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A two-echelon integrated inventory model under generalized lead time distribution with variable backordering rate

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Abstract

This paper investigates a generalized lead time distribution with a variable backordering rate in a two-echelon supply chain system. The vendor produces a single product and delivers to the buyer in equal sized batches. The delivery lead time follows a generalized stochastic variable. Shortages are allowed to occur and backordered partially. The backorder rate depends on the demand on stock-out period. Based on this notion, we formulate a mixed integer non-linear cost function which needs to be minimized with respect to reorder point, number of deliveries and lot size from the vendor to the buyer, to operate cooperatively in the integrated model. Analytically we proved the convexity of the generalized lead time distribution cost function with respect to the control parameters. Further, the uniqueness of optimality has been proved. To validate the proposed model, uniform, exponential and normal distributed lead times are presented in numerical example section. Sensitivity analysis also performed to the values of the parameters.

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Acknowledgements

The work of the authors are supported by Department of Science and Technology-Science and Engineering Research Board (DST-SERB), Government of India, New Delhi, under the Grant Number DST-SERB/SR/S4/MS: 814/13-Dated 24.04.2014.

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Authors and Affiliations

  1. Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram, Tamil Nadu, 624 302, India

    M. Ganesh Kumar & R. Uthayakumar

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  1. M. Ganesh Kumar
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  2. R. Uthayakumar
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Correspondence to M. Ganesh Kumar.

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Ganesh Kumar, M., Uthayakumar, R. A two-echelon integrated inventory model under generalized lead time distribution with variable backordering rate. Int J Syst Assur Eng Manag 10, 552–562 (2019). https://doi.org/10.1007/s13198-019-00769-x

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  • DOI: https://doi.org/10.1007/s13198-019-00769-x

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