Advertisement

Fuzzy Optimization and Decision Making

, Volume 9, Issue 2, pp 219–231 | Cite as

New fuzzy models for time-cost trade-off problem

  • Hua Ke
  • Weimin Ma
  • Xin Gao
  • Weihua Xu
Article

Abstract

The time-cost trade-off problem is a specific type of the project scheduling problem which studies how to modify project activities so as to achieve the trade-off between the completion time and the project cost. In real projects, the trade-off between the project cost and the completion time, and the uncertainty of the environment are both considerable aspects for managers. In this paper, three new fuzzy time-cost trade-off models are proposed, in which credibility theory is applied to describe the uncertainty of activity duration times. A searching method by integrating fuzzy simulation and genetic algorithm is produced to search the quasi-optimal schedules under some decision-making criteria. The purpose of the paper is to reveal how to obtain the optimal balance of the completion time and the project cost in fuzzy environments.

Keywords

Time-cost trade-off Credibility theory Fuzzy simulation Genetic algorithm 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Azaron A., Perkgoz C., Sakawa M. (2005) A genetic algorithm approach for the time-cost trade-off in PERT networks. Applied Mathematics and Computation 168(2): 1317–1339MATHCrossRefMathSciNetGoogle Scholar
  2. Butcher W. S. (1967) Dynamic programming for project cost-time curve. Journal of Construction Division 93(C01): 59–73Google Scholar
  3. Chanas S., Kamburowski J. (1981) The use of fuzzy variables in PERT. Fuzzy Sets and Systems 5(1): 11–19MATHCrossRefMathSciNetGoogle Scholar
  4. Charnes A., Cooper W. W. (1959) Chance-constrained programming. Management Science 6: 73–79MATHCrossRefMathSciNetGoogle Scholar
  5. Charnes A., Cooper W. W. (1962) A network interpretation and a direct sub-dual algorithm for critical path scheduling. Journal of Industrial Engineering 13: 213–219Google Scholar
  6. Chua D. K. H., Chan W. T., Govindan K. (1997) A time-cost trade-off model with resource consideration using genetic algorithm. Civil Engineering Systems 14: 291–311CrossRefGoogle Scholar
  7. Eshtehardian E., Afshar A., Abbasnia R. (2008) Time-cost optimization: Using GA and fuzzy sets theory for uncertainties in cost. Construction Management and Economics 26(7): 679–691CrossRefGoogle Scholar
  8. Feng C. W., Liu L., Burns S. A. (1997) Using genetic algorithms to solve construction time-cost trade-off problems. Journal of Construction Engineering and Management 11(3): 184–189Google Scholar
  9. Freeman R. J. (1960) A generalized network approach to project activity sequencing. IRE Transactions on Engineering Management 7(3): 103–107CrossRefGoogle Scholar
  10. Ghazanfari M., Shahanaghi K., Yousefli A. (2008) An application of possibility goal programming to the time-cost trade off problem. Journal of Uncertain Systems 2(1): 22–28Google Scholar
  11. Ghazanfari M., Yousefli A., Ameli M. S. J., Bozorgi-Amiri A. (2009) A new approach to solve time-cost trade-off problem with fuzzy decision variables. The International Journal of Advanced Manufacturing Technology 42: 408–414CrossRefGoogle Scholar
  12. Goldratt E. (1997) Critical chain. The North River Press, Great Barrington, MAGoogle Scholar
  13. Golenko-Ginzburg D., Gonik A. (1997) Stochastic network project scheduling with non-consumable limited resources. International Journal of Production Economics 48(1): 29–37CrossRefGoogle Scholar
  14. Gutjahr W. J., Strauss C., Wagner E. (2000) A stochastic branch-and-bound approach to activity crashing in project management. INFORMS Journal on Computing 12(2): 125–135MATHCrossRefGoogle Scholar
  15. Hapke M., Jaszkiewicz A., Slowinski R. (1994) Fuzzy project scheduling system for software development. Fuzzy Sets and Systems 67(11): 101–117CrossRefMathSciNetGoogle Scholar
  16. Hapke M., Slowinski R. (1993) A DSS for resource-constrained project scheduling under uncertainty. Journal of Decision Systems 2(2): 111–128Google Scholar
  17. Hapke M., Slowinski R. (1996) Fuzzy priority heuristics for project scheduling. Fuzzy Sets and Systems 83(3): 291–299CrossRefGoogle Scholar
  18. Hapke M., Slowinski R. (2000) Fuzzy set approach to multi-objective and multi-mode project scheduling under uncertainty. In: Hapke M., Slowinski R. (eds) Scheduling under fuzziness. Physica-Verlag, Heidelberg, pp 197–221Google Scholar
  19. Jin C., Ji Z., Lin Y., Zhao Y., Huang Z. (2005) Research on the fully fuzzy time-cost trade-off based on genetic algorithms. Journal of Marine Science and Application 4(3): 18–23CrossRefGoogle Scholar
  20. Kaufmann A., Gupta M. M. (1988) Fuzzy mathematical models in engineering and management science. Amsterdam, North-HollandMATHGoogle Scholar
  21. Ke H., Liu B. (2005) Project scheduling problem with stochastic activity duration times. Applied Mathematics and Computation 168(1): 342–353MATHCrossRefMathSciNetGoogle Scholar
  22. Ke H., Liu B. (2010) Fuzzy project scheduling problem and its hybrid intelligent algorithm. Applied Mathematical Modelling 34(2): 301–308MATHCrossRefMathSciNetGoogle Scholar
  23. Ke H., Ma W., Ni Y. (2009) Optimization models and a GA-based algorithm for stochastic time-cost trade-off problem. Applied Mathematics and Computation 215: 308–313MATHCrossRefMathSciNetGoogle Scholar
  24. Kelley J. E. Jr. (1961) Critical path planning and scheduling mathematical basis. Operations Research 9(3): 296–320MATHCrossRefMathSciNetGoogle Scholar
  25. Laslo Z. (2003) Activity time-cost tradeoffs under time and cost chance constraints. Computers & Industrial Engineering 44: 365–384CrossRefGoogle Scholar
  26. Leu S. S., Chen A. T., Yang C. H. (2001) A GA-based fuzzy optimal model for construction time-cost trade-off. International Journal of Project Management 19: 47–58CrossRefGoogle Scholar
  27. Liu B. (1997) Dependent-chance programming: A class of stochastic programming. Computers & Mathematics with Applications 34(12): 89–104MATHCrossRefMathSciNetGoogle Scholar
  28. Liu B., Iwamura K. (1998a) Chance constrained programming with fuzzy parameters. Fuzzy Sets and Systems 94: 227–237MATHCrossRefMathSciNetGoogle Scholar
  29. Liu B., Iwamura K. (1998b) A note on chance constrained programming with fuzzy coefficients. Fuzzy Sets and Systems 100: 229–233MATHCrossRefMathSciNetGoogle Scholar
  30. Liu B. (1999) Dependent-chance programming with fuzzy decisions. IEEE Transactions on Fuzzy Systems 7: 354–360CrossRefGoogle Scholar
  31. Liu B. (2002) Theory and practice of uncertain programming. Physica-Verlag, HeidelbergMATHGoogle Scholar
  32. Liu B., Liu Y. K. (2002) Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems 10: 445–450CrossRefGoogle Scholar
  33. Liu B. (2004) Uncertainty theory: An introduction to its axiomatic foundations. Springer-Verlag, BerlinMATHGoogle Scholar
  34. Liu B. (2006a) A survey of credibility theory. Fuzzy Optimization and Decision Making 5: 387–408CrossRefMathSciNetGoogle Scholar
  35. Liu Y. K. (2006b) Convergent results about the use of fuzzy simulation in fuzzy optimization problems. IEEE Transactions on Fuzzy Systems 14: 295–304CrossRefGoogle Scholar
  36. Long L. D., Ohsato A. (2008) Fuzzy critical chain method for project scheduling under resource constraints and uncertainty. International Journal of Project Management 26(6): 688–698CrossRefGoogle Scholar
  37. Özdamar L., Alanya E. (2001) Uncertainty modelling in software development projects (with case study). Annals of Operations Research 102(1–4): 157–178MATHCrossRefMathSciNetGoogle Scholar
  38. Phillips S. Jr., Dessouky M. I. (1997) Solving the project time/cost tradeoff problem using minimal cut concept. Management Science 24(4): 393–400CrossRefGoogle Scholar
  39. Prade H. (1979) Using fuzzy set theory in a scheduling problem: A case study. Fuzzy Sets and Systems 2(2): 153–165MATHCrossRefGoogle Scholar
  40. Siemens N. (1971) A simple CPM time-cost trade-off algorithm. Management Science 17(6): 354–363CrossRefMathSciNetGoogle Scholar
  41. Talbot F. B. (1982) Resource-constrained project scheduling with time-resource tradeoffs: The non-preemptive case. Management Science 28: 1197–1210MATHCrossRefGoogle Scholar
  42. Wang J. R. (1999) A fuzzy set approach to activity scheduling for product development. Journal of the Operational Research Society 50: 1217–1228MATHGoogle Scholar
  43. Wang J. R. (2002) A fuzzy project scheduling approach to minimize schedule risk for product development. Fuzzy Sets and Systems 127(2): 99–116MATHCrossRefMathSciNetGoogle Scholar
  44. Wollmer R. D. (1985) Critical path planning under uncertainty. Mathematical Programming Study 25: 164–171MATHMathSciNetGoogle Scholar
  45. Zadeh L. A. (1965) Fuzzy sets. Information and Control 8: 338–353MATHCrossRefMathSciNetGoogle Scholar
  46. Zadeh L. A. (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1: 3–28MATHCrossRefMathSciNetGoogle Scholar
  47. Zahraie B., Tavakolan M. (2009) Stochastic time-cost-resource utilization optimization using nondominated sorting genetic algorithm and discrete fuzzy sets. Journal of Construction Engineering and Management 135: 1162–1171CrossRefGoogle Scholar
  48. Zheng D. X. M., Ng S. T. (2005) Stochastic time-cost optimization model incorporating fuzzy sets theory and nonreplaceable front. Journal of Construction Engineering and Management 131(2): 176–186CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of Economics and ManagementTongji UniversityShanghaiChina
  2. 2.School of Mathematics and PhysicsNorth China Electric Power UniversityBeijingChina

Personalised recommendations