An improved procedure for solving minimum makespan on a flowshop

This paper presents numerous heuristics, derived from the NEH heuristic, aimed at minimizing the classical permutation flowshop scheduling problem. We compare the solution, based on Taillard's benchmark problems. We propose a better schedule by comparing these heuristics and identifying common partial sequences of consecutive jobs. We identify the closest heuristic to our result by using a standard distance measure used in the literature. We use this heuristic as an initial solution for a further standard improvement procedure. The obtained average relative percentage deviation values of our procedure is within a reasonable computational effort and appears to improve the published results on these problem sets.

I. Introduction

There is an extensive literature on the problem of minimizing makespan on a permutation flowshop. The classical setting of the problem features machines that are set up in series, with jobs that are processed on all the machines in the same order. The job sequences in permutation flowshop on the machines are assumed to be identical leading to no blocking in jobs that wait in these bufferes, until the next production stage is available. We refer the reader to Jarboui et al. (2008) and Ruiz et al. (2019).