Abstract
The Maximum Benefit Chinese Postman Problem (MBCPP) is an NP-hard problem that considers several benefits associated with each edge, one for each time the edge is traversed with a service. The objective is to find a closed walk with maximum benefit. We propose an IP formulation for the undirected MBCPP and, based on the description of its associated polyhedron, we propose a branch-and-cut algorithm and present computational results on instances with up to 1,000 vertices and 3,000 edges.
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References
Aráoz J., Fernández E., Franquesa C.: The clustered price-collecting arc-routing problem. Transp. Sci. 43, 287–300 (2009)
Aráoz J., Fernández E., Meza O.: Solving the prize-collecting rural postman problem. Eur. J. Oper. Res. 196, 886–896 (2009)
Aráoz J., Fernández E., Zoltan C.: Privatized rural postman problems. Comput. Oper. Res. 33, 3432–3449 (2006)
Archetti C., Feillet D., Hertz A., Speranza M.G.: The undirected capacitated arc routing problem with profits. Comput. Oper. Res. 37, 1860–1869 (2010)
Barahona F., Grötschel M.: On the cycle polytope of a binary matroid. J. Comb. Theory B 40, 40–62 (1986)
Fernández E., Fernández E., Franquesa C., Sanchis J.M.: The windy clustered prize-collecting problem. Transp. Sci. 45, 317–334 (2011)
Letchford A.N., Letchford A.N., Sanchis J.M.: A cutting-plane algorithm for the general routing problem. Math. Progr. 90, 291–316 (2001)
Plana I., Plana I., Sanchis J.M.: A branch & cut algorithm for the windy general routing problem and special cases. Networks 49, 245–257 (2007)
Corberán, Á., Plana, I., Sanchis, J.M.: Arc Routing Problems: Data Instances. http://www.uv.es/corberan/instancias.htm
Sanchis J.M., Sanchis J.M.: A polyhedral approach to the rural postman problem. Eur. J. Oper. Res. 79, 95–114 (1994)
Feillet D., Dejax P., Gendreau M.: The profitable arc tour problem: solution with a branch-and-price algorithm. Transp. Sci. 39, 539–552 (2005)
Franquesa, C.: The Clustered Prize-collecting Arc Routing Problem. PhD Thesis, Technical University of Catalonia, Barcelona (2008)
Ghiani G., Laporte G.: A branch-and-cut algorithm for the undirected rural postman problem. Math. Progr. 87, 467–481 (2000)
Lenstra J.K., Rinnooy Kan A.H.G.: On general routing problems. Networks 6, 593–597 (1976)
Letchford A.N., Reinelt G., Theis D.O.: Odd minimum cut-sets and b-matchings revisited. SIAM J. Discret. Math. 22, 1480–1487 (2008)
Malandraki C., Daskin M.S.: The maximum benefit chinese postman problem and the maximum benefit traveling salesman problem. Eur. J. Oper. Res. 65, 218–234 (1993)
Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley-Interscience Series in Discrete Mathematics and Optimization, Wiley, New York (1988)
Orloff C.S.: A fundamental problem in vehicle routing. Networks 4, 35–64 (1974)
Pearn W.L., Chiu W.C.: Approximate solutions for the maximum benefit Chinese postman problem. Int. J. Syst. Sci. 36, 815–822 (2005)
Pearn W.L., Wang K.H.: On the maximum benefit Chinese postman problem. OMEGA 31, 269–273 (2003)
Reinelt G., Theis D.O.: Transformation of facets of the general routing problem polytope. SIAM J. Optim. 16, 220–234 (2005)
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Corberán, Á., Plana, I., Rodríguez-Chía, A.M. et al. A branch-and-cut algorithm for the maximum benefit Chinese postman problem. Math. Program. 141, 21–48 (2013). https://doi.org/10.1007/s10107-011-0507-6
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DOI: https://doi.org/10.1007/s10107-011-0507-6
Keywords
- Chinese postman problem
- Maximum benefit Chinese postman problem
- Rural postman problem
- Facets
- Branch-and-cut