On the representation of timing for different structures within MRP theory

MRP Theory has been developed during the last 25 years for capturing processes concerning multi-level, multi-stage production-inventory systems in a compact way. Input–output analysis has been used to describe structures, and Laplace transforms to describe the timing relations. This theory has mainly dealt with assembly systems, in which each item has only one successor. The lead times for the assembly of an item have usually been constants and equal for all items entering a given successor. For such systems, the equations describing the flows of components may be written to include the generalised input matrix as the product of an input matrix containing needed amounts, and a diagonal lead time matrix with lead time operators along its main diagonal.