Skip to main content
SpringerLink
Log in

An Effective Solution Approach to Fuzzy Programming with Application to Project Scheduling

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

In the present paper, a novel solution approach is proposed for a class of fuzzy programming models. In this direction, we prove that the lower and upper bounds of their fuzzy optimal objective values at a possibility level, \(\alpha \in [0,1]\), can be calculated solving a pair of crisp mathematical programming models. Thus, their membership functions are simulated enumerating the upper and lower bounds obtained from a series of \(\alpha\)-level calculations. Motivated from real-world project scheduling applications, several numerical examples are considered to evaluate the accuracy, efficiency and applicability of our treatment. The results derived are compared with those of Chen and Tsai (Eur J Oper Res 212(2):386–397, 2011) to demonstrate that our method is easier to be utilized, with lower computational complexity, nonetheless without losing its effectiveness. Finally, the new approach does not suffer from the limitation to be applicable only to linear programming models that makes it suitable for a wider range of models and applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Su, T.S., Lin, Y.F.: Fuzzy multi-objective procurement/production planning decision problems for recoverable manufacturing systems. J. Manuf. Syst. 37(1), 396–408 (2015)

    Article  Google Scholar 

  2. Chen, S.P., Tsai, M.J.: Time-cost trade-off analysis of project networks in fuzzy environments. Eur. J. Oper. Res. 212(2), 386–397 (2011)

    Article  MathSciNet  Google Scholar 

  3. Wang, R., Zhou, J., Yi, X., Pantelous, A.A.: Solving the green-fuzzy vehicle routing problem using a revised hybrid intelligent algorithm. J. Ambient Intell. Humaniz. Comput. (2018). https://doi.org/10.1007/s12652-018-0703-9

    Article  Google Scholar 

  4. Verdegay, J.L.: Progress on fuzzy mathematical programming: a personal perspective. Fuzzy Sets Syst. 281, 219–226 (2015)

    Article  MathSciNet  Google Scholar 

  5. Zimmermann, H.J.: Description and optimization of fuzzy systems. Int. J. Gen. Syst. 2(1), 209–215 (1975)

    Article  Google Scholar 

  6. Chanas, S.: Fuzzy programming in multiobjective linear programming: a parametric approach. Fuzzy Sets Syst. 29(3), 303–313 (1989)

    Article  MathSciNet  Google Scholar 

  7. Sinha, S.: Fuzzy mathematical programming applied to multi-level programming problems. Comput. Oper. Res. 30(9), 1259–1268 (2003)

    Article  MathSciNet  Google Scholar 

  8. Tanaka, H., Asai, K.: Fuzzy linear programming problems with fuzzy numbers. Fuzzy Sets Syst. 13(1), 1–10 (1984)

    Article  MathSciNet  Google Scholar 

  9. Buckley, J.J., Feuring, T.: Evolutionary algorithm solution to fuzzy problems: fuzzy linear programming. Fuzzy Sets Syst. 109(1), 35–53 (2000)

    Article  MathSciNet  Google Scholar 

  10. Zhou, J., Yang, F., Wang, K.: Fuzzy arithmetic on LR fuzzy numbers with applications to fuzzy programming. J. Intell. Fuzzy Syst. 30(1), 71–87 (2016)

    Article  Google Scholar 

  11. Dubois, D., Prade, H.: Operations on fuzzy numbers. Int. J. Syst. Sci. 9(6), 613–626 (1978)

    Article  MathSciNet  Google Scholar 

  12. Yager, R.R.: On the specificity of a possibility distribution. Fuzzy Sets Syst. 50(3), 279–292 (1992)

    Article  MathSciNet  Google Scholar 

  13. Eslamipoor, R., Haji, M.J., Sepehriar, A.: Proposing a revised method for ranking fuzzy numbers. J. Intell. Fuzzy Syst. 25(2), 373–378 (2013)

    MathSciNet  MATH  Google Scholar 

  14. Baykasoglu, A., Gocken, T.: A direct solution approach to fuzzy mathematical programs with fuzzy decision variables. Expert Syst. Appl. 39(2), 1972–1978 (2012)

    Article  Google Scholar 

  15. Hatami, A., Kazemipoor, H.: Solving fully fuzzy linear programming with symmetric trapezoidal fuzzy numbers using Mehar’s method. J. Math. Comput. Sci. 4(2), 463–470 (2014)

    Google Scholar 

  16. Kaur, J., Kumar, A.: Mehar’s method for solving fully fuzzy linear programming problems with LR fuzzy parameters. Appl. Math. Model. 37(12–13), 7142–7153 (2013)

    Article  MathSciNet  Google Scholar 

  17. Pishvaee, M.S., Torabi, S.A.: A possibilistic programming approach for closed-loop supply chain network design under uncertainty. Fuzzy Sets Syst. 161(20), 2668–2683 (2010)

    Article  MathSciNet  Google Scholar 

  18. Ozceylan, E., Paksoy, T.: Interactive fuzzy programming approaches to the strategic and tactical planning of a closed-loop supply chain under uncertainty. Int. J. Prod. Res. 52(8), 2363–2387 (2014)

    Article  Google Scholar 

  19. Talaei, M., Moghaddam, B.F., Pishvaee, M.S., Bozorgi-Amiri, A., Gholamnejad, S.: A robust fuzzy optimization model for carbon-efficient closed-loop supply chain network design problem: a numerical illustration in electronics industry. J. Clean. Prod. 113, 662–673 (2016)

    Article  Google Scholar 

  20. Farrokh, M., Azar, A., Jandaghi, G., Ahmadi, E.: A novel robust fuzzy stochastic programming for closed loop supply chain network design under hybrid uncertainty. Fuzzy Sets Syst. 341, 69–91 (2017)

    Article  MathSciNet  Google Scholar 

  21. Chen, S.P., Ho, Y.H.: Optimal inventory policy for the fuzzy newsboy problem with quantity discounts. Inf. Sci. 228, 75–89 (2013)

    Article  MathSciNet  Google Scholar 

  22. Chen, S.P.: Effects of fuzzy data on decision making in a competitive supply chain. J. Oper. Res. Soc. 68(10), 1146–1160 (2017)

    Article  Google Scholar 

  23. Zadeh, L.A.: The concept of linguistic variable and its application to approximate reasoning. Inf. Sci. 8(3), 199–249 (1975)

    Article  MathSciNet  Google Scholar 

  24. Aminbakhsh, S., Sonmez, R.: Discrete particle swarm optimization method for the large-scale discrete time-cost trade-off problem. Expert Syst. Appl. 51, 177–185 (2016)

    Article  Google Scholar 

  25. Zou, X., Fang, S.C., Huang, Y.S., Zhang, L.H.: Mixed-integer linear programming approach for scheduling repetitive projects with time-cost trade-off consideration. J. Comput. Civil. Eng. 31(3), 06016003 (2017)

    Article  Google Scholar 

  26. Hu, X., Cui, N., Demeulemeester, E.: Effective expediting to improve project due date and cost performance through buffer management. Int. J. Prod. Res. 53(5), 1460–1471 (2015)

    Article  Google Scholar 

  27. Prade, H.: Using fuzzy set theory in a scheduling problem: a case study. Fuzzy Sets Syst. 2(2), 153–165 (1979)

    Article  Google Scholar 

  28. Pathak, B.K., Srivastava, S.: Integrated fuzzy-HMH for project uncertainties in time-cost trade-off problem. Appl. Soft. Comput. 21, 320–329 (2014)

    Article  Google Scholar 

  29. Vartouni, A.M., Khanli, L.M.: A hybrid genetic algorithm and fuzzy set applied to multi-mode resource-constrained project scheduling problem. J. Intell. Fuzzy Syst. 26(3), 1103–1112 (2014)

    MathSciNet  MATH  Google Scholar 

  30. Ke, H., Ma, J.: Modeling project time-cost trade-off in fuzzy random environment. Appl. Soft. Comput. 19, 80–85 (2014)

    Article  Google Scholar 

  31. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  Google Scholar 

  32. Cheng, C.H.: A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets Syst. 95(3), 307–317 (1998)

    Article  MathSciNet  Google Scholar 

  33. Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 100(1), 9–34 (1999)

    Article  MathSciNet  Google Scholar 

  34. Nahmias, S.: Fuzzy variables. Fuzzy Sets Syst. 1(2), 97–110 (1978)

    Article  MathSciNet  Google Scholar 

  35. Liu, B.: Uncertainty Theory. Springer, Berlin (2004)

    Book  Google Scholar 

  36. Baykasoglu, A., Gocken, T.: A review and classification of fuzzy mathematical programs. J. Intell. Fuzzy Syst. 19(3), 205–229 (2008)

    MATH  Google Scholar 

  37. Zhong, S., Pantelous, A.A., Beer, M., Zhou, J.: Constrained non-linear multi-objective optimization of preventive maintenance scheduling for offshore wind farms. Mech. Syst. Signal Process. 104, 347–369 (2018)

    Article  Google Scholar 

  38. Kaufmann, A., Gupta, M.M.: Introduction to Fuzzy Arithmetic: Theory and Applications. Thomson, Belmont (1991)

    MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to acknowledge the gracious support of this work by the National Natural Science Foundation of China (Grant No. 71501123) and the High-end Foreign Experts Recruitment Program of China (Grant No. GDW20183100431).

Author information

Authors and Affiliations

  1. School of Management, Shanghai University, Shanghai, 200444, China

    Qianyu Zhang, Jian Zhou & Ke Wang

  2. Department of Econometrics and Business Statistics, Monash Business School, Monash University, 20 Chancellors walk, Wellington Rd, Clayton Campus, Melbourne, VIC, 3800, Australia

    Athanasios A. Pantelous

Authors
  1. Qianyu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jian Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ke Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Athanasios A. Pantelous
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ke Wang.

Appendix

Appendix

Table 8 Triangular fuzzy parameters of the project network shown in Fig. 3
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Q., Zhou, J., Wang, K. et al. An Effective Solution Approach to Fuzzy Programming with Application to Project Scheduling. Int. J. Fuzzy Syst. 20, 2383–2398 (2018). https://doi.org/10.1007/s40815-018-0542-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-018-0542-z

Keywords

Search

Navigation