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. On occasion, there has been a need to deviate from this representation enabling lead times to vary depending on which input item that is considered. This paper deals with how to represent lead times and similar output delays (in diverging, arborescent systems), when the assumption of equal times is relaxed, in order to retain the basic structure of the fundamental balance equations involved. The intention of this paper is to create a general taxonomy for the representation of timing in algebraic form for a variety of systems covering both assembly systems and arborescent systems (such as extraction, distribution and remanufacturing), as well as systems with mixed properties. For instance, this method may be used directly for the evaluation of investments in capacity or in the location of activities in a production network, or even in a global supply chain.
