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Integer programming models and linearizations for the traveling car renter problem

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Abstract

The traveling car renter problem (CaRS) is an extension of the classical traveling salesman problem (TSP) where different cars are available for use during the salesman’s tour. In this study we present three integer programming formulations for CaRS, of which two have quadratic objective functions and the other has quadratic constraints. The first model with a quadratic objective function is grounded on the TSP interpreted as a special case of the quadratic assignment problem in which the assignment variables refer to visitation orders. The second model with a quadratic objective function is based on the Gavish and Grave’s formulation for the TSP. The model with quadratic constraints is based on the Dantzig–Fulkerson–Johnson’s formulation for the TSP. The formulations are linearized and implemented in two solvers. An experiment with 50 instances is reported.

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Acknowledgements

The researches of M. C. Goldbarg and E. F. G. Goldbarg are partially supported by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), Brazil, under Grants 301845/2013-1 and 308062/2014-0. The research of L. Corrales is partially supported by CONICET (Consejo Nacional de Investigaciones Científicas Y Técnicas).

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Authors and Affiliations

  1. Universidade Federal do Rio Grande do Norte, Natal, Brazil

    Marco C. Goldbarg & Elizabeth F. G. Goldbarg

  2. Universidade Federal de Alagoas, Maceió, Brazil

    Henrique P. L. Luna

  3. Universidade Federal Rural do Semi-Árido, Mossoró, Brazil

    Matheus S. Menezes

  4. Universidad Nacional del Centro de la Provincia de Buenos Aires, Tandil, Argentina

    Lucas Corrales

Authors
  1. Marco C. Goldbarg
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  2. Elizabeth F. G. Goldbarg
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  3. Henrique P. L. Luna
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  4. Matheus S. Menezes
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  5. Lucas Corrales
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Corresponding author

Correspondence to Elizabeth F. G. Goldbarg.

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Goldbarg, M.C., Goldbarg, E.F.G., Luna, H.P.L. et al. Integer programming models and linearizations for the traveling car renter problem. Optim Lett 12, 743–761 (2018). https://doi.org/10.1007/s11590-017-1138-5

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  • DOI: https://doi.org/10.1007/s11590-017-1138-5

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