Multi-Item Fuzzy Inventory Model Involving Three Constraints: A Karush-Kuhn-Tucker Conditions Approach
R. Kasthuri, P. Vasanthi, S. Ranganayaki, C. V. Seshaiah
DOI: 10.4236/ajor.2011.13017   PDF   HTML     5,234 Downloads   9,990 Views   Citations


In this paper, a multi-item inventory model with storage space, number of orders and production cost as constraints are developed in both crisp and fuzzy environment. In most of the real world situations the cost parameters, the objective functions and constraints of the decision makers are imprecise in nature. This model is solved with shortages and the unit cost dependent demand is assumed. Hence the cost parameters are imposed here in fuzzy environment. This model has been solved by Kuhn-Tucker conditions method. The results for the model without shortages are obtained as a particular case. The model is illustrated with numerical example.

Share and Cite:

R. Kasthuri, P. Vasanthi, S. Ranganayaki and C. Seshaiah, "Multi-Item Fuzzy Inventory Model Involving Three Constraints: A Karush-Kuhn-Tucker Conditions Approach," American Journal of Operations Research, Vol. 1 No. 3, 2011, pp. 155-159. doi: 10.4236/ajor.2011.13017.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol. 8, No. 3, 1965, pp. 338-353. doi:10.1016/S0019-9958(65)90241-X
[2] R. E. Bellman and L. A. Zadeh, “Decision-Making in a Fuzzy Environment,” Management Science, Vol. 17, No. 4, 1970, pp. B141-B164. doi:10.1287/mnsc.17.4.B141
[3] H. J. Zimmermann, “Description and Optimization of Fuzzy Systems,” International Journal of General Systems, Vol. 2, No. 4, 1976, pp. 209-215. doi:10.1080/03081077608547470
[4] G. Sommer, “Fuzzy Inventory Scheduling,” In: G. Lasker, Ed., Applied Systems and Cybernetics, Vol. 6, Academic Press, New York, 1981.
[5] K. S. Park, “Fuzzy Set Theoretic Interpretation of Economic Order Quantity,” IEEE Transactions on Systems, Man, and Cybernetics, Vol. 17, No. 6, 1987, pp. 1082-1084.
[6] H. A. Taha, “Operations Research: An Introduction,” Prentice-Hall of India, Delhi, 2005, pp. 725-728.
[7] P. K. Gupta and M. Mohan, “Problems in Operations Research (Methods & Solutions),” Sultan Chand Co., New Delhi, 2003, pp. 609-610.
[8] E. A. Silver and R. Peterson, “Decision Systems for Inventory Management and Production Planning,” John Wiley, New York, 1985.
[9] H. Tanaka, T. Okuda and K. Asai, “On Fuzzy Mathematical Programming,” Journal of Cybernetics, Vol. 3, No. 4, 1974, pp. 37-46. doi:10.1080/01969727308545912
[10] F. E. Raymond, “Quantity and Economic in Manufacturer,” McGraw Hill Book Co., New York, 1931.
[11] G. Hadley and T. M. Whitin, “Analysis of Inventory Systems,” Prentice-Hall, Englewood Cliffs, 1958.

Copyright © 2022 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.