Skip to main content
SpringerLink
Log in

An optimal inventory model for perishable items under successive price discounts with permissible delay in payments

  • Application Article
  • Published:
OPSEARCH Aims and scope Submit manuscript

Abstract

This article derives an optimal ordering policy for non-instantaneously deteriorating items under successive price discounts with delay in payments. Here successive price discounts is a strategy to sell almost all the items before decomposition. The cause of implementing this concept in the model is the fact that about 25% of vegetables and fruits of India gets decayed before selling, due to lack of facilities and awareness of business strategies, although poverty is its vital factor. Thus we propose to offer successive price discounts of 20% and 40% after selling the stock up to 50% and 90% respectively to raise the customer’s inflow and so also rotate the cycle early to avoid more deterioration. This type of business not only reduces the factory of decomposability but also saves the holding cost partially. In addition to, the delay in payment is another business strategy of the wholesaler by which he keeps the retailers in track and so also reduces the holding cost. In this case the wholesaler offers an interest-free credit period to the retailers till the settlement of the accounts. The retailers earn interest on selling the revenue during this opportunity. Supplier charges interest on the outstanding balance after exceeding the period. Besides the above, again the inventory cost does not remaining constant due to various factors like inflation, salary, house rent etc. so a time varying holding cost has been well thought out instead of constant holding cost. Once more customers’ flow not only depends upon the price instigating but also on timings, hence we assume an exponential demand function which depends on these variables. The main idea of the task is to determine optimal selling price, optimal refill schedule and optimal ordering quantity such that the total profit is maximized under exponential constraints. The literal idea of the work is (a) to avoid the deterioration through successive price discounts, (b) to attract the customers through successive price discounts, (c) to sell all the items through successive price discounts, (d) to rotate the cycle early through successive price discounts, (e) to keep the retailers in track through delay in payment, (f) to keep variable holding cost instead of constant holding cost due to market inflation, (g) to get the optimum results under exponential constraints.

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. Ghare, P.M., Schrader, G.H.: A Model for exponentially decaying inventory system. Int. J. Prod. Res. 21, 449–460 (1963)

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  4. Abad, P.L.: Optimal price and order size for a reseller under partial backordering. Comput. Oper. Res. 28, 53–65 (2001)

    Article  Google Scholar 

  5. Chung, H.J., Lin, C.N.: Optimal inventory replenishment models for deteriorating items taking account of time discounting. Comput. Oper. Res. 28, 67–83 (2001)

    Article  Google Scholar 

  6. Taleizadeh, A.A., Nematollahi, M.: An inventory control problem for deteriorating items with back-ordering and financial considerations. Appl. Math. Model. 38, 93–109 (2014)

    Article  Google Scholar 

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

    Article  Google Scholar 

  8. Taleizadeh, A.A., Stojkovska, I., Pentico, D.W.: An economic order quantity model with partial backordering and incremental discount. Comput. Ind. Eng. 82, 21–32 (2015)

    Article  Google Scholar 

  9. Dye, C.Y., Yang, C.T.: Optimal dynamic pricing and preservation technology investment for deteriorating products with reference price effects. Omega 62, 52–67 (2016)

    Article  Google Scholar 

  10. Mehta, N.J., Shah, N.H.: An inventory model for deteriorating items with exponentially increasing demand and shortages under inflation and time discounting. Investig Oper 23, 103–111 (2003)

    Google Scholar 

  11. 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 

  12. Zhang, J., Wang, Y., Lu, L., Tang, W.: Optimal dynamic pricing and replenishment cycle for non-instantaneous deterioration items with inventory-level-dependent demand. Int. J. Prod. Econ. 170, 136–145 (2015)

    Article  Google Scholar 

  13. Maihami, R., Isa, I.N.K.: Joint control of inventory and its pricing for non-instantaneously deteriorating items under permissible delay in payments and partial backlogging. Math. Comput. Model. 55, 1722–1733 (2012)

    Article  Google Scholar 

  14. 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)

    Article  Google Scholar 

  15. Yang, C.-T., Ouyang, L.-Y., Wu, H.-H.: Retailer’s optimal pricing and ordering policies for non-instantaneous deteriorating items with price-dependent demand and partial backlogging. Math. Probl. Eng. (2009). https://doi.org/10.1155/2009/198305

    Google Scholar 

  16. Taleizadeh, A.A., Pentico, D.W., Jabalameli, M.S., Aryanezhad, M.: An economic order quantity model with multiple partial prepayments and partial backordering. Math. Comput. Model. 57, 311–323 (2013)

    Article  Google Scholar 

  17. Zia, N.P., Taleizadeh, A.A.: A lot-sizing model with backordering under hybrid linked-to-order multiple advance payments and delayed payment. Transp. Res. Part E 82, 19–37 (2015)

    Article  Google Scholar 

  18. Tuan, H.W., Lin, S.C., Julian, P.: Improvement for amelioration inventory model with weibull distribution. Math. Probl. Eng. 2017, 8946547-1–8946547-8 (2017)

    Article  Google Scholar 

  19. Rangarajan, K., Karthikeyan, K.: EOQ Models for non-instantaneous/instantantaneous deteriorating items with cubic demand rate under inflation and permissible delay in payments. Ital. J. Pure Appl. Math. 37, 197–218 (2017)

    Google Scholar 

  20. Janssen, L., Claus, T., Sauer, J.: Literature review of deteriorating inventory models by key topics from 2012 to 2015. Int. J. Prod. Econ. 182, 86–112 (2016)

    Article  Google Scholar 

  21. Taleizadeh, A.A., Pentico, D.W.: An economic order quantity model with partial backordering and all-units discount. Int. J. Prod. Econ. 155, 172–184 (2014)

    Article  Google Scholar 

  22. Taleizadeh, A.A., Rasuli-Baghban, A.: Pricing and Lot sizing of a decaying item under group dispatching with time dependent demand and decay rates. Sci. Iranica. 25, 1656–1670 (2018)

    Google Scholar 

  23. Taleizadeh, A.A.: Lot-sizing model with advance payment pricing and disruption in supply under planned partial backordering. Int. Trans. Oper. Res. 24, 783–800 (2017)

    Article  Google Scholar 

  24. Taleizadeh, A.A., Noori-daryan, M., Cárdenas-Barrón, L.E.: Joint optimization of price, replenishment frequency, and replenishment cycle and production rate in vendor managed inventory system with deteriorating items. Int. J. Prod. Econ. 159, 285–295 (2015)

    Article  Google Scholar 

  25. Moussawi-Haidar, Lama, Jaber, Mohamad Y.: A joint model for cash and inventory management for a retailer under delay in payments. Comput. Ind. Eng. 66, 758–767 (2013)

    Article  Google Scholar 

  26. Soni, H.N., Patel, K.A.: Joint pricing and replenishment policies for non-instantaneous deteriorating items with imprecise deterioration free time and credibility constraint. Comput. Ind. Eng. 66, 944–951 (2013)

    Article  Google Scholar 

  27. Ghosh, S.K., Kharana, S., Chaudhari, K.S.: Optimal price and lot size determination for a perishable product under conditions of finite production, partial backordering and lost sale. Appl. Math. Comput. 217, 6047–6053 (2011)

    Google Scholar 

  28. Dye, C.-Y., Ouyang, L.-Y., Hsiesh, T.-P.: Inventory and pricing strategies for deteriorating items with shortages: a discounted cash flow approach. Comput. Ind. Eng. 52, 29–40 (2007)

    Article  Google Scholar 

  29. Chung, C.J., Widyadana, G.A., Wee, H.M.: Economic production quantity model for deteriorating inventory with random machine unavailability and shortage. Int. J. Prod. Res. 49, 883–902 (2011)

    Article  Google Scholar 

  30. Cheng, M., Zhang, B., Wang, G.: Optimal policy for deteriorating items with trapezoidal type demand and partial backlogging. Appl. Math. Mod. 35, 3552–3560 (2011)

    Article  Google Scholar 

  31. Hung, K.C.: An inventory model with generalized type demand, deterioration and backorder rates. Eur. J. Oper. Res. 208, 239–242 (2011)

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank all the anonymous reviewers and the associate editor for their valuable and constructive suggestions to improve the quality of the manuscript. We would also like to thank our management for their kind cooperation and encouragement.

Author information

Authors and Affiliations

  1. Department of Mathematics, National Institute of Science & Technology (Autonomous), Berhampur, Odisha, 761008, India

    Bhaskar Bhaula

  2. Department of Mathematics, Siksha ‘O’ Anusandhan University (Deemed to be University), Bhubaneswar, Odisha, 751030, India

    Jayanta Kumar Dash & M. Rajendra Kumar

Authors
  1. Bhaskar Bhaula
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jayanta Kumar Dash
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Rajendra Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bhaskar Bhaula.

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

Bhaula, B., Dash, J.K. & Rajendra Kumar, M. An optimal inventory model for perishable items under successive price discounts with permissible delay in payments. OPSEARCH 56, 261–281 (2019). https://doi.org/10.1007/s12597-018-0349-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12597-018-0349-6

Keywords

Search

Navigation