Multi-level, multi-stage capacity-constrained production-inventory systems in discrete time with non-zero lead times using MRP theory

In this paper, we remain in the discrete time framework and develop a methodology for the case that lead times are non-zero, whereas demand is deterministic. Our emphasis is on the design of the state space, the properties of which depend on the product structures (the input matrix), the distribution of lead times among the production processes (the lead time matrix), and on the historical sequences of the production vectors. Once an efficient state space is designed, dynamic programming may be applied as a solution method. The net present value principle is again applied.