Estimating Demand Uncertainty Using Dispersion of Team Forecasts or Distributions of Forecast Errors

Abstract

In this paper, we compare two fundamentally different judgmental demand forecasting approaches used to estimate demand and their corresponding demand distributions. In the first approach, parameters are obtained from a linear regression and maximum likelihood estimation (MLE) based on team forecasts and dispersion within the judgmental forecasts. The second approach ignores dispersion and instead estimates the demand distribution based on the mean demand forecast and the historic relative forecast errors as measured by A/F ratios — that is, the ratio of actual to forecast outcomes. We show that accounting for forecast dispersion (as a timely indicator of anticipated demand risk) explains demand uncertainty sublinearly whereas the mean demand forecast most often explains demand uncertainty as being more than linear. We use actual company data from an online retailer to show that the A/F ratio approach dominates the MLE approach in terms of de-biasing the mean demand forecast, predicting total season demand, predicting the percentage of demand actually served at a target service level, and maximizing realized gross profit. However, the MLE approach more closely follows the assumed standard normally distributed demand and hence yields better-fitting demand distributions. Product segmentation can further improve the forecast accuracy of both approaches. In the application case study described here, we fit the data and analyze accuracy of forecasts. The results indicate that, in order to maximize accuracy, demand forecasts should always employ product segmentation and should favor the A/F ratio approach for order quantities “close” to the mean; otherwise, the MLE approach is preferred.