Skip to main content
SpringerLink
Log in

An Imprecise EOQ Model for Non-instantaneous Deteriorating Item with Imprecise Inventory Parameters Using Interval Number

  • Review Article
  • Published:
International Journal of Applied and Computational Mathematics Aims and scope Submit manuscript

Abstract

In this paper, an imprecise EOQ model for non-instantaneous deteriorating item with different demand rate, shortages and salvage value is formulated and solved with inventory parameters like demand rate, holding cost, deteriorating cost, shortage cost and salvage value which are considered to be imprecise. The rate of deterioration here is assumed to be constant but imprecise. Here the impreciseness of the above inventory parameters are assumed as interval numbers which are made crisp representations them in parametric forms. For the first time, total average cost of the system is presented by introducing parametric functional form of interval number. The optimal order cycle, the optimal shortage period and the optimal order quantity of the proposed imprecise model are derived by minimizing the total average cost. A numerical example is presented to illustrate the solution of the proposed imprecise model. Finally a graphical representation of the optimal solution is provided to demonstrate the proposed approach. It is seen that at the lower ends of the intervals, the average total cost is maximum where as at the corresponding upper ends, the said cost is lowest.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Abad, P.L.: Optimal pricing and lot sizing under conditions of partial backlogging. Manag. Sci. 42, 1093–1104 (1996)

    Article  MATH  Google Scholar 

  2. Annadurai, K.: An optimal replenishment policy for decaying items with shortages and salvage value. Int. J. Manag. Eng. Manag. 8(1), 38–46 (2013)

    MathSciNet  Google Scholar 

  3. Bahari-Kashani, H.: Replenishment schedule for deteriorating items with time- proportional demand. J. Oper. Res. Soc. 40, 75–81 (1989)

    Article  MATH  Google Scholar 

  4. Chang, H.J., Dye, C.Y.: An EOQ model for deteriorating items with time varying demand and partial backlogging. J. Oper. Res. Soc. 50, 1176–1182 (1999)

    Article  MATH  Google Scholar 

  5. Chung, K.J., Ting, P.S.: A heuristic for replenishment for deteriorating items with a linear trend in demand. J. Oper. Res. Soc. 44, 1235–1241 (1993)

    Article  MATH  Google Scholar 

  6. Chang, S.C., Yao, J.S., Lee, H.M.: Economic reorder point for fuzzy backorder quantity. Eur. J. Oper. Res. 109, 183–202 (1998)

    Article  MATH  Google Scholar 

  7. Chang, S.: Fuzzy production inventory for fuzzy product quantity with triangular fuzzy number. Fuzzy Sets Syst. 107, 37–57 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. Deb, M., Chaudhuri, K.: A note on the heuristic for replenishment of trended inventories considering shortages. J. Oper. Res. Soc. 38, 459–463 (1987)

    Article  MATH  Google Scholar 

  9. Diabat, A., Taleizadeh, A.A., Lashgari, M.: A lot sizing model with partial down-stream delayed payment, partial up-stream advance payment, and partial backordering for deteriorating items. J. Manuf. Syst. 45, 322–342 (2017)

    Article  Google Scholar 

  10. Gen, M., Tsujimura, Y., Zheng, D.: An application of fuzzy set theory to inventory control models. Comput. Ind. Eng. 33(3), 553–556 (1997)

    Article  Google Scholar 

  11. Ghare, P.M., Schrader, G.F.: A model for an exponentially decaying inventory. J. Ind. Eng. 14, 238–243 (1963)

    Google Scholar 

  12. Giri, B.C., Chaudhuri, K.S.: Heuristic model for deteriorating items with shortages and time-varying demand and costs. Int. J. Syst. Sci. 28(2), 153–159 (1997)

    Article  MATH  Google Scholar 

  13. Goswami, A., Chaudhuri, K.S.: An EOQ model for deteriorating items with a linear trend in demand. J. Oper. Res. Soc. 42(12), 1105–1110 (1991)

    Article  MATH  Google Scholar 

  14. Goyal, S.K., Giri, B.C.: Recent trends in modeling of deteriorating inventory. Eur. J. Oper. Res. 134, 1–16 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  15. Goyal, S.K.: A heuristic for replenishment of trended inventories considering shortages. J. Oper. Res. Soc. 39, 885–887 (1988)

    Article  Google Scholar 

  16. Hariga, M.: Optimal EOQ models for deteriorating items with time varying demand. J. Oper. Res. Soc. 47, 1228–1246 (1996)

    Article  MATH  Google Scholar 

  17. Hariga, M.: The inventory lot-sizing problem with continuous time varying demand and shortages. J. Oper. Res. Soc. 45(7), 827–837 (1994)

    Article  MATH  Google Scholar 

  18. Harris, F.W.: Operations and Cost. A. W. Shaw Company, Chicago (1915)

    Google Scholar 

  19. Iqbal, W., Sarkar, B.: Recycling of lifetime dependent deteriorated products through different supply chains. Rairo Oper. Res. (2017). https://doi.org/10.1051/ro/2017051

    Google Scholar 

  20. Jaggi, C.K., Aggarwal, S.P.: EOQ model for deteriorating items with salvage values. Bull. Appl. Sci. 15E(1), 67–71 (1996)

    MATH  Google Scholar 

  21. Jalan, A.K., Chaudhuri, K.S.: Structural properties of an inventory system with deterioration and trended demand. Int. J. Syst. Sci. 30(6), 627–633 (1999)

    Article  MATH  Google Scholar 

  22. Kim, D.H.: A heuristic for replenishment of deteriorating items with linear trend in demand. Int. J. Prod. Econ. 39, 265–270 (1995)

    Article  Google Scholar 

  23. Lashgari, M., Taleizadeh, A.A., Sana, S.S.: An inventory control problem for deteriorating items with back-ordering and financial considerations under two levels of trade credit linked to order quantity. J. Ind. Manag. Optim. 12(3), 1091–1119 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  24. Lashgari, M., Taleizadeh, A.A., Sadjadi, S.J.: Ordering policies for non-instantaneous deteriorating items under hybrid partial prepayment, partial trade credit and partial backordering. J. Oper. Res. Soc. 1–30 (2018)

  25. Lee, H.M., Yao, J.S.: Economic order quantity in fuzzy sense for inventory without backorder model. Fuzzy Sets Syst. 105, 13–31 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  26. Lin, C., Tan, B., Lee, W.C.: An EOQ model f or deteriorating items with time-varying demand and shortages. Int. J. Syst. Sci. 31(3), 39–400 (2000)

    Article  Google Scholar 

  27. Majumdar, A., Jaggi, K.C, Sarkar, B.: A multi-retailer supply chain model with backorder and variable production cost. Rairo Oper. Res. (2017). https://doi.org/10.1051/ro/2017013

    Google Scholar 

  28. Mishra, P., Shah, N.H.: Inventory management of time dependent deteriorating items with salvage value. Appl. Math. Sci. 16, 793–798 (2008)

    MathSciNet  MATH  Google Scholar 

  29. Murdeshwar, T.M.: Inventory replenishment policies for linearly increasing demand considering shortages. J. Oper. Res. Soc. 39, 687–692 (1988)

    Article  MATH  Google Scholar 

  30. Pal, D., Mahapatra, G.S.: Dynamic behavior of a predator–prey system of combined harvesting with interval-valued rate parameters. Nonlinear Dyn. 83, 2113–2123 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  31. Pal, D., Mahapatra, G.S., Samanta, G.P.: Optimal harvesting of prey-predator system with interval biological parameters: a bioeconomic model. Math. Biosci. 241, 181–187 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  32. Pareek, S., Mishra, V.K., Rani, S.: An inventory model for time dependent deteriorating item with salvage value and shortages. Math. Today 25, 31–39 (2009)

    Google Scholar 

  33. Park, K.: Fuzzy-set theoretic interpretation of economic order quantity. IEEE Trans. Syst. Man Cybern. 17, 1082–1084 (1987)

    Article  Google Scholar 

  34. Roy, A.: An inventory model for deteriorating items with price dependent demand and time varying holding cost. Adv. Model. Opt. 10, 25–37 (2008)

    MathSciNet  MATH  Google Scholar 

  35. Sarkar, B.: Supply chain coordination with variable backorder, inspections, and discount policy for fixed lifetime products. Mathematical Problem in Engineering, Hindawi Publishing Corporation, Vol. 2016, Article ID 6318737 (2016)

  36. Sarkar, B.: A production-inventory model with probabilistic deterioration in two-echelon supply chain management. Appl. Math. Model. 37(5), 3138–3151 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  37. Sarkar, B., Sarkar, S.: Variable deterioration and demand-an inventory model. Econ. Model. 31, 548–556 (2013)

    Article  Google Scholar 

  38. Sarkar, B., Sana, S.S., Chaudhuri, K.: Inventory model with finite replenishment rate, trade credit policy and price-discount offer. J. Ind. Eng. Hindawi Publishing Corporation, Vol. 2013, Article ID 672504 (2013)

  39. Sarkar, B.: An EOQ model with delay-in-payments and time-varying deterioration rate. Math. Comput. Model. 55, 367–377 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  40. Singh, T., Pattnayak, H.: An EOQ model for deteriorating items with linear demand, variable deterioration and partial backlogging. J. Serv. Sci. Manag. 6(2), 186–190 (2013)

    Google Scholar 

  41. Taleizadeh, A.A., Niaki, S.T., Ghavamizadeh, M.R.: An inventory control problem for deteriorating items with backordering and financial engineering considerations. Appl. Math. Model. 38, 93–109 (2014)

    Article  MathSciNet  Google Scholar 

  42. Taleizadeh, A.A., Baghban, A.R.: Pricing and lot sizing of a decaying item under group dispatching with time-dependent demand and decay rates. Int. J. Sci. Technol. (2018). https://doi.org/10.24200/SCI.2017.4449 (Scientia Iranica)

    Google Scholar 

  43. Taleizadeh, A.A.: An economic order quantity model with partial backordering and advance payments for an evaporating item. Int. J. Prod. Econ. 155, 185–193 (2014)

    Article  Google Scholar 

  44. Taleizadeh, A.A., Daryan, M.N., Barron, L.E.C.: Joint optimization of price, replenishment frequency, replenishment cycle and production rate in vendor managed inventory system with deteriorating items. Int. J. Prod. Econ. 159, 285–295 (2014)

    Article  Google Scholar 

  45. Taleizadeh, A.A.: An economic order quantity model for deteriorating item in a purchasing system with multiple prepayments. Appl. Math. Model. 38, 5357–5366 (2014)

    Article  MathSciNet  Google Scholar 

  46. Tavakoli, S., Taleizadeh, A.A.: A lot sizing model for decaying item with full advance payment from the buyer and conditional discount from the supplier. Ann. Oper. Res. 259, 415–436 (2016)

    Article  Google Scholar 

  47. Vujosevic, M., Petrovic, D., Petrovic, R.: EOQ Formula when inventory cost is fuzzy. Int. J. Prod. Econ. 45, 499–504 (1996)

    Article  Google Scholar 

  48. Wee, H.M.: A deterministic lot-size inventory model for deteriorating items with shortages and a declining market. Comput. Oper. 22, 345–356 (1995)

    Article  MATH  Google Scholar 

  49. Whitin, T.M.: The Theory of Inventory Management, 2nd edn. Princeton University Press, Princeton (1957)

    Google Scholar 

  50. Wilson, R.H.: A scientific routine for stock control. Harv. Bus. Rev. 13, 116–128 (1934)

    Google Scholar 

  51. 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)

    Article  Google Scholar 

  52. Xu, H., Wang, H.: An economic ordering policy model for deteriorating items with time-proportional demand. Eur. J. Oper. Res. 24, 21–27 (1991)

    MathSciNet  MATH  Google Scholar 

  53. Yao, J.S., Lee, H.M.: Fuzzy inventory with backorder for fuzzy order quantity. Inf. Sci. 93, 283–319 (1996)

    Article  MATH  Google Scholar 

  54. Yao, J.S., Chang, S.C., Su, J.S.: Fuzzy inventory without backorder for fuzzy order quantity and fuzzy total demand quantity. Comput. Oper. Res. 27, 935–962 (2000)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West-Bengal, 711103, India

    Asim Kumar Das & Tapan Kumar Roy

Authors
  1. Asim Kumar Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tapan Kumar Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Asim Kumar Das.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Das, A.K., Roy, T.K. An Imprecise EOQ Model for Non-instantaneous Deteriorating Item with Imprecise Inventory Parameters Using Interval Number. Int. J. Appl. Comput. Math 4, 79 (2018). https://doi.org/10.1007/s40819-018-0510-1

Download citation

  • Published:

  • DOI: https://doi.org/10.1007/s40819-018-0510-1

Keywords

Mathematics Subject Classification

Search

Navigation