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A branch-and-price algorithm for the windy rural postman problem

Published online by Cambridge University Press:  09 March 2012

Hasan Murat Afsar ,
Nicolas Jozefowiez  and
Pierre Lopez
Hasan Murat Afsar
Affiliation:
Universitéde Technologie de Troyes (UTT), Institut Charles Delaunay, LOSI, 12 rue Marie Curie, 10010 Troyes, France. murat.afsar@utt.fr
Nicolas Jozefowiez
Affiliation:
CNRS, LAAS, 7 avenue du Colonel Roche, 31077 Toulouse Cedex 4, France Université de Toulouse, INSA, LAAS, 31400 Toulouse, France
Pierre Lopez
Affiliation:
CNRS, LAAS, 7 avenue du Colonel Roche, 31077 Toulouse Cedex 4, France Université de Toulouse, LAAS, 31400 Toulouse, France
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Abstract

In this paper, we propose an exact solution method for the windy rural postman problem (WRPP). The motivation to study this problem comes from some real-life applications, such as garbage collecting in a predefined sector with hills, where the traversing or the servicing speed can change following the direction. We present a Dantzig-Wolfe decomposition and a branch-and-price algorithm to solve the WRPP. To the best of our knowledge, Dantzig-Wolfe decomposition has never been used to solve that problem. The numerical results show that optimal solutions are found in a very reasonable amount of time on instances with up to 100 nodes and 180 edges.

Keywords

Branch-and-pricewindy rural postman problem
Type
Research Article
Information
RAIRO - Operations Research , Volume 45 , Issue 4 , October 2011 , pp. 353 - 364
Copyright
© EDP Sciences, ROADEF, SMAI, 2012

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References

Benavent, E., Corberán, A., Piñana, E., Plana, I. and Sanchis, J.M., New heuristic algorithms for the windy rural postman problem. Comput. Oper. Res. 32 (2005) 3111–3128. Google Scholar
Benavent, E., Carotta, A., Corberán, A., Sanchis, J.M. and Vigo, D., Lower bounds and heuristics for the windy rural postman problem. Eur. J. Oper. Res. 176 (2007) 855–869. Google Scholar
N. Christofides, V. Campos, A. Corberán and E. Mota, An algorithm for the rural postman problem. Technical Report 5, Imperial College Report ICOR815 (1981).
Christofides, N., Campos, V., Corberán, A. and Mota, E., An algorithm for the rural postman problem on a directed graph. Math. Program. Stud. 26 (1986) 155–166. Google Scholar
Corberán, A. and Sanchis, J.M., A polyhedral approach to the rural postman problem. Eur. J. Oper. Res. 79 (1994) 95–114. Google Scholar
Corberán, A., Letchford, A. and Sanchis, J.M., A cutting plane algorithm for the general routing problem. Math. Program. 90 (2001) 291–316. Google Scholar
Dantzig, G.B. and Wolfe, P., Decomposition principle for linear programs. Oper. Res. 8 (1960) 101–111. Google Scholar
Ghiani, G. and Laporte, G., A branch and cut algorithm for the undirected rural postman problem. Math. Program. 87 (2000) 467–481. Google Scholar
Grötschel, M. and Win, Z., A cutting plane algorithm for the windy postman problem. Math. Program. 55 (1992) 339–358. Google Scholar
Hertz, A., Laporte, G. and Nanchen, P., Improvement procedures for the undirected rural postman problem. Informs J. Comput. 11 (1999) 53–62. Google Scholar
Hertz, A., Laport, G. and Mittaz, M., A tabu search heuristic for the capacitated arc routing problem. Oper. Res. 48 (2000) 129–135. Google Scholar
Lenstra, J.K. and Rinnooy Kan, A.H.G., On general routing problems. Networks 6 (1976) 273–280. CrossRef
A.N. Letchford, Polyhedral results for some constrained arc-routing problems. Ph.D. thesis, Lancaster University (1996).
Minieka, E., The chinese postman problem for mixed networks. Manage. Sci. 25 (1979) 643–648. Google Scholar
Orloff, C.S., A fundamental problem in vehicle routing. Networks 4 (1974) 35–64. Google Scholar
J.M. Sanchis, El poliedro del problema del cartero rural. Ph.D. thesis, University of Valencia (1990) (in Spanish).
Win, Z., On the windy postman problem on eulerian graphs. Math. Program. 44 (1989) 97–112. Google Scholar