Nonparametric predictive inference for the single-period inventory model
In inventory theory, a known probability distribution is traditionally assumed for the random demand. In this paper, an alternative approach to inventory problems is presented, with the aim of basing the order strategy on information in the form of previously observed demands, adding only quite minimal further assumptions. Nonparametric Predictive Inference (NPI) is used to predict a future demand given observations of past demands. NPI makes only few modelling assumptions, which is achieved by quantifying uncertainty through lower and upper probabilities. As the first use of NPI in inventory theory, the basic scenario of inventory for a single period is considered. The performance of the NPI approach is investigated through simulations, which are also used to compare the method to the classical approach in which the probability distribution of the random demand is assumed to be known. Several cases are studied, some where the assumptions underlying the classical method are fully correct and other cases where the assumed model is not well aligned with the reality. The NPI approach performs well, already outperforming the classical method for relatively small data sets if there is substantial discrepancy between the classical method assumptions and reality.
In inventory theory, a known probability distribution is traditionally assumed for the random demand.