# American Institute of Mathematical Sciences

July  2016, 12(3): 1153-1172. doi: 10.3934/jimo.2016.12.1153

## Production inventory model with deteriorating items, two rates of production cost and taking account of time value of money

 1 Research and Development Centre, Bharathiar University, Coimbatore-641 046, Tamilnadu, India 2 RVS Technical Campus-Coimbatore, Coimbatore-641402, Tamilnadu, India 3 CSIR Emeritus Scientist in Mathematics, Government Arts College, Coimbatore, Tamilnadu, India

Received  October 2014 Revised  May 2015 Published  September 2015

This paper presents production-inventory model for deteriorating items with constant demand under the effect of inflation and time-value of money. Models are developed without shortages while using two production cost functions. In the first case, production cost is divided into two parts: an initial cost which occurs at the beginning of each cycle and is applied to the entire quantity produced during the cycle and a running cost that is incurred as production progresses and is applied to the initial units produced. In the second case, the production cost is incurred at the beginning of the cycle. Numerical examples are given to illustrate the theoretical results and made the sensitivity analysis of parameters on the optimal solutions. The validation of this model's result was coded in Microsoft Visual Basic 6.0
Citation: Vincent Choudri, Mathiyazhgan Venkatachalam, Sethuraman Panayappan. Production inventory model with deteriorating items, two rates of production cost and taking account of time value of money. Journal of Industrial and Management Optimization, 2016, 12 (3) : 1153-1172. doi: 10.3934/jimo.2016.12.1153
##### References:
 [1] J. A. Buzacott, Economic order quantities with inflation, Operational Research, 26 (1979), 553-558. [2] C.-Y. Dye, H.-J. Chang and C.-H. Wu, Purchase-inventory decision models for deteriorating items with a temporary sale price, Internat. J. Inform. Management Sci., 18 (2007), 17-35. [3] S. Eilon and R. V. Mallaya, Issuing and pricing policy of semi-perishables, in Proceedings of the 4th International Conference on Operational Research, Wiley-Interscience, New York, 1966. [4] P. M. Ghare and G. F. Schrader, A model for exponentially decaying inventory, J. Indust. Eng., 14 (1963), 238-243. [5] J. Min, et al., An EPQ model for deteriorating items with inventory-level-dependent demand and permissible delay in payments, Internat. J. Systems Sci., 43 (2012), 1039-1053. doi: 10.1080/00207721.2012.659685. [6] I. Moon and S. Lee, The effects of inflation and time-value of money on an economic order quantity model with a random product life cycle, European J. Oper. Res., 125 (2000), 588-601. doi: 10.1016/S0377-2217(99)00270-2. [7] G. Moslehi, M. Rasti Barzoki and M. Fathollah Bayati, The effect of inflation and time value of money on lot sizing by considering of rework in an inventory control model, Internat. J. Indust. Eng. Prod. Man., 22 (2011), 181-192. [8] A. Roy and G. P. Samanta, Inventory model with two rates of production for deteriorating items with permissible delay in payments, Internat. J. Systems Sci., 42 (2011), 1375-1386. doi: 10.1080/00207721003646256. [9] B. Sarkar and I. Moon, An EPQ model with inflation in an imperfect production system, Appl. Math. Comput., 217 (2011), 6159-6167. doi: 10.1016/j.amc.2010.12.098. [10] N. H. Shah, Inventory model for deteriorating items and time value of money for a finite time horizon under the permissible delay in payments, Internat. J. Systems Sci., 37 (2006), 9-15. doi: 10.1080/00207720500404334. [11] S. R. Singh and R. Jain, On reserve money for an EOQ model in an inflationary environment under supplier credit, OPSEARCH, 46 (2009), 303-320. doi: 10.1007/s12597-009-0020-3. [12] S. Singh, R. Dube and S. R. Singh, Production model with selling price dependent demand and partially backlogging under inflation, Internat. J. Math. Mod. Comput., 1 (2011), 1-7. [13] H.-M. Wee, Economic production lot size model for deteriorating items with partial back ordering, Comp. Indust. Eng., 24 (1993), 449-458. doi: 10.1016/0360-8352(93)90040-5. [14] H.-M. Wee and S.-T. Law, Economic production lot size for deteriorating items taking account of the time value of money, Comp. Oper. Res., 26 (1999), 545-558. doi: 10.1016/S0305-0548(98)00078-1. [15] J. C. P. Yu, et al., The effects of inflation and time value of money on a production model with a random product life cycle, Asia-Pac. J. Oper. Res., 27 (2010), 437-456. doi: 10.1142/S0217595910002788.

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##### References:
 [1] J. A. Buzacott, Economic order quantities with inflation, Operational Research, 26 (1979), 553-558. [2] C.-Y. Dye, H.-J. Chang and C.-H. Wu, Purchase-inventory decision models for deteriorating items with a temporary sale price, Internat. J. Inform. Management Sci., 18 (2007), 17-35. [3] S. Eilon and R. V. Mallaya, Issuing and pricing policy of semi-perishables, in Proceedings of the 4th International Conference on Operational Research, Wiley-Interscience, New York, 1966. [4] P. M. Ghare and G. F. Schrader, A model for exponentially decaying inventory, J. Indust. Eng., 14 (1963), 238-243. [5] J. Min, et al., An EPQ model for deteriorating items with inventory-level-dependent demand and permissible delay in payments, Internat. J. Systems Sci., 43 (2012), 1039-1053. doi: 10.1080/00207721.2012.659685. [6] I. Moon and S. Lee, The effects of inflation and time-value of money on an economic order quantity model with a random product life cycle, European J. Oper. Res., 125 (2000), 588-601. doi: 10.1016/S0377-2217(99)00270-2. [7] G. Moslehi, M. Rasti Barzoki and M. Fathollah Bayati, The effect of inflation and time value of money on lot sizing by considering of rework in an inventory control model, Internat. J. Indust. Eng. Prod. Man., 22 (2011), 181-192. [8] A. Roy and G. P. Samanta, Inventory model with two rates of production for deteriorating items with permissible delay in payments, Internat. J. Systems Sci., 42 (2011), 1375-1386. doi: 10.1080/00207721003646256. [9] B. Sarkar and I. Moon, An EPQ model with inflation in an imperfect production system, Appl. Math. Comput., 217 (2011), 6159-6167. doi: 10.1016/j.amc.2010.12.098. [10] N. H. Shah, Inventory model for deteriorating items and time value of money for a finite time horizon under the permissible delay in payments, Internat. J. Systems Sci., 37 (2006), 9-15. doi: 10.1080/00207720500404334. [11] S. R. Singh and R. Jain, On reserve money for an EOQ model in an inflationary environment under supplier credit, OPSEARCH, 46 (2009), 303-320. doi: 10.1007/s12597-009-0020-3. [12] S. Singh, R. Dube and S. R. Singh, Production model with selling price dependent demand and partially backlogging under inflation, Internat. J. Math. Mod. Comput., 1 (2011), 1-7. [13] H.-M. Wee, Economic production lot size model for deteriorating items with partial back ordering, Comp. Indust. Eng., 24 (1993), 449-458. doi: 10.1016/0360-8352(93)90040-5. [14] H.-M. Wee and S.-T. Law, Economic production lot size for deteriorating items taking account of the time value of money, Comp. Oper. Res., 26 (1999), 545-558. doi: 10.1016/S0305-0548(98)00078-1. [15] J. C. P. Yu, et al., The effects of inflation and time value of money on a production model with a random product life cycle, Asia-Pac. J. Oper. Res., 27 (2010), 437-456. doi: 10.1142/S0217595910002788.
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