An improved NEH heuristic to minimize makespan in permutation flow shops

For over 20 years the NEH heuristic of Nawaz, Enscore, and Ham [A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem. Omega, The International Journal of Management Science 1983;11:91–5] has been commonly regarded as the best heuristic for solving the NP-hard problem of minimizing the makespan in permutation flow shops. The strength of NEH lies mainly in its priority order according to which jobs are selected to be scheduled during the insertion phase. Framinan et al. [Different initial sequences for the heuristic of Nawaz, Enscore and Ham to minimize makespan, idle time or flowtime in the static permutation flowshop problem. International Journal of Production Research 2003;41:121–48] presented the results of an extensive study to conclude that the NEH priority order is superior to 136 different orders examined. Based upon the concept of Johnson's algorithm, we propose a new priority order combined with a simple tie-breaking method that leads to a heuristic that outperforms NEH for all problem sizes.