Quasicomplete factorization and the two machine flow shop problem Original Research Article

A connection is made between the Two Machine Flow Shop Problem (2MFSP) from job scheduling theory and the issue of quasicomplete factorization of rational matrix functions. A quasicomplete factorization is a factorization into elementary (i.e., degree one) factors such that the number of factors is minimal. For a companion based matrix function W, the number of factors in a quasicomplete factorization of W is related in a simple way to the minimum makespan of an instance J of 2MFSP which can be associated to W. As a consequence of this result, variants of the 2MFSP and other types of factorization can be related too.