JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A Special Case of Three Machine Flow Shop Scheduling
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
A Special Case of Three Machine Flow Shop Scheduling
Yang, Jaehwan;
  PDF(new window)
 Abstract
This paper considers a special case of a three machine flow shop scheduling problem in which operation processing time of each job is ordered such that machine 1 has the longest processing time, whereas machine 3, the shortest processing time. The objective of the problem is the minimization of the total completion time. Although the problem is simple, its complexity is yet to be established to our best knowledge. This paper first introduces the problem and presents some optimal properties of the problem. Then, it establishes several special cases in which a polynomial-time optimal solution procedure can be found. In addition, the paper proves that the recognition version of the problem is at least binary NP-complete. The complexity of the problem has been open despite its simple structure and this paper finally establishes its complexity. Finally, a simple and intuitive heuristic is developed and the tight worst case bound on relative error of 6/5 is established.
 Keywords
Three Machine Flow Shop;Computational Complexity;Total Completion Time;
 Language
English
 Cited by
 References
1.
Baker, K. R. and Trietsch, D. (2009), Flow shop scheduling, Principles of sequencing and scheduling, John Wiley and Sons, 225-249.

2.
Chen, B., Potts, C. N., and Woeginger, G. J. (1993), A review of machine scheduling: complexity, algorithms and approximability, Handbook of Combinatorial Optimization, Springer US, 1493-1641.

3.
Garey, M. R. and Johnson, D. S. (1979), Computers and intractibility: a guide to the theory of NP-completeness, New York: W. H. Freeman and Co.

4.
Garey, M. R., Johnson, D. S., and Sethi, R. (1976), The complexity of flowshop and jobshop scheduling, Mathematics of Operations Research, 1, 117-129. crossref(new window)

5.
Graham, R. L., Lawler, E. L., Lenstra, J. K., and Rinnooy Kan, A. H. G. (1979), Optimization and approximation in deterministic sequencing and scheduling: a survey, Annals of Discrete Mathematics, 5, 287-326. crossref(new window)

6.
Hoogeveen, J. A. and Kawaguchi, T. (1999), Minimizing total completion time in a two-machine flowshop:analysis of special cases, Mathematics of Operations Research, 24, 887-910. crossref(new window)

7.
Johnson, S. M. (1954), Optimal two- and three-stage production with setup times included, Naval Research Quarterly, 61-68.

8.
Lenstra, J. K., Rinnooy Kan, A. H. G., and Brucker, P. (1977), Complexity of machine scheduling problems, Annals of Discrete Mathematics, 1, 343-362. crossref(new window)

9.
Yang, J. (2013), No Tardiness Rescheduling with Order Disruptions, Industrial Engineering and Management Systems, 12, 51-62. crossref(new window)

10.
Yang, J. (2015), Hybrid Flow Shop with Parallel Machines at the First Stage and Dedicated Machines at the Second Stage, Industrial Engineering and Management Systems, 14, 22-31. crossref(new window)