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Linear and conic reformulations for the maximum capture location problem under multinomial logit choice

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Abstract

This paper presents three reformulations for the well-known maximum capture location problem under multinomial logit choice. The problem can be cast as an integer fractional program and it has been the subject of several linear reformulations in the past. Here we develop two linear and a conic reformulation based on alternative treatments of fractional programs. Numerical experiments conducted on established sets of instances have shown that conic reformulation has greatly improved the solution times as well as the size of the solvable problems as compared to the most successful reformulations to date.

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Acknowledgements

We are thankful to Knut Haase, Sven Muller, Ivana Ljubic, and Eduardo Moreno for sharing their data sets with us. The data sets analysed in this study are available from the corresponding author on reasonable request. We also greatly appreciate the invaluable comments of two anonymous referees.

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  1. Sabanci Business School, Sabanci University, 34956, Istanbul, Turkey

    F. Tevhide Altekin & Abdullah Dasci

  2. National Defense University, Naval Academy, 34940, Istanbul, Turkey

    Mumtaz Karatas

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  1. F. Tevhide Altekin
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  2. Abdullah Dasci
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Altekin, F.T., Dasci, A. & Karatas, M. Linear and conic reformulations for the maximum capture location problem under multinomial logit choice. Optim Lett 15, 2611–2637 (2021). https://doi.org/10.1007/s11590-020-01684-y

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