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Mathematical Modeling and Computational Algorithm to Solve Multi-Echelon Multi-Constraint Inventory Problem with Errors in Quality Inspection

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Journal of Mathematical Modelling and Algorithms in Operations Research

Abstract

In this research an integrated production-distribution inventory model is developed for a single-vendor single-buyer supply chain system with the consideration of quality inspection errors at the buyer’s end, the buyer’s warehouse has limited capacity and there is an upper bound on the purchase of products. Mathematical modeling is employed in this study for optimizing the replenishment lot-size and total number of deliveries from the vendor to the buyer in one production run with the objective of minimizing integrated expected total cost of the system while satisfying the constraints. We show that the model of this problem is a constrained non-linear programme and propose a simple Lagrangian multiplier algorithmic technique to solve it. The computational effort and time are small for the proposed algorithm and it is simple to implement. A numerical example is given to demonstrate the application and the performance of the proposed methodology. In addition, sensitivity analysis has been carried out to illustrate the behaviors of the proposed model and some managerial insights are also included.

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Authors and Affiliations

  1. Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram-624 302, TamilNadu, India

    S. Priyan & R. Uthayakumar

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  1. S. Priyan
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  2. R. Uthayakumar
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Correspondence to S. Priyan.

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Priyan, S., Uthayakumar, R. Mathematical Modeling and Computational Algorithm to Solve Multi-Echelon Multi-Constraint Inventory Problem with Errors in Quality Inspection. J Math Model Algor 14, 67–89 (2015). https://doi.org/10.1007/s10852-014-9258-8

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  • DOI: https://doi.org/10.1007/s10852-014-9258-8

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