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The Steiner travelling salesman problem with correlated costs

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  • Letchford, Adam N.
  • Nasiri, Saeideh D.

Abstract

The Steiner Travelling Salesman Problem (STSP) is a variant of the TSP that is suitable for instances defined on road networks. We consider an extension of the STSP in which the road traversal costs are both stochastic and correlated. This happens, for example, when vehicles are prone to delays due to rush hours, road works or accidents. Following the work of Markowitz on portfolio selection, we model this problem as a bi-objective mean-variance problem. Then, we show how to approximate the efficient frontier via integer programming. We also show how to exploit certain special structures in the correlation matrices. Computational results indicate that our approach is viable for instances with up to 100 nodes. It turns out that minimum variance tours can look rather different from minimum expected cost tours.

Suggested Citation

  • Letchford, Adam N. & Nasiri, Saeideh D., 2015. "The Steiner travelling salesman problem with correlated costs," European Journal of Operational Research, Elsevier, vol. 245(1), pages 62-69.
    • Handle: RePEc:eee:ejores:v:245:y:2015:i:1:p:62-69
    DOI: 10.1016/j.ejor.2015.02.044
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    1. Gendreau, Michel & Laporte, Gilbert & Seguin, Rene, 1996. "Stochastic vehicle routing," European Journal of Operational Research, Elsevier, vol. 88(1), pages 3-12, January.
    2. Gilbert Laporte & François Louveaux & Hélène Mercure, 1992. "The Vehicle Routing Problem with Stochastic Travel Times," Transportation Science, INFORMS, vol. 26(3), pages 161-170, August.
    3. Fleischmann, Bernhard, 1985. "A cutting plane procedure for the travelling salesman problem on road networks," European Journal of Operational Research, Elsevier, vol. 21(3), pages 307-317, September.
    4. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    5. Li, Xiangyong & Tian, Peng & Leung, Stephen C.H., 2010. "Vehicle routing problems with time windows and stochastic travel and service times: Models and algorithm," International Journal of Production Economics, Elsevier, vol. 125(1), pages 137-145, May.
    6. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    7. Astrid S. Kenyon & David P. Morton, 2003. "Stochastic Vehicle Routing with Random Travel Times," Transportation Science, INFORMS, vol. 37(1), pages 69-82, February.
    8. Warren P. Adams & Hanif D. Sherali, 1986. "A Tight Linearization and an Algorithm for Zero-One Quadratic Programming Problems," Management Science, INFORMS, vol. 32(10), pages 1274-1290, October.
    9. Edward P. C. Kao, 1978. "A Preference Order Dynamic Program for a Stochastic Traveling Salesman Problem," Operations Research, INFORMS, vol. 26(6), pages 1033-1045, December.
    10. Mavrotas, G. & Diakoulaki, D., 1998. "A branch and bound algorithm for mixed zero-one multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 107(3), pages 530-541, June.
    11. Letchford, Adam N. & Nasiri, Saeideh D. & Theis, Dirk Oliver, 2013. "Compact formulations of the Steiner Traveling Salesman Problem and related problems," European Journal of Operational Research, Elsevier, vol. 228(1), pages 83-92.
    12. Sanjay Chaudhuri & Mathias Drton & Thomas S. Richardson, 2007. "Estimation of a covariance matrix with zeros," Biometrika, Biometrika Trust, vol. 94(1), pages 199-216.
    13. Francis Sourd & Olivier Spanjaard, 2008. "A Multiobjective Branch-and-Bound Framework: Application to the Biobjective Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 472-484, August.
    14. S. Y. Teng & H. L. Ong & H. C. Huang, 2004. "An Integer L-Shaped Algorithm For Time-Constrained Traveling Salesman Problem With Stochastic Travel And Service Times," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 241-257.
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    Cited by:

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    2. Rostami, Borzou & Chassein, André & Hopf, Michael & Frey, Davide & Buchheim, Christoph & Malucelli, Federico & Goerigk, Marc, 2018. "The quadratic shortest path problem: complexity, approximability, and solution methods," European Journal of Operational Research, Elsevier, vol. 268(2), pages 473-485.

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