Skip to main content
SpringerLink
Log in

Optimal Replenishment Strategy for Inventory Mechanism with Step-Shaped Demand

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

This paper extends the classical economic order quantity inventory model to that the planning horizon consists of two stages—a finite planning horizon and an infinite planning horizon, the demand in each stage is deterministic and stable but differs. The main goal is to find the optimal replenishment and stocking policy in each stage in order to keep the total relevant cost as low as possible, which is formulated as a mixed integer optimization problem. Using the alternating minimization method and the optimization theory, we develop a closed-form solution to the optimal inventory model and provide an optimal replenishment strategy to the retailer. Some numerical experiments are made to test the validity of the model and the effect of the involved parameters to the replenishment policy. A numerical example shows a counterintuitive fact that the economic ordering quantity may not necessarily be optimal for this inventory mechanism.

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

Similar content being viewed by others

References

  1. Abad, P.L.: Optimal pricing and lot-sizing under conditions of perishability and partial backordering. Manag. Sci. 42(8), 1093–1104 (1996)

    Article  Google Scholar 

  2. Aggarwal, S.P., Jaggi, C.K.: Ordering policies of deteriorating items under permissible delay in payments. J. Oper. Res. Soc. 46(5), 658–662 (1995)

    Article  Google Scholar 

  3. Agi, M.A.N., Soni, H.N.: Joint pricing and inventory decisions for perishable products with age-, stock-, and price-dependent demand rate. J Oper. Res. Soc. 71(1), 85–99 (2020)

    Article  Google Scholar 

  4. Alfares, H.K., Ghaithan, A.M.: Inventory and pricing model with price-dependent demand, time-varying holding cost, and quantity discounts. Comput. Indus. Eng. 94, 170–177 (2016)

    Article  Google Scholar 

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

    Article  Google Scholar 

  6. Avinadav, T., Herbon, A., Spiegel, U.: Optimal inventory policy for a perishable item with demand function sensitive to price and time. Inter. J. Prod. Econ. 144(2), 497–506 (2013)

    Article  Google Scholar 

  7. Bakker, M., Riezebos, J., Teunter, R.H.: Review of inventory systems with deterioration since 2001. Eur. J. Oper. Res. 221(2), 275–284 (2012)

    Article  MathSciNet  Google Scholar 

  8. Benkherouf, I., Skouri, K., Konstantaras, I.: Optimal control of production, remanufacturing and refurbishing activities in a finite planning horizon inventory system. J. Optim. Theory Appl. 168(2), 677–698 (2016)

    Article  MathSciNet  Google Scholar 

  9. Caliskan, C.: A simple derivation of the optimal solution for the EOQ model for deteriorating items with planned backorders. Appl. Math. Model. 89(2), 1373–1381 (2021)

    Article  MathSciNet  Google Scholar 

  10. Chang, H.J., Dye, C.Y.: An EOQ model for deteriorating items with time varying demand and partial backlogging. J. Oper. Res. Soc. 50(11), 1176–1182 (1999)

    Article  Google Scholar 

  11. Cárdenas-Barróna, L.E., Shaikha, A.A., Tiwaric, S., Treviño-Garza, G.: An EOQ inventory model with nonlinear stock dependent holding cost, nonlinear stock dependent demand and trade credit. Comput. Indus. Eng. 139, 105557 (2020)

    Article  Google Scholar 

  12. Dobson, G., Pinker, E.J., Yildiz, O.: An EOQ model for perishable goods with age-dependent demand rate. Eur. J. Oper. Res. 257(1), 84–88 (2017)

    Article  MathSciNet  Google Scholar 

  13. Dye, C.Y.: Joint pricing and ordering policy for a deteriorating inventory with partial backlogging. Omega 35(2), 184–189 (2007)

    Article  Google Scholar 

  14. Goyal, S.K.: Economic order quantity under conditions of permissible delay in payments. J. Oper. Res. Soc. 36(11), 335–338 (1985)

    Article  Google Scholar 

  15. Harris, F.W.: How many parts to make at once. Fact. Mag. Manag. 10, 135–136 (1913)

    Google Scholar 

  16. Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, England (2013)

    MATH  Google Scholar 

  17. Kaya, O., Ghahroodi, S.R.: Inventory control and pricing for perishable products under age and price dependent stochastic demand. Math. Meth. Oper. Res. 88(1), 1–35 (2018)

    Article  MathSciNet  Google Scholar 

  18. Khanra, S., Mandal, B., Sarkar, B.: An inventory model with time dependent demand and shortages under trade credit policy. Econ. Model. 35, 349–355 (2013)

    Article  Google Scholar 

  19. Li, X.M.: Optimal policies and bounds for stochastic inventory systems with lost sales. J. Optim. Theory Appl. 164(1), 359–375 (2015)

    Article  MathSciNet  Google Scholar 

  20. Mandal, B., Phaujdar, S.: An inventorymodel for deteriorating items and stock-dependent consumption rate. J. Oper. Res. Soc. 40, 483–488 (1989)

    Article  Google Scholar 

  21. Mishra, U., Cárdenas-Barrón, L.E., Tiwari, S., Shaikh, A.A., Treviño-Garza, G.: An inventory model under price and stock dependent demand for controllable deterioration rate with shortages and preservation technology investment. Ann. Oper. Res. 254(1–2), 165–190 (2017)

    Article  MathSciNet  Google Scholar 

  22. Nocedal, J., Wright, S.T.: Numerical Optimization. Springer, New York (1999)

    Book  Google Scholar 

  23. Pando, V., San-José, L.A., García-Laguna, J., Sicilia, J.: Optimal lot-size policy for deteriorating items with stock-dependent demand considering profit maximization. Comput. Indus. Eng. 117, 81–93 (2018)

    Article  Google Scholar 

  24. Patriarca, R., Di Gravio, G., Costantino, F., Tronci, M.: EOQ inventory model for perishable products under uncertainty. Prod. Eng. 14(5–6), 601–612 (2020)

    Article  Google Scholar 

  25. San-José, L.A., Sicilia, J., González, M., Febles-Acosta, J.: Optimal inventory policy under power demand pattern and partial backlogging. Appl. Math. Model. 46(1), 618–630 (2017)

    Article  MathSciNet  Google Scholar 

  26. Sarkar, B., Mandal, P., Sarkar, S.: An EMQ model with price and time dependent demand under the effect of reliability and inflation. Appl. Math. Comput. 231, 414–421 (2014)

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  28. Thinakaran, N., Jayaprakas, J., Elanchezhian, C.: Survey on inventory model of EOQ and EPQ with partial backorder problems. Mater. Today Proc. 16(2), 629–635 (2019)

    Article  Google Scholar 

  29. Tiwari, S., Cárdenas-Barrón, L.E., Goh, M., Shaikh, A.A.: Joint pricing and inventory model for deteriorating items with expiration dates and partial backlogging under two-level partial trade credits in supply chain. Inter. J. Prod. Econ. 200, 16–36 (2018)

    Article  Google Scholar 

  30. Tiwari, S., Jaggi, C.K., Gupta, M., Crdenas-Barrn, L.E.: Optimal pricing and lot-sizing policy for supply chain system with deteriorating items under limited storage capacity. Inter. J. Prod. Econ. 200, 278–290 (2018)

    Article  Google Scholar 

  31. Wang, Y.J., Xing, W., Gao, H.X.: Optimal ordering policy for inventory mechanism with a stochastic short-term price discount. J. Indus. Manag. Optim. 16(3), 1187–1202 (2020)

    MathSciNet  MATH  Google Scholar 

  32. Wee, H.M.: Deteriorating inventory model with quantity discount, pricing and partial backordering. Inter. J. Prod. Econ. 59(1), 511–518 (1999)

    Article  Google Scholar 

  33. Whitin, T.M.: The Theory of Inventory Management. Princeton University Press, Princeton (1953)

    Google Scholar 

  34. Yan, X.: An EOQ model for perishable items with freshness-dependent demand and partial backlogging. Inter. J. Cont. Auto. 5(4), 19–38 (2012)

    Google Scholar 

  35. Yang, H.L., Teng, J.T., Chern, M.S.: A forward recursive algorithm for inventory lot size models with power-form demand and shortages. Eur. J. Oper. Res. 137(2), 394–400 (2002)

    Article  MathSciNet  Google Scholar 

  36. Yang, P.C., Wee, H.M., Wee, K.P.: An integrated vendor-buyer model with perfect and monopolistic competitions: an educational note. Inter. Trans. Oper. Res. 13(1), 75–83 (2006)

    Article  Google Scholar 

  37. Zhang, Y.G., Tang, X.W.: Retailers order strategy of delay in payments under cash discount and capital constraints. Sys. Eng. 27, 30–34 (2009)

    Google Scholar 

  38. Zipkin, P.H.: Foundations of Inventory Management. McGraw-Hill, New York (2000)

    MATH  Google Scholar 

Download references

Acknowledgements

We thank three anonymous referees for their careful reading of the paper and helpful comments and suggestions which greatly improved the presentation. This work is supported by the National Natural Science Foundation of China (Grant No.12071250).

Author information

Authors and Affiliations

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

    Yiju Wang & Jingfu Huang

  2. Faculty of Business Administration Fredericton, University of New Brunswick, Fredericton, Canada

    Donglei Du

Authors
  1. Yiju Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Donglei Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jingfu Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yiju Wang.

Additional information

Communicated by Anita Schöbel.

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

Wang, Y., Du, D. & Huang, J. Optimal Replenishment Strategy for Inventory Mechanism with Step-Shaped Demand. J Optim Theory Appl 190, 841–860 (2021). https://doi.org/10.1007/s10957-021-01909-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-021-01909-9

Keywords

Mathematics Subject Classifications (2010)

Search

Navigation