Inventory Model for Deteriorating Items with Quadratic Time Dependent Demand under Trade Credits

Tripathi, Rakesh; Singh, Dinesh; Mishra, Tushita

doi:10.22034/2015.4.06

Inventory Model for Deteriorating Items with Quadratic Time Dependent Demand under Trade Credits

Document Type : Research Paper

Authors

¹ Graphic Era University, Dehradun (UK) India

² Head Department of Mathematics SSRRPG College, Dehradun (UK) India

³ Department of Mathematics SGRRPG College Dehradun (UK) India

10.22034/2015.4.06

Abstract

In this paper, an EOQ model is developed for a deteriorating item with quadratic time dependent demand rate under trade credit. Mathematical models are also derived under two different situations i.e. Case I; the credit period is less than the cycle time for settling the account and Case II; the credit period is greater than or equal to the cycle time for settling the account. The numerical examples are also given to validate the proposed model. Sensitivity analysis is given to study the effect of various parameters on ordering policy and optimal total profit. Mathematica 7.1 software is used for finding optimal numerical solutions.

Keywords

Main Subjects

production & inventory management

References

Aggarwal,S.P. and Jagg,C.K. (1995). Ordering policies of deteriorating items under permissible delay in payments. Journal of Operational Research Society, Vol. 36,pp. 658-662.

Bahari, Kashani,H. (1989). Replenishment schedule for deteriorating items with time- proportion demand. Journal of Operational Research Society, Vol. 40, pp. 75-81.

Chang,H.J., Hung,C.H. and Dye,C.Y. (2001). An inventory model for deteriorating items with linear trend in demand under conditions of permissible delay in payments. Production, Planning and Control, Vol. 12, pp. 272-282.

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

Chung,K.J., Lin,J.J. (2004). Lot sizing decisions under trade credit depending on the ordering quantity. Computer and Operations Research, Vol. 31, pp. 909-928.

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

Chung,K.J., Chang,S.L. and Yang,W.D. (2001). The optimal cycle time for exponentially deteriorating products under trade credit financing. The Engineering Economist, Vol. 46, pp. 232- 242.

Chung,K.J. and Teng,P.S. (1993). A heuristic for replenishment of deteriorating items with a linear trend in demand. Journal of Operational Research Society, Vol. 44(12), pp. 1235-1241.

Dave, U. And Patel, L.K. (T, ) (1981). Policy inventory model for deteriorating items with time proportional demand. Journal of Operational Research Society, Vol. 32, pp. 137-142.

Davis,R.A. and Gaither,N. (1985). Optimal ordering policies under condition of extended payment privileges. Management Science, Vol. 31, pp. 499-509.

Donaldson, W.A. (1977). A simple inventory replenishment decision rule for on linear trend in demand. Journal of Operational Research Society, Vol. 28, pp. 663-670.

Giri,B.C. and Chaudhuri, K.S. (1996). An EOQ model for deteriorating item with time varying demand and costs. Journal of Operational Research Society, Vol. 47, pp. 1398-1405.

Goyal,S.K. (1985). EOQ under condition of permissible delay in payments. Journal of Operational Research Society, Vol. 36, pp. 335-338.

Jalan,A.K. and Chaudhuri,K.S. (1999). An EOQ model for deteriorating items in a declining market with SFI policy. Korean Journal of Computational and Applied Mathematics, Vol. 6(2), pp. 437-449.

Hariga, M. (1995). An EOQ model for deteriorating items with shortages and time-varrying demand. Journal of Operational Research Society, Vol. 46, pp. 398-404.

Huang,Y.F. (2003). Optimal retailer’s ordering policies in the EOQ model under trade credit financing. Journal of the Operational Research Society, Vol. 54, pp. 1011-1015.

Jalan,A.K., Chaudhary, K.S. (1999). Structured properties of an inventory system with deterioration and trended demand. International Journal of System Science, Vol. 30(6), pp. 627-633.

Jalan, A.K., Giri, R.R. and Chaudhuri, K.S. (1996). EOQ model for item with Weibull distribution deterioration, shortages and trended demand. International Journal of System Science, Vol. 27(9), pp. 851-855.

Khanna, S.Ghosh, S.K. and Chaudhuri, K.S. (2011). An EOQ model for a deteriorating item with time-dependent demand under permissible delay in payment. Applied Mathematics and Computation, Vol. 218, pp. 1-9.

Lin,C., Tan, B. And Lee,W.C. (2000). An EOQ model for deteriorating items with time-varying demand and shortages. International Journal of System Science, Vol. 31(3), pp. 391-400.

Mandal,B.N. and Phanjdar,S. (1989). Some EOQ models under conditions of permissible delay in payments. Journal of Management Sciences, Vol. 5(2), pp. 99-108.

Mitra, A., Fox, J.F. and Jesser (1984). A note on determining order qualities with a linear trend in demand. Journal of Operational Research Society, Vol. 35, pp. 141-144.

Rilchie, E. (1985). Stock replenishment qualities for unbounded linear increasing demand: an interesting consequence of the optimal policy. Journal of Operational Research Society, Vol. 36, pp. 737-739.

Shah,N.H. AND Shah,Y.K. (1992). A probabilistic order level system when delay in payments is permissible. Presented at Operational Research Society of India, 25, India.

Silver, E.A. and Meal, H.C. (1969). A simple modification of the EOQ for the case of a varying demand rate. Production and Inventory Management, Vol. 10(4), pp. 52-65.

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

Wee,H.M. (1995). A deterministic lot size inventory model for deteriorating items with shortages and a declining market, Computer and Operations Research, Vol. 22(3), pp. 345-356.