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An Economic Production Quantity Problem with Fuzzy Backorder and Fuzzy Demand

  • József Mezei
  • Kaj-Mikael Björk
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 206)

Abstract

Optimization models based on fuzzy set theory are relevant to the process industry, where there are many uncertainties that are inherently fuzzy. In this paper, we incorporate backorders (i.e the inventory to go below zero) and cycle time in a fuzzy Economic Production Quantity (EPQ) model. The uncertainties in the backorders and in the demand for different products are modeled using triangular possibility distributions. We illustrate the model with an example that describes a typical decision making problem in the paper industry.

Keywords

Economic Production Quantity Fuzzy Sets Signed Distance Production optimization Supply Chain Management 

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References

  1. 1.
    APICS Dictionary, 8th ed., American Production and Inventory Control Society, Falls Church, VA (1995)Google Scholar
  2. 2.
    Finland in Figures - National Accounts, Statistics Finland, http://www.stat.fi/tup/suoluk/suoluk_kansantalous_en.html (retrieved September 18, 2012)
  3. 3.
    Finland in Figures - Manufacturing, Statistics Finland, http://www.stat.fi/tup/suoluk/suoluk_teollisuus_en.html (retrieved September 18, 2012)
  4. 4.
    Harris, F.W.: How many parts to make at once. The Magazine of Management 10, 135–136 (1913)Google Scholar
  5. 5.
    Björk, K.-M.: Supply Chain Efficiency with Some Forest Industry Improvements. Doctoral dissertation (Business Administration), Abo Akademi University (2006) ISBN 952-12-1782-0 Google Scholar
  6. 6.
    Bj\"{o}rk, K.-M., Carlsson, C.: The Effect of Flexible Lead Times on a Paper Producer. International Journal of Production Economics 107(1), 139–150 (2007)CrossRefGoogle Scholar
  7. 7.
    Zadeh, L.A.: Outline of a new Approach to the Analysis of Complex Systems and Decision Processes. IEEE Transactions on Systems, Man and Cybernetics, SMC-3, 28–44 (1973)Google Scholar
  8. 8.
    Liberatore, M.J.: The EOQ model under stochastic lead time. Operations Research 27, 391–396 (1979)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Björk, K.-M., Carlsson, C.: The Outcome of Imprecise Lead Times on the Distributors. In: Proceedings of the 38th Annual Hawaii International Conference on System Sciences (HICSS 2005), pp. 81–90 (2005)Google Scholar
  10. 10.
    Carlsson, C., Fullér, R.: Soft computing and the Bullwhip effect. Economics and Complexity 2(3), 1–26 (1999)Google Scholar
  11. 11.
    Chang, S.-C., Yao, J.-S., Lee, H.-M.: Economic reorder point for fuzzy backorder quantity. European Journal of Operational Research 109, 183–202 (1998)MATHCrossRefGoogle Scholar
  12. 12.
    Björk, K.-M.: An Analytical Solution to a Fuzzy Economic Order Quantity Problem. International Journal of Approximate Reasoning 50, 485–493 (2009)MATHCrossRefGoogle Scholar
  13. 13.
    Yao, J.S., Wu, K.: Ranking fuzzy numbers based on decomposition principle and signed distance. Fuzzy Sets and Systems 116, 275–288 (2000)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Yao, J.-S., Ouyang, L.-Y., Chiang, J.: Models for a fuzzy inventory of two replaceable merchandises without backorders based on the signed distance of fuzzy sets. European Journal of Operational Research 150, 601–616 (2003)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Yao, J.S., Chiang, J.: Inventory without backorder with fuzzy total cost and fuzzy storing cost defuzzified by centroid and signed distance. European Journal of Operational Research 148, 401–409 (2003)MATHCrossRefGoogle Scholar
  16. 16.
    Björk, K.-M.: The economic production quantity problem with a finite production rate and fuzzy cycle time. In: 41th Annual Hawaii International Conference on System Sciences, HICSS 2008 (2008)Google Scholar
  17. 17.
    Björk, K.-M.: A Multi-item Fuzzy Economic Production Quantity Problem with a Finite Production Rate. International Journal of Production Economics 135(2), 702–707 (2011)Google Scholar
  18. 18.
    Kazemi, N., Ehsani, E., Jaber, M.Y.: An inventory model with backorders with fuzzy parameters and decision variables. International Journal of Approximate Reasoning 51, 964–972 (2012)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Lee, H.M., Yao, J.S.: Economic production quantity for fuzzy demand quantity, and fuzzy production quantity. European Journal of Operational Research 109, 203–211 (1998)MATHCrossRefGoogle Scholar
  20. 20.
    Bag, S., Chakraborty, D., Roy, A.R.: A production inventory model with fuzzy random demand and with flexibility and reliability considerations. Computers & Industrial Engineering 56, 411–416 (2009)CrossRefGoogle Scholar
  21. 21.
    Wang, X., Tang, W.: Fuzzy EPQ inventory models with backorder. Journal of Systems Science and Complexity 22, 313–323 (2009)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.IAMSRÅbo Akademi UniversityTurkuFinland
  2. 2.Arcada University of Applied SciencesHelsinkiFinland

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