Proportionate flowshops with general position-dependent processing times

Most scheduling studies assume constant (position-independent) job processing times. Most of the papers allowing position-dependent processing times consider only special cases, where the job processing times follow a specific function of the job-position. Polynomial time solutions have hardly been found for general position-dependent processing times in scheduling literature. In this note we provide one of these cases: we introduce a polynomial time solution for minimum makespan on an m-machine proportionate flowshop.

Research highlights
► We study a scheduling problem on a proportionate flowshop.
► The job processing times are assumed to be position-dependent.
► The objective function is minimum makespan.
► We introduce a polynomial time solution algorithm for the problem.