Properties of optimal order-up-to levels for the newsvendor problem with random capacity

It is known that for the newsvendor problem with uncertain capacity as well as uncertain demand, order-up-to policies are optimal. This paper explores the structure of these order-up-to policies in more detail for the multiple period and infinite horizon problems for some special cases. Through numerical examples and analytic proofs the relationships between parameters of the demand and supply distributions and optimal order-up-to levels are explored. The specific cases include normally and exponentially distributed demand in each period. An ‘all-or-nothing’ type capacity distribution is assumed in these cases. A linear relationship is shown to exist between the mean demand and the optimal order-up-to level in these cases.