Advertisement

Operational Research

, Volume 16, Issue 1, pp 25–50 | Cite as

Optimal ordering policy for an inventory system with linearly increasing demand and allowable shortages under two levels trade credit financing

  • B. C. Giri
  • S. SharmaEmail author
Original Paper

Abstract

To reduce default risk, a retailer may offer a partial down-stream trade credit to its credit-risk customers who should pay a portion of their purchasing costs at the time of receiving items as a collateral deposit, and then receive a permissible trade credit on the rest of the outstanding amount. To reflect this fact, we consider an inventory model with linear time dependent demand under two levels of trade credit and allowable shortages. Depending on the relationship between up-stream and down-stream trade credit periods, several cases are considered and the necessary and sufficient conditions are derived for finding the optimal solution. We also present a simple algorithm to determine the optimal solution. Numerical examples are provided to illustrate the solution procedure. Sensitivity analysis of important model-parameters is performed and some relevant managerial implications are discussed.

Keywords

Inventory Increasing demand Partial trade credit Shortages 

Notes

Acknowledgments

The authors are thankful to the honorable referees for their helpful comments and suggestions on the earlier version of the manuscript. The second author acknowledges the financial assistance provided by Jadavpur University under the State Govt. Fellowship Scheme.

References

  1. Aggarwal SP, Jaggi CK (1995) Ordering policies of deteriorating items under permissible delay in payments. J Oper Res Soc 46(5):658–662CrossRefGoogle Scholar
  2. Dave U (1985) Letters and viewpoints on “economic order quantity under conditions of permissible delay in payments”. J Oper Res Soc 46(5):1069–1070CrossRefGoogle Scholar
  3. Chen SC, Teng JT, Skouri K (2013) Economic production quantity models for deteriorating items with up-stream full trade credit and down-stream partial trade credit. Int J Prod Econ 155:302–309CrossRefGoogle Scholar
  4. Giri BC, Sharma S (2014) An integrated inventory model for a deteriorating item with allowable shortages and credit linked wholesale price. Optim Lett. doi: 10.1007/s11590-014-0810-2
  5. Goyal SK (1985) Economic order quantity under conditions of permissible delay in payments. J Oper Res Soc 36(4):335–338CrossRefGoogle Scholar
  6. Huang YF (2003) Optimal retailer’s ordering policies in the EOQ model under trade credit financing. J Oper Res Soc 54(9):1011–1015CrossRefGoogle Scholar
  7. Huang YF, Hsu KH (2008) An EOQ model under retailer partial trade credit policy in supply chain. Int J Prod Econ 112(2):655–664CrossRefGoogle Scholar
  8. Jamal AMM, Sarker BR, Wang S (1997) An ordering policy for deteriorating items with allowable shortages and permissible delay in payment. J Oper Res Soc 48(8):826–833CrossRefGoogle Scholar
  9. Khanra S, Ghosh SK, Chaudhuri KS (2011) An EOQ model for a deteriorating item with time dependent quadratic demand under permissible delay in payment. Appl Math Comput 218(1):1–9Google Scholar
  10. Khanra S, Mandal B, Sarkar B (2013) An inventory model with time dependent demand and shortages under trade credit policy. Econ Model 35:349–355CrossRefGoogle Scholar
  11. Maihami R, Abadi INK (2012) Joint control of inventory and its pricing for non-instantaneously deteriorating items under permissible delay in payments and partial backlogging. Math Comp Model 55(5–6):1722–1733CrossRefGoogle Scholar
  12. Ouyang LY, Teng JT, Chen LH (2006) Optimal ordering policy for deteriorating items with partial backlogging under permissible delay in payments. J Glob Optim 34(2):245–271CrossRefGoogle Scholar
  13. Ouyang LY, Teng JT, Goyal SK, Yang CT (2009) An economic order quantity model for deteriorating items with partially permissible delay in payments linked to order quantity. Eur J Oper Res 194(2):418–431CrossRefGoogle Scholar
  14. Petersen MA, Rajan RG (1997) Trade credit: theories and evidence. Rev Financ Stud 10(3):661–691CrossRefGoogle Scholar
  15. Shinn SW, Hwang H (2003) Optimal pricing and ordering policies for retailers under order-size-dependent delay in payments. Comp Oper Res 30(1):35–50CrossRefGoogle Scholar
  16. Teng JT (2002) On the economic order quantity under conditions of permissible delay in payments. J Oper Res Soc 53(8):915–918CrossRefGoogle Scholar
  17. Teng JT (2009) Optimal ordering policies for a retailer who offers distinct trade credits to its good and bad credit customers. Int J Prod Econ 119(2):415–423CrossRefGoogle Scholar
  18. Teng JT, Chang CT (2009) Optimal manufacturer’s replenishment policies in the EPQ model under two levels of trade credit policy. Eur J Oper Res 195(2):358–363CrossRefGoogle Scholar
  19. Teng JT, Chang CT, Goyal SK (2005) Optimal pricing and ordering policy under permissible delay in payments. Int J Prod Econ 97(2):121–129CrossRefGoogle Scholar
  20. Teng JT, Goyal SK (2007) Optimal ordering policies for a retailer in a supply chain with up-stream and down-stream trade credits. J Oper Res Soc 58(9):1252–1255CrossRefGoogle Scholar
  21. Teng JT, Min J, Pan Q (2012) Economic order quantity model with trade credit financing for non-decreasing demand. Omega 40(3):328–335CrossRefGoogle Scholar
  22. Teng JT, Yang HL, Chern MS (2013) An inventory model for increasing demand under two levels of trade credit linked to order quantity. Appl Math Model 37(14–15):7624–7632CrossRefGoogle Scholar
  23. Thangam A, Uthayakumar R (2010) Optimal pricing and lot-sizing policy for a two-warehouse supply chain system with perishable items under partial trade credit financing. Int J Oper Res 10(2):133–161CrossRefGoogle Scholar
  24. Wang WC, Teng JT, Lou KR (2014) Seller’s optimal credit period and cycle time in a supply chain for deteriorating items with maximum lifetime. Eur J Oper Res 232(2):315–321CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsJadavpur UniversityKolkataIndia

Personalised recommendations