Numerical assessment on makespan minimization by adopting NEH heuristics in permutation flow shop

Abstract

Permutation flow shop problem (PFSP) is one of the important subclass of scheduling, where the order in each process remains unchanged for all machines. Few algorithms have been developed for deciding the sequence of n jobs and m machines to minimize makespan in the flow shop. Throughout the last 30 years, the NEH heuristic developed by Nawaz, Enscore and Ham has been commonly regarded as the best heuristic for minimizing the makespan in permutation flow shops. This heuristic is basically divided into two main stages: generate an initial sequence with decreasing total processing time and insert into the schedule accordingly. In this paper, total of 50 flow-shop problems were solved with the number of machines and jobs being set at a range of 4 to 25. Whereas the process times of the jobs were randomly generated with range 1 to 10 using Microsoft Excel spreadsheet. Performance of the heuristic was validated using the relative percentage deviation (RPD) formula based on the makespan generated by CDS heuristic proposed by Campbell, Dudek and Smith. The generated results through Excel modeling showed that NEH heuristic outperforms CDS heuristic. This statement correspond with the previous studies. Therefore, the Excel modelling is said to be an encouraging direction for solving scheduling problems in future research.