Four model classes with differing rules are considered to show how to deal with the issues of backordering and shortages. For each model, N switchover levels and piecewise linear, state dependent and deterministic production rates between levels are considered. 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.