An EPQ Model with Increasing Demand and Demand Dependent Production Rate under Trade Credit Financing

Document Type : Research Paper

Author

Tianjin University of Finance and Economics, TianJin, China

Abstract

This paper investigates an EPQ model with the increasing demand and demand dependent production rate involving the trade credit financing policy, which is seldom reported in the literatures. The model considers the manufacturer was offered by the supplier a delayed payment time. It is assumed that the demand is a linear increasing function of the time and the production rate is proportional to the demand. That is, the production rate is also a linear function of time. This study attempts to offer a best policy for the replenishment cycle and the order quantity for the manufacturer to maximum its profit per cycle. First, the inventory model is developed under the above situation. Second, some useful theoretical results have been derived to characterize the optimal solutions for the inventory system. The Algorithm is proposed to obtain the optimal solutions of the manufacturer. Finally, the numerical examples are carried out to illustrate the theorems, and the sensitivity analysis of the optimal solutions with respect to the parameters of the inventory system is performed. Some important management insights are obtained based on the analysis.

Keywords

Main Subjects


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 Science, Vol. 32(3), pp. 345-352.

Chu P, Chang K H, Lan S P.(1998). Economic order quantity of deteriorating items under permissible delay in payments. Computer and Operations Research, Vol. 25(10), pp. 817-824.

Chung K J, Huang Y F.(2003). The optimal cycle time for EPQ inventory model under permissible delay in payments. International Journal of Production Economics, Vol. 84(3), pp. 307-318.

Chung K J, Liao J J. (2011).The simplified solution algorithm for an integrated supplier buyer inventory model with two-part trade credit in a supply chain system. European Journal of Operational Research, Vol. 213(1), pp. 156-165.

Chung Kun-Jen. (2010). The complete proof on the optimal ordering policy under cash discount and trade credit. International Journal of Systems Science, Vol. 141(4), pp. 467-475.

Goyal S K.(1985). Economic order quantity under conditions of permissible delay in payments [J]. Journal of the Operational Research Society, Vol. 36(4), pp. 335-338.

Huang Y F. (2003). Optimal retailer’s ordering policies in the EOQ model under trade credit financing [J]. Journal of the Operational research society, Vol. 54(9), pp. 1011-1015.
HuangY F.(2007). Optimal retailer’s replenishment decisions in the EPQ model under two levels of trade credit policy. European Journal of Operational Research, Vol. 176(3), pp. 1577-1597.

Jamal A 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 Society, Vol. 48(8), pp. 826-833.

Kreng V B, Tan S J. (2001). Optimal replenishment decision in an EPQ model with defective items under supply chain trade credit policy. Expert Systems with Applications, Vol. 38(8), pp. 9888-9899.

Liao Jui-Jung, Huang Kuo-Nan, Chung Kun-Jen. (2012). Lot-sizing decisions for deteriorating items with two warehouses under an order-size-dependent trade credit. International Journal of Production Economics, Vol. 137(1), pp. 102-115.

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, Vol. 171(2), pp. 557-566.

Min Jie, Zhou Yong-Wu, Liu Gui-Qing.(2012). An EPQ model for deteriorating items with inventory-level-dependent demand and permissible delay in payments. International Journal of Systems Science, Vol. 43(6), pp. 1039-1053.

Qiu Hao, Liang Liang, Yu Yu-gang, Du Shao-fu.(2007). EOQ model under three Levels of ordersize-dependent delay in payments. Journal of Systems & Management, Vol. 16(6), pp. 669-672.

Sarkar Biswajit. (2012).An EOQ model with delay in payments and time varying deterioration rate. Mathematical and Computer Modelling, Vol. 545(3-4), pp. 367-377.

Skouri K, I Konstantaras, Manna S K. (2011).Chaudhuri. Inventory models with ramp type demand rate, time dependent deterioration rate, unit production cost and shortages . Annals of Operations Research, Vol. 191(1), pp. 73-95.

Soni H N, Patel K A. (2012). Optimal strategy for an integrated inventory system involving variable production and defective items under retailer partial trade credit policy [J]. Decision Support Systems, Vol. 54(1), pp. 235-247.

Soni. N Hardik (2013).Optimal replenishment policies for non-instantaneous deteriorating items with price and stock sensitive demand under permissible delay in payment. International Journal of Production Economics, Vol. 146, pp. 259-268.

Teng J T, Min J, Pan Q H. (2012). Economic order quantity model with trade credit financing for non-decreasing demand. Omega, Vol. 40(3), pp. 328-335.

Teng J T. (2002). On the economic order quantity under conditions of permissible delay in payments. Journal of the Operational Research Society, Vol. 53(8), pp.915-918.
Teng Jinn-Tsair, Chang Chun-Tao, Chern Maw-Sheng. (2012).Vendor–buyer inventory models with trade credit financing under both non-cooperative and integrated environments. International Journal of Systems Science, Vol. 43(11), pp. 2050-2060.

Tsao Y C, Sheen G J. (2008). Dynamic pricing, promotion and replenishment policies for a deteriorating item under permissible delay in payments. Computers & Operations Research, Vol. 35(11), pp. 3562-3580.

Wu J, Ouyang L Y, Cárdenas-Barrón L E. (2014). Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing [J]. European Journal of Operational Research, Vol. 237(3), pp. 898-908.

Zhong Y G, Zhou Y W.(2013). Improving the supply chain's performance through trade credit under inventory-dependent demand and limited storage capacity. International Journal of Production Economics, Vol. 143(2), pp. 364-370.