Flowshop/No-idle Scheduling to Minimize Total Elapsed Time

Abstract

This paper studies four n-job, m-machine flowshop problems when processing times of jobs on various machines follow certain conditions. The objective is to obtain a sequence, which minimizes total elapsed time under no-idle constraint. Under no-idle constraint, the machines work continuously without idle-interval. We prove two theorems. We introduce simple algorithms without using branch and bound technique. Numerical examples are also given to demonstrate the algorithms.