A capacity-constrained multi-level inventory and production control problem

This paper presents a mathematical formulation of a capacity constrained multistage inventory and production control problem. It argues that most practical multistage inventory and production control problems can be summarised in the formulation. The model has a strong connection to the model of Billington, McClain and Thomas and is also inspired of a paper from Bard and Golany. The revised Billington/McClain/Thomas model is formulated in a dynamic programming recursion. A numerical solution to a simple problem is presented. A scheduling problem concerning capacity constrained models are enlightened. Further, the paper points to differences and relationships between this capacity constrained model, MRP, Kanban and Cover-Time Planning.