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A production-repairing inventory model considering demand and the proportion of defective items as rough intervals

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Abstract

This paper explores a production inventory model in an imperfect production system under a rough interval environment. The occurrences of shortages are allowed and are fully backlogged. In this paper, two models are presented. In the first model, the demand of the product is considered as a rough interval. In the second model, both the demand and the defective rate are considered as rough intervals. In reality, these two factors cannot be assessed exactly due to a lack of available data. Moreover, there are few scenarios where the demand of the product is assessed in two-layer information. The inner layer demand is obvious, and it may extend up to the outer layer depending on the situation. Also, the same thing may happen for the defective rate of the product. In those cases, it is more reasonable to express the demand and the defective rate as rough intervals instead of fuzzy or interval numbers. Based on the expected value of rough intervals, the necessary and sufficient conditions are determined analytically to obtain the optimal inventory policies. The main advantage of this method is that the optimal profit and the optimal lot size are determined as crisp numbers rather than rough intervals. Obtaining a precise value for these two quantities is desirable for any production manager. Numerical examples for both models are provided to illustrate the solution methodology. Sensitivity analysis of the optimal solutions concerning the key parameters is conducted for identifying several managerial implications.

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Acknowledgements

The authors would like to thank the learned anonymous reviewers and the editor for their valuable suggestions, constructive comments, and excellent observations which have substantially helped to improve the quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Sonamukhi College, Bankura, 722 207, India

    Subhendu Ruidas & Mijanur Rahaman Seikh

  2. Department of Mathematics, Kazi Nazrul University, Asansol, 713 340, India

    Mijanur Rahaman Seikh

  3. Department of Mathematics, Midnapore College(Autonomous), Midnapore, 721 101, India

    Prasun Kumar Nayak

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  1. Subhendu Ruidas
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  2. Mijanur Rahaman Seikh
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  3. Prasun Kumar Nayak
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Correspondence to Mijanur Rahaman Seikh.

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Ruidas, S., Seikh, M.R. & Nayak, P.K. A production-repairing inventory model considering demand and the proportion of defective items as rough intervals. Oper Res Int J 22, 2803–2829 (2022). https://doi.org/10.1007/s12351-021-00634-5

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  • DOI: https://doi.org/10.1007/s12351-021-00634-5

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