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.

15 Supply Chain Formulas Every Planner Must Know — Safety Stock, EOQ, MAPE, Reorder Point

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

90%

Z = 1.28

95%

Z = 1.65

99%

Z = 2.33

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.

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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