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

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  • M. Ganesh Kumar

    (The Gandhigram Rural Institute (Deemed to be University))

  • R. Uthayakumar

    (The Gandhigram Rural Institute (Deemed to be University))

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.

Suggested Citation

  • M. Ganesh Kumar & R. Uthayakumar, 2019. "A two-echelon integrated inventory model under generalized lead time distribution with variable backordering rate," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(4), pages 552-562, August.
    • Handle: RePEc:spr:ijsaem:v:10:y:2019:i:4:d:10.1007_s13198-019-00769-x
    DOI: 10.1007/s13198-019-00769-x
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    References listed on IDEAS

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    Cited by:

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    2. Mandeep Mittal & Mahesh Kumar Jayaswal & Vijay Kumar, 2022. "Effect of learning on the optimal ordering policy of inventory model for deteriorating items with shortages and trade-credit financing," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(2), pages 914-924, June.
    3. Sudip Adak & G. S. Mahapatra, 2021. "Effect of inspection and rework of probabilistic defective production on two-layer supply chain incorporating deterioration and reliability dependent demand," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 12(3), pages 565-578, June.

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