Inventory Model for Deteriorating Items Involving Fuzzy with Shortages and Exponential Demand

Document Type: Research Paper

Authors

The Gandhigram Rural Institute, Deemed University, Gandhigram, India

Abstract

This paper considers the fuzzy inventory model for deteriorating items for power demand under fully backlogged conditions. We define various factors which are affecting the inventory cost by using the shortage costs. An intention of this paper is to study the inventory modelling through fuzzy environment. Inventory parameters, such as holding cost, shortage cost, purchasing cost and deterioration cost are assumed to be the trapezoidal fuzzy numbers. In addition, an efficient algorithm is developed to determine the optimal policy, and the computational effort and time are small for the proposed algorithm. It is simple to implement, and our approach is illustrated through some numerical examples to demonstrate the application and the performance of the proposed methodology.

Keywords

Main Subjects


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

Chandrasekhara Reddy, B. and Ranganatham, G. (2012).An EOQ Model with Exponentially Increasing Demand fewer than Two Levels of Storage, Journal of perspective- Gurgaon, Vol.16, pp. 121-127.

Chang, H. J. and Dye, C. Y. (2001). An inventory model for deteriorating items with partial backlogging and permissible delay in payments, International Journal of Systems Science, Vol. 32, pp. 345-352.

Chang, 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 & Control, Vol. 12, pp. 274-282.

Chang, C. T., Teng, J. T. and Goyal, S.K. (2008). Inventory lot-size models under trade credits: a review, Asia-Pacific Journal of Operational Research, Vol. 25, pp. 89-112. 

Chang, C. T., Wu, S. J. and. Chen, L. C. (2009). Optimal payment time with deteriorating items under inflation and permissible delay in payments, International Journal of Systems Science, Vol. 40. pp. 985-993.

Dutta, D. and Pavan Kumar. (2013). Fuzzy Inventory Model for Deteriorating Items with Shortages under Fully Backlogged Condition, International Journal of Soft Computing and Engineering (IJSCE), Vol.3, pp. 393-398.

Goyal, S. K. (1985). Economic order quantity under conditions of permissible delay in payments, Journal of the Operational Research Society, Vol. 36, pp. 335-338.

Halkos, G. and Kevork, I. (2012). Validity and precision of estimates in the classical newsvendor model with exponential and Rayleigh demand, MPRA Paper No. 36460, posted 6. 12:22 UTC.

Halkos, G. and Kevork, I. (2013). Evaluating alternative frequentist inferential approaches for optimal order quantities in the newsvendor model under exponential demand, International transactions in Operational research Vol. 20, pp. 837–857.

Horng-Jinh Chang and Chung-Yuan Dye. (1999). An EOQ Model for Deteriorating Items with Exponential Time-Varying Demand and Partial Backlogging, Information and Management Sciences, Vol. 10, pp. 1-11.

Hwang, H. and Shinn, S. W. (1997). Retailer’s pricing and lot sizing policy for exponentially deteriorating products under the conditions of permissible delay in payments, Computers & Operations Research, Vol. 24, pp. 539-547.

Jaggi, C. K., Pareek, S., Sharma, A. and Nidhi, A. (2012). Fuzzy inventory model for deteriorating items with time varying demand and shortages, American Journal of Operational Research, Vol. 2, pp. 81-92.

Jamal, A. M. M., Sarker, B. R. and Wang, S. (1997). An ordering policy for deteriorating items with allowable shortages and permissible delay in payments, Journal of the Operational Research Society, Vol. 48, pp. 826-833.

Kapil Kumar Bansal and Navin Ahalawat. (2012). Integrated Inventory Models for Decaying Items with Exponential Demand under Inflation, International Journal of Soft Computing and Engineering, Vol.2, pp. 578-587.

Liang, Y. and Zhou, F. (2011). A two-warehouse inventory model for deteriorating conditionally permissible delay in payment, Applied Mathematical Modelling, Vol. 35, pp. 2221-2231.

Maragatham, M. and Lakshmidevi, P. K. (2014). A Fuzzy Inventory Model for Deteriorating Items with Price Dependent Demand, Intern. J. Fuzzy Mathematical Archive, Vol. 5, pp. 39-47.

Mary Latha, K. F. and Uthayakumar, R. (2014). An Inventory Model for Increasing Demand with Probabilistic Deterioration, Permissible Delay and Partial Backlogging, International Journal of Information and Management Science, Vol. 25, pp. 297-316. 

Nithya, K. and Ritha, W. (2012). Fuzzy Economic Order Quantity for Items with Imperfect Quality and Inspection Errors in an Uncertain Environment on Fuzzy Parameters, Journal of Informatics and Mathematical Sciences, Vol.4, pp. 269–283.

Nirmal Kumar Duari and Prof. Tripti Chakraborty. (2012). A Marketing Decision Problem in a Periodic Review Model with Exponential Demand and Shortages, IOSR Journal of Mathematics, Vol.1, pp. 35-38.

Raafat, F. (1991), Survey of literature on continuously deteriorating inventory models, Journal of the Operational Research Society, Vol. 42, pp. 27-37.

Ritha, W. and Rexlin Jeyakumari, S. (2013). Fuzzy Inventory model for Imperfect quality items with shortages, Annals of pure and applied Mathematics, Vol. 4, pp. 127-137.

Sarah Ryan, M. (2003). Capacity Expansion for Random Exponential Demand Growth with Lead Times, for publication in Management Science, Vol.50, pp. 1-23.

Sanhita, B and Tapan Kumar, R. (2012). Arithmetic Operations on Generalized Trapezoidal Fuzzy Number and its Applications, Turkish Journal of Fuzzy Systems. An Official Journal of Turkish Fuzzy Systems Association, Vol.3, pp. 16-44.

Savitha Pathak and Seema Sarkar (Mondal). (2012). Fuzzy Inventory Models of Perishable Multi-items for Integrated and Non-integrated Businesses with Possibility/Necessity Measure of Trapezoidal Fuzzy Goal, International Journal of Modelling and Optimization, Vol. 2, pp. 119-129.

Shah, N. H. (1993).Probabilistic time-scheduling model for an exponentially decaying inventory when delay in payments is permissible, International Journal of Production Economics, Vol. 32, pp. 77-82.

Shah, N. H. (2006). Inventory mode for deteriorating items and time value of money for a finite time horizon under permissible delay in payments, International Journal of Systems Science, Vol. 37, pp. 9-15.

Soni, H., Gor, A. S. and Shah, N. H. (2006) An EOQ model for progressive payment scheme under DCF approach, Asia-Pacific Journal of Operational Research, Vol. 23, pp. 500-524.

Sushil Kumar. and Rajput, U. S. 2015. Fuzzy Inventory Model for Deteriorating Items with Time Dependent Demand and Partial Backlogging, Scientific Research Publishing, Applied Mathematics, Vol. 6, pp. 496-509.

Syed, J. K. and Aziz, L. A. (2007). Fuzzy Inventory model without shortages using signed distance method, Applied Mathematics and Information Sciences an International Journal, Vol. 1, pp. 203-209.