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Optimization of Weibull deteriorating items inventory model under the effect of price and time dependent demand with partial backlogging

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Abstract

In this study, we have discussed the development of an inventory model when the deterioration rate of the item follows Weibull two parameter distributions under the effect of selling price and time dependent demand, since, not only the selling price, but also the time is a crucial factor to enhance the demand in the market as well as affecting the overall finance. In the present model, shortages are approved and also partially backlogged. Optimum inventory level, the optimal length of a cycle and the expressions for profit function under various cost considerations are obtained using differential equations. These are illustrated graphically with the help of numerical examples. The sensitivity analysis of the standards of the parameters has been performed to study the effect on inventory optimizations.

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Acknowledgement

One of the authors Mr. Shiv Kumar is grateful to the Indian School of Mines, Dhanbad authorities for financial support in the form of a Research Fellowship and facilitating the best facility. The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. Department of Applied Mathematics, Indian School of Mines, Dhanbad, 826004, India

    SHIV KUMAR & ABHAY KUMAR SINGH

  2. Department of Mathematics, National Institute of Technology, Dimapur, Nagaland, 797103, India

    MANOJ KUMAR PATEL

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  1. SHIV KUMAR
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  2. ABHAY KUMAR SINGH
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  3. MANOJ KUMAR PATEL
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Correspondence to SHIV KUMAR.

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KUMAR, S., SINGH, A.K. & PATEL, M.K. Optimization of Weibull deteriorating items inventory model under the effect of price and time dependent demand with partial backlogging. Sādhanā 41, 977–984 (2016). https://doi.org/10.1007/s12046-016-0533-4

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  • DOI: https://doi.org/10.1007/s12046-016-0533-4

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