A collaborative inventory system with permissible delay in payment for deteriorating items. (English) Zbl 1170.90320

Summary: A collaborative inventory system of single vendor and single buyer is developed to maximize the total profit of the whole system. However, the optimal solution for the whole system is not always beneficial to both players. To ensure mutual benefit, a negotiation factor is incorporated to share the profit between the two players according to their contributions. The permissible delay in payment is a win-win strategy for sharing profit in the collaborative system. A deteriorating inventory model with finite replenishment rate and price sensitive demand is assumed to occur in a high-tech, short life cycle and perishable electronic product. A numerical example is provided to illustrate our models. The sensitivity analysis of the demand rate, replenishment rate, deterioration factor, and other related parameters shows that the percentage extra total profit is significant when both the collaboration strategy and the deterioration factor are considered.


90B05 Inventory, storage, reservoirs
90B50 Management decision making, including multiple objectives
Full Text: DOI


[1] Clark, A.J.; Scarf, H., Optimal policies for a multi-echelon inventory problem, Management sciences, 6, 475-490, (1960)
[2] Banerjee, A., A joint economic-lot-size model for purchaser and vendor, Decision sciences, 17, 292-311, (1986)
[3] Goyal, S.K., A joint economic-lot-size model for purchaser and vendor: A comment, Decision sciences, 19, 236-241, (1988)
[4] Ha, D.; Kim, S.L., Implementation of JIT purchasing: an integrated approach, Production planning & control, 8, 2, 152-157, (1997)
[5] Monahan, J.P., A quantity discount-pricing model to increase vendor profits, Management science, 30, 720-726, (1984)
[6] Lal, P.; Staelin, R., An approach for developing an optimal discount pricing policy, Management science, 30, 1524-1539, (1984)
[7] Lee, L.E.; Rosenblatt, M.J., A generalized quantity discount-pricing model to increase supplier’s profits, Management science, 32, 1177-1185, (1986) · Zbl 0605.90022
[8] Kim, K.H.; Hwang, H., An incremental discount-pricing schedule with multiple customers and single price break, European journal of operation research, 35, 71-79, (1988)
[9] Chakravarty, A.K.; Martin, G.E., An optimal joint buyer – seller discount pricing model, Computers and operations research, 15, 271-281, (1988)
[10] Weng, Z.K.; Wong, R.T., General models for the supplier’s all-unit quantity discount policy, Navel research logistics, 40, 971-991, (1993) · Zbl 0800.90117
[11] Weng, Z.K., Modeling quantity discount under general price-sensitive demand functions: optimal policies and relations, European journal of operational research, 86, 300-314, (1995) · Zbl 0906.90102
[12] Li, S.X.; Hung, Z.; Ashley, A., Inventory channel coordination and bargaining in a manufacturer – retailer system, Annals of operations research, 68, 47-60, (1996) · Zbl 0867.90064
[13] Wee, H.M., Optimal buyer – seller discount pricing and ordering policy for deteriorating items, The engineering economist winter, 43, 2, 151-168, (1998)
[14] Yang, P.C.; Wee, H.M., Optimal strategy in vendor – buyer alliances with quantity discount, International journal of computer integrated manufacturing, 16, 6, 455-463, (2003)
[15] Kingsman, B.G., The effect of payment rules on ordering and stocking in purchasing, Journal of the operational research society, 34, 1085-1098, (1983)
[16] Goyal, S.K., Economic order quantity under conditions of permissible delay in payment, Journal of the operational research society, 36, 335-338, (1985) · Zbl 0568.90025
[17] Davis, R.A.; Gaither, N., Optimal ordering policies under conditions of extended payment privileges, Management sciences, 31, 499-509, (1985) · Zbl 0609.90028
[18] Mandal, B.N.; Phaujdar, S., Some EOQ models under permissible delay in payments, International journal of managements science, 5, 2, 99-108, (1989)
[19] Jaggi, C.K.; Aggarwall, S.P., Ordering policies of deteriorating items under permissible delay in payments, Journal of the operational research society, 46, 658-662, (1995) · Zbl 0830.90032
[20] Chung, K.J., A theorem on the determination of economic order quantity under conditions of permissible delay in payments, Computer and operations research, 25, 49-52, (1998) · Zbl 0906.90051
[21] Wee, H.M., Economic production lot size model for deteriorating items with partial back-ordering, Computers & industrial engineering, 24, 3, 449-458, (1993)
[22] Ghare, P.M.; Schrader, S.F., A model for exponentially decaying inventory, Journal of industrial engineering, 14, 5, 238-243, (1963)
[23] Covert, R.P.; Philip, G.C., An EOQ model for items with Weibull distribution deterioration, AIIE transactions, 5, 323-326, (1973)
[24] Kang, S.; Kim, I., A study on the price and production level of the deteriorating inventory system, International journal of production research, 21, 449-460, (1983)
[25] Raafat, F.; Wolfe, P.M.; Eldin, H.K., An inventory model for deteriorating items, Computers & industrial engineering, 20, 89-94, (1991)
[26] Yang, P.C.; Wee, H.M., Economic ordering policy of deteriorated item for vendor and buyer: an integrated approach, Production planning and control, 11, 5, 474-480, (2000)
[27] H.M. Wee, S.L. Chung, Managing deteriorating items through VMI using a genetic algorithm, Working Paper in Chung Yuan Christian University, Taiwan, 2003
[28] Spiegel, M.R., Applied differential equations, (1960), Prentice-Hall Englewood Cliffs, NJ · Zbl 0145.32302
[29] Misra, R.B., Optimal production lot size model for a system with deteriorating inventory, International journal of production research, 15, 495-505, (1975)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.