Inventory Model for Deteriorating Items with Four level System and Shortages

Document Type: Research Paper

Author

Graphic Era University, Dehradun (UK) India

Abstract

This paper presents an inventory model for deteriorating items in which shortages are allowed. It is assumed that the production rate is proportional to the demand rate and greater than demand rate. The inventory model is developed by considering four different circumstances. The optimal of the problem is obtained with the help of Mathematica 7 software. Numerical examples are given to illustrate the model for different parameters. Sensitivity analysis of the model has been developed to examine the effect of changes in the values of the different parameters for optimal inventory policy. Truncated Taylor’s series is used for finding closed form optimal solution.

Keywords


Aggarwal, S.P. and Jaggi, C.K. (1995). Ordering policies of deteriorating items under permissible delay in payments. Journal of operational Research Society, Vol. 46, pp. 658-662.

Agarwal, R., Rajput, D. and Varshney, N.K. (2009). Integrated inventory system with the effect of inflation and credit period. International Journal of Applied Engineering Research, Vol. 4(11), pp. 2337-2348.

Baker, R.C. and Urban, T.L. (1988). A deterministic inventory system with inventory- level dependent demand rate. Journal of operational Research Society, Vol. 39, pp. 823-831.

Bhunia,A.K. , Jaggi,C.K. , Sharma,A. and Sharma,R. (2014). A two- warehouse inventory model for deteriorating items under permissible delay in payments with partial backlogging. Applied Mathematics and Computation, Vol. 232, pp.1125-1137.

Chakrabarty, T., Giri, B.C. and Chaudhuri, K.S. (1998). A EOQ model for items with Weibull distribution deterioration shortages and trended demand. An extension of Phillip model. Computer and Operations Research, Vol. 25, (718), pp. 649- 657.

Chung, K.J. (1998). A theorem on the determination of economic order quantity under conditions of permissible delay in payments. Computers and Operations Research, Vol. 25, pp. 49-52

Chung, H.J. Hung, C.H. and 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, Vol. 12, pp. 274-282

Covert, R.P. and Philip, G.C. (1973). An EOQ model for items with Weibull distribution deterioration. AIIE Transaction, Vol. 5, pp. 323-326.

Datta, T.K., and Pal, A.K. (1991). Effects of inflation and time- value of money on an inventory model with linear time – dependent demand rate and shortages. European Journal of Operational Research, Vol. 52, pp. 1-8.

Datta, T.K., and Pal, A.K. (1991). Effects of inflation and time- value of money on an inventory model with linear time – dependent demand rate and shortages. European Journal of Operational Research, Vol. 52, pp. 1-8.

Deb,M and Chaudhuri,K.S. (1987). A note on the heuristic for replenishment of trended inventories considering shortages. Journal of Operational Research Society, Vol. 38, pp. 459-463.

Ghare, P.M. and Schrader, G.H. (1963). A model for exponentially decaying inventory system. Journal of Industrial Engineering, Vol. 15, pp. 238–243

Ghiami,Y. Williams,T. and Wu,Y. (2013). A two- echelon inventory model for a deteriorating item with stock- dependent demand, partial backlogging and capacity constraints. European Journal of Operational Research, Vol. 231, pp. 587-597.

Goyal, S.K. (1985). Economic order quantity under conditions of permissible delay in payments. Journal of operational Research Society, 36, 335-338. Gupta, R. and Vrat, P. (1986). Inventory model for stock – dependent consumption rate. Opsearch, Vol. 23(1), pp. 19-24.

Lin, J. and Julian, H.C. (2012). A demand independent inventory control. Yugoslav Journal of operations Research, Vol. 22, pp. 1-7.

Mandal, B.N. and Phaujdar, S. (1989). An inventory model for deteriorating items and stockdependent consumption rate. Journal of operational Research Society, Vol. 40(5), pp. 483-488.

Meher, M.K., Panda, G.C., and Sahu,S.K. (2012). An inventory model with Weibull deterioration rate under the Delay in Payment in Demand Decling Market. Applied Mathematical Sciences, Vol. 6(23), pp. 1121-1133.

Misra, R.B. (1979). A note on optimal inventory management under inflation. Noval Res. Logist, Vol. 26, pp. 161-165.

Misra, R.B. (1975). Optimal Production lot size model for a system with deteriorating inventory. International Journal of Production Economics, Vol.  13 , pp. 495–505 .

Ouyang, L.Y. and Chang, C.T. (2013). Optimal production lot with imperfect production process under permissible delay in payment and complete backlogging. International Journal of Production Economics, Vol. 144, pp. 610-617.

Philip, G.C. (1974).A generalized EOQ model for items with Weibull distribution deterioration. AIIE transactions, Vol. 6, pp. 159–162.

Ray, J. Chaudhuri, K.S. (1997). An EOQ model with stock- dependent demand, shortages, inflation and time- discounting. International Journal of Production Economics, Vol. 53, pp. 171-180.

Sarkar, B. (2012). An EOQ model with delay in payments and time varying deterioration rate. Mathematical and Computer Modelling, Vol. 55(3-4), pp. 367-377.

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

Silver, E.A. and Meal, H.C. (1973). A heuristic for selecting lot size quantities for the case of a deterministic time – varying demand rate and discrete opportunities of replenishment. Journal of operational Research Society, Vol. 14, pp. 64 – 74.

Soni, H.N. (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., Chang, C.T. and Goyal, S.K. (2005). Optimal Pricing and ordering policy under permissible delay in payments. International Journal of Production Economics, Vol. 97, pp. 121-129.

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.

Tripathi , R.P. Misra, S.S. and Shukla, H.S. (2011). A cash flow oriented EOQ model of deteriorating items with time- dependent demand rate under permissible delay in payments. International Journal of Business and Information Technology, Vol. 1(2), pp. 153-158.

Tripathi, R.P. and Kumar, M. (2011). Credit financing in economic ordering policies of time – dependent deteriorating items. International Journal of Business Management and Social Sciences, Vol. 2(3), pp. 75-84.

Tripathi, R.P. and Pandey, H.S. (2013). An EOQ model for deteriorating Items with Weibull Time- Dependent Demand Rate under Trade Credits. International Journal of Information and Management Sciences, Vol. 24(4), pp. 329-347.

Tripathi, R.P. (2011). Inventory model with time dependent demand rate under inflation when supplier credit linked to order quantity. International Journal of Business and Information Technology, Vol. 1(3), pp. 174–183.

Tripathi, R.P. (2011). EOQ model with time- dependent demand rate and time- dependent holding cost function. International Journal of Operations Research and Information System, Vol. 2(3), pp. 79-92.

Tripathy, C.K., and Mishra, U. (2011). Ordering policy for linear deteriorating items for decling demand with permissible delay in payments. International Journal of Open Problems and Computational Mathematics, Vol. 5(3), pp. 152–160.

Tripathy, C. K., and Mishra, U. (2010). An inventory model for Weibull Time- dependent demand rate with completely backlogged shortages. International Mathematical Forum, Vol. 5(54). pp. 2675-2687.

Urban, T.L.(2012). An extension of inventory models incorporating financing agreements with both suppliers and customers. Applied Mathematical Modelling, Vol. 36, pp. 6323-6330.

Yang, H.L., Teng, J.T. and Chern, M.S. (2010). An inventory model under inflation for deteriorating items with stock- dependent consumption rate and partial backlogging shortages. International Journal of Production Economics, Vol. 123, pp. 8-19.