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Discontinuity, Nonlinearity, and Complexity 11(4) (2022) 583--598 | DOI:10.5890/DNC.2022.12.002

Rituparna Pakhira$^1$, Uttam Ghosh$^1$, Susmita Sarkar$^1$, Lakshmi Narayan Mishra$^2$

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Abstract

In current years, fractional calculus has received much attention because it can include memory effect to the inventory model. In the paper, fractional order derivative and integration have been applied to include the memory dependency to the polynomial type demand rate inventory model under the fuzzy environment. The advantage of fractional order derivative and integration have been applied to the EOQ model taking fuzzy environment. Inventory cost parameters, for example holding cost, purchasing cost and ordering cost are thought to be triangular fuzzy numbers. Two type memory indices (i) differential memory index, (ii) integral memory index have been established where differential memory index is associated with the fractional order derivative and integral memory index is associated with the fractional order integration. Defuzzification has been considered using graded mean integration method and signed distance method. Numerical examples and graphical presentations are considered to explain importance of the work.

Acknowledgments

The authors would like to thank the reviewers and the editor for the valuable comments and suggestions for the improvement of this article.

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