Transient Aspects of MRP Theory - Abridged

Abstract

MRP theory concerns production-inventory systems, in which produced items are made up of sets of sub-items, either produced or purchased (imported into the system) and required to be available a lead-time before the product is completed. The hierarchical dependence of relations between items is captured by the use of input matrices from Input-Output Analysis, the necessary advanced timing by applying the methodology of Laplace transforms, and the production-economic consequences by the net present value (NPV). This theory has been developed for about 40 years, but little attention has been given to transient aspects, i.e. when there happens to be an initial available inventory of items usable in future production. In this paper, we attempt to highlight the theoretical consequences from having a positive initial available inventory.