Abstract
This paper studies the target visitation arc routing problem on an undirected graph. This problem combines the well-known undirected rural postman problem and the linear ordering problem. In this problem, there is a set of required edges partitioned into targets, which must be traversed and there are pairwise preferences for the order in which some targets are serviced, which generates a revenue if the preference is satisfied. The aim is to find a tour that traverses all required edges at least once, and offers a compromise between the revenue generated by the order in which targets are serviced, and the routing cost of the tour. A linear integer programming formulation including some families of valid inequalities is proposed. Despite the difficulty of the problem, the model can be used to solve to optimality around 62% of the test instances.
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Acknowledgements
Thanks are due to the referees for their valuable comments. This research was partially supported by the Spanish Ministry of Economy and Competitiveness through Grant MTM2015-63779-R (MINECO/FEDER), and by the Canadian Natural Sciences and Engineering Research Council under the Grant 2015-06189. This support is gratefully acknowledged.
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Rodríguez-Pereira, J., Laporte, G. The target visitation arc routing problem. TOP 30, 60–76 (2022). https://doi.org/10.1007/s11750-021-00601-5
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DOI: https://doi.org/10.1007/s11750-021-00601-5