Capacity Constraints in Multi-Stage Production-Inventory Systems Applying Material Requirments Planning Theory

Abstract: In this thesis, capacity-constrained aspects of multi-level, multi-stage productionplanning are investigated. The aim has been to extend Material Requirements Planning Theory (MRP Theory) to cover more general problems dealing with capacity constraints, in particular when non-zero lead times are present and the processes take place in continuous time.MRP Theory deals with multi-level production systems with multiple items taking place either within a discrete or continuous time framework. External demand is considered either deterministic or stochastic. Lead times are assumed to be given constants, and the Net Present Value Principle has been applied as the objective function. The Bill-of-Materials, capturing component as well as capacity requirements, in volume as well as in advanced timing due to lead times, has been described using a generalised input matrix involving Laplace transforms or z transforms.In order to be able to apply Dynamic Programming as a solution method, the system state has been defined and designed in terms of a matrix, in which historical values of cumulative production and cumulative demand are given state variables. A high power computer has been used to calculate solutions to numerical examples.Moreover, this thesis examines the fundamental equations of MRP Theory in order to analyse the possibility to obtain closed-form expressions for the time development of the system, when standard ordering rules of MRP are applied.In addition, capacity-constrained production planning problems and procedures in a paper mill have been surveyed and are presented in the form of a case study.