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Constructing a fuzzy flow-shop sequencing model based on statistical data. (English) Zbl 1006.68018
Summary: This study investigated an approach for incorporating statistics with fuzzy sets in the flow-shop sequencing problem. This work is based on the assumption that the precise value for the processing time of each job is unknown, but that some sample data are available. A combination of statistics and fuzzy sets provides a powerful tool for modeling and solving this problem. Our work intends to extend the crisp flow-shop sequencing problem into a generalized fuzzy model that would be useful in practical situations. In this study, we constructed a fuzzy flow-shop sequencing model based on statistical data, which uses level ($1- \alpha$, $1- \beta$) interval-valued fuzzy numbers to represent the unknown job processing time. Our study shows that this fuzzy flow-shop model is an extension of the crisp flow-shop problem and the results obtained from the fuzzy flow-shop model provides the same job sequence as that of the crisp problem.

##### MSC:
 68M20 Performance evaluation of computer systems; queueing; scheduling
##### Keywords:
fuzzy sets; flow-shop sequencing
Full Text:
##### References:
 [1] Baker, K. R.: Introduction to sequencing and scheduling. (1974) [2] Campbell, H.; Dudek, R.; Smith, M.: A heuristic algorithm forthe n-job m-machine sequencing problem. Management science B 16, 630-637 (1970) · Zbl 0194.50504 [3] Jr., E. G. Coffman: Computer and job-shop scheduling theory. (1976) · Zbl 0359.90031 [4] Dannenbring, D.: An evaluation of flow shop sequencing heuristics. Management science 23, 1174-1182 (1977) · Zbl 0371.90063 [5] Dudek, R. A.; Panwalkar, S. S.; Smith, M. L.: The lessons of flowshop scheduling research. Operations research 40, 7-13 (1992) · Zbl 0825.90554 [6] Garey, M.; Johnson, D.; Sethi, R.: The complexity of flowshop and jobshop scheduling. Mathematics of operations research 1, 117-129 (1976) · Zbl 0396.90041 [7] Gen, M.; Cheng, R.: Genetic algorithms and engineering design. (1997) [8] Gorzalezang, M. B.: A method of inference in approximate reasoning based on interval-valued fuzzy set. Fuzzy sets and systems 21, 1-17 (1981) [9] Ho, J.; Chang, Y.: A new heuristic for the n-job m-machine flow shop problem. European journal of operational research 52, 194-202 (1991) · Zbl 0725.90045 [10] Hundal, T. S.; Rajgopal, J.: An extension of palmer’s heuristic for the flow-shop scheduling problem. International journal of production research 26, 1119-1124 (1998) [11] Ishibuchi, H.; Yamamoto, N.; Murata, T.; Tanaka, H.: Genetic algorithms and neighborhood search algorithms for fuzzy flowshop scheduling problems. Fuzzy sets and systems 67, 81-100 (1994) [12] Ishii, H.; Tada, M.; Masuda, T.: Two scheduling problems with fuzzy due dates. Fuzzy sets and systems 46, 339-347 (1992) · Zbl 0767.90037 [13] Kaufmann, A.; Gupta, M. M.: Introduction to fuzzy arithmetic theory and applications. (1991) · Zbl 0754.26012 [14] R.M. Kerr, W. Slany, Research issues and challenges in fuzzy scheduling, CD-Technical Report 94/68, Christian Doppler Laboratory for Expert Systems, Technical University of Vienna, Austria, 1994 [15] Mccahon, C. S.; Lee, E. S.: Fuzzy job sequencing for a flowshop. European journal of operational research 62, 294-301 (1992) · Zbl 0762.90039 [16] Morton, T.; Pentico, D.: Heuristic scheduling systems -- with applications to production systems and project management. (1993) [17] Nawaz, M.; Enscore, E.; Ham, I.: A heuristic algorithm for the m-machine n-job flow shop sequencing problem. Omega 11, 11-95 (1983) [18] Palmer, D.: Sequencing jobs through a multi-stage process in the minimum total time -- a quick method of obtaining a near optimum. Operations research quarterly 16, 101-107 (1965) [19] Taillard, E.: Some efficient heuristic methods for the flowshop sequencing problem. European journal of operational research 47, 65-74 (1990) · Zbl 0702.90043 [20] Weiss, N. A.; Hassett, M. J.: Introductory statistics. (1987) [21] Yao, J. S.; Wu, K. M.: Ranking fuzzy numbers based on decomposition principle and signed distance. Fuzzy sets and systems 116, 275-288 (2000) · Zbl 1179.62031