Abstract
We describe a solution procedure for a capacitated arc routing problem with refill points and multiple loads. This problem stems from the road network marking in Quebec, Canada. Two different types of vehicles are used: the first type (called servicing vehicle—SV) with a finite capacity to service the arcs and the other (called refilling vehicle—RV) to refill the SV vehicle. The RV can deliver multiple loads, which means that it meets the SV several times before returning to the depot. The problem consists of simultaneously determining the vehicle routes that minimize the total cost of the two vehicles. We present an integer formulation and a route first-cluster second heuristic procedure. Computational results are provided.
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Amaya CA, Langevin A and Trépanier M ( 2007 ). The capacitated arc routing problem with refill points . Opns Res Lett 35 : 45 – 53 .
Assad AA and Golden BL ( 1995 ). Arc routing methods and applications . In: Ball MO, Magnanti TL, Monma CL and Nemhauser GL (eds) . Network Routing, Handbooks in Operations Research and Management Science . North-Holland: Amsterdam, The Netherlands, pp . 375 – 483 .
Belenguer JM and Benavent E ( 1998 ). The capacitated arc routing problem: Valid inequalities and facets . Comput Optim Appl 10 : 165 – 187 .
Belenguer JM, Benavent E, Lacomme P and Prins C ( 2006 ). Lower and upper bounds for the mixed capacitated arc routing problem . Comput Opns Res 33 : 3363 – 3383 .
Benavent E, Campos V, Corberán A and Mota E ( 1990 ). The capacitated arc routing problem: Lower Bounds . Networks 22 : 669 – 690 .
Christofides N, Campos V, Corberán A and Mota E ( 1986 ). An algorithm for the rural postman problem on a directed graph . Math Program Stud 26 : 155 – 166 .
Dror M ( 2000 ). Arc Routing: Theory, Solutions and Applications . Kluwer Academic Publishers: Boston .
Eglese R and Letchford A ( 2000 ). Polyhedral theory for arc routing problems . In: Dror M (ed) . Arc Routing: Theory, Solutions and Applications . Kluwer Academic Publishers: Boston, pp . 199 – 226 .
Golden BL and Wong RT ( 1981 ). Capacitated arc routing problems . Networks 11 : 305 – 315 .
In: Gross J and Yellen J (eds) . Handbook of Graph Theory. Discrete Mathematics and its Applications . CRC Press: London .
Hertz A ( 2005 ). Recent trends in arc routing . In: Golumbic MC and Ben-Arroyo Hartman I (eds) . Graph Theory, Combinatorics and Algorithmics: Interdisciplinary Applications . Springer: Berlin, pp . 215 – 236 .
Hertz A and Mittaz M ( 2000 ). Heuristics algorithms . In: Dror M (ed) . Arc Routing: Theory, Solutions and Applications . Kluwer Academic Publishers: Boston, pp . 327 – 386 .
Hirabayashi R, Saruwatari Y and Nishida N ( 1992 ). Tour construction algorithm for the capacitated arc routing problems . Asia Pac J Opns Res 9 : 155 – 175 .
Marzolf F, Trépanier M and Langevin A ( 2006 ). Road network monitoring: Algorithms and a case study . Comput Opns Res 33 : 3494 – 3507 .
Perrier N, Langevin A and Amaya A ( 2008 ). Vehicle routing for urban snow plowing operations . Transport Sci 42 ( 1 ): 44 – 56 .
Sniezek J, Bodin L, Levy L and Ball M ( 2002 ). Capacitated arc routing problem with vehicle-site dependencies: The Philadelphia experience . In: Toth P and Vigo D (eds) . The Vehicle Routing Problem, SIAM Monographs on Discrete Mathematics and Applications . SIAM: Philadelphia, pp . 287 – 330 .
Ulusoy G ( 1985 ). The fleet size and mix problem for capacitated arc routing . Eur J Opl Res 22 : 329 – 337 .
Wøhlk S ( 2006 ). New lower bound for the capacitated arc routing problem . Comput Opns Res 33 : 3458 – 3472 .
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Amaya, CA., Langevin, A. & Trépanier, M. A heuristic method for the capacitated arc routing problem with refill points and multiple loads. J Oper Res Soc 61, 1095–1103 (2010). https://doi.org/10.1057/jors.2009.58
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DOI: https://doi.org/10.1057/jors.2009.58