Applying Bayesian methodology with a uniform prior to the single period inventory model

We consider the application of the Bayesian approach to parameter estimation to the single period inventory model. We assume complete prior ignorance of the values that the (single) unknown parameter of the demand distribution might take and express this by using a uniform prior over the permitted range of parameter values. Direct analytical and numerical comparisons are made for three distributions and the results show that over a wide range of parameter values, including most of those which are likely to be of practical interest, the application of Bayesian methodology produces better decisions (resulting in lower expected total cost) than the approach of using a point estimate for the parameter, with no increase in computation or complexity. This suggests that this methodology could usefully be applied to this and other decision models and also provides a strong justification for the use of the full Bayesian approach when a meaningful prior is available.