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An EPQ model for delayed deteriorating items with quadratic demand and linear holding cost

  • S. DariEmail author
  • B. Sani
Theoretical Article
  • 6 Downloads

Abstract

In this paper, an EPQ model for delayed deteriorating items is presented, where the demand before deterioration sets in is assumed to be time dependent quadratic demand and the holding (carrying) cost is assumed to be linearly dependent on time. Three stages are considered as follows: (1) production build up period, (2) period before deterioration starts and, (3) period after deterioration sets in. There is no demand during production build up period and the demand before deterioration begins is assumed to be quadratic time dependent while that after deterioration sets in is assumed to be constant. It is also assumed that shortages are not allowed. The purpose of this paper is to investigate the optimal set of production rates that minimizes the total inventory cost per unit time, the best cycle length and the economic production quantity. A numerical example is given to illustrate the applicability of the model and sensitivity analysis carried out on the example to see the effect of changes on some system parameters.

Keywords

Delayed deterioration Quadratic demand EPQ model Linear holding cost 

Notes

Acknowledgements

The authors thank the unknown referees and the editor for their constructive suggestions and remarks, which greatly helped to improve the appearance of the paper.

References

  1. 1.
    Agatamudi, L.R., Geremew, M.: An EOQ model for deteriorating items with power demand and time—varying holding cost. IOSR J. Math. 12(5), 40–45 (2016)CrossRefGoogle Scholar
  2. 2.
    Baraya, Y.M., Sani, B.: An economic production quantity (EPQ) model for delayed deteriorating items with stock-dependent demand rate and time dependent holding cost. J. Niger. Assoc. Math. Phys. 19, 123–130 (2011)Google Scholar
  3. 3.
    Biswajit, S., Sumon, S.: An improved inventory model with partial backlogging, time varying deterioration and stock-dependent demand. Econ. Model. 30, 924–932 (2013)CrossRefGoogle Scholar
  4. 4.
    Chang, C., Cheng, M., Ouyang, L.: Optimal pricing and ordering policies for non-instantaneously deteriorating items under order-size-dependent delay in payments. Appl. Math. Model. 39, 747–763 (2015)CrossRefGoogle Scholar
  5. 5.
    Dari, S., Sani, B.: An EPQ model for items that exhibit delay in deterioration with reliability consideration. J. Niger. Assoc. Math. Phys. 24, 163–172 (2013)Google Scholar
  6. 6.
    Dari, S., Sani, B.: An EPQ model for items that exhibit delay in deterioration with reliability consideration and linear time dependent demand. ABACUS 42, 1–16 (2015)Google Scholar
  7. 7.
    Geetha, K.V., Uthayakumar, R.: Economic design of an inventory policy for non-instantaneous deteriorating items under permissible delay in payments. J. Comput. Appl. Math. 233, 2492–2505 (2010)CrossRefGoogle Scholar
  8. 8.
    Karabi, D.C., Biplab, K., Mantu, D., Tapan, K.D.: An inventory model for deteriorating items with stock-dependent demand, time-varying holding cost and shortages. OPSEARCH 52(1), 55–79 (2015)CrossRefGoogle Scholar
  9. 9.
    Kumar, S., Malik, A.K., Abhishek, S., Yadav, S.K., Yashveer, S.: An inventory model with linear holding cost and stock- dependent demand for non-instantaneous deteriorating items. In: Advancement in Science and Technology AIP Conference Proceedings no. 1715, p. 020058 (2016)Google Scholar
  10. 10.
    Meenakshi, S., Ranjana, G.: An EPQ model for deteriorating items with time and price dependent demand under markdown policy. OPSEARCH 51(1), 148–158 (2014)CrossRefGoogle Scholar
  11. 11.
    Mohan, R., Venkateswarlu, R.: Inventory management model with quadratic demand, variable holding cost with salvage value. Res. J. Manag. Sci. 3(1), 18–22 (2013)Google Scholar
  12. 12.
    Mohan, R.: Quadratic demand, variable holding cost with time dependent deterioration without shortages and salvage value. IOSR J. Math. (IOSR-JM) 13(2), 59–66 (2017)CrossRefGoogle Scholar
  13. 13.
    Monika, V., Shon, S.K.: Two levels of storage model for non-instantaneous deteriorating items with stock dependent demand, time varying partial backlogging under permissible delay in payments. Int. J. Oper. Res. Optim. 1, 133–147 (2010)Google Scholar
  14. 14.
    Musa, A., Sani, B.: Inventory ordering policies of delayed deteriorating items under permissible delay in payments. Int. J. Prod. Econ. 136, 84–92 (2012)CrossRefGoogle Scholar
  15. 15.
    Osagiede, F.E.U., Osagiede, A.A.: Inventory policy for a deteriorating item: quadratic demand with shortages. J. Sci. Technol. 27(2), 91–97 (2007)Google Scholar
  16. 16.
    Ouyang, L.Y., Wu, K.S., Yang, C.T.: A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments. Comput. Ind. Eng. 51, 637–651 (2006)CrossRefGoogle Scholar
  17. 17.
    Pando, V., Luis, S., Laguna, J., Sicilia, J.: An economic lot-size model with non-linear holding cost hinging on time and quantity. Int. J. Prod. Econ. 145, 294–303 (2013)CrossRefGoogle Scholar
  18. 18.
    Reza, M., Isa, N.K.: Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand. Int. J. Prod. Econ. 136, 116–122 (2012)CrossRefGoogle Scholar
  19. 19.
    Sarkar, T., Ghosh, S.K., Chaudhuri, K.S.: An optimal inventory replenishment policy for a deteriorating item with time-quadratic demand and time-dependent partial backlogging with shortages in all cycles. Appl. Math. Comput. 218, 9147–9155 (2012)Google Scholar
  20. 20.
    Sharmila, D., Uthayakumar, R.: Inventory model for deteriorating items with quadratic demand, partial backlogging and partial trade credit. Oper. Res. Appl. Int. J. (ORAJ) 2(4), 51–70 (2015)Google Scholar
  21. 21.
    Sh-Tyan, L., Hui-Ming, W., Wen-Chang, H.: An integrated production-inventory model with imperfect production processes and Weibull distribution deterioration under inflation. Int. J. Prod. Econ. 106, 248–260 (2007)CrossRefGoogle Scholar
  22. 22.
    Sugapriya, C., Jeyaraman, K.: An EPQ model for non-instantaneous deteriorating item in which holding cost varies with time. Electron. J. Appl. Stat. Anal. 1, 16–23 (2008)Google Scholar
  23. 23.
    Umakanta, M.: An EOQ model with time dependent weibull deterioration, quadratic demand and partial backlogging. Int. J. Appl. Comput. Math. 2, 545–563 (2016)CrossRefGoogle Scholar
  24. 24.
    Venkateswarlu, R., Mohan, R.: An inventory model for time varying deterioration and price dependent quadratic demand with salvage value. Indian J. Comput. Appl. Math. 1(1), 21–27 (2013)Google Scholar
  25. 25.
    Vinod, K.M., Lal, S.S., Rakesh, K.: An inventory model for deteriorating items with time-dependent demand and time-varying holding cost under partial backlogging. J. Ind. Eng. Int. 9(4), 2–5 (2013)Google Scholar
  26. 26.
    Vinod, K.M.: Deteriorating inventory model with controllable deterioration rate for time-dependent demand and time-varying holding cost. Yugosl. J. Oper. Res. 24(1), 87–98 (2014)CrossRefGoogle Scholar
  27. 27.
    Wu, K.S., Ouyang, L.Y., Yang, C.T.: An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging. Int. J. Prod. Econ. 101, 369–384 (2006)CrossRefGoogle Scholar
  28. 28.
    Yang, P., Wee, H.: An integrated multi-lot-size production inventory model for deteriorating item. Comput. Oper. Res. 30, 671–682 (2003)CrossRefGoogle Scholar

Copyright information

© Operational Research Society of India 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesKaduna State UniversityKadunaNigeria
  2. 2.Department of MathematicsAhmadu Bello UniversityZariaNigeria

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