Mathematical Solution of Parts Requirements Problems

Abstract

This paper describes a matrix algebraic theory and techniques for defining and solving general parts requirements problems. These include problems to check bills of materials for feasibility, to generate and up-date total requirements, to explode the gross requirements necessary to produce a given product mix, to net the gross requirements against surplus inventory and to generate the capacity and cost restraints in LP models to determine optimal product and resource mixes. The intent of the work is two-fold: (1) to demonstrate the use of matrix algebraic techniques to speed and compact the logical and numerical operations in solving parts requirements problems and (2) to develop a concise and unambiguous mathematical theory for parts requirements problems so that production engineers, mathematicians and programmers can cooperate more easily in their definition and solution.