Distribution free procedures for some inventory models

Stochastic inventory models, such as continuous review models and periodic review models, require information on the lead time demand. However, information about the form of the probability distribution of the lead time demand is often limited in practice. The authors relax the assumption that the cumulative distribution function, say F, of the lead time demand is completely known and merely assumed that the first two moments of F are known and finite. The minmax distribution free approach for the inventory model consists of finding the most unfavourable distribution for each decision variable and then minimizing over the decision variable. The authors solve both the continuous review model and the periodic review model with a mixture of backorders and lost sales using the minmax distribution free approach.