An Production Inventory Model with Imperfect Production and Risk

  • Kartik Patra
Original Paper


A single item production system has been considered in this proposed work. It is also assumed that the system produced some imperfect items. For this purpose a screening process has been considered here to separate the perfect quality items and imperfect quality items. The perfect quality items have a demand in the market which is depended on the advertisement of the product as well as the selling price of the product. The imperfect quality items are sold in a lot after the production period. As the depreciation rate of the product increases and number of imperfect product increases then there will be a risk in the system of loss in profit. So a risk function has been considered here depending on the depreciation rate of the demand and imperfect production rate of the item. Keeping these phenomenon the proposed model has been maximize for profit and minimize for the risk with numerical illustration.


Imperfect product Risk Screening process Advertizement 


  1. 1.
    Taft, E.W.: The most economical production lot. Iron Age 101, 1410–1412 (1918)Google Scholar
  2. 2.
    Harris, F.W.: Operations and Cost. Factory Management Service. A.W. Shaw co, Chicago (1915)Google Scholar
  3. 3.
    Goyal, S.K., Gunasekaran, A.: An integrated production inventory marketing model for deteriorating items. Comput. Ind. Eng. 28(4), 755–762 (1995)CrossRefGoogle Scholar
  4. 4.
    Cho, I.D.: Analysis of optimal production and adverting policies. Int. J. Syst. Sci. 27(12), 1297–1305 (1996)CrossRefzbMATHGoogle Scholar
  5. 5.
    Rosenblatt, M.J., Lee, H.L.: Economic production cycles with imperfect production processes. IIE Trans. 18(1), 48–55 (1986)CrossRefGoogle Scholar
  6. 6.
    Salameh, M.K., Jaber, M.Y.: Economic production quantity model for items with iperfect quality. Int. J. Prod. Econ. 64, 59–64 (2000)CrossRefGoogle Scholar
  7. 7.
    Skouri, K., Papachristos, S.: A continuous review inventory model, with deteriorating items, time-varying demand, linear replenishment cost, partially time-varying backlogging. Appl. Math. Model. 26(5), 603–617 (2002)CrossRefzbMATHGoogle Scholar
  8. 8.
    Roy, A., Maity, K., Kar, S., Maiti, M.: A production-inventory model with remanufacturing for defective and usable items in fuzzy-environment. Comput. Ind. Eng. 56(1), 87–96 (2009)CrossRefGoogle Scholar
  9. 9.
    Sicilia, J., Gonzlez-De-la-Rosa, M., Febles-Acosta, J., Alcaide-Lpez-de-Pablo, D.: An inventory model for deteriorating items with shortages and time-varying demand. Int. J. Prod. Econ. 155, 155–162 (2014)CrossRefGoogle Scholar
  10. 10.
    Patra, K., Mondal, S.K.: A single item inventory model with variable production rate and defective items. Int. J. Appl. Comput. Math. (2015). Google Scholar
  11. 11.
    Das, B.C., Das, B., Mondal, S.K.: An integrated production-inventory model with defective item dependent stochastic credit period. Comput. Ind. Eng. 110, 255–263 (2017)CrossRefGoogle Scholar
  12. 12.
    Manna, A.K., Dey, J., Mondal, S.K.: Imperfect production inventory model with production rate dependent defective rate and advertisement dependent demand. Comput. Ind. Eng. 104, 9–22 (2017)CrossRefGoogle Scholar
  13. 13.
    Mandal, B.N., Phaujdar, S.: An inventory model for deteriorating items and stock dependent consumption rate. J. Oper. Res. Soc. 40, 483–488 (1989)CrossRefzbMATHGoogle Scholar
  14. 14.
    El-Gohary, A.A., Tadj, L., Al-Rasheed, A.F.: Using optimal control to adjust the production rate of a deteriorating inventory system. J. Taibah Univ. Sci. 2, 69–77 (2009)CrossRefGoogle Scholar
  15. 15.
    Teng, J.T., Chang, C.T.: Economic production quantity models for deteriorating items with price and stock dependent demand. Comput. Oper. Res. 32, 297–308 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Mishra, V.K., Singh, L., Kumar, R.: An inventory model for deteriorating items with time-dependent demand and time-varying holding cost under partial backlogging. J. Ind. Eng. Int. 9(4), 1–5 (2013)Google Scholar
  17. 17.
    Uthayakumar, R., Karuppasamy, S.K.: A pharmaceutical inventory model for variable demand and variable holding cost with partially backlogged under permissible delay in payments in healthcare industries. Int. J. Appl. Comput. Math. 3(Suppl 1), 327 (2017)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Chen, S.M., Munif, A., Chen, G.S., Liu, H.C., Kuo, B.C.: Fuzzy risk analysis based on ranking generalized fuzzy numbers with different left heights and right heights. Expert Syst. Appl. 39(2012), 6320–6334 (2012)CrossRefGoogle Scholar
  19. 19.
    Chen, S.M., Wang, C.H.: Fuzzy risk analysis based on ranking fuzzy numbers using \(\alpha \)-cuts, belief features and signal/noise ratios. Expert Syst. Appl. 36(2009), 5576–5581 (2009)CrossRefGoogle Scholar
  20. 20.
    Chen, S.M., Sanguansat, K.: Analyzing fuzzy risk based on a new fuzzy ranking method between generaized fuzzy numbers. Expert Syst. Appl. 38, 2163–2171 (2011)CrossRefGoogle Scholar
  21. 21.
    Patra, K., Mondal, S.K.: Risk analysis in diabetes prediction based on a new approach of ranking of generalized trapezoidal fuzzy numbers. Cybernet. Syst. Int. J. 43(8), 623–650 (2012)CrossRefzbMATHGoogle Scholar
  22. 22.
    Patra, K., Mondal, S.K.: Fuzzy risk analysis using area and height based similarity measure on generalized trapezoidal fuzzy numbers and its application. Appl. Soft Comput. 28, 276–284 (2015)CrossRefGoogle Scholar
  23. 23.
    Patra, K., Mondal, S.K.: Risk analysis in a production inventory model with fuzzy demand, variable production rate and production time dependenet selling price. Opsearch. 52(3), 505–529 (2015)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer (India) Private Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsVivekananda Satabarshiki MahavidyalayaManikparaIndia

Personalised recommendations