Service differentiation in a single-period inventory model with numerous customer classes

We study critical‐level inventory‐management policies as means to provide differentiated ( $\mathit{\alpha }$ and $\mathit{\beta }$ ) service levels to more than two classes of customers. First, we derive closed‐form expressions for the service levels of a single‐period critical‐level policy with an arbitrary number of customer classes (with Poisson demand). Based on the service‐level expressions, we derive additional structural insights and provide an efficient algorithm with which to compute the essential system parameters, that is, the minimum required starting inventory and the associated critical levels. Based on these results, we conduct numerical experiments and develop structural insights into the system’s behavior.