A Fuzzified Production Model with Time Varying Demand Under Shortages and Inflation

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 236)

Abstract

We develop an inventory model with time-dependent demand rate and deterioration, allowing shortages. The production rate is assumed to be finite and proportional to the demand rate. The shortages are partially backlogged with time-dependent rate. Inflation is also taken in this model. Inflation plays a very significant role in inventory policy. We developed the model in both fuzzy and crisp sense. The model is solved logically to obtain the optimal solution of the problem. It is then illustrated with the help of numerical examples. Sensitivity of the optimal solution with respect to changes in the values of the system parameters is also studied.

Keywords

Time-dependent demand Shortages Deterioration Fuzzy 

References

  1. 1.
    Bierman, H., Thomas, J.: Inventory decisions under inflationary condition. Deci. Sci. 8(1), 151–155 (1977)CrossRefGoogle Scholar
  2. 2.
    Brahmbhatt, A.C.: Economic order quantity under variable rate of inflation and mark-up prices. Productivity 23, 127–130 (1982)Google Scholar
  3. 3.
    Buzacott, J.A.: Economic order quantities with inflation. Oper. Res. Quart. 26(3), 553–558 (1975)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Chakrabarti, T., Giri, B.C., Chaudhuri, K.S.: An EOQ model for items weibull distribution deterioration shortages and trended demand: an extension of philip’s model. Comp. Oper. Res. 25, 649–657 (1998)CrossRefGoogle Scholar
  5. 5.
    Chang, H.C., Yao, J.S., Ouyang, L.Y.: Fuzzy mixture inventory model with variable lead-time based on probabilistic fuzzy set and triangular fuzzy number. Math. Comp. Mode. 39(2–3), 287–304 (2004)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Chang, H.C., Yao, J.S., Ouyang, L.Y.: Fuzzy mixture inventory model involving fuzzy random variable lead time demand and fuzzy total demand. Euro. J. Oper. Res. 169(1), 65–80 (2006)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Chen, S.H., Wang, C.C.: Backorder fuzzy inventory model under functional principle. Inf. Sci. 95, 71–79 (1996)CrossRefGoogle Scholar
  8. 8.
    Covert, R.P., Philip, G.C.: An EOQ model for items with weibull distribution deterioration. AIIE Trans. 5, 323–326 (1973)CrossRefGoogle Scholar
  9. 9.
    Dave, U.: On a discrete-in-time order-level inventory model for deteriorating items. Oper. Res. 30, 349–354 (1979)MATHGoogle Scholar
  10. 10.
    Ghare, P.M., Schrader, S.F.: A model for exponentially decaying inventory. J. Ind. Eng. 14, 238–243 (1963)Google Scholar
  11. 11.
    Goyal, S.K., Gunasekaran, A.: An integrated production-inventory-marketing model for deteriorating items. Comp. Ind. Eng 28(4), 755–762 (1995)CrossRefGoogle Scholar
  12. 12.
    Goyal, S.K., Giri, B.C.: Recent trends in modeling of deteriorating inventory. Euro. J. Oper. Res. 134, 1–16 (2001)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Kang, S., Kim, I.: A study on the price and production level of the deteriorating inventory system. Int. J. Prod. Res. 21, 899–908 (1983)CrossRefMATHGoogle Scholar
  14. 14.
    Lee, H.M., Yao, J.S.: Economic order quantity in fuzzy sense for inventory without backorder model. Fuzzy Sets Syst. 105, 13–31 (1999)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Misra, R.B.: Optimum production lot-size model for a system with deteriorating inventory. Int. J. Prod. Res. 13(5), 495–505 (1975)CrossRefGoogle Scholar
  16. 16.
    Misra, R.B.: A study of inflation effects on inventory system. Logi. Spect. 9(3), 260–268 (1997)Google Scholar
  17. 17.
    Moon, I., Yun, W.: A note on evaluating inventory systems: a net present value frame work. Eng. Econ. 39(1), 93–99 (1993)CrossRefGoogle Scholar
  18. 18.
    Nayebi, M.A., Sharifi, M., Shahriari, M.R., Zarabadipour, O.: Fuzzy-chance constrained multi-objective programming applications for inventory control model. App. Math. Sci. 6(5), 209–228 (2012)MATHGoogle Scholar
  19. 19.
    Raafat, F.: Survey of literature on continuously deteriorating inventory models. J. Oper. Res. Soci. 42, 27–37 (1991)MATHGoogle Scholar
  20. 20.
    Simmons, D., Cheng, J.: An alternative approach to computing economic run quantity. Int. J. Prod. Res. 56(3), 837–847 (2008)CrossRefGoogle Scholar
  21. 21.
    Singh, S.R., Bhatia, D.: Fuzzy inventory model for non-instantaneous perishable products under inflation. Int. J. Man. Res. Tech. 4(2), 261–270 (2010)Google Scholar
  22. 22.
    Singh, S.R., Kumar, T., Gupta, C.B.: Optimal replenishment policy for ameliorating item with shortages under inflation and time value of money using genetic algorithm. Int. J. Comp. App. 27(1), 5–17 (2011)MathSciNetGoogle Scholar
  23. 23.
    Teng, J.T., Chang, C.T.: Economic production quantity models for deteriorating itemswith price- and stock-dependent demand. Comp. Oper. Res. 32(2), 297–308 (2005)CrossRefMATHMathSciNetGoogle Scholar
  24. 24.
    Vojosevic, M., Petrovic, D., Petrovic, R.: EOQ formula when inventory cost is fuzzy. Int. J. Prod. Eco. 45, 499–504 (1996)CrossRefGoogle Scholar
  25. 25.
    Wee, H.M.: Economic production lot-size model for deteriorating items with partial backordering. Comp. Ind. Eng. 20(2), 187–197 (1993)Google Scholar
  26. 26.
    Wee, H.M., Jong, J.F.: An integrated multi-lot-size production inventory modelfor deteriorating items. Manage. Syst. 5, 97–114 (1998)Google Scholar
  27. 27.
    Yang, P.C., Wee, H.M.: Economic order policy of deteriorated item for vendor and buyer: an integrated approach. Prod. Plan. Cont. 11, 474–480 (2000)CrossRefGoogle Scholar
  28. 28.
    Yao, J.S., Chang, S.C., Su, J.S.: Fuzzy inventory without backorder for fuzzy order quantity and fuzzy total demand quantity. Comp. Oper. Res. 27, 935–962 (2000)CrossRefMATHGoogle Scholar
  29. 29.
    Zadeh, L.: Fuzzy sets. Inf. control 8, 338–353 (1965)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Centre of Mathematical SciencesBanasthali UniversityBanasthaliIndia
  2. 2.Department of MathematicsD.N. CollegeMeerutIndia

Personalised recommendations