A single-period production model with uncertain output and demand

Single-period production models with uncertain output as well as demand are analyzed. The output level is assumed to be a product of the input level and a random multiplier. We compare optimal input levels in situations where cost is proportional to the input level to those with cost proportional to the (random) output level. We also show that the optimal policies are, in general, not of the familiar "order-up-to" type.