1. Safety Stock Formula
The buffer inventory held to protect against demand variability and lead time uncertainty. The most searched formula in supply chain planning.
Basic Safety Stock
SS = Z × σd × √LT
Z = service level z-score (1.28 for 90%, 1.65 for 95%, 2.33 for 99%) · σd = std dev of demand · LT = lead time in periods
Excel: =NORM.S.INV(0.95) * STDEV(demand_range) * SQRT(lead_time)
Safety Stock with Lead Time Variability
SS = Z × √(LT × σd² + d̄² × σLT²)
d̄ = average demand per period · σLT = std dev of lead time · Accounts for BOTH demand and supply uncertainty
2. Economic Order Quantity (EOQ)
The optimal order size that minimises total inventory cost — balancing ordering cost against holding cost.
EOQ Formula
EOQ = √(2DS / H)
D = annual demand · S = ordering cost per order · H = holding cost per unit per year
Excel: =SQRT(2 * annual_demand * order_cost / holding_cost)
3. Reorder Point (ROP)
The inventory level at which a new order should be placed to avoid stockout during replenishment lead time.
Reorder Point
ROP = (d̄ × LT) + Safety Stock
d̄ = average daily demand · LT = lead time in days · Safety stock provides the buffer
Excel: =AVERAGE(daily_demand) * lead_time + safety_stock
4. MAPE — Mean Absolute Percentage Error
The industry standard forecast accuracy metric. Expresses error as a percentage of actual demand.
MAPE
MAPE = (1/n) × Σ(|Actual - Forecast| / Actual) × 100%
Below 20% = good · Below 10% = excellent · Above 30% = needs intervention
Excel: =AVERAGE(ABS(actual-forecast)/actual) * 100
5. Forecast Bias
The systematic tendency to consistently over-forecast or under-forecast. MAPE alone cannot detect bias.
Forecast Bias
Bias = (1/n) × Σ(Actual - Forecast)
Positive = chronic under-forecasting (stockout risk) · Negative = chronic over-forecasting (excess inventory)
6. Tracking Signal
The cumulative bias detection alarm. When it exceeds ±4, the forecast is systematically biased.
Tracking Signal
TS = CFE / MAD
CFE = Σ(Actual - Forecast)
MAD = (1/n) × Σ|Actual - Forecast|
|TS| > 4 = bias confirmed · |TS| > 6 = critical · Recalibrate model immediately
7. Inventory Turnover
How many times inventory is sold and replaced in a year. Higher turns = more efficient capital use.
Inventory Turnover
Turns = COGS / Average Inventory
FMCG: 8-12x · Manufacturing: 4-8x · Spare parts: 2-4x · Luxury: 1-3x
Excel: =COGS / AVERAGE(inventory_start, inventory_end)
8. Days of Supply (DOS / DIO)
Days of Supply
DOS = Average Inventory / (COGS / 365)
Also: DOS = 365 / Inventory Turnover · Lower is generally better · Target depends on lead time + safety stock
9. Fill Rate
Fill Rate (Line Level)
Fill Rate = (Units Shipped / Units Ordered) × 100%
Order fill rate = (Complete Orders / Total Orders) × 100% · Target: 95-98%
10. OTIF — On-Time In-Full
OTIF
OTIF = (Orders On-Time AND In-Full / Total Orders) × 100%
Both conditions must be met simultaneously · Walmart penalty: 3% of COGS · Target: 92-96%
11. Cash-to-Cash Cycle Time
Cash-to-Cash (C2C)
C2C = DIO + DSO - DPO
DIO = Days Inventory Outstanding · DSO = Days Sales Outstanding · DPO = Days Payable Outstanding
Lower is better · Negative C2C = you collect cash before paying suppliers (e.g. Amazon)
12. GMROI — Gross Margin Return on Inventory
GMROI
GMROI = Gross Margin / Average Inventory Cost
GMROI > 1 = each $1 of inventory generates > $1 margin · Target: 2.5-4.0x · Below 1.0 = losing money on inventory
13. Perfect Order Rate
Perfect Order Rate
POR = (On-Time × In-Full × Damage-Free × Accurate Docs) × 100%
All four conditions must be met · Industry benchmark: 88-94% · Each failure adds cost
14. Total Cost of Ownership (TCO)
TCO
TCO = Purchase Price + Ordering Cost + Holding Cost + Shortage Cost + Quality Cost + Transport Cost
Unit price is only 40-60% of true cost · TCO reveals the real cost of sourcing decisions
15. Bullwhip Effect Ratio
Bullwhip Ratio
BWR = (σ_orders / μ_orders) / (σ_demand / μ_demand)
BWR > 1 = bullwhip present (order variability exceeds demand variability) · BWR = 1 = perfect signal · BWR > 2 = severe amplification
The best supply chain professionals don't just know these formulas — they know which formula to apply to which problem, and when the formula breaks down in practice.
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Frequently Asked Questions
Everything you need to know
What is the safety stock formula?
Safety Stock = Z × σd × √LT, where Z is the service level z-score (e.g. 1.65 for 95%), σd is the standard deviation of demand, and LT is the lead time in periods. For variable lead time: SS = Z × √(LT × σd² + d² × σLT²).
How do you calculate EOQ (Economic Order Quantity)?
EOQ = √(2DS/H), where D is annual demand, S is ordering cost per order, and H is holding cost per unit per year. EOQ minimises total inventory cost by balancing ordering and holding costs.
What is the reorder point formula?
Reorder Point = (Average Daily Demand × Lead Time) + Safety Stock. When inventory drops to this level, a new order should be placed to avoid stockouts.
How do you calculate MAPE?
MAPE = (1/n) × Σ(|Actual - Forecast| / Actual) × 100%. MAPE below 20% is good, below 10% is excellent. Above 30% requires intervention.
What is the inventory turnover formula?
Inventory Turnover = Cost of Goods Sold / Average Inventory. Higher turns mean more efficient use of working capital. Typical benchmarks: FMCG 8-12x, manufacturing 4-8x, spare parts 2-4x.
How do you calculate fill rate?
Fill Rate = (Units Shipped / Units Ordered) × 100%. Also called line fill rate. Order fill rate measures the percentage of complete orders shipped. Target: 95-98%.
What is the OTIF formula?
OTIF = (Orders Delivered On-Time AND In-Full / Total Orders) × 100%. Both conditions must be met simultaneously. Industry target: 92-96%. Walmart penalty: 3% of COGS for non-compliance.
How do you calculate cash-to-cash cycle time?
Cash-to-Cash = Days Inventory Outstanding + Days Sales Outstanding - Days Payable Outstanding. Lower is better. Negative C2C means you collect cash before paying suppliers.