Introducing capacity limitations into multi-level, multi-stage production-inventory systems applying the input–output/Laplace transform approach

The Laplace transform and Input–Output Analysis have been used to formulate a theoretical basis for Material Requirements Planning. In this paper, as a first step to incorporating capacity limitations into this theory, we introduce alternative formulations of a model for capacity-constrained production-inventory systems in a deterministic environment applying the same approach. We focus our attention on the way in which the balance equations constraining the system need to be modified. A numerical example is given to explain the model.