Integral stock norms in divergent systems with lot-sizes

In this paper an overview is given of integral stock norm formulae for several periodic review production-inventory systems. The stock norm formulae for all systems are simple and coherent. These formulae are used to study the 2-stage divergent system with lot-sizing. At first glance, integral control of divergent systems seems to be questionable due to the fact that the inventory levels of the final products are unbalanced most of the time. Such imbalance requires additional inventory in the system to obtain the same service level compared to a similar system without imbalance. However, the results of this paper show that in most cases the impact of imbalance is small. This result implies, that many divergent systems can be controlled efficiently with an integral control rule. Furthermore, systems with depot as well as without depot will be considered and compared. It will appear that the following rule holds in general: the positive effect of decreased imbalance in case a depot is present is small compared with the negative effect of decreased ability to satisfy customers’ demand. The only exception to this rule are systems with a large lot-size for the common component combined with large coefficients of variation for the final poducts’ demand. Attention will be restricted to the identical products case.