Myopic policies for some inventory models with uncertain demand distributions

The majority of papers on stochastic inventory theory make the assumption that the distribution of consumer demand in each time period is known with certainty. While this assumption is unsupported in many applied contexts, it is conventionally held that more realistic models are more difficult to solve and will not yield simple operational policies. This paper shows that a simple inventory policy based upon a critical fractile can be optimal or near-optimal in some inventory models with parameter adaptive demand processes. In these, some parameter of the demand distribution is not known with certainty, and estimates of the parameter are updated in a statistical fashion as demand is observed through time. Examples include exponentially smoothed forecasts and Bayesian updating of parameter estimates. Bounds on the value loss relative to optimal cost, when using the critical fractile policy, can be calculated directly from the problem data. Some numerical examples illustrate the technique.