Skip to main content
SpringerLink
Log in

Optimal replenishment and stocking strategies for inventory mechanism with a dynamically stochastic short-term price discount

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

This paper considers an inventory mechanism with a non-deterministic short-term price discount. In the mechanism, the supplier has a tendency to offer retailers a short-term price discount for a future occasion. Subsequently, when the discount occurs, the discount stock would start to reduce gradually. Therefore the discount might terminate ahead of schedule once the discount stock is depleted, which means that the discount possibility will gradually decrease from 1 ever after the start of the discount. For this system, to maximize the retailer’s profit, we establish an optimal replenishment and stocking strategies model. Based on the retailer’s cost-benefit analysis, we present a solution method for the model and provide an optimal ordering policy to the retailer. The given numerical experiments illustrate the validity of the model.

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
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Arcelus, F.J., Shah, N.H., Srinivasan, G.: Retailers response to special sales: price discount vs trade credit. Omega 29(5), 417–428 (2001)

    Article  Google Scholar 

  2. Arcelus, F.J., Shah, N.H., Srinivasan, G.: Retailer’s pricing, credit and inventory policies for deteriorating items in response to temporary price/credit incentives. Int. J. Prod. Econ. 81–82, 153–162 (2003)

    Article  Google Scholar 

  3. Ardalan, A.: Optimal ordering policies in response to a sale. IIE Trans. 20, 292–294 (1988)

    Article  Google Scholar 

  4. Ardalan, A.: Optimal prices and order quantities when temporary price discounts result in increase in demand. Eur. J. Oper. Res. 72, 52–61 (1994)

    Article  MATH  Google Scholar 

  5. Aull-Hyde, R.: Evaluation of supplier-restricted purchasing options under temporary price discounts. IIE Tran. 24, 184–186 (1992)

    Article  Google Scholar 

  6. Aull-Hyde, R.: A backlog inventory model during restricted sale periods. J. Oper. Res. Soc. 47(9), 1192–1200 (1996)

    Article  MATH  Google Scholar 

  7. Baker, R.C., Vilcassim, N.: Continuos review price change inventory model. Prod. Invent. Manag. 24, 67–72 (1983)

    Google Scholar 

  8. Cárdenas-Barrón, L.E., Smith, N.R., Goyal, S.K.: Optimal order size to take advantage of a one-time discount offer with allowed backorders. Appl. Math. Model. 34, 1642–1652 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Chang, H.J., Lin, W.F., Ho, J.F.: Closed-form solutions for Wee’s and Martin’s EOQ models with a temporary price discount. Int. J. Prod. Econ. 131, 528–534 (2011)

    Article  Google Scholar 

  10. Chu, P., Chen, P.S., Niu, T.: Note on supplier-restricted order quantity under temporary price discounts. Math. Methods Oper. Res. 58, 141–147 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  11. Davis, R.A., Gaither, N.: Optimal ordering policies under conditions of extended payment privileges. Manag. Sci. 31, 499–509 (1985)

    Article  MATH  Google Scholar 

  12. Fan, S.J.: A new extracting formula and a new distinguishing means on the one variable cubic equation. J Hainan Teach. Coll. 2(2), 91–98 (1989)

    Google Scholar 

  13. Gaither, N., Park, M.S.: Analysis of constrained, on-time, multi-item discount offers. IIE Tran. 23(3), 228–235 (1991)

    Article  Google Scholar 

  14. Goyal, S.K.: Economic ordering policy during special discount periods for dynamic inventory problems under certainty. Eng. Costs Prod. Econ. 20, 101–104 (1990)

    Article  Google Scholar 

  15. Hsu, W.K., Yu, H.F.: EOQ model for imperfective items under a one-time-only discount. Omega 37, 1018–1026 (2009)

    Article  Google Scholar 

  16. Hu, F., Lim, C.C., Lu, Z.: The retailer’s optimal decision on order quantity and credit periods under two-level trade credit policy. J. Glob. Optim. 62, 833–852 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  17. Kindi, M.A., Sarker, B.R.: Optimal inventory system with two backlog costs in response to a discount offer. Prod. Plan. & Cont. 22, 25–333 (2011)

    Article  Google Scholar 

  18. Lev, B., Weiss, H.J.: Inventory models with cost changes. Oper. Res. 38, 56–63 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  19. Sari, D.P., Rusdiansyah, A., Huang, L.: Models of joint economic lot-sizing problem with time-based temporary price discounts. Int. J. Prod. Econ. 139(1), 145–154 (2012)

    Article  Google Scholar 

  20. Sarker, B.R., Kindi, M.A.: Optimal ordering policies in response to a discount offer. Int. J. Prod. Econ. 100(2), 195–211 (2006)

    Article  Google Scholar 

  21. Shaposhnik, Y., Herer, Y.T., Naseraldin, H.: Optimal ordering for a probabilistic one-time discount. Eur. J. Oper. Res. 244(3), 803–814 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  22. Taleizadeh, A.A., Pentico, D.W., Aryanezhad, M., Ghoreyshi, S.M.: An economic order quantity model with partial backordering and a special sale price. Eur. J. Oper. Res. 221(3), 571–583 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  23. Tersine, R., Schwarzkopf, A.: Optimal stock replenishment strategies in response to temporary price reductions. J. Bus. Logist. 10(2), 123–145 (1989)

    Google Scholar 

  24. Thi, H.A.L., Tran, D.Q.: New and efficient algorithms for transfer prices and inventory holding policies in two-enterprise supply chains. J. Glob. Optim. 60, 5–24 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  25. Wang, Y.J., Sun, X.F., Meng, F.X.: On the conditional and partial trade credit policy with capital constraints: a Stackelberg model. Appl. Math. Model. 40, 1–18 (2016)

    Article  MathSciNet  Google Scholar 

  26. Wang, C.W., Wang, Y.J.: A superlinearly convergent projection method for constrained systems of nonlinear equations. J. Glob. Optim. 40, 283–296 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  27. Waters, C.D.J.: Inventory Control and Management. Wiley, New Jersey (2003)

    Google Scholar 

  28. Wee, H.M., Yu, J.: A deteriorating inventory model with a temporary price discount. Int. J. Prod. Econ. 53(1), 81–90 (1997)

    Article  Google Scholar 

  29. Zhang, Y.G., Tang, X.W.: Retailer’s order strategy of delay in payments under cash discount and capital constraints. Syst. Eng. 27, 30–34 (2009)

    Google Scholar 

Download references

Acknowledgements

The authors are in debt to two anonymous referees for numerous insightful comments and suggestions, which have greatly improved the paper.

Author information

Authors and Affiliations

  1. School of Management Science, Qufu Normal University, Rizhao, 276800, Shandong, China

    Yiju Wang, Hengxia Gao & Wei Xing

Authors
  1. Yiju Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hengxia Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei Xing
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Yiju Wang or Wei Xing.

Additional information

This work is supported by the Natural Science Foundation of China (11671228, 71471101) and Shandong Provincial Natural Science Foundation (ZR2015GZ008).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y., Gao, H. & Xing, W. Optimal replenishment and stocking strategies for inventory mechanism with a dynamically stochastic short-term price discount. J Glob Optim 70, 27–53 (2018). https://doi.org/10.1007/s10898-017-0522-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-017-0522-0

Keywords

Search

Navigation