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The two numbers and how they are calculated
ADI — average demand interval
How many periods there are, on average, for every period that has demand.
ADI = number of periods ÷ number of periods with demand > 0
ADI 1.0 means demand every month. ADI 3.0 means demand in roughly one month out of three. Some texts compute ADI as the mean gap between successive demands, which ignores the zeros before the first order and after the last; over a reasonable history the two agree closely, and this page uses the count form above.
CV² — squared coefficient of variation of demand sizes
How much the order sizes vary, measured only over the months that had demand. Zeros are left out, because their effect is already in ADI.
CV² = ( standard deviation of non-zero demands ÷ mean of non-zero demands )²
This calculator uses the sample standard deviation, Excel's STDEV.S. To reproduce both numbers in Excel with 36 months of demand in B2:B37:
ADI: =COUNT(B2:B37)/COUNTIF(B2:B37,">0")
CV²: =(STDEV.S(IF(B2:B37>0,B2:B37))/AVERAGEIF(B2:B37,">0"))^2
In Excel 2019 and earlier, confirm the CV² formula with Ctrl+Shift+Enter, because it works on an array.
The four demand patterns
Syntetos, Boylan and Croston (2005) derived the cut-offs ADI = 1.32 and CV² = 0.49 by comparing where Croston's method and its SBA correction outperform one another. They split SKUs into four quadrants:
| Pattern | ADI | CV² | What it looks like | Models worth testing |
|---|---|---|---|---|
| Smooth | < 1.32 | < 0.49 | Demand most months, sizes fairly steady | SES, Holt, Holt-Winters, ARIMA |
| Erratic | < 1.32 | ≥ 0.49 | Demand most months, sizes swing widely | Same family; expect wider intervals |
| Intermittent | ≥ 1.32 | < 0.49 | Many zero months, similar order sizes | Croston, SBA, TSB, ADIDA |
| Lumpy | ≥ 1.32 | ≥ 0.49 | Many zero months, very uneven order sizes | SBA, TSB, ADIDA; hardest to forecast |
Worked example
The sample loaded in the calculator is 36 months with demand in 11 of them: 14, 9, 21, 6, 12, 17, 8, 11, 15, 7 and 13.
- ADI = 36 ÷ 11 = 3.27, well above 1.32: orders arrive about one month in three.
- Mean of the non-zero sizes = 133 ÷ 11 = 12.09; sample standard deviation = 4.55; CV² = (4.55 ÷ 12.09)² = 0.14, below 0.49: when an order comes, its size is fairly predictable.
- Pattern: intermittent. Candidate models are Croston, SBA, TSB and ADIDA. A smoothing model built for continuous demand would chase every zero and every order.
Want the same numbers in a spreadsheet? The Croston and SBA Excel template calculates ADI, CV² and the pattern alongside the forecast.
Four mistakes that change the answer
- Deleting zero months. ADI is built from them. Remove the zeros and every SKU looks as if it sells every month — smooth or erratic, never intermittent.
- Mixing time buckets. Weekly data is far more intermittent than the same demand summed monthly. Classify in the bucket you forecast in.
- Too little history. With three or four demand months, CV² rests on three or four numbers. Treat the class as provisional below about 24 months.
- Counting returns as demand. Net negative lines off first, or they distort both the zero count and the size spread.
Sources
- Croston, J. D. (1972). Forecasting and stock control for intermittent demands. Operational Research Quarterly, 23(3), 289–303. Journal record
- Syntetos, A. A. & Boylan, J. E. (2001). On the bias of intermittent demand estimates. International Journal of Production Economics, 71(1–3), 457–466. Journal record
- Syntetos, A. A., Boylan, J. E. & Croston, J. D. (2005). On the categorization of demand patterns. Journal of the Operational Research Society, 56(5), 495–503. Journal record
- Kostenko, A. V. & Hyndman, R. J. (2006). A note on the categorization of demand patterns. Journal of the Operational Research Society, 57(10), 1256–1257. Paper (PDF)