It is well-known that the classical Johnson's Rule leads to optimal schedules on a two-stage flowshop. However, it is still unclear how Johnson's Rule would help in approximation algorithms for scheduling an arbitrary number of parallel two-stage flowshops with the objective of minimizing the makespan. Thus within the paper, we study the problem and propose a new efficient algorithm that incorporates Johnson's Rule applied on each individual flowshop with a carefully designed job assignment process to flowshops. The algorithm is successfully shown to have a runtime O(nlogn)\documentclass[12pt]...
