Inventory Reorder Point & Safety Stock
Calculate optimal reorder points and safety stock with demand variability. Enter values for instant results with step-by-step formulas.
Formula
ROP = (Daily Demand × Lead Time) + Safety Stock; SS = Z × √(LT×σD² + D²×σLT²)
Worked Examples
Example 1: Electronics Retailer
Problem:Daily demand: 100 units (σ=20). Lead time: 7 days (σ=2 days). Target 95% service level. Order cost $50. Holding cost 25% of $10 unit cost.
Solution:Step 1: Calculate Z-score for 95% = 1.65\n\nStep 2: Combined standard deviation\nσcombined = √(7×20² + 100²×2²)\n= √(2800 + 40000) = √42800 = 207 units\n\nStep 3: Safety Stock\nSS = 1.65 × 207 = 342 units (3.4 days supply)\n\nStep 4: Demand during lead time\nDDLT = 100 × 7 = 700 units\n\nStep 5: Reorder Point\nROP = 700 + 342 = 1,042 units\n\nStep 6: EOQ\nAnnual demand = 100 × 365 = 36,500\nHolding cost = $10 × 25% = $2.50/unit/year\nEOQ = √(2×36500×50/2.50) = 1,208 units\n\nOrder 1,208 units when inventory hits 1,042.
Result:ROP: 1,042 units | Safety Stock: 342 units | EOQ: 1,208 units | 30 orders/year
Example 2: Food Distributor (High Variability)
Problem:Daily demand: 500 units (σ=150). Lead time: 3 days (σ=1 day). 97% service level. Order cost $100. Holding cost 35% of $5 unit.
Solution:High variability scenario:\nDemand CV = 150/500 = 30% (high)\nLead time CV = 1/3 = 33% (high)\n\nZ-score for 97% = 1.88\n\nσcombined = √(3×150² + 500²×1²)\n= √(67500 + 250000) = √317500 = 564 units\n\nSafety Stock = 1.88 × 564 = 1,060 units\n\nDDLT = 500 × 3 = 1,500 units\nROP = 1,500 + 1,060 = 2,560 units\n\nEOQ = √(2×182500×100/1.75) = 4,564 units\n\nHigh variability requires 2+ days safety stock despite short lead time.
Result:ROP: 2,560 units | Safety Stock: 1,060 (2.1 days) | High variability = high buffer
Example 3: Pharmaceutical - 99% Service
Problem:Daily demand: 50 units (σ=5). Lead time: 14 days (σ=1 day). 99% service (critical medicine). Order cost $200. Holding cost 20% of $100 unit.
Solution:Critical item - 99% service level:\nZ-score = 2.33\n\nLow demand variability (CV=10%) but strict service requirement.\n\nσcombined = √(14×5² + 50²×1²)\n= √(350 + 2500) = √2850 = 53 units\n\nSafety Stock = 2.33 × 53 = 124 units (2.5 days)\n\nDDLT = 50 × 14 = 700 units\nROP = 700 + 124 = 824 units\n\nEOQ = √(2×18250×200/20) = 604 units\n\nHigh unit cost makes holding expensive; order more frequently.
Result:ROP: 824 units | SS: 124 units | EOQ: 604 | 30 orders/year | $12K holding cost
Frequently Asked Questions
What is a reorder point?
The reorder point (ROP) is the inventory level at which a new order should be placed to replenish stock before it runs out. It accounts for demand during lead time plus safety stock buffer. When inventory drops to ROP, trigger a purchase order. ROP = (Average Daily Demand × Lead Time) + Safety Stock.
What is safety stock?
Safety stock is extra inventory held to protect against uncertainty in demand and lead time. It acts as a buffer against stockouts when demand exceeds forecast or suppliers deliver late. Higher service levels require more safety stock. Typical ranges: 1-4 weeks of average demand depending on variability and service requirements.
How do I calculate safety stock with variable demand and lead time?
Combined formula: SS = Z × √(LT × σD² + D² × σLT²) where Z is service level factor, LT is lead time, σD is demand standard deviation, D is average demand, and σLT is lead time standard deviation. This captures both sources of uncertainty simultaneously.
How does lead time variability affect inventory?
Lead time variability often has bigger impact than demand variability. A supplier who sometimes delivers in 3 days, sometimes 10 days, requires far more safety stock than one consistently delivering in 7 days. Work with suppliers to reduce variability, not just average lead time.