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

Author

Listed:
  • Dipak Kumar Jana

    (Ramkrishna Mahato Govt. Engg. College)

  • Asim Kumar Das

    (Government General Degree College)

  • Sahidul Islam

    (University of Kalyani)

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.

Suggested Citation

  • Dipak Kumar Jana & Asim Kumar Das & Sahidul Islam, 2024. "Effect of memory on an inventory model for deteriorating item: fractional calculus approach," OPSEARCH, Springer;Operational Research Society of India, vol. 61(4), pages 2360-2378, December.
    • Handle: RePEc:spr:opsear:v:61:y:2024:i:4:d:10.1007_s12597-024-00767-z
    DOI: 10.1007/s12597-024-00767-z
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    References listed on IDEAS

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    1. Tarasov, Vasily E. & Tarasova, Valentina V., 2018. "Macroeconomic models with long dynamic memory: Fractional calculus approach," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 466-486.
    2. Wu, Kun-Shan & Ouyang, Liang-Yuh & Yang, Chih-Te, 2006. "An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging," International Journal of Production Economics, Elsevier, vol. 101(2), pages 369-384, June.
    3. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Logistic map with memory from economic model," Papers 1712.09092, arXiv.org.
    4. Tarasova, Valentina V. & Tarasov, Vasily E., 2017. "Logistic map with memory from economic model," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 84-91.
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