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An inventory model for partial backlogging items with memory effect

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Abstract

Inventory control is considered one of the most widely documented topics in the reality. Fractional derivatives and integration is the part of fractional calculus. Fractional calculus is the generalized part of ordinary calculus. The memory of physical phenomena is a highly concerning topic but it is neglected with describing in terms of integer-order differential equation. To discuss the memory of the inventory model, fractional derivative tools are considered. A fractional derivative at any point gives the previous marginal output and current point output for any current point input. In this model, a shortage is considered, and during the shortage period, demand is partially backlogged. Depending on the low partial backlogging rate and high partial backlogging rate, the result of the memory effect varies on the total average cost and optimal ordering interval. Moreover, in order to show the relationship between fractional models and ordinary classical model, two types of memory indices have been considered: (i) differential memory index and (ii) integral memory index. For a certain memory effect, minimized total average cost is the same for low partial backlogging rate and high partial backlogging rate.

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Acknowledgements

We would also like to show our gratitude to the reviewers for valuable comments and suggestions.

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Authors and Affiliations

  1. Academy of Technology, Adisaptagram, Hooghly, West Bengal, India

    Rituparna Pakhira

  2. Department of Applied Mathematics, University of Calcutta, Kolkata, 700009, India

    Uttam Ghosh

  3. School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala, Punjab, 147004, India

    Harish Garg

  4. Department of Mathematics, Graphic Era Deemed to be University, Dehradun, Uttarakhand, 248002, India

    Harish Garg

  5. Applied Science Research Center, Applied Science Private University, Amman, 11931, Jordan

    Harish Garg

  6. College of Technical Engineering, The Islamic University, Najaf, Iraq

    Harish Garg

  7. Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh, India

    Vishnu Narayan Mishra

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  1. Rituparna Pakhira
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Contributions

R. Pakhira involved in conceptualization, methodology, data creation, and software; U. Ghosh involved in conceptualization and review; H. Garg involved in conceptualization, review, and editing; V. N. Mishra involved in conceptualization and review.

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Correspondence to Uttam Ghosh.

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Pakhira, R., Ghosh, U., Garg, H. et al. An inventory model for partial backlogging items with memory effect. Soft Comput 27, 9533–9550 (2023). https://doi.org/10.1007/s00500-023-08087-y

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