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Annals of Operations Research

, Volume 229, Issue 1, pp 677–702 | Cite as

An inventory model with trade-credit policy and variable deterioration for fixed lifetime products

  • Biswajit SarkarEmail author
  • Sharmila Saren
  • Leopoldo Eduardo Cárdenas-Barrón
Article

Abstract

The purpose of this study is two-fold. The first is to consider supplier’s and retailer’s trade-credit policy for fixed lifetime products and the second is to extend Mahata’s 2012 model with time varying deterioration where Mahata (Expert Syst Appl 39(3):3537–3550, 2012) wrote exponential deterioration but actually he considered constant deterioration. We assume that the suppliers offer full trade-credit to retailers but retailers offer partial trade-credit to their customers. Some numerical examples along with graphical representations are given to illustrate the model.

Keywords

Inventory Trade-credit policy Variable deterioration Fixed lifetime 

Notes

Acknowledgments

The authors would like to thank the reviewers for their very helpful comments to improve the paper. This work was supported by the research fund of Hanyang University (HY-2014-N, Project number 201400000002202) for new Faculty members.

References

  1. Abad, P. L., & Jaggi, C. K. (2003). A joint approach for setting unit price and the length of the credit period for a seller when end demand is price sensitive. International Journal of Production Research, 83(2), 115–122.CrossRefGoogle Scholar
  2. Aggarwal, S. P., & Jaggi, C. K. (1995). Ordering policies of deteriorating items under permissible delay in payments. Journal of the Operational Research Society, 46(5), 658–662.CrossRefGoogle Scholar
  3. Arcelus, F. J., Shah, N. H., & Srinivasan, G. (2003). Retailer’s pricing credit and inventory policies for deteriorating items in response to temporary price/credit incentives. International Journal of Production Economics, 81–82, 153–162.CrossRefGoogle Scholar
  4. Chang, H. J., Huang, C. H., & Dye, C. Y. (2001). An inventory model for deteriorating items with linear trend demand under the condition of permissible delay in payment. Production Planning and Control, 12(3), 274–282.CrossRefGoogle Scholar
  5. Chen, X., & Wang, A. (2012). Trade-credit contract with limited liability in the supply chain with budget constraints. Annals of Operations Research, 196(1), 153–165.CrossRefGoogle Scholar
  6. Chen, S.-C., Cárdenas-Barrón, L. E., & Teng, J. T. (2014). Retailers economic order quantity when the supplier offers conditionally permissible delay in payments link to order quantity. International Journal of Production Economics, 155, 284–291.CrossRefGoogle Scholar
  7. Chung, K. J. (2011). The simplified solution procedures for the optimal replenishment decisions under two-level of trade-credit policy depending on the order quantity in a supply chain system. Expert Systems with Applications, 38(10), 13482–13486.CrossRefGoogle Scholar
  8. Chung, K. J., & Cárdenas-Barrón, L. E. (2013). The simplified solution procedure for deteriorating items under stock-dependent demand and two-level trade-credit in the supply chain management. Applied Mathematical Modelling, 37(7), 4653–4660.CrossRefGoogle Scholar
  9. Chung, K. J., Cárdenas-Barrón, L. E., & Ting, P. S. (2014). An inventory model with non-instantaneous receipt and exponentially deteriorating items for an integrated three layer supply chain system under two levels of trade-credit. International Journal of Production Economics, 155, 310–317.CrossRefGoogle Scholar
  10. Ghare, P. M., & Schrader, G. H. (1963). A model for exponentially decaying inventory system. Journal of Industrial Engineering, 14(5), 238–243.Google Scholar
  11. Goyal, S. K. (1985). Economic order quantity under conditions of permissible delay in payments. Journal of Operational Research Society, 36(4), 335–338.CrossRefGoogle Scholar
  12. Ho, C. H. (2011). The optimal integrated inventory policy with price-and-credit-linked demand under two-level trade credit. Computers and Industrial Engineering, 60(1), 117–126.CrossRefGoogle Scholar
  13. Huang, Y. F. (2006). An inventory model under two-level of trade-credit and limited storage space derived without derivatives. Applied Mathematical Modelling, 30(5), 418–436.CrossRefGoogle Scholar
  14. Khanra, S., Mandal, B., & Sarkar, B. (2013). An inventory model with time dependent demand and shortages under trade-credit policy. Economic Modelling, 35, 349–355.CrossRefGoogle Scholar
  15. Khouja, M., & Mehrez, A. (1996). Optimal inventory policy under different supplier credit policies. Journal of Manufacturing Systems, 15(5), 334–339.CrossRefGoogle Scholar
  16. Li, Y., Zhen, X., & Cai, X. (2014). Trade-credit insurance, capital constraint, and the behavior of manufacturers and banks. Annals of Operations Research. doi: 10.1007/s10479-014-1602-x.
  17. Liao, H. C., Tsai, C. H., & Su, C. T. (2000). An inventory model with deteriorating items under inflation when a delay in payment is permissible. International Journal of Production Economics, 63(2), 207–214.CrossRefGoogle Scholar
  18. Mahata, G. C. (2012). An EPQ-based inventory model for exponentially deteriorating items under retailer partial trade-credit policy in supply chain. Expert Systems with Applications, 39(3), 3537–3550.CrossRefGoogle Scholar
  19. Manna, S. K., & Chaudhuri, K. S. (2006). An EOQ model with ramp type demand rate, time dependent deterioration rate, unit production cost and shortages. European Journal of Operational Research, 171(2), 557–566.CrossRefGoogle Scholar
  20. Ouyang, L. Y., Yang, C. T., Chan, Y. L., & Cárdenas-Barrón, L. E. (2013). A comprehensive extension of the optimal replenishment decisions under two-level of trade-credit policy depending on the order quantity. Applied Mathematics and Computation, 224, 268–277.CrossRefGoogle Scholar
  21. Philip, G. C. (1974). A generalized EOQ model for items with Weibull distribution. AIIE Transactions, 6(2), 159–162.CrossRefGoogle Scholar
  22. Sana, S. S. (2008). A deterministic EOQ model with delay in payments and time varying deterioration rate. European Journal of Operational Research, 184(2), 509–533.CrossRefGoogle Scholar
  23. Sarkar, B., Sana, S. S., & Chaudhuri, K. (2010). A finite replenishment model with increasing demand under inflation. International Journal of Mathematics in Operational Research, 2(3), 347–385.CrossRefGoogle Scholar
  24. Sarkar, B. (2012a). An EOQ model with delay in payments and stock dependent demand in the presence of imperfect production. Applied Mathematics and Computation, 218(17), 8295–8308.CrossRefGoogle Scholar
  25. Sarkar, B. (2012b). An EOQ model with delay in payments and time varying deterioration rate. Mathematical and Computer Modelling, 55(3–4), 367–377.CrossRefGoogle Scholar
  26. Sarkar, B., Saren, S., & Wee, H. M. (2013). An inventory model with variable demand, component cost and selling price for deteriorating items. Economic Modelling, 30, 306–310.CrossRefGoogle Scholar
  27. Sarkar, B., & Sarkar, S. (2013a). Variable deterioration and demand-an inventory model. Economic Modelling, 31, 548–556.CrossRefGoogle Scholar
  28. Sarkar, B., & Sarkar, S. (2013b). An improved inventory model with partial backlogging, time varying deterioration and stock-dependent demand. Economic Modelling, 30, 924–932.CrossRefGoogle Scholar
  29. Sarkar, M., & Sarkar, B. (2013c). An economic manufacturing quantity model with probabilistic deterioration in a production system. Economic Modelling, 31, 245–252.Google Scholar
  30. Sarkar, B. (2013). A production-inventory model with probabilistic deterioration in two-echelon supply chain management. Applied Mathematical Modelling, 37(5), 3138–3151.CrossRefGoogle Scholar
  31. Sarkar, B., Gupta, H., Chaudhuri, K., & Goyal, S. K. (2014). An integrated inventory model with variable lead time, defective units and delay in payments. Applied Mathematics and Computation, 237, 650–658.CrossRefGoogle Scholar
  32. Sarker, B. R., Jamal, A. M. M., & Wang, S. (2000). Supply chain model for perishable products under inflation and permissible delay in payment. Computers and Operations Research, 27(1), 59–75.CrossRefGoogle Scholar
  33. Sarker, B. R., Mukherjee, S., & Balan, C. V. (1997). An order-level lot size inventory model with inventory-level dependent demand and deterioration. International Journal of Production Economics, 48(3), 227–236.CrossRefGoogle Scholar
  34. Sett, B. K., Sarkar, B., & Goswami, A. (2012). A two-warehouse inventory model with increasing demand and time varying deterioration. Scientia Iranica, 19(6), 1969–1977.CrossRefGoogle Scholar
  35. Shah, Y. K. (1977). An order-level lot size inventory model for deteriorating items. AIIE Transactions, 9(1), 108–112.CrossRefGoogle Scholar
  36. Shah, N. H., Soni, H. N., & Patel, K. A. (2013). Optimizing inventory and marketing policy for non-instantaneous deteriorating items with generalized type deterioration and holding cost rates. Omega, 41(2), 421–430.CrossRefGoogle Scholar
  37. Soni, H. N. (2013). Optimal replenishment policies for deteriorating items with stock sensitive demand under two-level trade-credit and limited capacity. Applied Mathematical Modelling, 37(8), 5887–5895.CrossRefGoogle Scholar
  38. Skouri, K., Konstantaras, I., Manna, S. K., & Chaudhuri, K. S. (2011). Inventory models with ramp type demand rate, time dependent deterioration rate, unit production cost and shortages. Annals of Operations Research, 191(1), 73–95.CrossRefGoogle Scholar
  39. Teng, J. T. (2002). On the economic order quantity under conditions of permissible delay in payments. Journal of Operational Research, 53(8), 915–918.CrossRefGoogle Scholar
  40. Teng, J. T. (2009). Optimal ordering policies for a retailer who offers distinct trade-credits to its good and bad credit customers. International Journal of Production Economics, 119(2), 415–423.CrossRefGoogle Scholar
  41. Thangam, A., & Uthaykumar, R. (2008). Analysis of partial trade-credit financing in a supply chain in EPQ-based models. Advanced Modelling and Optimization, 10, 177–198.Google Scholar
  42. Wu, J., Ouyang, L. Y., Cárdenas-Barrón, L. E., & Goyal, S. K. (2014). Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade-credit financing. European Journal of Operational Research, 237(3), 898–908.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Biswajit Sarkar
    • 1
    Email author
  • Sharmila Saren
    • 2
  • Leopoldo Eduardo Cárdenas-Barrón
    • 3
  1. 1.Department of Industrial and Management EngineeringHanyang UniversityAnsanSouth Korea
  2. 2.Department of Applied Mathematics with Oceanology and Computer ProgrammingVidyasagar UniversityMidnaporeIndia
  3. 3.Department of Industrial and Systems Engineering, School of EngineeringTecnológico de MonterreyMonterreyMexico

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