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Effect of memory on an inventory model for deteriorating item: fractional calculus approach

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Abstract

It is incontrovertible that involvement of memory has a great impact in inventory model. For any company, long past experience as well as short past experience have similar significant importance to manage the profit. Our proposed inventory model is leaded by two important factors: constant demand and deterioration. Here, we have introduced memory effect through the feasible ideas of fractional calculus. Also, we consider the order of fractional derivative as memory index. We calculate various type of costs viz total holding cost, purchasing cost, deterioration cost, shortage cost, salvage value. Additionally, optimal ordering interval, optimal starting shortage time and minimized total average cost are computed theoretically using the fractional calculus techniques. Effect of memory is justified by choosing a suitable numerical example. Finally sensitivity analysis for the model has been presented.

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Acknowledgements

We are thankful to the Editor and Reviewers for their constructive comments and suggestions, which helps a lot for significant improvement of our work.

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The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Ramkrishna Mahato Govt. Engg. College, Purulia, West Bengal, 723103, India

    Dipak Kumar Jana

  2. Department of Mathematics, Government General Degree College, Chapra, Nadia, West Bengal, 741123, India

    Asim Kumar Das

  3. Department of Mathematics, University of Kalyani, Kalyani, West Bengal, 741235, India

    Sahidul Islam

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  1. Dipak Kumar Jana
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  2. Asim Kumar Das
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  3. Sahidul Islam
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Contributions

DKJ has conducted the study with potential contribution to present the analytical and numerical result. AKD has significant contribution to interpret the concept of memory which has been utilized in the form of fractional differential calculus, calculate the analytical outcomes and analyze the results. The entire process has been significantly monitored and supervised by SI. All authors participated in writing the manuscript.

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Correspondence to Asim Kumar Das.

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Jana, D.K., Das, A.K. & Islam, S. Effect of memory on an inventory model for deteriorating item: fractional calculus approach. OPSEARCH (2024). https://doi.org/10.1007/s12597-024-00767-z

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