stockouts and inventory levels.