Makespan In Permutation Flow Shops Research Articles

A new job priority rule for the NEH-based heuristic to minimize makespan in permutation flowshops

The permutation flowshop scheduling problem is a vital production management concern of industries such as electronic product manufacturing and integrated circuit fabrication. In many studies, jobs are prioritized independently according to their features or properties. This article develops a new perspective by introducing the self-attention mechanism into scheduling for the first time. The job similarities are characterized by the dot-product of processing time matrices and taken as job priorities. Based on this idea, a new priority rule denoted by PRSAT is proposed, and a heuristic named NEHLJP2 is presented with makespan minimization. The computational results with the Taillard and VRF benchmarks and 640 random instances demonstrate that the new priority rule and heuristic dominate the existing ones at a nominal cost of computation time.

A memetic algorithm with novel semi-constructive evolution operators for permutation flowshop scheduling problem

This paper proposes a memetic algorithm (MA) with novel semi-constructive crossover and mutation operators (MASC) to minimize makespan in permutation flowshop scheduling problem (PFSP). MASC combines the strengths of genetic algorithm (GA), simulated annealing (SA), and Nawaz–Enscore–Ham (NEH) algorithm. The aim is to enhance GA in identifying promising areas in the search space, whose local optima will be subsequently located by SA. This is achieved by means of novel crossover and mutation operators that construct chromosomes by using two different types of genes: static and dynamic genes. MASC is tested on the well-known Taillard’s benchmark instances. The proposed operators are compared with traditional operators. The results show that the proposed operators produce considerable improvements. These improvements reach up to 20.79% in the average relative error of best solution and 11.86% in the average relative error of average solution. MASC is compared with fourteen well-known and state-of-the-art algorithms. These algorithms include MA, whale optimization, ant colony optimization, particle swarm optimization, artificial bee colony, monkey search, and iterated greedy. The results show that MASC outperforms all the compared algorithms except three iterated greedy algorithms. Moreover, the improvement in the average relative error of best solution achieved on the best-so-far MA is 37.92%. Therefore, MASC can be considered as one of the best-so-far methods for PFSP.

Improved solution for minimizing makespan in permutation flow shop

ABSTRACTFlow shop is one of the scheduling systems in which the jobs are processed on different machines in a fixed order so as to optimize certain scheduling criteria. The general flow shop problem is shown to be NP-complete. In this paper, a simple constructive heuristic algorithm is proposed for optimizing flow shop scheduling problem with the objective to minimize the makespan. Experimental results show the superiority of the proposed algorithm over well-known heuristics when tested on existing benchmark problems in scheduling literature. Based upon the concept of CL-heuristic [a high-performing constructive heuristic for minimizing makespan in permutation flowshops, Journal of Industrial and Production Engineering, 2013; 30(6): 355–362], we propose a new tie-breaking rule in the proposed approach. An illustrative example is given in the paper to explain the working of the proposed procedure. Statistical tests are performed to establish the effectiveness of the proposed heuristic.

Minimizing Makespan in Permutation Flow Shop Scheduling with Proportional Deterioration

The [Formula: see text]-job and [Formula: see text]-machine permutation flow shop scheduling problem with a proportional deterioration is considered in which all machines process the jobs in the same order, i.e., a permutation schedule. A proportional deterioration means that the job deterioration as an increasing function that is proportional to a linear function of time. The objective is to minimize the makespan, i.e., the maximum completion time. When some dominant relationships between [Formula: see text] machines can be satisfied, we show that some special cases of the problem can be polynomial solvable. For the general case, we also propose a heuristic algorithm and give the computational experiments.

A high-performing constructive heuristic for minimizing makespan in permutation flowshops

Minimizing makespan in permutation flowshops is one of the most frequently investigated problems in scheduling theory. The NEH heuristic is commonly regarded as the best current constructive heuristic for solving this NP-hard problem. In this paper, we propose a novel constructive heuristic with an effective tie-breaking strategy to improve the scheduling quality of this problem. Experimental results reveal that the proposed approach outperforms NEH for all problem sizes on the standard benchmark problem set of Taillard. This study thus appears to successfully demonstrate a high-performing constructive heuristic that can serve as a new foundation for future research on this extremely challenging scheduling problem.

New high performing heuristics for minimizing makespan in permutation flowshops

The well-known NEH heuristic from Nawaz, Enscore and Ham proposed in 1983 has been recognized as the highest performing method for the permutation flowshop scheduling problem under the makespan minimization criterion. This performance lead is maintained even today when compared against contemporary and more complex heuristics as shown in recent studies. In this paper we show five new methods that outperform NEH as supported by careful statistical analyses using the well-known instances of Taillard. The proposed methods try to counter the excessive greediness of NEH by carrying out re-insertions of already inserted jobs at some points in the construction of the solution. The five proposed heuristics range from extensions that are slightly slower than NEH in most tested instances to more comprehensive methods based on local search that yield excellent results at the expense of some added computational time. Additionally, NEH has been profusely used in the flowshop scheduling literature as a seed sequence in high performing metaheuristics. We demonstrate that using some of our proposed heuristics as seeds yields better final results in comparison.

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.

On the NEH heuristic for minimizing the makespan in permutation flow shops

Over the last 20 years the NEH heuristic of Nawaz, Enscore, and Ham published in this journal has been commonly regarded as the best heuristic for minimizing the makespan in permutation flow shops. In recent years some authors claimed to develop new heuristics that are competitive or outperform NEH. Our study reveals that these claims are not justified. We also address the issue of a fair comparison of the NEH results with those obtained by metaheuristics. Finally we conduct a thorough analysis of NEH leading to its modification which secures the optimality in the two-machine case and improves the general performance.