2 Demand Forecasting

Learn how to build, evaluate, interpret, and apply demand forecasts to supply chain decisions while accounting for patterns, uncertainty, and forecast errors.

Understand the role of a forecast

estimates future customer demand from historical observations and relevant business information. In a supply chain, forecasts help guide purchasing, production, staffing, transportation, and inventory decisions. Because a forecast is an informed estimate rather than a promise, it should support decisions without being treated as a guarantee.

Build a useful forecasting workflow

A practical process starts by defining the decision: what demand is being forecast, at what level, how often the forecast will be updated, and how far ahead it must look. The horizon should match the decision. For example, a retailer replenishing weekly may need weekly forecasts, while a manufacturer planning capacity may need forecasts months ahead.

Prepare time-stamped demand history using consistent units and periods. Check for missing values, duplicates, stockouts, returns, unusual spikes, product changes, and changes in how demand was recorded. Sales do not always equal demand: a stockout, for example, can make recorded sales lower than customers’ actual desired purchases.

Plot demand over time and look for level changes, , , unusual observations, and changes in variability. Consider relevant business knowledge about promotions, price changes, holidays, and supply disruptions. Begin with simple, explainable, reproducible baseline forecasts; a more complex method is useful only if it performs better in realistic evaluation or better supports the decision.

Evaluate forecasts out of sample by holding back later observations, or use rolling-origin evaluation. At each origin, fit the forecast using only information available at that time, then compare it with what actually happened. Test the horizons that matter operationally. Finally, communicate the forecast, uncertainty, assumptions, and relevant business adjustments; compare actual demand with forecasts as new data arrive, investigate persistent errors, and refresh the process on a suitable schedule.

Establish baseline forecasts

Let $y_t$ be observed demand in period $t$ , and let $\hat y_{T+h|T}$ be the forecast for period $T+h$ , made using information through period $T$ . These baseline methods provide comparisons for more involved approaches.

Mean method: Forecast every future period using the historical average: $\hat y_{T+h|T} = \bar y$ . It can be a useful reference for a stable series without a clear or seasonal pattern.
Naïve method: Forecast future periods using the latest observation: $\hat y_{T+h|T} = y_T$ . It is a strong, simple benchmark when the most recent level is informative.
Seasonal naïve method: Forecast each future period using demand from the matching season in the most recent cycle. With monthly data and yearly , next January’s forecast is last January’s demand. This is a natural baseline when seasonal patterns repeat.
Drift method: Extend the average historical change per period. It allows a simple linear but assumes the historical average rate of change continues.

If a product has a recurring holiday peak, the seasonal naïve method is a useful comparison for methods intended to model both the seasonal pattern and underlying growth or decline.

Recognize and

is the sustained upward or downward movement in a series. is a pattern that recurs at a known interval. A cycle is a longer-term rise and fall that does not necessarily repeat at a fixed interval. Random variation and one-off events can obscure these patterns.

A series can be understood as a combination of components. In an additive pattern, seasonal effects are roughly constant in size as demand rises or falls:

y_t = T_t + S_t + R_t,

where $T_t$ is the -cycle, $S_t$ is the seasonal component, and $R_t$ is the remainder. In a multiplicative pattern, seasonal swings grow or shrink in proportion to the demand level:

y_t = T_t \times S_t \times R_t.

For example, a product might sell about $200$ more units in a busy month regardless of its baseline volume, an additive pattern. Alternatively, busy-month demand might consistently be about $\text{30\%}$ above its usual level, a multiplicative pattern. Decomposition separates patterns to aid understanding; a forecast can project the and reapply the expected seasonal pattern. Since patterns may change, and should be checked rather than assumed permanent.

Measure forecast accuracy

is the actual outcome minus the forecast:

e_t = y_t - \hat y_t.

Positive errors indicate underforecasting, and negative errors indicate overforecasting. Accuracy measures summarize errors across forecast periods and should be calculated on forecasts made before the outcomes were known, not just on the data used to fit a model.

Mean absolute error (MAE): $\operatorname{mean}(|e_t|)$ . It is expressed in the original units, describes typical absolute error, and is relatively easy to interpret.
Root mean squared error (RMSE): $\sqrt{\operatorname{mean}(e_t^2)}$ . It is also expressed in the original units and penalizes large errors more heavily than MAE.
: $100 \times \operatorname{mean}(|e_t/y_t|)$ . It is easy to communicate as a percentage, but is undefined when actual demand is zero and can become misleadingly large when actual demand is near zero.
Mean absolute scaled error (MASE): Compares absolute forecast errors with a simple benchmark error calculated from the training data. It can help compare series on different scales; a value below $1$ indicates better average performance than that benchmark under the chosen scaling.

No single measure captures every cost of . If underforecasting causes expensive stockouts while overforecasting mainly creates modest holding costs, both errors matter but can have different operational consequences. Examine error direction as well as magnitude, and evaluate performance separately by product, location, season, and forecast horizon where useful.

Use forecasts with uncertainty

A forecast has two important parts: a point forecast, the central estimate of future demand, and an indication of uncertainty. Prediction intervals show a range of plausible outcomes; a wider interval signals greater uncertainty. Uncertainty generally increases farther into the future, so a point forecast alone can conceal risk.

Use forecasts as inputs to decisions, not as automatic orders. A buyer can combine a demand forecast with supplier lead time, current inventory, and the consequences of stockouts to set replenishment plans. A production planner may use the same forecast together with capacity constraints and planned promotions. Record significant human adjustments and their reasons so their value can later be assessed.

Monitor errors regularly. Persistent errors in one direction may reveal bias, such as repeatedly underestimating demand during a growing . Sudden errors may instead reflect a one-time event, missing data, or a changed demand pattern. Investigating the cause is usually more useful than simply replacing a forecast with a more complicated model. Forecasts based on past patterns cannot anticipate every structural change, so important known events and assumptions should be made explicit.