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Interval Type-2 Fuzzy Vendor Managed Inventory System and Its Solution with Particle Swarm Optimization

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Abstract

The vendor managed inventory (VMI) is the most commonly known marketing and distribution methodology among the service provider and the retailer in a supply chain environment. The VMI framework's critical feature is to satisfy the demand of the products or items by the supplier rapidly generated from the retailers with the number of orders (order quantities). Due to the business's changing conditions, necessities of the particular product, production cycle, and manufacturing expenses, the VMI system's demand and order quantity are highly uncertain. Therefore, the total cost of a VMI system possesses higher-order uncertainties for a real-world scenario. This paper proposes a novel interval type-2 fuzzy vendor managed inventory (IT2FVMI) system, in which demand and order quantity are represented by the interval type-2 fuzzy numbers. The proposed IT2FVMI model aims to minimize the overall cost for the single vendor-retailer business, merchandise of multi-product, and a centralized warehouse of retailers' inventory managed by the vendor. Since the proposed model is an NP-hard, a particle swarm optimization (PSO) based solution approach is developed for solving it appropriately. Moreover, we have also formulated the classical/crisp VMI model and type-1 fuzzy vendor managed inventory (T1FVMI) model via considering demand and order quantity as the deterministic and the type-1 fuzzy numbers, respectively. The proposed solution technique is capable of solving both crisp VMI and T1FVMI problems. An appropriate real-world application is considered to conduct experimental simulations for the five test problems that displayed the various situations, and the minimum costs of the models are obtained. All the three models are thoroughly analyzed, and from comparison, it is demonstrated that the proposed IT2FVMI model outperforms both T1FVMI and crisp VMI models by providing a more trustworthy solution in terms of minimum cost, statistical analysis, and significantly faster convergence.

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Acknowledgements

The authors gratefully acknowledge the helpful feedback received from the reviewers and the editors that have significantly helped enhance the paper. The fourth author, Dr. Q. M. Danish Lohani, gratefully acknowledges SERB, DST, Government of India to support this research under the scheme of the MATRICS program (Grant File No. SERB/F/10728/2019-20).

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  1. Department of Computer Science, South Asian University, New Delhi, 110021, India

    Zubair Ashraf, Deepika Malhotra & Pranab K. Muhuri

  2. Department of Mathematics, South Asian University, New Delhi, 110021, India

    Q. M. Danish Lohani

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Ashraf, Z., Malhotra, D., Muhuri, P.K. et al. Interval Type-2 Fuzzy Vendor Managed Inventory System and Its Solution with Particle Swarm Optimization. Int. J. Fuzzy Syst. 23, 2080–2105 (2021). https://doi.org/10.1007/s40815-021-01077-y

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