The interruption of production on machines which are set up for a specific product incurs idle time costs but reduces inventory holding costs. This phenomenon is generally ignored in multi-stage inventory models. Interrupted production runs are economical when the additional costs generated by restarting the machines and by idle time are off-set by the reduced frequency of major set-up costs and by decreased inventory holding costs. Under these circumstances, the machine idle-time can be optimized for each stage. An appropriate production/inventory model for this situation and a suitable optimization method are developed; the method is illustrated by an example.