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A pollution sensitive fuzzy EPQ model with endogenous reliability and product deterioration based on lock fuzzy game theoretic approach

Soft Computing volume 27, pages 3065–3081 (2023)Cite this article

Abstract

This article deals with a cost minimization objective function of an economic production quantity (EPQ) inventory model with production breakdown and deterioration. The process reliability and the environmental pollution due to over production have also been considered. The model has been split into two different scenarios according to the breaking time before and after the production period. In scenario 1, no machinery failure occurs during production run time and that of scenario 2 the failure occurs during production run time. We develop a deterministic cost minimization problem first then we fuzzify the model by considering the production rate, the demand rate and all the cost components as lock fuzzy numbers. We convert the fuzzy model into equivalent game problem by considering Gaussian normal strategic probabilities. The model has been solved with the help of different key vectors employed by the decision maker. We have shown that the value of the game might be changed with the change of different key vectors. A comparative study has been made with the numerical results of the general fuzzy and crisp models. Finally, graphical illustrations and sensitivity analysis have been done followed by a conclusion.

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Acknowledgements

The authors are thankful to the honourable Editor-in-Chief, Associate Editors and the anonymous reviewers for their valuable comments and suggestions to improve the quality of this article.

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Authors and Affiliations

  1. Department of Mathematics, Midnapore College (Autonomous), Midnapore, 721101, India

    Kousik Bhattacharya & Sujit Kumar De

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  1. Kousik Bhattacharya
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  2. Sujit Kumar De
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Correspondence to Sujit Kumar De.

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Bhattacharya, K., De, S.K. A pollution sensitive fuzzy EPQ model with endogenous reliability and product deterioration based on lock fuzzy game theoretic approach. Soft Comput 27, 3065–3081 (2023). https://doi.org/10.1007/s00500-022-07485-y

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Keywords

  • EPQ
  • Failure rate
  • Reliability
  • Deterioration
  • Game theory
  • Lock fuzzy set
  • Optimization