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A production-reliability-inventory model for a series-parallel system with mixed strategy considering shortage, warranty period, credit period in crisp and stochastic sense

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Abstract

This paper deals with a combined study of production, reliability and inventory consisting of a single manufacturer and a single retailer with two types of model structures: crisp and stochastic. In the crisp model, manufacturer produces a single type of items with system reliability dependent production cost by offering credit period and warranty period to the retailer and the retailer’s demand has been considered as dependent on system reliability, credit period and selling price. Here, raw-materials’ shortages are allowed within the available stock of produced items. In the stochastic model, volume, cost and weight of the produced items have been considered as random parameters, because in reality, these parameters are not fixed. Again, there may be constraint violation in real life situations, so the constraints are treated as chance constraint here. To deal with this stochastic model we have used chance constraint programming technique. The novelty of this current model is the combination of production, reliability and inventory considering raw-materials’ shortages along with crisp and stochastic sense to find the number of active and cold standby components, number of replenishment and raw-materials’ shortage period which maximize the profit and system reliability. We have done numerical simulations based on different cases of crisp and stochastic models and solved the problems using elitist non-dominated sorting genetic algorithm (NSGA-II) and compared the results. Also, a comparison between active and mixed strategies is presented here. Sensitivity analyses provide managerial insights with the impact of several important parameters on profit, demand and system reliability.

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Acknowledgements

The authors wish to thank the handling editor and the anonymous reviewers for their valuable comments and suggestions, which improved the quality of the manuscript.

Funding

This work is supported by the Department of Science and Technology(DST), New Delhi, India, through the letter No.DST/INSPIRE/03/2016/001272.

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Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, W.B., 721102, India

    Anushri Maji & Shyamal Kumar Mondal

  2. Department of Mathematics, The University of Burdwan, Burdwan, W.B., 713104, India

    Asoke Kumar Bhunia

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  1. Anushri Maji
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  2. Asoke Kumar Bhunia
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  3. Shyamal Kumar Mondal
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Contributions

AM: Conceptualization, methodology, formal analysis, writing–original draft, visualization, writing–review & editing, funding acquisition. AKB: conceptualization, methodology, writing–review & editing. SKM: conceptualization, methodology, formal analysis, visualization, writing–review & editing, supervision.

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Correspondence to Shyamal Kumar Mondal.

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Maji, A., Bhunia, A.K. & Mondal, S.K. A production-reliability-inventory model for a series-parallel system with mixed strategy considering shortage, warranty period, credit period in crisp and stochastic sense. OPSEARCH 59, 862–907 (2022). https://doi.org/10.1007/s12597-022-00578-0

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