Fuzzy Inventory Model for Deteriorating Items with Time Dependent Demand and Partial Backlogging


In this paper we developed a fuzzy inventory model for deteriorating items with time dependent demand rate. Shortages are allowed and completely backlogged. The backlogging rate of unsatisfied demand is assumed to be a decreasing exponential function of waiting time. The demand rate, deterioration rate and backlogging rate are assumed as a triangular fuzzy numbers. The purpose of our study is to defuzzify the total profit function by signed distance method and centroid method. Further a numerical example is also given to demonstrate the developed crisp and fuzzy models. A sensitivity analysis is also given to show the effect of change of the parameters.

Share and Cite:

Kumar, S. and Rajput, U. (2015) Fuzzy Inventory Model for Deteriorating Items with Time Dependent Demand and Partial Backlogging. Applied Mathematics, 6, 496-509. doi: 10.4236/am.2015.63047.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Harris, F. (1915) Operations and Cost. AW Shaw CO., Chicago.
[2] Zadeh, L.A. (1965) Fuzzy Set. Information Control, 8, 338-353.
[3] Zadeh, L.A. and Bellman, R.E. (1970) Decision Making in a Fuzzy Environment. Management Science, 17, 140-164.
[4] Jain, R. (1976) Decision Making in the Presence of Fuzzy Variables. IIIE Transactions on Systems, Man and Cybernetics, 17, 698-703.
[5] Dubois, D. and Prade, H. (1978) Operations on Fuzzy Numbers. International Journal of System Science, 9, 613-626.
[6] Kacpryzk, J. and Staniewski, P. (1982) Long Term Inventory Policy Making through Fuzzy Decision Making Methods. Fuzzy Sets and System, 8, 117-132.
[7] Zimmerman, H.J. (1983) Using Fuzzy Sets in Operational Research. European Journal of Operation Research, 13, 201-206.
[8] Urgeletti Tinarelli, G. (1983) Inventory Control Models and Problems. European Journal of Operation Research, 14, 1-12.
[9] Park, K.S. (1987) Fuzzy Set Theoretical Interpretation of Economic Order Quantity. IEEE Transactions on Systems, Man and Cybernetics, 17, 1082-1084.
[10] Vujosevic, M. and Petrovic, D. (1996) EOQ Formula When Inventory Cost Is Fuzzy. International Journal of Production Economics, 45, 499-504.
[11] Yao, J.S. and Lee, H.M. (1999) Fuzzy Inventory with or without Backorder for Fuzzy Order Quantity with Trapezoidal Fuzzy Number. Fuzzy Sets and Systems, 105, 311-337.
[12] Yao, J.S. and Lee, H.M. (1999) Economic Order Quantity in Fuzzy Sense for Inventory without Backorder Model. Fuzzy Sets and Systems, 105, 13-31.
[13] Kao, C.K. and Hsu, W.K. (2002) A Single Period Inventory Model with Fuzzy Demand. Computers and Mathematics with Applications, 43, 841-848.
[14] Hsieh, C.H. (2002) Optimization of Fuzzy Production Inventory Models. Information Sciences, 146, 29-40.
[15] Yao, J.S. and Chiang, J. (2003) Inventory without Backorder with Fuzzy Total Cost and Fuzzy Storing Cost Defuzzified by Centroid and Signed Distance. European Journal of Operational Research, 148, 401-409.
[16] Kumar, Sujit De, Kundu, P.K. and Goswami, A. (2007) An Economic Production Quantity Inventory Model Involving Fuzzy Demand Rate and Fuzzy Deterioration Rate. Journal of Applied Mathematics and Computing, 12, 251-260.
[17] Syed, J.K. and Aziz, L.A. (2007) Fuzzy Inventory Model without Shortages by Using Signed Distance Method. Applied Mathematics and Information Sciences, 1, 203-209.
[18] De, P.K. and Rawat, A. (2011) A Fuzzy Inventory Model without Shortages Using Triangular Fuzzy Number. Fuzzy Information and Engineering, 3, 59-68.
[19] Jaggi, C.K., Pareek, S., Sharma, A. and Nidhi (2012) Fuzzy Inventory Model for Deteriorating Items with Time Varying Demand and Shortages. American Journal of Operational Research, 2, 81-92.
[20] Saha, S. and Chakrabarti, T. (2012) Fuzzy EOQ Model with Time Dependent Demand and Deterioration with Shortages. IOSR Journal of Mathematics, 2, 46-54.
[21] Dutta, D. and Kumar, P. (2012) Fuzzy Inventory Model without Shortage Using Trapezoidal Fuzzy Number with Sensitivity Analysis. IOSR Journal of Mathematics, 4, 32-37.
[22] Dutta, D. and Kumar, P. (2013) Optimal Ordering Policy for an Inventory Model for Deteriorating Items without Shortages by Considering Fuzziness in Demand Rate, Ordering Cost and Holding Cost. International Journal of Advanced Innovation and Research, 2, 320-325.
[23] Jain, D.K., Das, B. and Roy, T.K. (2013) A Fuzzy Generic Algorithm Approach for an Inventory Model for Deteriorating Items with Backorders under Fuzzy Inflation and Discounting over Random Planning Horizon. Advances in Operations Research, 2013, 1-15.

Copyright © 2021 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.