Skip to main content
Log in

An accurate and reliable mathematical analytic solution procedure for the EOQ model with non-instantaneous receipt under supplier credits

  • Original Paper
  • Published:
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

Recently, Huang and Hsu (J Oper Res Soc Jpn 50:1–13, 2007) investigated the retailer’s optimal replenishment policy with non-instantaneous receipt under trade credit and cash discount. Basically, their inventory model is correct and interesting. However, they ignored explorations of interrelations of functional behaviors of the annual total cost to locate the optimal solutions so much so that the accuracy and reliability of the process of the proof of their solution procedure are questionable. The main purpose of this paper is to provide accurate and reliable mathematical analytic solution procedures to improve the findings in the aforementioned work of Huang and Hsu (J Oper Res Soc Jpn 50:1–13, 2007). Some related recent works on the subject-matter of this investigation are also cited with a view to providing incentive and motivation for making further advances along the lines of the supply chain management and associated inventory problems which we have discussed in this article.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Borde, S.F., McCarty, D.E.: Determining the cash discount in the firm’s credit policy: an evaluation. J. Financ. Strat. Decis. 11, 41–49 (1998)

    Google Scholar 

  2. Cárdenas-Barrón, L.E., Chung, K.-J., Kazemi, N., Shekarian, E.: Optimal inventory system with two backlog costs in response to a discount offer: corrections and complements. Oper. Res. Int. J. 18, 97–104 (2018)

    Article  Google Scholar 

  3. Chung, K.-J., Liao, J.-J., Lin, S.-D., Chuang, S.-T., Srivastava, H.M.: Manufacturer’s optimal pricing and lot-sizing policies under trade-credit financing. Math. Methods Appl. Sci. 43, 3099–3116 (2020)

    Article  MathSciNet  Google Scholar 

  4. Chung, K.-J., Liao, J.-J., Lin, S.-D., Chuang, X., Srivastava, H.M.: The inventory model for deteriorating items under conditions involving cash discount and trade credit. Mathematics 7, 1–20 (2019). (Article ID 596)

    Google Scholar 

  5. Chung, K.-J., Liao, J.-J., Lin, S.-D., Chuang, S.-T., Srivastava, H.M.: Mathematical analytic techniques and the complete squares method for solving an inventory modelling problem with a mixture of backorders and lost sales. Rev. Real Acad. Cie. Exactas Fís. Nat. Ser. A Mat. 114, 1–10 (2020). (Article ID 28)

    Article  MathSciNet  Google Scholar 

  6. Chung, K.-J., Liao, J.-J., Ting, P.-S., Lin, S.-D., Srivastava, H.M.: A unified presentation of inventory models under quantity discounts, trade credits and cash discounts in the supply chain management. Rev. Real Acad. Cie. Exactas Fís. Nat. Ser. A ísicas y Naturales Serie A Matemáticas 112, 509–538 (2018)

    MathSciNet  MATH  Google Scholar 

  7. Chung, K.-J., Lin, S.-D., Srivastava, H.M.: The complete and concrete solution procedures for integrated vendor–buyer cooperative inventory models with trade credit financing in supply chain management. Appl. Math. Inf. Sci. 10, 155–171 (2016)

    Article  Google Scholar 

  8. Hill, N., Riener, K.: Determining the cash discount in the firm’s credit policy. Financ. Manag. 8, 68–73 (1979)

    Article  Google Scholar 

  9. Huang, Y.-F., Chung, K.-J.: Optimal replenishment and payment policies in the EOQ model under cash discount and trade credit. Asia-Pac. J. Oper. Res. 20, 177–190 (2003)

    MathSciNet  MATH  Google Scholar 

  10. Huang, Y.-F., Hsu, K.-H.: An EOQ model with non-instantaneous receipt under supplier credits. J. Oper. Res. Soc. Jpn 50, 1–13 (2007)

    MATH  Google Scholar 

  11. Khan, M.A.A., Shaikh, A.A., Panda, G., Konstantaras, I., Cárdenas-Barrón, L.E.: The effect of advance payment with discount facility on supply decisions of deteriorating products whose demand is both price and stock dependent. Int. Trans. Oper. Res. 27, 1343–1367 (2020)

    Article  MathSciNet  Google Scholar 

  12. Liao, J.-J., Huang, K.-N., Chung, K.-J., Lin, S.-D., Chuang, S.-T., Srivastava, H.M.: Optimal ordering policy in an economic order quantity (EOQ) model for non-instantaneous deteriorating items with defective quality and permissible delay in payments. Rev. Real Acad. Cie. Exactas Fís. Nat. Ser. A Mat. 114, 1–26 (2020). (Article ID 41)

    Article  MathSciNet  Google Scholar 

  13. Liao, J.-J., Huang, K.-N., Chung, K.-J., Lin, S.-D., Ting, P.-S., Srivastava, H.M.: Determination of the optimal ordering policy for the retailer with limited capitals when a supplier offers two levels of trade credit. Math. Methods Appl. Sci. 40, 7686–7696 (2017)

    Article  MathSciNet  Google Scholar 

  14. Liao, J.-J., Huang, K.-N., Chung, K.-J., Lin, S.-D., Ting, P.-S., Srivastava, H.M.: Retailer’s optimal ordering policy in the EOQ model with imperfect-quality items under limited storage capacity and permissible delay. Math. Methods Appl. Sci. 41, 7624–7640 (2018)

    Article  MathSciNet  Google Scholar 

  15. Liao, J.-J., Huang, K.-N., Chung, K.-J., Lin, S.-D., Ting, P.-S., Srivastava, H.M.: Mathematical analytic techniques for determining the optimal ordering strategy for the retailer under the permitted trade-credit policy of two levels in a supply chain system. Filomat 32, 4195–4207 (2018)

    Article  MathSciNet  Google Scholar 

  16. Liao, J.-J., Huang, K.-N., Chung, K.-J., Ting, P.-S., Lin, S.-D., Srivastava, H.M.: Some mathematical analytic arguments for determining valid optimal lot size for deteriorating items with limited storage capacity under permissible delay in payments. Appl. Math. Inf. Sci. 10, 915–925 (2016)

    Article  Google Scholar 

  17. Liao, J.-J., Huang, K.-N., Chung, K.-J., Ting, P.-S., Lin, S.-D., Srivastava, H.M.: Lot-sizing policies for deterioration items under two-level trade credit with partial trade credit to credit-risk retailer and limited storage capacity. Math. Methods Appl. Sci. 40, 2122–2139 (2017)

    Article  MathSciNet  Google Scholar 

  18. Modak, N.M., Panda, S., Sana, S.S.: Optimal inventory policy in hospitals: a supply chain model. Rev. Real Acad. Cie. Exactas Fís. Nat. Ser. A Mat. 114, 1–21 (2020). (Article ID 109)

    Article  MathSciNet  Google Scholar 

  19. Rashid, M., Mitra, D.: Price elasticity of demand and an optimal cash discount rate in credit policy. Financ. Rev. 34, 113–126 (1999)

    Article  Google Scholar 

  20. Sarker, B.R., Kindi, M.A.: Optimal ordering policies in response to a discount offer. Int. J. Prod. Econ. 100, 195–211 (2006)

    Article  Google Scholar 

  21. Srivastava, H.M., Chung, K.-J., Liao, J.-J., Lin, S.-D., Chuang, S.-T.: Some modified mathematical analytic derivations of the annual total relevant cost of the inventory model with two levels of trade credit in the supply chain system. Math. Methods Appl. Sci. 42, 3967–3977 (2019)

    Article  MathSciNet  Google Scholar 

  22. Stokes, J.R.: Dynamic cash discounts when sale volume is stochastic. Q. Rev. Econ. Financ. 45, 144–160 (2005)

    Article  Google Scholar 

  23. Tiwari, S., Kazemi, N., Modak, N.M., Cárdenas-Barrón, L.E., Sarkar, S.: The effect of human errors on an integrated stochastic supply chain model with setup cost reduction and backorder price discount. Int. J. Prod. Econ. 226, 1–15 (2020). (, Article ID 107643)

    Article  Google Scholar 

  24. Udayakumar, R., Geetha, K.V.: An EOQ model for non-instantaneous deteriorating items with two levels of storage under trade credit policy. J. Ind. Eng. Int. 14, 343–365 (2018)

    Article  Google Scholar 

  25. Varberg, D., Purcell, E.J., Steven, S.E.: Calculus, 9th edn, pp. 87–88. Pearson Education Incorporated, Upper Saddle River (2007)

    Google Scholar 

  26. Wójtowicz, M.: counterexample to the Fortune’s Formula investing method. Rev. Real Acad. Cie. Exactas Fís. Nat.Seri. A Mat. 113, 749–767 (2019)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to H. M. Srivastava.

Ethics declarations

Conflict of interest

The authors declare no conflicts of interest

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Srivastava, H.M., Chung, KJ., Liao, JJ. et al. An accurate and reliable mathematical analytic solution procedure for the EOQ model with non-instantaneous receipt under supplier credits. RACSAM 115, 1 (2021). https://doi.org/10.1007/s13398-020-00944-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13398-020-00944-x

Keywords

Mathematics Subject Classification

Navigation