Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing and back order

Document Type: Research Paper

Authors

1 Department of Industrial Engineering, College of Engineering, University of Tehran Tehran , Iran

2 School of Industrial Engineering, Iran University of Science & Technology, Tehran, Iran

Abstract

In a supplier-retailer-buyer supply chain, the supplier frequently offers the retailer a trade credit of  periods, and the retailer in turn provides a trade credit of  periods to her/his buyer to stimulate sales and reduce inventory. From the seller’s perspective, granting trade credit increases sales and revenue but also increases opportunity cost (i.e., the capital opportunity loss during credit period) and default risk (i.e., the percentage that the buyer will not be able to pay off her/his debt obligations). Hence, how to determine credit period is increasingly recognized as an important strategy to increase seller’s profitability. Also, many products such as fruits, vegetables, high-tech products, pharmaceuticals, and volatile liquids not only deteriorate continuously due to evaporation, obsolescence and spoilage but also have their expiration dates. In this paper along with deterioration and expiration date, we consider shortages that are very rarely investigated by researches. Therefore, this paper proposes an economic order quantity model for the retailer where: (a) the supplier provides an up-stream trade credit and the retailer also offers a down-stream trade credit, (b) the retailer’s down-stream trade credit to the buyer not only increases sales and revenue but also opportunity cost and default risk, (c) deteriorating items not only deteriorate continuously but also have their expiration dates and (d) there is a shortage allowed in each time period. We then show that the retailer’s optimal credit period and cycle time not only exist but also are unique. Furthermore, we discuss several special cases including for non-deteriorating items. Finally, we run some numerical examples to illustrate the problem and provide managerial insights. 

Keywords

Main Subjects


Aggarwal, S. P., & Jaggi, C. K. (1995). Ordering policies of deteriorating items under permissible delay in payments. Journal of the operational Research Society46(5), 658-662.

 

Bakker, M., Riezebos, J., & Teunter, R. H. (2012). Review of inventory systems with deterioration since 2001. European Journal of Operational Research221(2), 275-284.

 

Chakrabarti, T., & Chaudhuri, K. S. (1997). An EOQ model for deteriorating items with a linear trend in demand and shortages in all cycles. International Journal of Production Economics49(3), 205-213.

 

Chang, H. J., & Dye, C. Y. (2001). An inventory model for deteriorating items with partial backlogging and permissible delay in payments. International Journal of Systems Science32(3), 345-352.

 

Chern, M. S., Pan, Q., Teng, J. T., Chan, Y. L., & Chen, S. C. (2013). Stackelberg solution in a vendor–buyer supply chain model with permissible delay in payments. International Journal of Production Economics144(1), 397-404.

                      

Chen, S. C., Teng, J. T., & Skouri, K. (2014). Economic production quantity models for deteriorating items with up-stream full trade credit and down-stream partial trade credit. International Journal of Production Economics155, 302-309.

 

Covert, R. P., & Philip, G. C. (1973). An EOQ model for items with Weibull distribution deterioration. AIIE transactions5(4), 323-326.

 

Dave, U., & Patel, L. K. (1981). (T, S i) policy inventory model for deteriorating items with time proportional demand. Journal of the Operational Research Society32(2), 137-142.

 

Dye, C. Y. (2013). The effect of preservation technology investment on a non-instantaneous deteriorating inventory model. Omega41(5), 872-880.Ghare, P. M., & Schrader, G. F. (1963). A model for exponentially decaying inventory. Journal of industrial Engineering14(5), 238-243.

 

Goswami, A., & Chaudhuri, K. S. (1991). An EOQ model for deteriorating items with shortages and a linear trend in demand. Journal of the Operational Research Society42(12), 1105-1110.

 

Goyal, S. K. (1985). Economic order quantity under conditions of permissible delay in payments. Journal of the operational research society36(4), 335-338.

 

Goyal, S. K., & Giri, B. C. (2001). Recent trends in modeling of deteriorating inventory. European Journal of operational research134(1), 1-16.

 

Goyal, S. K. (2007). Optimal ordering policies for a retailer in a supply chain with up-stream and down-stream trade credits. The Journal of the Operational Research Society58(9), 1252-1255.

 

Hariga, M. (1996). Optimal EOQ models for deteriorating items with time-varying demand. Journal of the Operational Research Society47(10), 1228-1246.

 

Huang, Y. F. (2003). Optimal retailer's ordering policies in the EOQ model under trade credit financing. Journal of the Operational Research Society54(9), 1011-1015.

 

Jamal, A. M. M., Sarker, B. R., & Wang, S. (1997). An ordering policy for deteriorating items with allowable shortage and permissible delay in payment. Journal of the Operational Research Society48(8), 826-833.

 

Kreng, V. B., & Tan, S. J. (2011). Optimal replenishment decision in an EPQ model with defective items under supply chain trade credit policy. Expert Systems with Applications38(8), 9888-9899.

 

Liao, J. J. (2008). An EOQ model with noninstantaneous receipt and exponentially deteriorating items under two-level trade credit. International Journal of Production Economics113(2), 852-861.

 

Lou, K. R., & Wang, W. C. (2013). Optimal trade credit and order quantity when trade credit impacts on both demand rate and default risk. Journal of the Operational Research Society64(10), 1551-1556.

 

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 Applications39(3), 3537-3550.

 

Min, J., Zhou, Y. W., & Zhao, J. (2010). An inventory model for deteriorating items under stock-dependent demand and two-level trade credit. Applied Mathematical Modelling34(11), 3273-3285.

Ouyang, L. Y., & Chang, C. T. (2013). Optimal production lot with imperfect production process under permissible delay in payments and complete backlogging. International Journal of Production Economics144(2), 610-617.

 

Papachristos, S., & Skouri, K. (2000). An optimal replenishment policy for deteriorating items with time-varying demand and partial–exponential type–backlogging. Operations Research Letters27(4), 175-184.

 

Raafat, F. (1991). Survey of literature on continuously deteriorating inventory models. Journal of the Operational Research society42(1), 27-37.

 

Sachan, R. S. (1984). On (T, S i) policy inventory model for deteriorating items with time proportional demand. Journal of the operational research society35(11), 1013-1019.

 

Sarkar, B. (2012). An EOQ model with delay in payments and time varying deterioration rate. Mathematical and Computer Modelling55(3), 367-377.

 

Seifert, D., Seifert, R. W., & Protopappa-Sieke, M. (2013). A review of trade credit literature: Opportunities for research in operations. European Journal of Operational Research231(2), 245-256.

 

Shah, N. H. (1993). Probabilistic time-scheduling model for an exponentially decaying inventory when delays in payments are permissible. International Journal of Production Economics32(1), 77-82.

 

Skouri, K., Konstantaras, I., Papachristos, S., & Ganas, I. (2009). Inventory models with ramp type demand rate, partial backlogging and Weibull deterioration rate. European Journal of Operational Research192(1), 79-92.

 

Skouri, K., Konstantaras, I., Papachristos, S., & Teng, J. T. (2011). Supply chain models for deteriorating products with ramp type demand rate under permissible delay in payments. Expert Systems with Applications38(12), 14861-14869.

 

Teng, J. T., Chern, M. S., Yang, H. L., & Wang, Y. J. (1999). Deterministic lot-size inventory models with shortages and deterioration for fluctuating demand. Operations Research Letters24(1), 65-72.

 

Teng, J. T., & Lou, K. R. (2012). Seller’s optimal credit period and replenishment time in a supply chain with up-stream and down-stream trade credits. Journal of Global Optimization53(3), 417-430.

 

Teng, J. T. (2002). On the economic order quantity under conditions of permissible delay in payments. Journal of the Operational Research Society53(8), 915-918.

 

Teng, J. T., Krommyda, I. P., Skouri, K., & Lou, K. R. (2011). A comprehensive extension of optimal ordering policy for stock-dependent demand under progressive payment scheme. European Journal of Operational Research215(1), 97-104.

 

Teng, J. T., Min, J., & Pan, Q. (2012). Economic order quantity model with trade credit financing for non-decreasing demand. Omega40(3), 328-335.

 

Teng, J. T., Yang, H. L., & Chern, M. S. (2013). An inventory model for increasing demand under two levels of trade credit linked to order quantity. Applied Mathematical Modelling37(14), 7624-7632.

 

Wang, X., Ouyang, Y., Liu, J., Zhu, M., Zhao, G., Bao, W., & Hu, F. B. (2014). Fruit and vegetable consumption and mortality from all causes, cardiovascular disease, and cancer: systematic review and dose-response meta-analysis of prospective cohort studies. Bmj349, g4490.

 

Wang, W. C., Teng, J. T., & Lou, K. R. (2014). Seller’s optimal credit period and cycle time in a supply chain for deteriorating items with maximum lifetime. European Journal of Operational Research232(2), 315-321.

 

Wee, H. M., & Widyadana, G. A. (2013). A production model for deteriorating items with stochastic preventive maintenance time and rework process with FIFO rule. Omega41(6), 941-954.