Managing individual customer service constraints under stochastic demand

In recent years management of customer requirements has been the foremost concern of most manufacturers. In this paper, we consider a single-period problem in which the manufacturer faces stochastic demand and individual service level constraints from multiple customers. We present a formulation for the problem that utilizes the structure of the underlying allocation problem and provide an algorithm that generates the optimal procurement quantity under the optimal random allocation policy. For a special case when there are two identical customers and their demand is jointly uniform, we derive an analytical expression for the optimal procurement quantity.