Fuzzy scheduling: Modelling flexible constraints vs. coping with incomplete knowledge

European Journal of Operational Research

Volumn 147, Issue 2, 2003, Pages 231-252

  Dubois, Didier ^a   Fargier, Helene ^a   Fortemps, Philippe ^b  

^a IRIT   (France)

^b Mons Institute of Technology (FPMs) MATHRO   (Belgium)

Author keywords

Constraint propagation; Fuzzy intervals; Possibility theory; Scheduling; Uncertainty

Indexed keywords

CONSTRAINT THEORY; FUZZY SETS; KNOWLEDGE ENGINEERING; MATHEMATICAL MODELS; SCHEDULING;

FLEXIBLE CONSTRAINTS;

OPERATIONS RESEARCH;

EID: 0037410423     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-2217(02)00558-1     Document Type: Review

References (76)

1. Baas S.M., Kwakernaak H. Rating and ranking of multiple aspect alternatives using fuzzy sets. Automatica. 13:1977;47-58.
2. Bellman R.E., Zadeh L.A. Decision-making in a fuzzy environment. Management Science. 17(4):1970;B141-B164.
3. Bensana E., Bel G., Dubois D. OPAL, a multi-knowledge-based system for industrial job-shop scheduling. International Journal of Production Research. 26(5):1988;795-816.
4. Birge J.R., Dempster M.A.H. Stochastic programming approaches to stochastic scheduling. Journal of Global Optimization. 9:1996;383-409.
5. Blazewicz, J., Cellary, W., Slowinski, R., Weglarz, J. (Eds.) 1986. Scheduling under resource constraint - Deterministic Models. Annals of Operations Research, vol. 7, J.C. Baltzer AG.
6. Bortolan G., Degani R. A review of some methods for comparing fuzzy subsets. Fuzzy Sets and Systems. 15:1985;1-19.
7. Buckley J.J. Fuzzy PERT. Evans G., Karwowski W., Wilhelm M. Applications of the Fuzzy Set Methodologies in Industrial Engineering. 1989;103-114 Elsevier.
8. Chanas S., Kamburowski J. The use of fuzzy variables in PERT. Fuzzy Sets and Systems. 5:1981;11-19.
9. Chanas S., Kuchta D. Discrete fuzzy optimization. Slowinski R. Fuzzy Sets in Decision Analysis, Operations Research and Statistics. The Handbooks of Fuzzy Sets Series. 1988;249-277 Kluwer Academic Publishers, Boston.
10. Chanas S., Zielinski P. The computational complexity of interval critical path method. European Journal of Operational Research. 136(3):2002;541-550.
11. Chanas, S., Zielinski P., 2001. Critical path analysis in the network with fuzzy activity times, to appear in Fuzzy Sets and Systems, 122 (2), 195-204.
12. Chanas S., Dubois D., Zielinski P. Necessary criticality in the network with imprecise activity times. IEEE Transactions on Systems, Man and Cybernetics. 32:2002;393-407.
13. Chen S.-J., Hwang C.-L. Fuzzy Multiple Attribute Decision Making, Lecture Notes in Economics and Mathematical Systems. vol. 375:1992;Springer Verlag, Berlin.
14. Dubois, D., 1983. Modèles mathématiques de l'imprécis et de l'incertain en vue d'applications aux techniques d'aide á la décision, Thèse d'état de l'Université Scientifique et Médicale de Grenoble.
15. Dubois D. Fuzzy knowledge in an artificial intelligence system for job-shop scheduling. Evans G., Karwowski W., Wilhelm M. Applications of the Fuzzy Set Methodologies in Industrial Engineering. 1989;73-89 Elsevier.
16. Dubois D., Fortemps P. Computing improved optimal solutions to fuzzy constraint satisfaction problems. European Journal of Operational Research. 118:1999;95-126.
17. Dubois D., Koning J.L. A decision engine based on rational aggregation of heuristic knowledge. Decision Support Systems. 11:1994;337-361.
18. Dubois D., Prade H. Algorithmes de plus courts chemins pour traiter des donnees floues. RAIRO-Recherche Opérationnelle/Operations Research. 12:1978;212-227.
19. Dubois D., Prade H. Fuzzy Sets and Systems - Theory and Applications. 1980;Academic Press, New York.
20. Dubois D., Prade H. The mean value of a fuzzy number. Fuzzy Sets and Systems. 24:1987;279-300.
21. Dubois D., Prade H. Possibility Theory. 1988;Plenum Press, New York.
22. Dubois D., Prade H. Fundamentals of Fuzzy Sets. The Handbooks of Fuzzy Sets Series. 2000;Kluwer Academic Publishers, Boston.
23. Dubois D., Fargier H., Prade H. Fuzzy constraints in job-shop scheduling. Journal of Intelligent Manufacturing. 6:1995;215-234.
24. Dubois D., Fargier H., Prade H. Possibility theory in constraint satisfaction problems: Handling priority, preference and uncertainty. Applied Intelligence. 6:1996;287-309.
25. Dubois D., Kerre E., Mesiar R., Prade H. Fuzzy interval analysis. Dubois D., Prade H. Fundamentals of Fuzzy sets. The Handbooks of Fuzzy Sets Series. 2000;483-581 Kluwer Academic Publishers, Boston.
26. Dubois, D., Fargier, H., Galvagnon, V., 2001. On latest starting times and floats in activity networks with ill-known durations. European Journal of Operational Research 147 (2), this issue.
27. Dubois D., Prade H., Sabbadin R. Decision-theoretic foundations of qualitative possibility theory. European Journal of Operational Research. 128:2002;459-478.
28. Erschler J., Esquirol P. Decison-aid in job shop scheduling: A knowledge based approach. Proceedings of the 1986 IEEE Conference on Robotics and Automation, San Franscisco. 1986;1751-1756.
29. Erschler J., Roubellat F., Vernhes J.P. Finding some essential characteristics of the feasible solutions for a scheduling problem. Operations Research. 24:1976;774-783.
30. Esquirol P., Lopez P. L'ordonnancement. 1999;Economica, Paris.
31. Fargier, H., 1994. Problèmes de satisfaction de contraintes flexibles: Application à l'ordonnancement de production. Thèse de Doctorat, Université Paul Sabatier, Toulouse.
32. Fargier H. Fuzzy scheduling: Principles and experiments. Dubois D., Prade H., Yager R.R. Fuzzy Information Engineering: A Guided Tour of Applications. 1997;655-669 Wiley, New York.
33. Fargier H., Galvagnon V. Le Problm̀e du PERT flou dans les graphes série-paralléle. Actes des Rencontres Francophones sur la Logique Floue et ses Applications (LFA'99), Valenciennes. 1999;277-284 Cepadues, Toulouse.
34. Fargier H., Galvagnon V., Dubois D. Fuzzy PERT in series-parallel graphs. Ninth IEEE International Conference on Fuzzy Systems, San Antonio, Texas. 2000;717-722.
35. Fodor J., Roubens M. Fuzzy Preference Modelling and Multicriteria Decision Support. 1994;Kluwer Academic Publishers, Dordrecht. section 7.2.2.
36. Fortemps P. Job-shop scheduling with imprecise durations: A fuzzy approach. IEEE Transactions on Fuzzy Systems. 5:1997;557-569.
37. Fortemps P., Hapke M. On the disjunctive graph for project scheduling. Foundations of Computing and Decision Sciences. 22:1997;195-209.
38. Fortemps P., Roubens M. Ranking and defuzzification methods based on area compensation. Fuzzy Sets and Systems. 82:1996;319-330.
39. Fox M.S. Constraint-Directed Search: A Case Study of Job-Shop Scheduling. 1987;Pitman, London.
40. Gazdik I. Fuzzy network planning FNET. IEEE Transactions on Reliability. 32:1983;303-313.
41. Grabot B., Geneste L. Dispatching rules in scheduling: A fuzzy approach. International Journal of Production Research. 32:1994;903-915.
42. Guiffrida A.L., Nagi R. Fuzzy set theory applications in production management research: A literature survey. Journal of Intelligent Manufacturing. 9:1998;39-56.
43. Hapke M., Jaszkiewicz A., Slowinski R. Fuzzy project scheduling system for software development. Fuzzy Sets and Systems. 21:1994;101-117.
44. Hintz G.W., Zimmermann H.-J. A method to control flexible manufacturing systems. European Journal of Operational Research. 41:1989;321-334.
45. Ishibuchi H., Yamamoto N., Misaki S., Tanaka H. Local search algorithms for flowshop scheduling with fuzzy due-dates. International Journal of Production Economics. 33:1994;53-66.
46. Ishii H., Tada M., Masuda T. Two scheduling problems with fuzzy due-dates. Fuzzy Sets and Systems. 46:1992;339-347.
47. Kaufmann A., Gupta M.M. Fuzzy Mathematical Models in Engineering and Management Science. 1988;Amsterdam, North Holland.
48. Kerr, R.M., Walker, R.N., 1989. A job shop scheduling system based on fuzzy arithmetics. In: Proceedings of the third International Conference on Expert Systems and the Leading Edge in Production and Operation Management, Hilton Head, SC pp. 433-450.
49. Lin K.C., Chern M.S. The fuzzy shortest path problem and its most vital arcs. Fuzzy Sets and Systems. 58:1993;343-353.
50. Litoiu M., Tadei R. Real-time task scheduling allowing fuzzy due-dates. European Journal of Operational Research. 100:1997;475-481.
51. Litoiu M., Tadei R. Real-time scheduling with fuzzy deadlines and processing times. Fuzzy Sets and Systems. 117:2000;35-46.
52. Lootsma F. Stochastic and fuzzy PERT. European Journal of Operational Research. 43:1989;174-183.
53. Lootsma F. Fuzzy Logic for Planning and Decision-Making. 1997;Kluwer Academic Publishers, Dordrecht.
54. MacCahon C.S. Using PERT as an approximation of fuzzy project network analysis. IEEE trans. Engineering Management. 40:1993;146-153.
55. MacCahon C.S., Lee E.S. Project network analysis with fuzzy activity times. Computers and Mathematics with Applications. 15:1988;829-838.
56. MacCahon C.S., Lee E.S. Fuzzy job sequencing for a flow shop. European Journal of Operational Research. 62:1992;294-301.
57. MacCarthy B., Liu J. Addressing the gap in scheduling research: A review optimization and heuristic methods in production scheduling. International Journal of Production Research. 31:1993;59-79.
58. Mares M. Network analysis of fuzzy technologies. Evans G., Karwowski W., Wilhelm M. Applications of the Fuzzy Set Methodologies in Industrial Engineering. 1989;115-125 Elsevier.
59. Nasution S.H. Fuzzy critical path method. IEEE Transactions on Man, Machine and Cybernetics. 24(1):1993;48-57.
60. Özelkan E.C., Duckstein L. Optimal fuzzy counterparts of priority rules. European Journal of Operational Research. 113:1999;593-609.
61. Pirlot M., Vincke P. Semiorders: Properties, representations, applications. 1997;Kluwer Academic Publishers, Dordrecht.
62. Prade H. Using fuzzy set theory in a scheduling problem: A case study. Fuzzy Sets and Systems. 2:1979;153-165.
63. Rommelfanger H.J. FULPAL: An interactive method for solving (multiobjective) fuzzy linear programming problems. Slowinski R., Teghem J. Stochastic versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty. 1990;321-330 Kluwer.
64. Rommelfanger H.J. Network analysis and information flow in fuzzy environment. Fuzzy Sets and Systems. 67:1994;119-128.
65. Sadeh N., Fox M. Variable and value ordering heuristics for the jobshop scheduling constraint-satisfaction problem. Artificial Intelligence. 86:1996;1-41.
66. Slany W. Scheduling as a fuzzy multiple criteria decision problem. Fuzzy Sets and Systems. 78:1996;197-222.
67. Slowinski R., Hapke M. Scheduling under Fuzziness. 2000;Physica-Verlag, Heidelberg, Germany.
68. Stanfield P., King R., Jones J. Scheduling arrivals to a production system in a fuzzy environment. European Journal of Operational Research. 93:1996;75-87.
69. Turksen I.B., Fazel Zarandi M.H. Production planning and scheduling: Fuzzy and crisp/approaches. Zimmermann H.-J. Practical Applications of Fuzzy Technologies. The Handbook of Fuzzy sets Series. 1999;479-530 Kluwer Academic Publishers, Dordrecht.
70. vanLaarhoven P.J.M., Aarts E.H.L., Lenstra J.K. Job-shop scheduling by simulated annealing. Operations Research. 40:1992;112-125.
71. Wang H.F., Fu C.C. Fuzzy project scheduling models under inflation conditions. International Journal of Uncertainty, Fuzziness and Knowledge-based Systems. 4:1996;514-597.
72. Werners B., Weber R. Decision and planning in research and development. Zimmermann H.-J. Practical Applications of Fuzzy Technologies. The Handbook Fuzzy sets Series. 1999;445-478 Kluwer Academic Publishers, Dordrecht.
73. Yager R.R. A procedure for ordering fuzzy subsets of the unit interval. Information Sciences. 24:1981;143-161.
74. Zadeh L.A. Calculus of fuzzy restrictions. Zadeh L.A., Fu K.S., Tanaka K., Shimura M. Fuzzy Sets and their Applications Cognitive and Decision Processes. 1975;1-39 Academic Press, New York.
75. Zadeh L.A. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems. 1978;13-28.
76. Zimmermann H.-J. Applications of fuzzy set theory to mathematical programming. Information Sciences. 36:1985;28-58.