Analysis of production/inventory systems with several production rates

The authors consider four model classes with differing rules as to how to deal with the issue of backordering and shortages. For each model they assume N switchover levels and piecewise linear, state dependent and deterministic production rates between levels. The authors compute relevant functionals such as the stationary law of the inventory level, holding costs, switching and unsatisfied demand costs, and consider these with respect to two objective functions, namely, the long-run average cost, and the expected discounted cost.