Fuzzy distances and their applications on fuzzy scheduling
DOI:
https://doi.org/10.15587/1729-4061.2013.14759Keywords:
fuzzy scheduling problem, single machine scheduling, local search methods (Threshold accepted (TA), Tabu search (TS), Memetic algorithm (MA))Abstract
The aim of this paper is to develop a fuzzy scheduling problem for solving a multi-objective functions on single machine scheduling problems when processing time and due date are a triangular fuzzy numbers. We are used fuzzy distance function concepts which introduced by Lam and Cai. The objective is to minimize the maximum fuzzy lateness and maximum fuzzy completion time. In this paper we compare and test different local search methods (Threshold accepted (TA), Tabu search (TS), and Memetic algorithm (MA)) computational experience 1000 jobs with reasonable time. For comprise results we use probability and cost considerations in project schedulingReferences
- Brucker P. (2007). "Scheduling Algorithms", Springer Berlin Heidelberg New York, Fifth Edition.
- Chanas, S., Kasperski, A. (2001). "Minimizing maximum lateness in a single machine scheduling problem with fuzzy processing times and fuzzy due dates", Engineering Application of Artificial Intelligence, 14, 377-386.
- Chanas, S., Kasperski, A. (2003). "On two single machine scheduling problems with fuzzy processing times and fuzzy due dates", European Journal of Operational Research, 147, 281-296.
- Dubois, D., Prade H. (1980). "Fuzzy sets and systems: theory and applications", Academic press, Inc.
- França P. M. (1999). Mendes A. and Moscato P., "A memetic algorithm for the total tardiness single machine scheduling problem" European Journal of OR.
- Glover F. (1994). "A user's guide to tabu search", Annals of Operations Research, 41, 3-28.
- Goguen J. (1973). "The Fuzzy Tychonoff Theorem", J. Math. Anal. Appl, 43, 734-742.
- Han, S., Ishii, H., Fujii, S. (1994). "One machine scheduling problem with fuzzy due dates", European Journal Operation. Research , 79, 1-12.
- Heilpern, S. (1997). "Representation and application of fuzzy numbers", Fuzzy Sets and Systems, 91, 259-268.
- Hussam A., Faria A., Hanan A. and Fathalh A., "On Fuzzy Distances and their Applications on Cost Function ", to appear.
- Ishii, H., Tada, M. (1995). "Single machine scheduling problem with fuzzy precedence relation", European Journal of Operational Research, 87, 284-288.
- Kaufmann, A., Gupta, M. (1991). " Introduction to fuzzy arithmetic theory and applications", Van Nostrand Reinhold.
- Lam, S., Cai X. (1999). "Distance measures of fuzzy numbers computational intelligence and applications", Springer, Berlin, 207-214.
- Lam, S., Cai, X. (2002). "Single machine scheduling with nonlinear lateness cost functions and fuzzy due dates nonlinear analysis ", Real World Application, 3333, 307-316,
- Moscato, P. (1989). "On evolution, search, optimization, genetic algorithm and martial arts: toward memetic algorithms", Caltech Concurrent Computation Program c3p Technical Report, California, 826.
- Nachammai, A. (2012). "Solving fuzzy linear Fractional programming problem using Metric distance Ranking", Applied Mathematical Sciences, 6, 1275-1285.
- Tanaka, K., Vlach, M. (1997). "Single machine scheduling with fuzzy due dates", Seventh IFSA World Congress Prague, 195-199.
- Zadeh, L. (1965). "Fuzzy sets" Information and Control, 8, 338-353.
- Брукер, П. Scheduling Algorithms [Текст] / П. Брукер // Springer Berlin Heidelberg New York, пятое издание. - 2007.
- Шана, C. Minimizing maximum lateness in a single machine scheduling problem with fuzzy processing times and fuzzy due dates [Текст] / С. Шана, А. Касперски // Engineering Application of Artificial Intelligence, 2001. - Vol.14. - P. 377-386.
- Шана, C. On two single machine scheduling problems with fuzzy processing times and fuzzy due dates [Текст] / С. Шана, А. Касперски // Европейский журнал исследования операций, 2003. - Vol.147. - P.281-296.
- Дюбуа, Д. Fuzzy sets and systems: theory and applications [Текст] / Д. Дюбуа, Х. Prade // Academic press, Inc. 1980.
- Франция, P. М. A memetic algorithm for the total tardiness single machine scheduling problem [Текст] / P. М. Франция, А. Мендес, П. Moscato, // Европейский журнал исследования операций.-1999.
- Гловер, Ф. A user's guide to tabu search [Текст] / Ф. Гловер // Annals of Operations Research, 1994. - Вып.41. - С. 3-28.
- Гоген, Дж. The Fuzzy Tychonoff Theorem [Текст] / Дж. Гоген // Дж. Математика Анальный. Appl.,1973. - Т.43. - С.734-742.
- Хан, С. One machine scheduling problem with fuzzy due dates [Текст] / С. Хан, Х. Исии, С. Фуджи // Европейский журнал исследования операций, 1994. - Вып.79. - С. 1-12.
- Хейлперн, С. Representation and application of fuzzy numbers [Текст] / С. Хейлперн // Нечетких множеств и системы, 1997. - Вып.91. - С. 259-268.
- Хуссам А. , Фариа А., Ханан А. and Фадала А. On Fuzzy Distances and their Applications on Cost Function [Текст] / А. Хуссам , А. Фариа, А. Ханан, А. Фадала // to appear.
- Исии, Х. Single machine scheduling problem with fuzzy precedence relation [Текст] / Х. Исии М. Тада // Европейский журнал исследования операций, 1995. - Вып.87. - С. 284-288.
- Кауфман, А. Introduction to fuzzy arithmetic theory and applications [Текст] / Кауфман А. и М. Гупта // Van Nostrand Reinhold.-1991.
- Лам С. Distance measures of fuzzy numbers computational intelligence and applications [Текст] / С. Лам, X. Цай, // Springer, Berlin, 1999. - С.207-214.
- Лам, С. Single machine scheduling with nonlinear lateness cost functions and fuzzy due dates nonlinear analysis [Текст] / С. Лам, X. Цай, // Real World Application, 2002. - Вып.3333. - С.307-316.
- Москато, П. On evolution, search, optimization, genetic algorithm and martial arts: toward memetic algorithms [Текст] / Москато П. // Caltech Concurrent Computation Program c3p Technical Report, California, 1989. – 826с.
- Nachammai, A. "Solving fuzzy linear Fractional programming problem using Metric distance Ranking" [Текст] / A. Nachammai // Applied Mathematical Sciences, 2012. - Vol.6. - P.1275-1285.
- Танака, К. Single machine scheduling with fuzzy due dates [Текст] / К. Танака, М. Влах // Seventh IFSA World Congress Prague, 1997. - С.195-199.
- Заде, Л. Fuzzy sets [Текст] / Заде, Л. // Information and Control, 1965. - Вып.8. - С.338-353.
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