Category of routing problem minimizing total distance and time
Arc routing problems (ARP) are a category of general routing problems (GRP), which also includes node routing problems (NRP). The objective in ARPs and NRPs is to traverse the edges and nodes of a graph, respectively.[1] The objective of arc routing problems involves minimizing the total distance and time, which often involves minimizing deadheading time, the time it takes to reach a destination. Arc routing problems can be applied to garbage collection, school bus route planning, package and newspaper delivery, deicing and snow removal with winter service vehicles that sprinkle salt on the road,[2] mail delivery, network maintenance, street sweeping, police and security guard patrolling,[1] and snow ploughing.[3][4] Arc routings problems are NP hard, as opposed to route inspection problems that can be solved in polynomial-time.
For a real-world example of arc routing problem solving, Cristina R. Delgado Serna & Joaquín Pacheco Bonrostro applied approximation algorithms to find the best school bus routes in the Spanish province of Burgos secondary school system. The researchers minimized the number of routes that took longer than 60 minutes to traverse first. They also minimized the duration of the longest route with a fixed maximum number of vehicles.[5]
There are generalizations of arc routing problems that introduce multiple mailmen, for example the k Chinese Postman Problem (KCPP).
^ abChen, Huanfa; Cheng, Tao; Shawe-Taylor, John (2018-01-02). "A Balanced Route Design for Min-Max Multiple-Depot Rural Postman Problem (MMMDRPP): a police patrolling case". International Journal of Geographical Information Science. 32 (1): 169–190. doi:10.1080/13658816.2017.1380201. ISSN 1365-8816. S2CID 29526595.
^Omer, Masoud (2007). "Efficient routing of snow r outing of snow removal vehicles vehicles".
^Dussault, Benjamin; Golden, Bruce; Wasil, Edward (October 2014). "The downhill plow problem with multiple plows". Journal of the Operational Research Society. 65 (10): 1465–1474. doi:10.1057/jors.2013.83. ISSN 0160-5682. S2CID 36977043.
^Eiselt, H. A.; Gendreau, Michel; Laporte, Gilbert (April 1995). "Arc Routing Problems, Part I: The Chinese Postman Problem". Operations Research. 43 (2): 231–242. doi:10.1287/opre.43.2.231. hdl:11059/14013. ISSN 0030-364X.
^Delgado Serna, Cristina R.; Pacheco Bonrostro, Joaquín (2001), Voß, Stefan; Daduna, Joachim R. (eds.), "Minmax Vehicle Routing Problems: Application to School Transport in the Province of Burgos", Computer-Aided Scheduling of Public Transport, Berlin, Heidelberg: Springer, pp. 297–317, doi:10.1007/978-3-642-56423-9_17, ISBN 978-3-642-56423-9, retrieved 2022-05-01
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