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An Aspect of Bilevel Fixed Charge Fractional Transportation Problem

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Abstract

Bilevel Programming Problem (BLPP) is a hierarchical optimization problem. Here, the constraint set of the upper level problem, called the leader, is ascertained by the lower level problem, called the follower. In this paper, a BLPP is considered where the leader’s problem is a fractional transportation problem and the follower’s problem is a fixed charge transportation problem. Hence, a bilevel fixed charge fractional transportation problem (BLFCFTP) is formulated. The problem is also explained through graphical representation. The problem comes from a food chain industry which is utilizing its used vegetable cooking oil for the production of biodiesel. The mathematical model of the problem is presented and is also explained through graphical representation. The problem pertains to a food chain industry wherein the used vegetable cooking oil is utilized for the production of biodiesel. Another example quotes Indore city where waste is converted into bio-CNG which is used to run public transport. The managerial importance of the work is that it will promote a sustainable and environment friendly practice. This will result in reduction of waste and check environmental pollution. An algorithm to solve BLFCFTP is developed. The examples explaining the algorithm are exhibited by a viable situation. These examples are subsequently deciphered in MATLAB.

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Acknowledgements

We would like to thank the honorable reviewers’ for their valuable comments which has helped us to improve the quality of the manuscript to a great extent.

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Authors and Affiliations

  1. Department of Applied Sciences and Humanities, Indira Gandhi Delhi Technical University For Women, New Delhi, 110006, India

    Bindu Kaushal & Shalini Arora

  2. Keshav Mahavidyalaya, University of Delhi, Delhi, India

    Ritu Arora

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  1. Bindu Kaushal
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Kaushal, B., Arora, R. & Arora, S. An Aspect of Bilevel Fixed Charge Fractional Transportation Problem. Int. J. Appl. Comput. Math 6, 14 (2020). https://doi.org/10.1007/s40819-019-0755-3

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