KEVOS® MAKEOS · Planning
Exponential Smoothing Forecast (Next-Period Demand, Forecast Error, Best Smoothing Constant)
From the last few periods of demand, what does single exponential smoothing forecast for next period, how large is its error on my history, and which smoothing constant would have done best?
Single exponential smoothing forecast from up to twelve periods of demand or usage: the smoothed values from your smoothing constant, the one-step forecast errors on the history, the mean squared error and its square root as a share of average demand, the forecast for the next period, and the smoothing constant with the smallest error found by trial over 0.01 to 1, against the error you accept.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Number of periods used | periods | How many periods below to use, oldest first. |
| Smoothing constant α | Weight on the latest actual demand (0 to 1); larger reacts faster but follows noise. | |
| Forecast error accepted (RMSE) | % of average | Largest root mean squared forecast error you accept, as a share of average demand. |
| Demand in each period, oldest first | ||
| Period 1 demand | units | Actual demand or usage in period 1, oldest first. |
| Period 2 demand | units | Actual demand or usage in period 2, oldest first. |
| Period 3 demand | units | Actual demand or usage in period 3, oldest first. |
| Period 4 demand | units | Actual demand or usage in period 4, oldest first. |
| Period 5 demand | units | Actual demand or usage in period 5, oldest first. |
| Period 6 demand | units | Actual demand or usage in period 6, oldest first. |
| Period 7 demand | units | Actual demand or usage in period 7, oldest first. |
| Period 8 demand | units | Actual demand or usage in period 8, oldest first. |
| Period 9 demand | units | Actual demand or usage in period 9, oldest first. |
| Period 10 demand | units | Actual demand or usage in period 10, oldest first. |
| Period 11 demand | units | Actual demand or usage in period 11, oldest first. |
| Period 12 demand | units | Actual demand or usage in period 12, oldest first. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Number of periods used
- What it is
- How many of the demand periods listed below are used, counting from the oldest.
- Units and format
- Enter a number in periods: periods. The form accepts 3 periods to 12 periods. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12 periods as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Periods beyond this count are ignored.
- Get it right
- Use at least eight periods to judge the error and choose a smoothing constant.
What this means: Smoothing constant α
- What it is
- The smoothing constant: the weight given to the latest actual demand when updating the forecast, between 0 and 1.
- Units and format
- Enter a plain number with no unit. The form accepts 0.01 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger constant follows recent demand more closely but also follows random noise.
- Get it right
- Start with the best value the tool finds on your history, then round it; values of 0.1 to 0.3 suit steady demand.
What this means: Forecast error accepted (RMSE)
- What it is
- The largest root mean squared forecast error you accept, as a share of average demand over the periods used.
- Units and format
- Enter a number in % of average: % of average. The form accepts 0.1 % of average to 100 % of average. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 % of average as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line.
- Get it right
- Set it from the safety stock or capacity buffer you are prepared to hold against forecast error.
Demand in each period, oldest first
What this means: Period 1 demand
- What it is
- Actual demand or usage in period 1, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 71 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the smoothed values after it and the forecast errors; recent periods weigh most in the forecast.
- Get it right
- The first period also starts the smoothing (S₂ = y₁), so avoid starting on an unusual period.
What this means: Period 2 demand
- What it is
- Actual demand or usage in period 2, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 70 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the smoothed values after it and the forecast errors; recent periods weigh most in the forecast.
- Get it right
- Use actual demand for period 2, not shipments limited by stock-outs.
What this means: Period 3 demand
- What it is
- Actual demand or usage in period 3, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 69 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the smoothed values after it and the forecast errors; recent periods weigh most in the forecast.
- Get it right
- Use actual demand for period 3, not shipments limited by stock-outs.
What this means: Period 4 demand
- What it is
- Actual demand or usage in period 4, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 68 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the smoothed values after it and the forecast errors; recent periods weigh most in the forecast.
- Get it right
- Use actual demand for period 4, not shipments limited by stock-outs.
What this means: Period 5 demand
- What it is
- Actual demand or usage in period 5, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 64 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the smoothed values after it and the forecast errors; recent periods weigh most in the forecast.
- Get it right
- Use actual demand for period 5, not shipments limited by stock-outs.
What this means: Period 6 demand
- What it is
- Actual demand or usage in period 6, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 65 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the smoothed values after it and the forecast errors; recent periods weigh most in the forecast.
- Get it right
- Use actual demand for period 6, not shipments limited by stock-outs.
What this means: Period 7 demand
- What it is
- Actual demand or usage in period 7, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 72 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the smoothed values after it and the forecast errors; recent periods weigh most in the forecast.
- Get it right
- Use actual demand for period 7, not shipments limited by stock-outs.
What this means: Period 8 demand
- What it is
- Actual demand or usage in period 8, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 78 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the smoothed values after it and the forecast errors; recent periods weigh most in the forecast.
- Get it right
- Use actual demand for period 8, not shipments limited by stock-outs.
What this means: Period 9 demand
- What it is
- Actual demand or usage in period 9, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 75 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the smoothed values after it and the forecast errors; recent periods weigh most in the forecast.
- Get it right
- Use actual demand for period 9, not shipments limited by stock-outs.
What this means: Period 10 demand
- What it is
- Actual demand or usage in period 10, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 75 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the smoothed values after it and the forecast errors; recent periods weigh most in the forecast.
- Get it right
- Use actual demand for period 10, not shipments limited by stock-outs.
What this means: Period 11 demand
- What it is
- Actual demand or usage in period 11, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 75 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the smoothed values after it and the forecast errors; recent periods weigh most in the forecast.
- Get it right
- Use actual demand for period 11, not shipments limited by stock-outs.
What this means: Period 12 demand
- What it is
- Actual demand or usage in period 12, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 70 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the smoothed values after it and the forecast errors; recent periods weigh most in the forecast.
- Get it right
- Use actual demand for period 12, not shipments limited by stock-outs.
Method and formulas
- S₂ = y₁; Sₜ = α yₜ₋₁ + (1 − α) Sₜ₋₁ for t ≥ 3, where Sₜ is the forecast for period t (NIST e-Handbook 6.4.3.1).
- Errors eₜ = yₜ − Sₜ for t = 2 to n; MSE = Σ eₜ² ÷ (n − 1); RMSE = √MSE.
- Next-period forecast Sₙ₊₁ = α yₙ + (1 − α) Sₙ (NIST 6.4.3.2); the best α is found by trial over 0.01 to 1 in steps of 0.01, as NIST suggests.
- Example: next-period forecast 72.402 with RMSE 4.0616 (5.7206 % of average); best α 1.
Limitations
- Single smoothing does not follow a trend or seasonal pattern (NIST 6.4.3.2): its forecasts lag a rising or falling demand.
- Few periods make both the error and the best α uncertain; the start value S₂ = y₁ matters most when α is small.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Forecast next month’s demand for a stocked part
- Choose a smoothing constant for an inventory system
- Check whether simple smoothing is good enough for an item
Who it is for
- Production and inventory planners
- Purchasing staff
- Operations managers
What you get
- Smoothed values and forecast errors
- Mean squared error and RMSE
- Forecast for the next period
- Best smoothing constant on this history
Interpreting the result
- A best α near 1 means the latest period is the best guess (demand moves like a random walk); a best α near 0 means demand is steady around a level.
References
- NIST/SEMATECH e-Handbook of Statistical Methods, 6.4.3.1 Single Exponential Smoothing — https://www.itl.nist.gov/div898/handbook/pmc/section4/pmc431.htm
- NIST/SEMATECH e-Handbook of Statistical Methods, 6.4.3.2 Forecasting with Single Exponential Smoothing — https://www.itl.nist.gov/div898/handbook/pmc/section4/pmc432.htm
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Method explained here · Library collection
Demand forecasting for small manufacturers: matching supply with demand without drowning in stock
In Manufacturing Operations and Design for Manufacture
What it covers: Practical forecasting and planning for small manufacturers: simple forecasting methods, measuring forecast error, safety stock, reorder points, order quantities and a monthly planning meeting.
Useful alongside · KEVOS® original book
Measuring forecast error and reading base rates
In Demand and Benefit Forecasts by the Numbers
What it covers: Bias, MAE, MAPE and RMSE on the 2023 budget (all 12 months over, MAPE 9.7%), naive benchmarks that beat it, six annual ratios as a base rate, and a −8.9% error reported as −1.0%.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.