Two NEH Heuristic Improvements for Flowshop Scheduling Problem with Makespan Criterion

Christophe Sauvey,Nathalie Sauer

doi:10.3390/a13050112

Abstract

Since its creation by Nawaz, Enscore, and Ham in 1983, NEH remains the best heuristic method to solve flowshop scheduling problems. In the large body of literature dealing with the application of this heuristic, it can be clearly noted that results differ from one paper to another. In this paper, two methods are proposed to improve the original NEH, based on the two points in the method where choices must be made, in case of equivalence between two job orders or partial sequences. When an equality occurs in a sorting method, two results are equivalent, but can lead to different final results. In order to propose the first improvement to NEH, the factorial basis decomposition method is introduced, which makes a number computationally correspond to a permutation. This method is very helpful for the first improvement, and allows testing of all the sequencing possibilities for problems counting up to 50 jobs. The second improvement is located where NEH keeps the best partial sequence. Similarly, a list of equivalent partial sequences is kept, rather than only one, to provide the global method a chance of better performance. The results obtained with the successive use of the two methods of improvement present an average improvement of 19% over the already effective results of the original NEH method.

Highlights

Since its creation by Nawaz, Enscore, and Ham in 1983, NEH remains the best heuristic method to solve flowshop scheduling problems
An examination was made of the flowshop scheduling problem and its resolution with the NEH method, which is the best heuristic method, to date, for solving this kind of problem
The second occurs recurrently in the method process when, at each step, insertions of a new job in the current partial sequence leading to the best partial makespan are kept

Summary

Introduction

Since its creation by Nawaz, Enscore, and Ham in 1983, NEH remains the best heuristic method to solve flowshop scheduling problems. In order to propose the first improvement to NEH, the factorial basis decomposition method is introduced, which makes a number computationally correspond to a permutation. This method is very helpful for the first improvement, and allows testing of all the sequencing possibilities for problems counting up to 50 jobs. Since Johnson’s work and famous rule [1], a large number of problems have interested academic researchers globally This class of problems, in which jobs are processed by a series of machines in exactly the same order, is one of the most widely studied scheduling problems. This heuristic, known as CDS, builds m-1 schedules by clustering the m original

Methods

Results

Conclusion