Using Customers' Reported Forecasts to Predict Future Sales

We consider a supplier who must predict future orders using forecasts provided by their customers. Our goal is to improve the supplier's operations through a better understanding of the customers's forecast behavior. Unfortunately, customer forecasts cannot be used directly. They may be biased since the customer may want to mislead the supplier into believing that orders may be larger than expected to secure favorable terms or simply because the customer is a poor forecaster. There are several unusual elements in our problem. Analysts typically observe the actual process which may be biased due to asymmetric loss function. Also units are discrete not continuous. We believe the forecasting process can be modeled in a multi stage process. The customer first computes the distribution of demand at a future date which we assume to follow an ARMA(1,1) model. The customer then submits an integral forecast(multiples of lot sizes), which minimizes his expected loss due to forecast errors. We show that the customer may bias his forecasts under an asymmetric loss functions. We provide an estimator which can be used by the supplier to estimate the forecast generation model of the customer by looking at his forecasts.