Optimization Letters

, Volume 12, Issue 4, pp 743–761 | Cite as

Integer programming models and linearizations for the traveling car renter problem

  • Marco C. Goldbarg
  • Elizabeth F. G. GoldbargEmail author
  • Henrique P. L. Luna
  • Matheus S. Menezes
  • Lucas Corrales
Original Paper


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.


Traveling car renter problem Traveling salesman Integer programming Combinatorial optimization 



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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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Universidade Federal do Rio Grande do NorteNatalBrazil
  2. 2.Universidade Federal de AlagoasMaceióBrazil
  3. 3.Universidade Federal Rural do Semi-ÁridoMossoróBrazil
  4. 4.Universidad Nacional del Centro de la Provincia de Buenos AiresTandilArgentina

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