An EPQ model under cash discount and permissible delay in payments derived without derivatives
DOI:
https://doi.org/10.2298/YJOR0702177HKeywords:
economic production quantity, EPQ, permissible delay in payments, trade credit, cash discount, algebraic methodAbstract
The main purpose of this paper is to investigate the case where the retailer’s unit selling price and the purchasing price per unit are not necessarily equal within the economic production quantity (EPQ) framework under cash discount and permissible delay in payments. We establish the retailer’s inventory system as a cost minimization problem to determine the retailer’s optimal inventory cycle time, optimal order quantity and optimal payment time. This paper provides an algebraic approach to determine the optimal cycle time, optimal order quantity and optimal payment time. This approach provides one theorem to efficiently determine the optimal solution. Some previously published results of other researchers are deduced as special cases. Finally, numerical examples are given to illustrate the result and the managerial insights are also obtained.References
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 Economics, 83(2): 115
Aggarwal, S.P., Jaggi, C.K. (1995) Ordering policies of deteriorating items under permissible delay in payments. Journal of the Operational Research Society, 46, 658-662
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
Cardenas-Barron, L.E. (2001) The economic production quantity (EPQ) with shortage derived algebraically. International Journal of Production Economics, 70(3): 289
Chang, C. T. (2002) Extended economic order quantity model under cash discount and payment delay. International Journal of Information and Management Sciences, 13, 57-69
Chang, C.T., Ouyang, L.Y., Teng, J.T. (2003) An EOQ model for deteriorating items under supplier credits linked to ordering quantity. Applied Mathematical Modelling, 27(12): 983
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, 32(3): 345
Chang, H.J., Dye, C.Y. (2005) The effect of credit period on the optimal lot size for deteriorating items with time varying demand and deterioration rates. Asia-Pacific Journal of Operational Research, 22(2): 211
Chang, H.J., Hung, C.H., Dye, C.Y. (2001) An inventory model for deteriorating items with linear trend demand under the condition of permissible delay in payments. Production Planning and Control, 12, 274-282
Chang, H., Dye, C., Chuang, B. (2002) An inventory model for deteriorating items under the condition of permissible delay in payments. Yugoslav Journal of Operations Research, vol. 12, br. 1, str. 73-84
Chen, M.S., Chuang, C.C. (1999) An analysis of light buyer's economic order model under trade credit. Asia-Pacific Journal of Operational Research, 16, 23-34
Chung, K.J., Goyal, S.K., Huang, Y.F. (2005) The optimal inventory policies under permissible delay in payments depending on the ordering quantity. International Journal of Production Economics, 95(2): 203
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, 84 307-318
Chung, K.J., Huang, Y.F. (2003) Economic ordering policies for items under permissible delay in payments. Journal of Information and Optimization Sciences, 24 329-344
Chung, K.J., Huang, Y.F., Huang, C.K. (2002) The replenishment decision for EOQ inventory model under permissible delay in payments. Opsearch, 39 327-340
Chung, K.J., Liao, J.J. (2004) Lot-sizing decisions under trade credit depending on the ordering quantity. Computers and Operations Research, 31(6): 909
Chung, K. (1998) A theorem on the determination of economic order quantity under conditions of permissible delay in payments. Computers and Operations Research, 25, 49-52
Goyal, S.K. (1985) Economic order quantity under conditions of permissible delay in payments. J Oper Res Soc, vol. 36, 335-338
Grubbstrom, R.W., Erdem, A. (1999) The EOQ with backlogging derived without derivatives. International Journal of Production Economics, 59(1-3): 529
Huang, Y.F. (2003) Optimal retailer's ordering policies in the EOQ model under trade credit financing. Journal of the Operational Research Society, 54(9): 1011
Huang, Y.F., Chung, K.J. (2003) Optimal replenishment and payment policies in the EOQ model under cash discount and trade credit. Asia-Pacific Journal of Operational Research, 20, 177-190
Huang, Y.F. (2004) Optimal retailer’s replenishment policy for the EPQ model under supplier’s trade credit policy. Production Planning and Control, 15(1): 27
Huang, Y. (2004) Retailer's replenishment policies under conditions of permissible delay in payments. Yugoslav Journal of Operations Research, vol. 14, br. 2, str. 231-246
Hwang, H., Shinn, S.W. (1997) Retailer's pricing and lot sizing policy for exponentially deteriorating products under the condition of permissible delay in payments. Computers and Operations Research, vol. 24, str. 539-547
Jamal, A.M.M., Sarker, B.R., Wang, S. (1997) An ordering policy for deteriorating items with allowable shortages and permissible delay in payment. J Oper Res Soc, vol. 48, str. 826-833
Jamal, A.M.M., Sarker, B.R., Wang, S. (2000) Optimal payment time for a retailer under permitted delay of payment by the wholesaler. International Journal of Production Economics, 66, 59-66
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, 207-214
Ouyang, L.Y., Chang, C.T., Teng, J.T. (2005) An EOQ model for deteriorating items under trade credits. Journal of the Operational Research Society, 56(6): 719
Ouyang, L.Y., Chen, M.S., Chuang, K.W. (2002) Economic order quantity model under cash discount and payment delay. International Journal of Information and Management Sciences, 13, 1-10
Salameh, M.K., Abboud, N.E., El-Kassar, A.N., Ghattas, R.E. (2003) Continuous review inventory model with delay in payments. International Journal of Production Economics, 85(1): 91
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, 59-75
Sarker, B.R., Jamal, A.M.M., Wang, S. (2000) Optimal payment time under permissible delay in payment for products with deterioration. Production Planning and Control, 11, 380-390
Shinn, S.W., Hwang, H. (2003) Optimal pricing and ordering policies for retailers under order size-dependent delay in payments. Computers and Operations Research, 30, 35-50
Teng, J.T. (2002) On the economic order quantity under conditions of permissible delay in payments. J Oper Res Soc, 53, 915-918
Wu, K.S., Ouyang, L.Y. (2003) An integrated single-vendor single-buyer inventory system with shortage derived algebraically. Production Planning and Control, 14,555-561
Yang, P.C., Wee, H.M. (2002) The economic lot size of the integrated vendor-buyer inventory system derived without derivatives. Optimal Control Applications and Methods, 23(3): 163
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