Multi Objective Production–Distribution Decision Making Model Under Fuzzy Random Environment

  • Muhammad Nazim
  • Muhammad Hashim
  • Abid Hussain Nadeem
  • Liming Yao
  • Jamil Ahmad
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 280)


Today the most important concern of the managers is to make their firms viable in the competitive trade world. Managers are looking effective tools for decision making in the complex business world. This paper addresses a hierarchical multi objective production-distribution planing problem under fuzzy random environment. A mathematical model is presented to describe the purpose problem. To deal the uncertain environment, the fuzzy random variables are first transformed into trapezoidal fuzzy numbers, and by using the expected value operation, the trapezoidal fuzzy numbers are subsequently defuzzified. For solving the multi-objective problem a weighted sum base genetic algorithm is applied. Finally, the result of a numerical example are presented to demonstrate the practical and efficiency of the optimized model.


Multi-objective optimization Fuzzy lead-time Fuzzy inventory cost parameters Inventory planing Interactive fuzzy decision making method 



The authors wish to thank the anonymous referees for their helpful and constructive comments and suggestions. The work is supported by the National Natural Science Foundation of China (Grant No. 71301109), the Western and Frontier Region Project of Humanity and Social Sciences Research, Ministry of Education of China (Grant No. 13XJC630018), the Philosophy and Social Sciences Planning Project of Sichuan province (Grant No. SC12BJ05), and the Initial Funding for Young Teachers of Sichuan University (Grant No. 2013SCU11014).


  1. 1.
    Aliev RA, Fazlollahi B et al (2007) Fuzzy-genetic approach to aggregate production-distribution planning in supply chain management. Inf Sci 177(20):4241–4255CrossRefGoogle Scholar
  2. 2.
    Averbakh I (2010) On-line integrated production-distribution scheduling problems with capacitated deliveries. Eur J Oper Res 200(2):377–384CrossRefGoogle Scholar
  3. 3.
    Liu B (2002) Theory and practice of uncertain programming. Physica-Verlag, Heidelberg pp 235–238Google Scholar
  4. 4.
    Bilgen B, Ozkarahan I (2004a) Strategic tactical and operational production-distribution models: a review. Int J Technol Manage 28(2):151–171CrossRefGoogle Scholar
  5. 5.
    Erengüç ŞS, Simpson NC, Vakharia AJ (1999) Integrated production/distribution planning in supply chains: an invited review. Eur J Oper Res 115(2):219–236CrossRefGoogle Scholar
  6. 6.
    Fogel DB (2006) Evolutionary computation: Toward a new philosophy of machine intelligence, vol 1. Wiley.comGoogle Scholar
  7. 7.
    Gen M, Cheng R (1997) Genetic algorithms and engineering design. Wiley, New JerseyGoogle Scholar
  8. 8.
    Glodberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addion Wesley, ReadingGoogle Scholar
  9. 9.
    Heilpern S (1992) The expected value of a fuzzy number. Fuzzy Sets Syst 47(1):81–86CrossRefGoogle Scholar
  10. 10.
    Hua G, Wang S, Chan CK (2009) A fractional programming model for internation facility location. J Ind Manage Optim 5:629–649 (in Chinese)CrossRefGoogle Scholar
  11. 11.
    Holland J (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann ArborGoogle Scholar
  12. 12.
    Kruse R, Meyer KD (1987) Statistics with vague data, vol 6. Springer.Google Scholar
  13. 13.
    Kwakernaak H (1978) Fuzzy random variables-I. definitions and theorems. Inf Sci 15(1):1–29Google Scholar
  14. 14.
    Kwakernaak H (1979) Fuzzy random variables-II, algorithms and examples for the discrete case. Inf Sci 17(3):253–278CrossRefGoogle Scholar
  15. 15.
    Lee YH, Kim SH (2002) Production-distribution planning in supply chain considering capacity constraints. Comput Ind Eng 43(1):169–190CrossRefGoogle Scholar
  16. 16.
    Liang TF (2008a) Fuzzy multi-objective production/distribution planning decisions with multi-product and multi-time period in a supply chain. Comput Ind Eng 55(3):676–694CrossRefGoogle Scholar
  17. 17.
    Liang TF (2008b) Integrating production-transportation planning decision with fuzzy multiple goals in supply chains. Int J Prod Res 46(6):1477–1494CrossRefGoogle Scholar
  18. 18.
    Liang TF, Cheng HW et al (2011) Application of fuzzy sets to aggregate production planning with multiproducts and multitime periods. IEEE Trans Fuzzy Syst 19(3):465–477CrossRefGoogle Scholar
  19. 19.
    Michalewicz Z (1996) Genetic algorithms \(+\) data structures \(=\) evolution programs. springer.Google Scholar
  20. 20.
    Petrovic D, Roy R, Petrovic R (1998) Modelling and simulation of a supply chain in an uncertain environment. Eur J Oper Res 109(2):299–309CrossRefGoogle Scholar
  21. 21.
    Sarmiento AM, Nagi R (1999) A review of integrated analysis of production-distribution systems. IIE Trans 31(11):1061–1074Google Scholar
  22. 22.
    Selim H, Araz C, Ozkarahan I (2008a) Collaborative production-distribution planning in supply chain: a fuzzy goal programming approach. Transp Res Part E: Logistics Transp Rev 44(3):396–419CrossRefGoogle Scholar
  23. 23.
    Vidal CJ, Goetschalckx M (1997a) Strategic production-distribution models: A critical review with emphasis on global supply chain models. Eur J Oper Res 98(1):1–18Google Scholar
  24. 24.
    Wang RC, Liang TF (2004a) Application of fuzzy multi-objective linear programming to aggregate production planning. Comput Ind Eng 46(1):17–41CrossRefGoogle Scholar
  25. 25.
    Xu JP, Pei W (2013) Production-distribution planing of construction supply chain management under fuzzy random environment for large-scale construction projects. J Ind Manage Optim 9(1):31–56 (in Chinese)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Muhammad Nazim
    • 1
  • Muhammad Hashim
    • 1
  • Abid Hussain Nadeem
    • 1
  • Liming Yao
    • 1
  • Jamil Ahmad
    • 1
  1. 1.Uncertainty Decision-Making LaboratorySichuan UniversityChengdu  People’s Republic of China

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