Two-machine proportionate flowshop scheduling with breakdowns to minimize maximum lateness

Abstract

This paper addresses the problem of scheduling in a two-machine proportionate flowshop with a maximum lateness objective function, where machines are subject to random breakdowns. It is shown that, under appropriate conditions, the Longest Processing Time policy minimizes the objective function with probability 1 if only the first machine is subject to breakdowns. It is also shown that when only the second machine suffers breakdowns, the Shortest Processing Time policy minimizes the objective function with probability 1.