Batch sizing with controllable production rates in a multi-stage production system

In a recent paper, Glock (2010a, Batch sizing with controllable production rates. International Journal of Production Research, 48 (20), 5925-5942) studied the impact of a variable production rate on the inventory build-up and the total costs in a two-stage production system. In this paper, we extend Glock's (2010a) model to a multi-stage production system where the production rate at each producing stage may be varied within given limits. We compare our model to the classical case with a fixed production rate and show that treating the production rate as a variable is an appropriate measure to reduce excessive inventory in a production system.