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April  2015, 11(2): 479-492. doi: 10.3934/jimo.2015.11.479

The EPQ model with deteriorating items under two levels of trade credit in a supply chain system

Pin-Shou Ting 1,

1. 

Department of International Business Management, Shih Chien University, Taipei, Taiwan

Received  October 2013 Revised  March 2014 Published  September 2014

There are two kinds of two levels of trade credit policies addressed by Huang [15] and Teng [29], respectively. Liao [24] presents the EPQ model with deteriorating items under two-level trade credit policy from the viewpoint of Huang [15], while Chang, Teng and Chern [2] discuss the model from the viewpoint of Teng [29]. However, errors are found in the process of the modeling in Chang et al. [2]. The main purpose of this study is to improve the model of Chang et al. [2] and develop a more general EPQ inventory model. A theorem is also provided for practitioners to make right decisions.
Keywords: permissible delay in payments., trade credit, EPQ, Inventory, deteriorating items.
Mathematics Subject Classification: Primary: 90B05; Secondary: 65H0.
Citation: Pin-Shou Ting. The EPQ model with deteriorating items under two levels of trade credit in a supply chain system. Journal of Industrial & Management Optimization, 2015, 11 (2) : 479-492. doi: 10.3934/jimo.2015.11.479
References:
[1]

F. J. Arcelus, N. H. Shah and G. Srinivasan, Retailer's pricing, credit and inventory policies for deteriorating items in response to temporary price/credit incentives, International Journal of Production Economics, 81-82 (2003), 153-162. doi: 10.1016/S0925-5273(02)00269-4.  Google Scholar

[2]

C. T. Chang, J. T. Teng and M. S. Chern, Optimal manufacturer's replenishment policies for deteriorating items in a supply chain with up-stream and down-stream trade credits, International Journal of Production Economics, 127 (2010), 197-202. doi: 10.1016/j.ijpe.2010.05.014.  Google Scholar

[3]

C. K. Chen and Y. X. Liao, A deteriorating inventory model for an intermediary firm under return on inventory investment maximization, Journal of Industrial and Management Optimization, 10 (2014), 989-1000. doi: 10.3934/jimo.2014.10.989.  Google Scholar

[4]

L. H. Chen and F. S. Kang, Coordination between vendor and buyer considering trade credit and items of imperfect quality, International Journal of Production Economics, 123 (2010), 52-61. doi: 10.1016/j.ijpe.2009.06.043.  Google Scholar

[5]

S. C. Chen, J. T. Teng and K. Skouri, Economic production quantity models for deteriorating items with up-stream full trade credit and down-stream partial trade credit, International Journal of Production Economics, 155 (2014), 302-309. doi: 10.1016/j.ijpe.2013.07.024.  Google Scholar

[6]

C. Y. Chiu, M. F. Yang, C. J. Tang and Y. Lin, Integrated imperfect production inventory model under permissible delay in payments depending on the order quantity, Journal of Industrial and Management Optimization, 9 (2013), 945-965. doi: 10.3934/jimo.2013.9.945.  Google Scholar

[7]

P. Chu, K. J. Chung and S. P. Lan, Economic order quantity of deteriorating items under permissible delay in payments, Computers and Operations Research, 25 (1998), 817-824. doi: 10.1016/S0305-0548(98)00006-9.  Google Scholar

[8]

K. J. Chung, Comments on the EOQ model under retailer partial trade credit policy in the supply chain, International Journal of Production Economics, 114 (2008), 308-312. doi: 10.1016/j.ijpe.2008.02.010.  Google Scholar

[9]

K. J. Chung and T. S. Huang, The optimal retailer's ordering policies for deteriorating items with limited storage capacity under trade credit financing, International Journal of Production Economics, 106 (2007), 127-145. doi: 10.1016/j.ijpe.2006.05.008.  Google Scholar

[10]

K. J. Chung and Y. F. Huang, The optimal cycle time for EPQ inventory model under permissible delay in payments, International Journal of Production Economics, 84 (2003), 307-318. doi: 10.1016/S0925-5273(02)00465-6.  Google Scholar

[11]

K. J. Chung and J. J. Liao, Lot-sizing decisions under trade credit depending on the ordering quantity, Computers and Operations Research, 31 (2004), 909-928. doi: 10.1016/S0305-0548(03)00043-1.  Google Scholar

[12]

K. J. Chung and J. J. Liao, The optimal ordering policy in a DCF analysis for deteriorating items when trade credit depends on the order quantity, International Journal of Production Economics, 100 (2006), 116-130. doi: 10.1016/j.ijpe.2004.10.011.  Google Scholar

[13]

P. M. Ghare and G. F. Schrader, A model for exponentially decaying inventories, Journal of Industrial Engineering, 14 (1963), 238-243. Google Scholar

[14]

S. K. Goyal, Economic order quantity under conditions of permissible delay in payments, Journal of Operational Research Society, 36 (1985), 335-338. doi: 10.2307/2582421.  Google Scholar

[15]

Y. F. Huang, Optimal retailer's ordering policies in the EOQ model under trade credit financing, Journal of Operational Research Society, 54 (2003), 1011-1015. doi: 10.1057/palgrave.jors.2601588.  Google Scholar

[16]

Y. F. Huang, An inventory model under two levels of trade credit and limited storage space derived without derivatives, Applied Mathematical Modelling, 30 (2006), 418-436. doi: 10.1016/j.apm.2005.05.009.  Google Scholar

[17]

Y. F. Huang, Optimal retailer's replenishment decisions in the EPQ model under two levels of trade credit policy, European Journal of Operational Research, 176 (2007), 1577-1591. doi: 10.1016/j.ejor.2005.10.035.  Google Scholar

[18]

Y. F. Huang and K. H. Hsu, An EOQ model under retailer partial trade credit policy in supply chain, International Journal of Production Economics, 112 (2008), 655-664. doi: 10.1016/j.ijpe.2007.05.014.  Google Scholar

[19]

C. K. Jaggi and S. P. Aggarwal, Credit financing in economics ordering policies of deteriorating items, International Journal of Production Economics, 34 (1994), 151-155. doi: 10.1016/0925-5273(94)90031-0.  Google Scholar

[20]

C. K. Jaggi, S. K. Goyal and S. K. Goel, Retailer's optimal replenishment decisions with credit-linked demand under permissible delay in payments, European Journal of Operational Research, 190 (2008), 130-135. doi: 10.1016/j.ejor.2007.05.042.  Google Scholar

[21]

V. B. Kreng and S. J. Tan, The optimal replenishment decisions under two levels of trade credit policy depending on the order quantity, Expert Systems with Applications, 37 (2010), 5514-5522. doi: 10.1016/j.eswa.2009.12.014.  Google Scholar

[22]

J. J. Liao, On an EPQ model for deteriorating items under permissible delay in payments, Applied Mathematical Modelling, 31 (2007), 393-403. doi: 10.1016/j.apm.2005.11.016.  Google Scholar

[23]

J. J. Liao, A note on an EOQ model for deteriorating items under supplier credit linked to ordering quantity, Applied Mathematical Modelling, 31 (2007), 1690-1699. doi: 10.1016/j.apm.2006.05.003.  Google Scholar

[24]

J. J. Liao, An EOQ model with noninstantaneous receipt and exponentially deteriorating items under two-level trade credit, International Journal of Production Economics, 113 (2008), 852-861. doi: 10.1016/j.ijpe.2007.09.006.  Google Scholar

[25]

J. J. Liao and K. J. Chung, An EOQ model for deterioration items under trade credit policy in a supply chain system, Journal of the Operations Research Society of Japan, 52 (2009), 46-57.  Google Scholar

[26]

J. Min, Y. W. Zhou and J. Zhao, An inventory model for deteriorating items under stock-dependent demand and two-level trade credit, Applied Mathematical Modelling, 34 (2010), 3273-3285. doi: 10.1016/j.apm.2010.02.019.  Google Scholar

[27]

K. Skouri and I. Konstantara, Two-warehouse inventory models for deteriorating products with ramp type demand rate, Journal of Industrial and Management Optimization, 9 (2013), 855-883. doi: 10.3934/jimo.2013.9.855.  Google Scholar

[28]

H. Soni and N. H. Shah, Optimal ordering policy for stock-dependent demand under progressive payment scheme, European Journal of Operational Research, 184 (2008), 91-100. doi: 10.1016/j.ejor.2006.10.048.  Google Scholar

[29]

J. T. Teng, Optimal ordering policies for a retailer who offers distinct trade credits to its good and bad credit customers, International Journal of Production Economics, 119 (2009), 415-423. doi: 10.1016/j.ijpe.2009.04.004.  Google Scholar

[30]

J. T. Teng and C. T. Chang, Optimal manufacturer's replenishment policies in the EPQ model under two levels of trade credit policy, European Journal of Operational Research, 195 (2009), 358-363. doi: 10.1016/j.ejor.2008.02.001.  Google Scholar

[31]

J. T. Teng, C. T. Cheng, M. S. Chern and Y. L. Chan, Retailer's optimal ordering policies with trade credit financing, International Journal of Systems Science, 38 (2007), 269-278. doi: 10.1080/00207720601158060.  Google Scholar

[32]

J. T. Teng and S. K. Goyal, Optimal ordering policies for a retailer in a supply chain with up-stream and down-stream trade credit, Journal of the Operational Research Society, 58 (2007), 1252-1255. Google Scholar

[33]

J. T. Teng, J. Chen and S. K. Goyal, A comprehensive note on: An inventory model under two levels of trade credit and limited storage space derived without derivatives, Applied Mathematical Modelling, 33 (2009), 4388-4396. doi: 10.1016/j.apm.2009.03.010.  Google Scholar

[34]

A. Thangam and R. Uthayakumar, Two-echelon trade credit financing for perishable items in a supply chain when demand depends on both selling price and credit period, Computers and Industrial Engineering, 57 (2009), 773-786. doi: 10.1016/j.cie.2009.02.005.  Google Scholar

[35]

Y. C. Tsao and G. J. Shreen, Dynamic pricing, promotion and replenishment policies for a deteriorating item under permissible delay in payments, Computers and Operations Research, 35 (2008), 3562-3580. doi: 10.1016/j.cor.2007.01.024.  Google Scholar

[36]

D. E. Varberg, J. Purcell and S. E. Rigdon,, Calculus, $9^{th}$ edition, Pearson Education, New Jersey, 2007. Google Scholar

[37]

C. T. Yang, L. Y. Ouyang, H. F. Yen and K. L. Lee, Joint pricing and ordering policies for deteriorating item with retail price-dependent demand in response to announced supply price increase, Journal of Industrial and Management Optimization, 9 (2013), 437-454. doi: 10.3934/jimo.2013.9.437.  Google Scholar

show all references

References:
[1]

F. J. Arcelus, N. H. Shah and G. Srinivasan, Retailer's pricing, credit and inventory policies for deteriorating items in response to temporary price/credit incentives, International Journal of Production Economics, 81-82 (2003), 153-162. doi: 10.1016/S0925-5273(02)00269-4.  Google Scholar

[2]

C. T. Chang, J. T. Teng and M. S. Chern, Optimal manufacturer's replenishment policies for deteriorating items in a supply chain with up-stream and down-stream trade credits, International Journal of Production Economics, 127 (2010), 197-202. doi: 10.1016/j.ijpe.2010.05.014.  Google Scholar

[3]

C. K. Chen and Y. X. Liao, A deteriorating inventory model for an intermediary firm under return on inventory investment maximization, Journal of Industrial and Management Optimization, 10 (2014), 989-1000. doi: 10.3934/jimo.2014.10.989.  Google Scholar

[4]

L. H. Chen and F. S. Kang, Coordination between vendor and buyer considering trade credit and items of imperfect quality, International Journal of Production Economics, 123 (2010), 52-61. doi: 10.1016/j.ijpe.2009.06.043.  Google Scholar

[5]

S. C. Chen, J. T. Teng and K. Skouri, Economic production quantity models for deteriorating items with up-stream full trade credit and down-stream partial trade credit, International Journal of Production Economics, 155 (2014), 302-309. doi: 10.1016/j.ijpe.2013.07.024.  Google Scholar

[6]

C. Y. Chiu, M. F. Yang, C. J. Tang and Y. Lin, Integrated imperfect production inventory model under permissible delay in payments depending on the order quantity, Journal of Industrial and Management Optimization, 9 (2013), 945-965. doi: 10.3934/jimo.2013.9.945.  Google Scholar

[7]

P. Chu, K. J. Chung and S. P. Lan, Economic order quantity of deteriorating items under permissible delay in payments, Computers and Operations Research, 25 (1998), 817-824. doi: 10.1016/S0305-0548(98)00006-9.  Google Scholar

[8]

K. J. Chung, Comments on the EOQ model under retailer partial trade credit policy in the supply chain, International Journal of Production Economics, 114 (2008), 308-312. doi: 10.1016/j.ijpe.2008.02.010.  Google Scholar

[9]

K. J. Chung and T. S. Huang, The optimal retailer's ordering policies for deteriorating items with limited storage capacity under trade credit financing, International Journal of Production Economics, 106 (2007), 127-145. doi: 10.1016/j.ijpe.2006.05.008.  Google Scholar

[10]

K. J. Chung and Y. F. Huang, The optimal cycle time for EPQ inventory model under permissible delay in payments, International Journal of Production Economics, 84 (2003), 307-318. doi: 10.1016/S0925-5273(02)00465-6.  Google Scholar

[11]

K. J. Chung and J. J. Liao, Lot-sizing decisions under trade credit depending on the ordering quantity, Computers and Operations Research, 31 (2004), 909-928. doi: 10.1016/S0305-0548(03)00043-1.  Google Scholar

[12]

K. J. Chung and J. J. Liao, The optimal ordering policy in a DCF analysis for deteriorating items when trade credit depends on the order quantity, International Journal of Production Economics, 100 (2006), 116-130. doi: 10.1016/j.ijpe.2004.10.011.  Google Scholar

[13]

P. M. Ghare and G. F. Schrader, A model for exponentially decaying inventories, Journal of Industrial Engineering, 14 (1963), 238-243. Google Scholar

[14]

S. K. Goyal, Economic order quantity under conditions of permissible delay in payments, Journal of Operational Research Society, 36 (1985), 335-338. doi: 10.2307/2582421.  Google Scholar

[15]

Y. F. Huang, Optimal retailer's ordering policies in the EOQ model under trade credit financing, Journal of Operational Research Society, 54 (2003), 1011-1015. doi: 10.1057/palgrave.jors.2601588.  Google Scholar

[16]

Y. F. Huang, An inventory model under two levels of trade credit and limited storage space derived without derivatives, Applied Mathematical Modelling, 30 (2006), 418-436. doi: 10.1016/j.apm.2005.05.009.  Google Scholar

[17]

Y. F. Huang, Optimal retailer's replenishment decisions in the EPQ model under two levels of trade credit policy, European Journal of Operational Research, 176 (2007), 1577-1591. doi: 10.1016/j.ejor.2005.10.035.  Google Scholar

[18]

Y. F. Huang and K. H. Hsu, An EOQ model under retailer partial trade credit policy in supply chain, International Journal of Production Economics, 112 (2008), 655-664. doi: 10.1016/j.ijpe.2007.05.014.  Google Scholar

[19]

C. K. Jaggi and S. P. Aggarwal, Credit financing in economics ordering policies of deteriorating items, International Journal of Production Economics, 34 (1994), 151-155. doi: 10.1016/0925-5273(94)90031-0.  Google Scholar

[20]

C. K. Jaggi, S. K. Goyal and S. K. Goel, Retailer's optimal replenishment decisions with credit-linked demand under permissible delay in payments, European Journal of Operational Research, 190 (2008), 130-135. doi: 10.1016/j.ejor.2007.05.042.  Google Scholar

[21]

V. B. Kreng and S. J. Tan, The optimal replenishment decisions under two levels of trade credit policy depending on the order quantity, Expert Systems with Applications, 37 (2010), 5514-5522. doi: 10.1016/j.eswa.2009.12.014.  Google Scholar

[22]

J. J. Liao, On an EPQ model for deteriorating items under permissible delay in payments, Applied Mathematical Modelling, 31 (2007), 393-403. doi: 10.1016/j.apm.2005.11.016.  Google Scholar

[23]

J. J. Liao, A note on an EOQ model for deteriorating items under supplier credit linked to ordering quantity, Applied Mathematical Modelling, 31 (2007), 1690-1699. doi: 10.1016/j.apm.2006.05.003.  Google Scholar

[24]

J. J. Liao, An EOQ model with noninstantaneous receipt and exponentially deteriorating items under two-level trade credit, International Journal of Production Economics, 113 (2008), 852-861. doi: 10.1016/j.ijpe.2007.09.006.  Google Scholar

[25]

J. J. Liao and K. J. Chung, An EOQ model for deterioration items under trade credit policy in a supply chain system, Journal of the Operations Research Society of Japan, 52 (2009), 46-57.  Google Scholar

[26]

J. Min, Y. W. Zhou and J. Zhao, An inventory model for deteriorating items under stock-dependent demand and two-level trade credit, Applied Mathematical Modelling, 34 (2010), 3273-3285. doi: 10.1016/j.apm.2010.02.019.  Google Scholar

[27]

K. Skouri and I. Konstantara, Two-warehouse inventory models for deteriorating products with ramp type demand rate, Journal of Industrial and Management Optimization, 9 (2013), 855-883. doi: 10.3934/jimo.2013.9.855.  Google Scholar

[28]

H. Soni and N. H. Shah, Optimal ordering policy for stock-dependent demand under progressive payment scheme, European Journal of Operational Research, 184 (2008), 91-100. doi: 10.1016/j.ejor.2006.10.048.  Google Scholar

[29]

J. T. Teng, Optimal ordering policies for a retailer who offers distinct trade credits to its good and bad credit customers, International Journal of Production Economics, 119 (2009), 415-423. doi: 10.1016/j.ijpe.2009.04.004.  Google Scholar

[30]

J. T. Teng and C. T. Chang, Optimal manufacturer's replenishment policies in the EPQ model under two levels of trade credit policy, European Journal of Operational Research, 195 (2009), 358-363. doi: 10.1016/j.ejor.2008.02.001.  Google Scholar

[31]

J. T. Teng, C. T. Cheng, M. S. Chern and Y. L. Chan, Retailer's optimal ordering policies with trade credit financing, International Journal of Systems Science, 38 (2007), 269-278. doi: 10.1080/00207720601158060.  Google Scholar

[32]

J. T. Teng and S. K. Goyal, Optimal ordering policies for a retailer in a supply chain with up-stream and down-stream trade credit, Journal of the Operational Research Society, 58 (2007), 1252-1255. Google Scholar

[33]

J. T. Teng, J. Chen and S. K. Goyal, A comprehensive note on: An inventory model under two levels of trade credit and limited storage space derived without derivatives, Applied Mathematical Modelling, 33 (2009), 4388-4396. doi: 10.1016/j.apm.2009.03.010.  Google Scholar

[34]

A. Thangam and R. Uthayakumar, Two-echelon trade credit financing for perishable items in a supply chain when demand depends on both selling price and credit period, Computers and Industrial Engineering, 57 (2009), 773-786. doi: 10.1016/j.cie.2009.02.005.  Google Scholar

[35]

Y. C. Tsao and G. J. Shreen, Dynamic pricing, promotion and replenishment policies for a deteriorating item under permissible delay in payments, Computers and Operations Research, 35 (2008), 3562-3580. doi: 10.1016/j.cor.2007.01.024.  Google Scholar

[36]

D. E. Varberg, J. Purcell and S. E. Rigdon,, Calculus, $9^{th}$ edition, Pearson Education, New Jersey, 2007. Google Scholar

[37]

C. T. Yang, L. Y. Ouyang, H. F. Yen and K. L. Lee, Joint pricing and ordering policies for deteriorating item with retail price-dependent demand in response to announced supply price increase, Journal of Industrial and Management Optimization, 9 (2013), 437-454. doi: 10.3934/jimo.2013.9.437.  Google Scholar

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