5 Forecasting for Operations

Purpose of demand forecasting

Demand forecasting estimates how much customers will want and when. Operations managers use forecasts to plan purchasing, production, staffing, inventory, transportation, and capacity. A forecast is an estimate, not a sales target or a guarantee; its usefulness depends on the decision it supports, the time horizon, and the information available.

Selecting a forecasting method

Start by defining the item or service, the time period, the forecast horizon, and the required level of detail. For example, a forecast might concern weekly demand for one product at one warehouse. Then inspect historical demand for its level, trend, seasonality, unusual events, and missing data.

Compare candidate methods against a simple benchmark, such as forecasting the next period with the latest observation. Choose a method that performs well for the horizon relevant to the decision. No method is best for every demand pattern or horizon.

Common method families

• Judgmental methods: Expert estimates, sales-force input, customer surveys, or structured approaches such as Delphi. These can be useful for new products or major changes when there is little relevant history. Document assumptions and apply judgment systematically to reduce bias.

• Naïve and seasonal naïve methods: Forecast the next period using the latest observation, or use demand from the matching period in the previous seasonal cycle. These methods provide simple benchmarks and can work well when demand is stable or strongly seasonal.

• Moving averages and exponential smoothing: Average recent observations, with exponential smoothing giving greater weight to newer observations. These methods are useful when recent demand is informative; smoothing methods can also represent trend and seasonality.

• Trend, regression, and causal models: Relate demand to time or potential drivers such as price, promotions, weather, or economic conditions. Use these when the drivers are relevant and their future values are available or can be estimated.

Combine statistical forecasts with judgment only when there is specific, relevant information the model does not already include, such as a confirmed promotion.

Measuring and evaluating forecast error

A Forecast error is the difference between actual demand and the forecast. Using the convention that actual demand minus forecast defines the error:

A positive error means demand exceeded the forecast, so demand was under-forecast. A negative error means the forecast was too high. State the sign convention when reporting errors because some systems define the difference in the opposite order.

Measures of error

• Mean absolute error (MAE): The average of $|e_t|$. It reports typical error in demand units and is straightforward to interpret.

• Mean squared error (MSE): The average of squared errors, $\frac{1}{n}\sum_{t=1}^{n} e_t^2$. Squaring gives large misses greater influence.

• Root mean squared error (RMSE): The square root of the mean squared error, $\sqrt{\frac{1}{n}\sum_{t=1}^{n} e_t^2}$. It is expressed in the original demand units.

• Mean absolute percentage error (MAPE): The average of $\left|\frac{e_t}{\text{actual demand}_t}\right| \times 100\%$. It expresses error as a percentage, but is undefined when actual demand is zero and can be misleading when actual demand is close to zero.

• Mean error or bias: The average signed error, $\frac{1}{n}\sum_{t=1}^{n} e_t$. A persistent positive or negative mean indicates systematic under- or over-forecasting. Absolute-error measures show the size of misses but not their direction.

For actual demand of $100$, $120$, and $110$ units and forecasts of $90$, $130$, and $100$, the errors are $+10$, $-10$, and $+10$. The MAE is $10$ units, while the mean error is about $+3.3$ units, indicating a modest net tendency to under-forecast. Reporting both helps distinguish typical miss size from directional bias.

Testing forecasts and representing uncertainty

Evaluate forecasts on data not used to fit the method. For time-series demand, preserve chronological order: fit on earlier periods and test on later ones, or repeatedly move the training window forward. Compare methods at the horizon used in practice, and review results by product, location, and period when aggregate scores could hide local problems.

Forecasts are uncertain. Prediction intervals or low/base/high scenarios help decision makers see a plausible range instead of treating a point estimate as certain.

Using forecasts in operations

Forecasts inform decisions across the operating system:

• Inventory and purchasing: Estimate replenishment needs and assess the risk of stockouts or excess stock. Uncertainty and lead time matter as well as average demand.

• Production and capacity: Plan output, equipment use, and capacity before demand arrives. Longer-term forecasts can inform capacity decisions.

• Staffing and scheduling: Anticipate workload by day, shift, or season and arrange labor accordingly.

• Supply chains: Share demand expectations with suppliers and distribution partners so purchasing, production, and transport plans can be coordinated.

The cost of an error is not always symmetric. Under-forecasting may cause lost sales or missed service, while over-forecasting may create excess inventory or idle capacity. Use the forecast together with the consequences of each decision; the method with the lowest average error does not automatically produce the best operating decision.