An Empirical Bayes Approach to Due Date Assignment

We consider a model in which there are m products and for each i=1,...,m, there are ni observations of the service times associated with the th i product. Assuming the service times associated with the th i product follow an exponential distribution with parameter i θ , and i θ 's are independent random variables with a common gamma distribution, with unknown parameters α and β , we provide two empirical Bayes, under the squared error loss, forecasts of the (ni+1) th service time for each i. Our proposed empirical Bayes forecasts are obtained by replacing the structural parameters α and β with their consistent estimators in the Bayes solution. A simulation study comparing the performance of our empirical Bayes forecasts with the performance of the Bayes forecasts, which would be available only if α and β were known, is also provided.