Skip to main content

A Bilevel Programming Model for an Agriculture Production-Distribution System with Fuzzy Random Parameters

  • Conference paper
  • First Online:
Proceedings of the Eighth International Conference on Management Science and Engineering Management

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 280))

Abstract

In this paper, we focus on a production-distribution system consists of a producer and a distribution center. We formulate a bilevel multiobjective programming model for it. The upper model is to maximize the producer’s profit and the lower model is to maximize both the distribution center’s profit and customers’ satisfaction degree. Some decision parameters, including unit production cost, customers’ demand and unit sale price, are assumed as fuzzy random variables due to complex decision environment. Chance-constrained technique are used to tackle the uncertainty of this model. A modified genetic algorithm is be used to solve the problem. A numerical example illustrates the effectiveness and efficiency of the model and the algorithm.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Aliev R, Fazlollahi B et al (2007) Fuzzy-genetic approach to aggregate production-distribution planning in supply chain management. Inf Sci 177(20):4241–4255

    Article  Google Scholar 

  2. Bard J (1984) Optimality conditions for the bilevel programming problem. Naval Res Logistics Q 31(1):13–26

    Article  Google Scholar 

  3. Ben-Ayed O, Blair CE (1990) Computational difficulties of bilevel linear programming. Oper Res 38(3):556–560

    Article  Google Scholar 

  4. Boudia M, Prins C (2009) A memetic algorithm with dynamic population management for an integrated production-distribution problem. Eur J Oper Res 195(3):703–715

    Article  Google Scholar 

  5. Charnes A, Cooper WW (1959) Chance-constrained programming. Manage Sci 6(1):73–79

    Article  Google Scholar 

  6. Dempe S, Gadhi N (2010) Second order optimality conditions for bilevel set optimization problems. J Global Optim 47(2):233–245

    Article  Google Scholar 

  7. Gil M (2001) Fuzzy random variables. Inf Sci 133:1–2

    Google Scholar 

  8. Hu T, Guo X et al (2010) A neural network approach for solving linear bilevel programming problem. Knowl-Based Syst 23(3):239–242

    Article  Google Scholar 

  9. Kwakernaak H (1978) Fuzzy random variables-I. Definitions and theorems. Inf Sci 15(1):1–29

    Google Scholar 

  10. Kwakernaak H (1979) Fuzzy random variables-II. Algorithms and examples for the discrete case. Inf Sci 17(3):253–278

    Article  Google Scholar 

  11. López-Diaz M, Gil M (1997) Constructive definitions of fuzzy random variables. Stat Probab Lett 36(2):135–143

    Article  Google Scholar 

  12. Luhandjula M (1996) Fuzziness and randomness in an optimization framework. Fuzzy Sets Syst 77(3):291–297

    Article  Google Scholar 

  13. Lukač Z, Šorić K, Rosenzweig V (2008) Production planning problem with sequence dependent setups as a bilevel programming problem. Eur J Oper Res 187(3):1504–1512

    Article  Google Scholar 

  14. Puri M, Ralescu D (1986) Fuzzy random variables. J Math Anal Appl 114(2):409–422

    Article  Google Scholar 

  15. Vicente L, Savard G, Júdice J (1994) Descent approaches for quadratic bilevel programming. J Optim Theory Appl 81(2):379–399

    Article  Google Scholar 

  16. Yan C, Banerjee A, Yang L (2011) An integrated production-distribution model for a deteriorating inventory item. Int J Prod Econ 133(1):228–232

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported by the Programs of NSFC (Grant No. 70831005, 71273036, 71302134), Projects of International Cooperation and Exchanges NSFC (Grant No. 71011140076), the Research Foundation of Ministry of Education for the Doctoral Program of Higher Education of China (Grant No. 20130181110063), “985” Program of Sichuan University (Innovative Research Base for Economic Development and Management), Sichuan University Young Teachers Scientific Research Start Funds (Grant No. 2012SCU11016) and the Key Program of Sichuan System Science and Enterprise Development Research Center (Grant No.Xq13B04).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhimiao Tao .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Tao, Z., Qian, X. (2014). A Bilevel Programming Model for an Agriculture Production-Distribution System with Fuzzy Random Parameters. In: Xu, J., Cruz-Machado, V., Lev, B., Nickel, S. (eds) Proceedings of the Eighth International Conference on Management Science and Engineering Management. Advances in Intelligent Systems and Computing, vol 280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55182-6_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-55182-6_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-55181-9

  • Online ISBN: 978-3-642-55182-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics