Optimizing a Production Inventory Model with Exponential Demand Rate, Exponential Deterioration and Shortages

  • M. Dhivya LakshmiEmail author
  • P. Pandian
Conference paper
Part of the Trends in Mathematics book series (TM)


A production inventory model having an exponential deterioration rate with an exponential demand rate and shortages is considered. In this model, the production rate is a function of the demand rate. The total inventory cost per cycle, the cycle length, the shortage and the production lengths are optimized. Numerical example of the proposed model is presented.


  1. 1.
    Baker, R.C., Urban, T.L.: A deterministic inventory system with an inventory level dependent demand rate. J. Oper. Res. Soc. 39(9), 823–831 (1988)zbMATHGoogle Scholar
  2. 2.
    Begum, R., Sahu, S.K., Sahoo, R.R.: An inventory model with exponential demand rate, finite production rate and shortages. J. Sci. Res. 1(3), 473–483 (2009)Google Scholar
  3. 3.
    Begum, R., Sahu, S.K., Sahoo, R.R.: An inventory model for deteriorating items with quadratic demand and partial backlogging. Br. J. Appl. Sci. Technol. 2(2), 112–131 (2012)Google Scholar
  4. 4.
    Bhanu Priya Dash, Trailokyanath Singh, Hadibandhu Pattnayak.: An inventory model for deteriorating items with exponential declining demand and time-varying holding cost. Am. J. Oper. Res. 4, 1–7 (2014)Google Scholar
  5. 5.
    Geetha, K., Anusheela, N., Raja, A.: An optimum inventory model for time dependent demand with shortages. Int. J. Math. Archive. 7(10), 99–102 (2016)Google Scholar
  6. 6.
    Ghare, P., Schrader, G.: A model for an exponentially decaying inventory. J. Ind. Eng.14, 238–243 (1963)Google Scholar
  7. 7.
    Gupta, R., Vrat, P.: Inventory model for stock-dependent consumption rate. Opsearch. 23, 19–24 (1986)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Harris, F.: Operations and cost. Chicago AW Shaw Co (1915)Google Scholar
  9. 9.
    Jhuma Bhowmick, Samanta, G.P.: A deterministic inventory model of deteriorating items with two rates of production, shortages and variable production cycle. International Scholarly Research Notices. ISRN Applied Mathematics. 2011, (2011). Scholar
  10. 10.
    Liang-Yuh Ouyang, Kun-Shan WU, Mei-Chuan Cheng.: An inventory model for deteriorating items with exponential declining demand and partial backlogging. Yugosl. J. Oper. Res. 15(2), 277–288 (2005)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Madhu Jain, Sharma, G.C., Shalini Rathore.: Economic production quantity models with shortage, price and stock-dependent demand for deteriorating items. IJE Transactions A: Basics. 20(2), 159–168 (2007)Google Scholar
  12. 12.
    Niketa J. Mehta, Nita H. Shah.: An inventory model for deteriorating items with exponentially increasing demand and shortages under inflation and time discounting. Investigacao Operacional. 23, 103–111 (2003)Google Scholar
  13. 13.
    Rekha Rani Chaudhary, Vikas Sharma.: Optimal inventory model with weibull deterioration with trapezoidal demand and shortages. Int. J. Eng. Res. Technol. 2(3), 1–10 (2013)Google Scholar
  14. 14.
    Sahoo, C.K., Sahoo, S.K.: An Inventory Model with Linear Demand Rate, Finite Rate of Production with Shortages and Complete Backlogging. Proceedings of the 2010 International Conference on Industrial Engineering and Operations Management. Dhaka Bangladesh (2010)Google Scholar
  15. 15.
    Samanta, G.P., Ajanta Roy.: A production inventory model with deteriorating items and shortages. Yugosl. J. Oper. Res. 14(2), 219–230 (2004)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Sarkar, S., Chakrabarti, T.: An EPQ model having weibull distribution deterioration with exponential demand and production with shortages under permissible delay in payments. Mathematical Theory and Modeling. 3(1), 1–6 (2013)Google Scholar
  17. 17.
    Seyed Reza Moosavi Tabatabaei, Seyed Jafar Sadjadi, Ahmad Makui.: Optimal pricing and marketing planning for deteriorating items. PLOS ONE. 12(3), pp. 1–21 (2017)Google Scholar
  18. 18.
    Sharmila, D., Uthayakumar, R.: Inventory model for deteriorating items involving fuzzy with shortages and exponential demand. Int. J. Supply. Oper. Manag. 2(3), 888–904 (2015)Google Scholar
  19. 19.
    Sheikh, S.R., Raman Patel.: Production inventory model with different deterioration rates under shortages and linear demand. International Refereed Journal of Engineering and Science. 5(3), 01–07 (2016)Google Scholar
  20. 20.
    Shital S. Patel.: Production inventory model for deteriorating items with different deterioration rates under stock and price dependent demand and shortages under inflation and permissible delay in payments. Global J. Pure. Appl. Math. 13(7), 3687–3701 (2017)Google Scholar
  21. 21.
    Shukla, H.S., Vivek Shukla, Sushil Kumar Yadav.: EOQ model for deteriorating items with exponential demand rate and shortages. Uncertain Supply Chain Management. 1, 67–76 (2013)Google Scholar
  22. 22.
    Sunil V. Kawale, Pravin B. Bansode.: An inventory model for time varying holding cost and weibull distribution for deterioration with fully backlogged shortages. Int. J. Math. Trends. Technol. 4(10), 201–206 (2013)Google Scholar
  23. 23.
    Wee, H.M.: A deterministic lot-size inventory model for deteriorating items with shortages and a declining market. Comput. Oper. Res. 22, 345–356 (1995)zbMATHGoogle Scholar
  24. 24.
    Whitin, T.M.: The theory of inventory management. Princeton University Press. New Jersey USA (1957)Google Scholar

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsVITVelloreIndia

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