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A Fuzzy Graph Theory Approach to the Facility Location Problem: A Case Study in the Indian Banking System

Author

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  • Anushree Bhattacharya

    (Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India
    These authors contributed equally to this work.)

  • Madhumangal Pal

    (Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India
    These authors contributed equally to this work.)

Abstract

A fuzzy graph G is stated to have a set of trees as its tree cover if all the vertices of G are in their union. The maximum weight tree in the tree cover is assumed to be the cost of a tree cover for a fuzzy graph. For an integer β > 0 , finding a set of trees to cover all the vertices of a graph with minimum cost and at most β number of spanning trees is known as the β -tree cover problem. Combining the tree-covering concept and facility location problem in a fuzzy environment for solving critical real-life problems in the recent era is a more fruitful approach. This issue strongly inspires us to develop a model with a practical algorithm. This paper provides an algorithm and complexity analysis to determine the number of rooted trees s covering the given fuzzy graph. In addition, a model is constructed with three optimization programming problems in the facility location problem and a tree covering fuzzy graphs. The model includes two types of the facility location problem, simultaneously addressing a variable covering radius and a fixed covering radius. A numerical example is provided to further describe the model, then, in the application part of the paper, the proposed model is applied to solve the real-life problem of maximizing demand saturation by minimizing the number of small denominations in the Indian banking system. This problem involves the data input of different indicators in the banking system along with details of the denominations of banknotes.

Suggested Citation

  • Anushree Bhattacharya & Madhumangal Pal, 2023. "A Fuzzy Graph Theory Approach to the Facility Location Problem: A Case Study in the Indian Banking System," Mathematics, MDPI, vol. 11(13), pages 1-19, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2992-:d:1186945
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    References listed on IDEAS

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    1. Constantine Toregas & Ralph Swain & Charles ReVelle & Lawrence Bergman, 1971. "The Location of Emergency Service Facilities," Operations Research, INFORMS, vol. 19(6), pages 1363-1373, October.
    2. S. L. Hakimi, 1965. "Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems," Operations Research, INFORMS, vol. 13(3), pages 462-475, June.
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    1. Murugan Kaviyarasu & Mohammed Alqahtani & Murugesan Rajeshwari & Gopikumar Sudalaimuthu, 2024. "Complex t-Intuitionistic Fuzzy Graph with Applications of Rubber Industrial Water Wastes," Mathematics, MDPI, vol. 12(13), pages 1-30, June.

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