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A Multi-item Inventory Model with Fuzzy Rough Coefficients via Fuzzy Rough Expectation

  • Totan Garai
  • Dipankar Chakraborty
  • Tapan Kumar Roy
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 225)

Abstract

In this paper, we concentrated on developing a multi-item inventory model under fuzzy rough environment. Here, demand and holding cost rates are assumed as the functions of stock level. Fuzzy rough expectation method is used to transform the present fuzzy rough inventory model into its equivalent crisp model. A numerical example is provided to illustrate the proposed model. To show the validity of the proposed models, few sensitivity analyses are also presented under the major parameter, and the results are illustrated numerically and graphically.

Keywords

Multi-item inventory Trapezoidal fuzzy rough variable Fuzzy rough expectation 

References

  1. 1.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)CrossRefzbMATHGoogle Scholar
  2. 2.
    Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1, 3–28 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Ishii, H., Konno, T.: A stochastic inventory problem with fuzzy shortage cost. Eur. J. Oper. Res. 106, 90–94 (1998)CrossRefGoogle Scholar
  4. 4.
    Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Int. J. Gen. Syst. 17, 191–208 (1990)CrossRefzbMATHGoogle Scholar
  5. 5.
    Morsi, N.N., Yakout, M.M.: Axiomatics for fuzzy rough sets. Fuzzy Sets Syst. 100, 327–342 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Radzikowska, M.A., Kerre, E.E.: A comparative study of rough sets. Fuzzy Sets Syst. 126, 137–155 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Liu, B.: Theory and Practice of Uncertain Programming. Physica-Verlag, Heidelberg (2002)CrossRefzbMATHGoogle Scholar
  8. 8.
    Mondal, M., Maity, K.A., Maiti, K.M., Maiti, M.: A production-repairing inventory model with fuzzy rough coefficients under inflation and time value of many. Appl. Math. Model. 37, 3200–3215 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Xu, J., Zhao, L.: A multi-objective decision-making model with fuzzy rough coefficients and its application to the inventory problem. Inf. Sci. 180, 679–696 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Maiti, M.K., Maiti, M.: Production policy for damageable items with variable cost function in an imperfect production process via genetic algorithm. Math. Comput. Model. 42, 977–990 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Khouja, M.: The economic production lot size model under volume flexibility. Comput. Oper. Res. 22, 515–525 (1995)CrossRefzbMATHGoogle Scholar
  12. 12.
    Maity, K.A.: One machine multiple-product problem with production-inventory system under fuzzy inequality constraint. Appl. Soft Comput. 11, 1549–1555 (2011)CrossRefGoogle Scholar
  13. 13.
    Xu, J., Zaho, L.: A class of fuzzy rough expected value multi-objective decision making model and its application to inventory problems. Comput. Math. Appl. 56, 2107–2119 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Lushu, S., Nair, K.P.K.: Fuzzy models for single-period inventory model. Fuzzy Sets Syst. 132, 273–289 (2002)CrossRefzbMATHGoogle Scholar
  15. 15.
    Li, F.D.: An approach to fuzzy multi-attribute decision-making under uncertainty. Inf. Sci. 169, 97–112 (2005)CrossRefzbMATHGoogle Scholar
  16. 16.
    Balkhi, Z.T., Foul, A.: A multi-item production lot size inventory model with cycle dependent parameters. Int. J. Math. Model. Methods Appl. Sci. 3, 94–104 (2009)Google Scholar
  17. 17.
    Hartley, R.: An existence and uniqueness theorem for an optimal inventory problem with forecasting. J. Math. Anal. Appl. 66, 346–353 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Lee, H., Yao, J.S.: Economic production quantity for fuzzy demand quantity and fuzzy production quantity. Eur. J. Oper. Res. 109, 203–211 (1998)CrossRefzbMATHGoogle Scholar
  19. 19.
    Taleizadeh, A.A., Sadjadi, S.J., Niaki, S.T.A.: Multi-product EPQ model with single machine, back-ordering and immediate rework process. Eur. J. Ind. Eng. 5, 388–411 (2011)CrossRefGoogle Scholar
  20. 20.
    Dutta, P., Chakraborty, D., Roy, R.A.: An inventory model for single-period products with reordering opportunities under fuzzy demand. 53, 1502–1517 (2007)Google Scholar
  21. 21.
    Chang, T.C.: An EOQ model with deteriorating items under inflation when supplier credits linked to order quantity. Int. J. Prod. Econ. 88, 6159–6167 (2004)CrossRefGoogle Scholar
  22. 22.
    Shi, Y., Yao, L., Xu, J.: A probability maximization model based on rough approximation and its application to the inventory problem. Int. J. Approx. Reason. 52, 261–280 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Wang, Y.: Mining stock price using fuzzy rough set system. Expert Syst. Appl. 24, 13–23 (2003)CrossRefGoogle Scholar
  24. 24.
    Taleizadeh, A.A., Wee, M.H., Jolai, F.: Revisiting a fuzzy rough economic order quantity model for deteriorating items considering quantity discount and prepayment. Math. Comput. Model. 57, 1466–1479 (2013)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Kazemi, N., Olugu, U.E., Rashid, H.S., Ghazilla, R.A.R.: A fuzzy EOQ model with back orders and forgetting effect on fuzzy parameters: an empirical study. Comput. Ind. Eng. 96, 140–148 (2016)CrossRefGoogle Scholar
  26. 26.
    Bazan, E., Jaber, Y.M., Zanoni, S.: A review of mathematical inventory models for reverse logistics and the future of its modelling: an environmental perspective. Appl. Math. Model. 40, 4151–4178 (2016)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Das, C.B., Das, B., Mondal, K.S.: An integrated production inventory model under interactive fuzzy credit period for deteriorating item with several markets. Appl. Soft Comput. 28, 453–465 (2015)CrossRefGoogle Scholar
  28. 28.
    Xu, J., Zaho, L.: Fuzzy Link Multiple-Object Decision Making. Springer, Berlin (2009)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Totan Garai
    • 1
  • Dipankar Chakraborty
    • 2
  • Tapan Kumar Roy
    • 1
  1. 1.Department of MathematicsIndian Institute of Engineering Science and Technology, ShibpurHowrahIndia
  2. 2.Department of MathematicsHeritage Institute of TechnologyAnandapur, KolkataIndia

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