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Fermatean fuzzy vehicle routing problem with profit: solution algorithms, comparisons and developments

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Abstract

In this work, a fermatean fuzzy vehicle routing problem with profits (FFVRPP) is considered. Fermatean fuzzy numbers are used to represent the various coefficients of the problem. The objectives of FFVRPP is to obtain a set of routes that originates and terminates at the source node while keeping in mind the objective function and route restriction constraints. The objective function here is to maximizes the difference between the profit function and the expense function. The route restriction constraints provides an upper bound on the number of customers that can be served in single visit of any vehicle. We propose two stage solution methodologies for solving FFVRPP where the first stage corresponds to the selection of subset of customers which gives the maximum profit and the second stage corresponds to formation of routes for the selected customers such that the expenses incurred in serving them comes out to be a minimum. The inclusion of qualitative factors like relationship of customers with the seller and the risk of transportation of goods across various edges with the help of fermatean fuzzy numbers makes the model more realistic and applicable in real life situations. Three different methodologies based on various clustering and routing algorithms are proposed to solve the problem. The feasibility and richness of the proposed algorithms is demonstrated with the help of a numerical example.

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Abbreviations

FFVRPP:

Fermetean fuzzy vehicle routing problem with profits

VRPP:

Vehicle routing problem with profits

VRP:

Vehicle routing problem

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Acknowledgements

The authors would like to thank the anonymous reviewers and the senior associate editor, Prof. Manoj Kumar Tiwari for their insightful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, VNIT Nagpur, Nagpur, 440010, India

    V P Singh, Kirti Sharma & Bishwajeet Singh

  2. Department of Mathematics, Islamic Azad University, Qaemshahr Branch, Qaemshahr, Iran

    Ali Ebrahimnejad

  3. Department of Mathematics, IIT Kharagpur, Kharagpur, 721302, India

    Debjani Chakraborty

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  1. V P Singh
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Correspondence to V P Singh.

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Singh, V.P., Sharma, K., Singh, B. et al. Fermatean fuzzy vehicle routing problem with profit: solution algorithms, comparisons and developments. Sādhanā 48, 166 (2023). https://doi.org/10.1007/s12046-023-02238-5

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  • DOI: https://doi.org/10.1007/s12046-023-02238-5

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