On the Parts Requirements Problem

The parts requirements (or “explosion”) problem is that of finding the total numbers of components, subassemblies, and assemblies needed to fulfill an order, given the individual requirements needed in each assembly. In this paper two methods are presented for solving the problem, together with the so-called “spare parts” and “netting” problems. The first method involves the use of the inverse of the matrix I − Q where Q is the quantity matrix. The second method is a generalization of the successive multiplication algorithm, first discussed in a special case by Elmaghraby. Mathematical proofs of the methods are presented, as is computational experience with small problems.