Abstract
The vehicle routing problem is one of the most important problems in the field of supply chain management, of logistics, of combinatorial optimization, and, in general, of operational research. The interest in this problem has been recently increased both from theoretical and practical aspects. In this chapter, a number of the most important variants of the vehicle routing problem are presented. In some of them, the basic formulation of the problem is, also, given.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Adulyasak, Y., Cordeau, J.F., Jans, R.: Optimization-based adaptive large neighborhood search for the production routing problem. Transp. Sci. 48(1), 20–45 (2014)
Angelelli, E., Speranza, M.G.: The periodic vehicle routing problem with intermediate facilities. Eur. J. Oper. Res. 137(2), 233–247 (2002)
Archetti, C., Speranza, M.G., Hertz, A.: A tabu search algorithm for the split delivery vehicle routing problem. Transp. Sci. 40(1), 64–73 (2006)
Archetti, C., Speranza, M.G., Vigo, D.: Vehicle routing problems with profits. In: Toth, P., Vigo, D. (eds.) Vehicle Routing: Problems, Methods and Applications, 2nd edn. MOS-Siam Series on Optimization, pp. 272–297. Siam, Philadelphia (2014)
Assad, A.A., Golden, B.L.: Arc routing methods and applications. In: Ball, M.O., Magnanti, T.L., Momma, C.L., Nemhauser, G.L. (eds.) Network Routing, Handbooks in Operations Research and Management Science, vol. 8, pp. 375–483. Elsevier Science B. V., Amsterdam (1995)
Baldacci, R., Battarra, M., Vigo, D.: Routing a heterogeneous fleet of vehicles. In: Golden, B.L., Raghavan, S., Wasil, E.A. (eds.) The Vehicle Routing Problem: Latest Advances and New Challenges. Operations Research/Computer Science Interfaces Series, vol. 43, pp. 3–27. Springer, New York (2008)
Ball, M.O., Magnanti, T.L., Momma, C.L., Nemhauser, G.L. (eds.): Network Routing, Handbooks in Operations Research and Management Science, vol. 8. Elsevier Science B V, Amsterdam (1995)
Bard, J.F., Huang, L., Dror, M., Jaillet, P.: A branch and cut algorithm for the VRP with satellite facilities. IIE Trans. 30, 821–834 (1998)
Battarra, M., Cordeau, J.-F., Iori, M.: Pickup-and-delivery problems for goods transportation. In: Toth, P., Vigo, D. (eds.) Vehicle Routing: Problems, Methods and Applications, 2nd edn. MOS-Siam Series on Optimization, pp. 161–192. Siam, Philadelphia (2014)
Bektas, T., Repoussis, P.P., Tarantilis, C.D.: Dynamic vehicle routing problems. In: Toth, P., Vigo, D. (eds.) Vehicle Routing: Problems, Methods and Applications, 2nd edn. MOS-Siam Series on Optimization, pp. 299–347. Siam, Philadelphia (2014)
Bertsimas, D.J.: A vehicle routing problem with stochastic demands. Oper. Res. 40, 574–585 (1992)
Bianchi, L., Birattari, M., Manfrin, M., Mastrolilli, M., Paquete, L., Rossi-Doria, O., Schiavinotto, T.: Hybrid metaheuristics for the vehicle routing problem with stochastic demands. J. Math. Model. Alg. 5(1), 91–110 (2006)
Bodin, L.D., Golden, B.L.: Classification in vehicle routing and scheduling. Networks 11, 97–108 (1981)
Bodin, L.D., Golden, B.L., Assad, A.A., Ball, M.: The state of the art in the routing and scheduling of vehicles and crews. Comput. Oper. Res. 10, 63–212 (1983)
Braca, J., Bramel, J., Posner, B., Simchi Levi, D.: A computerized approach to the New York City school bus routing problem. IIE Trans. 29(8), 693–702 (1997)
Brandao, J.: A tabu search algorithm for the open vehicle routing problem. Eur. J. Oper. Res. 157(3), 552–564 (2004)
Campbell, A., Clarke, L., Kleywegt, A., Sawelsberg, M.: The inventory routing problem. In: Crainic, T.G., Laporte, G. (eds.) Fleet Management and Logistics, pp. 95–113. Kluwer Academic Publishers, Boston (1998)
Campbell, A., Clarke, L., Sawelsberg, M.: Inventory routing in practice. In: Toth, P., Vigo, D. (eds.) The Vehicle Routing Problem. Monographs on Discrete Mathematics and Applications, pp. 309–330. Siam, Philadelphia (2002)
Caretto, C., Baker, B.: A GRASP interactive approach to the vehicle routing problem with backhauls. In: Ribeiro, C.C., Hansen, P. (eds.) Essays and Surveys on Metaheuristics, pp. 185–199. Kluwer Academic Publishers, Norwell (2002)
Casco, D.O., Golden, B.L., Wasil, E.A.: Vehicle routing with backhauls: models, algorithms, and case studies. In: Golden, B.L., Assad, A.A. (eds.) Vehicle Routing: Methods and Studies, pp. 127–147. North Holland, Amsterdam (1988)
Christiansen, M., Fagerholt, K., Ronen, D.: Ship routing and scheduling: status and perspectives. Transp. Sci. 38(1), 1–18 (2004)
Christiansen, M., Fagerholt, K., Nygreen, B., Ronen, D.: Ship routing and scheduling in the new millennium. Eur. J. Oper. Res. 228, 467–483 (2013)
Christofides, N.: Vehicle routing. In Lawer, E.L., Lenstra, J.K., Rinnoy Kan, A.H.G., Shmoys, D.B. (eds.) The Travelling Salesman Problem: A Guided Tour of Combinatorial Optimization, pp. 431–448. Wiley, Hoboken (1985)
Christofides, N., Mignozzi, A., Toth, P.: The vehicle routing problem. In: Christofides, N. (ed.) Combinatorial Optimization, pp. 315–338. Wiley, Hoboken (1979)
Cordeau, J.F., Deasulniers, G., Desrosiers, J., Solomon, M.M., Soumis, F.: VRP with time windows. In: Toth, P., Vigo, D. (eds.) The Vehicle Routing Problem. Monographs on Discrete Mathematics and Applications, 157–193. Siam, Philadelphia (2002)
Cordeau, J.F., Laporte, G., Ropke, S.: Recent Models and Algorithms for One-to-One Pickup and Delivery Problems. In: Golden, B.L., Raghavan, S., Wasil, E.A. (eds.) The Vehicle Routing Problem: Latest Advances and New Challenges. Operations Research/Computer Science Interfaces Series, vol. 43, pp. 327–357. Springer, New York (2008)
Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Manag. Sci. 6(1), 80–91 (1959)
Daskin, M.: Network and Discrete Location. Models, Algorithms and Applications. Wiley, New York (1995)
Doerner, K.F., Salazar-Gonzalez, J.J.: Pickup-and-delivery problems for people transportation. In: Toth, P., Vigo, D. (eds.) Vehicle Routing: Problems, Methods and Applications, 2nd edn. MOS-Siam Series on Optimization, pp. 193–212. Siam, Philadelphia (2014)
Dror, M.: Arc Routing Theory, Solutions and Applications. Kluwer Academic Publishers, Boston (2000)
Eiselt, H.A., Laporte, G.: A Historical perspective on arc routing. In: Dror, M. (ed.) Arc Routing Theory, Solutions and Applications, pp. 1–16. Kluwer Academic Publishers, Boston (2000)
Fedegruen, A., Simchi-Levi, D.: Analysis of vehicle routing and inventory routing problems. In: Ball, M.O., Magnanti, T.L., Momma, C.L., Nemhauser, G.L. (eds.) Network Routing. Handbooks in Operations Research and Management Science, vol. 8, pp. 297–373. Elsevier Science B. V., Amsterdam (1995)
Fisher, M.L.: Vehicle routing. In: Ball, M.O., Magnanti, T.L., Momma, C.L., Nemhauser, G.L. (eds.) Network Routing. Handbooks in Operations Research and Management Science, vol. 8, pp. 1–33. North Holland, Amsterdam (1995)
Fisher, M.L., Jaikumar, R.: A generalized assignment heuristic for vehicle routing. In: Golden, B., Bodin, L. (eds.) Proceedings of the International Workshop on Current and Future Directions in the Routing and Scheduling of Vehicles and Crews, pp. 109–124. Wiley, Hoboken (1979)
Fisher, M.L., Jaikumar, R., Wassenhove, L.N.V.: A mutliplier adjustment method for the generalized assignment problem. Manag. Sci. 32(9), 1095–1103 (1986)
Francis, P.M., Smilowitz, K.R., Tzur, M.: The period vehicle routing problem and its extensions. In: Golden, B. et al. (eds.) The Vehicle Routing Problem: Latest Advances and New Challenges, pp. 73–102. Springer, New York (2008)
Gendreau, M., Potvin, J.Y.: Dynamic vehicle routing and dispatching. In: Crainic, T.G., Laporte, G. (eds.) Fleet Management and Logistics, pp. 115–125. Kluwer Academic Publishers, Boston (1998)
Gendreau, M., Laport, G., Seguin, R.: A tabu search heuristic for the vehicle routing problem with stochastic demands and customers. Oper. Res. 44, 469–477 (1995)
Gendreau, M., Laport, G., Seguin, R.: An exact algorithm for the vehicle routing problem with stochastic demands and customers. Oper. Res. 29, 143–155 (1995)
Gendreau, M., Laport, G., Seguin, R.: Stochastic vehicle routing. Eur. J. Oper. Res. 88, 3–12 (1996)
Gendreau, M., Laporte, G., Potvin, J.-Y.: Vehicle routing: modern heuristics. In: Aarts, E.H.L., Lenstra, J.K. (eds.) Local Search in Combinatorial Optimization, pp. 311–336. Wiley, Chichester (1997)
Gendreau, M., Laporte, G., Potvin, J.-Y.: Metaheuristics for the capacitated VRP. In: Toth, P., Vigo, D. (eds.) The Vehicle Routing Problem. Monographs on Discrete Mathematics and Applications, pp. 129–154. Siam, Philadelphia (2002)
Gerdessen, J.H.: Vehicle routing problem with trailers. Eur. J. Oper. Res. 93, 135–147 (1996)
Golden, B.L., Assad, A.A.: Vehicle Routing: Methods and Studies. North Holland, Amsterdam (1988)
Golden, B.L., Wong, R.T.: Capacitated arc routing algorithms. Networks 11, 305–315 (1981)
Golden, B.L., Wasil, E.A., Kelly, J.P., Chao, I.M.: The impact of metaheuristics on solving the vehicle routing problem: algorithms, problem sets, and computational results. In: Crainic, T.G., Laporte, G. (eds.) Fleet management and logistics, pp. 33–56. Kluwer Academic Publishers, Boston (1998)
Golden, B.L., Raghavan, S., Wasil, E.A. (eds.): The vehicle routing problem: latest advances and new challenges. Operations Research/Computer Science Interfaces Series, vol. 43. Springer, New York (2008)
Gribkovskaia, I., Laporte, G.: One-to-many-to-one single vehicle pickup and delivery problems. In: Golden, B.L., Raghavan, S., Wasil, E.A. (eds.) The Vehicle Routing Problem: Latest Advances and New Challenges. Operations Research/Computer Science Interfaces Series, vol. 43, pp. 359–377. Springer, New York (2008)
Hachicha, M., Hodgson, M.J., Laporte, G., Semet, F.: Heuristics for the multi-vehicle covering tour problem. Comput. Oper. Res. 27, 29–42 (2000)
Hertz, A., Mittaz, M.: Heuristic algorithms. In: Dror, M. (ed.) Arc Routing Theory, Solutions and Applications, pp. 327–386. Kluwer Academic Publishers, Boston (2000)
Irnich, S., Schneider, M., Vigo, D.: Four variants of the vehicle routing problem. In: Toth, P., Vigo, D. (eds.) Vehicle Routing: Problems, Methods and Applications, 2nd edn. MOS-Siam Series on Optimization, pp. 241–271. Siam, Philadelphia (2014)
Ke, L., Archetti, C., Feng, Z.: Ants can solve the team orienteering problem. Comput. Ind. Eng. 54(3), 648–665 (2008)
Lahyani, R., Khemakhem, M., Semet, F.: Rich vehicle routing problems: from a taxonomy to a definition. Eur. J. Oper. Res. 241, 1–14 (2015)
Laporte, G., Semet, F.: Classical heuristics for the capacitated VRP. In: Toth, P., Vigo, D. (eds.) The Vehicle Routing Problem. Monographs on Discrete Mathematics and Applications, pp. 109–128. Siam, Philadelphia (2002)
Laporte, G., Gendreau, M., Potvin, J.-Y., Semet, F.: Classical and modern heuristics for the vehicle routing problem. Int. Trans. Oper. Res. 7, 285–300 (2000)
Lin, C., Choy, K.L., Ho, G.T.S., Chung, S.H., Lam, H.Y.: Survey of green vehicle routing problem: past and future trends. Expert Syst. Appl. 41, 1118–1138 (2014)
Marinakis, Y.: An improved particle swarm optimization algorithm for the capacitated location routing problem and for the location routing problem with stochastic demands. Appl. Soft Comput. 37, 680–701 (2015)
Marinakis, Y., Migdalas, A.: Heuristic solutions of vehicle routing problems in supply chain management. In: Pardalos, P.M., Migdalas, A., Burkard, R. (eds.) Combinatorial and Global Optimization, pp. 205–236. World Scientific Publishing Co., Singapore (2002)
Marinakis, Y., Marinaki, M.: A bilevel genetic algorithm for a real life location routing problem. Int. J. Log. Res. Appl. 11(1), 49–65 (2008)
Migdalas, A.: Bilevel programming in traffic planning: models, methods and challenge. J. Global Optim. 7, 381–405 (1995)
Min, H., Jayaraman, V., Srivastava, R.: Combined location-routing problems: a synthesis and future research directions. Eur. J. Oper. Res. 108, 1–15 (1998)
Montane, F.A.T., Galvao, R.D.: A tabu search algorithm for the vehicle routing problem with simultaneous pick-up and delivery service. Comput. Oper. Res. 33, 595–619 (2006)
Montoya-Torres, J.R., Franco, J.L., Isaza, S.N., Jimenez, H.F., Herazo-Padilla, N.: A literature review on the vehicle routing problem with multiple depots. Comput. Ind. Eng. 79, 115–129 (2015)
Nagy, G., Salhi, S.: Location-routing: issues, models and methods. Eur. J. Oper. Res. 177, 649–672 (2007)
Pearn, W.L., Assad, A.A., Golden, B.L.: Transforming arc routing into node routing problems. Comput. Oper. Res. 14(4), 285–288 (1987)
Pereira, F.B., Tavares, J.: Bio-inspired algorithms for the vehicle routing problem. Studies in Computational Intelligence, vol. 161. Springer, Berlin (2008)
Pillac, V., Gendreau, M., Gueret, C., Medaglia, A.L.: A review of dynamic vehicle routing problems. Eur. J. Oper. Res. 225, 1–11 (2013)
Powell, W.B., Jaillet, P., Odoni, A.: Stochastic and dynamic networks and routing. In: Ball, M.O., Magnanti, T.L., Momma, C.L., Nemhauser, G.L. (eds.) Network Routing. Handbooks in Operations Research and Management Science, vol. 8, pp. 141–295. Elsevier Science B V, Amsterdam (1995)
Prodhon, C., Prins, C.: A survey of recent research on location-routing problems. Eur. J. Oper. Res. 238, 1–17 (2014)
Psaraftis, H.N.: Scheduling large-scale advance request dial-a-ride systems. Am. J. Math. Manag. Sci. 6, 327–368 (1986)
Psaraftis, H.N.: Dynamic vehicle routing problems. In: Golden, B.L., Assad, A.A. (eds.) Vehicle Routing: Methods and Studies, pp. 223–248. North Holland, Amsterdam (1988)
Psaraftis, H.N.: Dynamic vehicle routing: status and prospects. Ann. Oper. Res. 61, 143–164 (1995)
Renaud, J., Laporte, G., Boctor, F.F.: A Tabu search heuristic for the multidepot vehicle routing problem. Comput. Oper. Res. 23(3), 229–235 (1996)
Ronen, D.: Cargo ships routing and scheduling: survey of models and problems. Eur. J. Oper. Res. 12, 119–126 (1983)
Ronen, D.: Ships scheduling: the last decade. Eur. J. Oper. Res. 71(3), 325–333 (1993)
Sariklis, D., Powell, S.: A heuristic method for the open vehicle routing problem. J. Oper. Res. Soc. 51(5), 564–573 (2000)
Sevkli, A.Z., Sevilgen, F.E.: Discrete particle swarm optimization for the team orienteering problem. Turk. J. Electr. Eng. Comput. Sci. 20(2), 231–239 (2012)
Solomon, M.M.: Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper. Res. 35(2), 254–265 (1987)
Solomon, M.M., Desrosiers, J.: Time window constrained routing and scheduling problems. Transp. Sci. 22(1), 1–13 (1988)
Stewart, W.R., Golden, B.L.: Stochastic vehicle routing: a comprehensive approach. Eur. J. Oper. Res. 14, 371–385 (1983)
Tarantilis, C.D.: Solving the vehicle routing problem with adaptive memory programming methodology. Comput. Oper. Res. 32(9), 2309–2327 (2005)
Tiwari, A., Chang, P.C.: A block recombination approach to solve green vehicle routing problem. Int. J. Prod. Econ., 164, 379–387 (2015)
Toth, P., Vigo, D.: The Vehicle Routing Problem. Monographs on Discrete Mathematics and Applications. Siam, Philadelphia (2002)
Toth, P., Vigo, D.: VRP with backhauls. In: Toth, P., Vigo, D. (eds.) The Vehicle Routing Problem. Monographs on Discrete Mathematics and Applications, pp. 195–224. Siam, Philadelphia (2002)
Toth, P., Vigo D.: Vehicle Routing: Problems, Methods and Applications, 2nd edn. MOS-Siam Series on Optimization. Siam, Philadelphia (2014)
Vansteenwegen, P., Souffriau, W., Berghe, G.V., Oudheusden, D.V.: A guided local search metaheuristic for the team orienteering problem. Eur. J. Oper. Res. 196, 118–127 (2009)
Xiao, Y., Zhao, Q., Kaku, I., Xu, Y.: Development of a fuel consumption optimization model for the capacitated vehicle routing problem. Comput. Oper. Res. 39(7), 1419–1431 (2012)
Yang, W.H., Mathur, K., Ballou, R.H.: Stochastic vehicle routing problem with restocking. Transp. Sci. 34, 99–112 (2000)
Yusoff, M., Ariffin, J., Mohamed, A.: A multi-valued discrete particle swarm optimization for the evacuation vehicle routing problem. In: Tan, Y. et al. (eds.) ICSI 2011, Part I. Lecture Notes in Computer Science, vol. 6728, pp. 182–193. Springer, Berlin (2011)
Zhang, T., Chaovalitwongse, W.A., Zhang, Y.: Scatter search for the stochastic travel-time vehicle routing problem with simultaneous pick-ups and deliveries. Comput. Oper. Res. 39, 2277–2290 (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Marinakis, Y., Marinaki, M., Migdalas, A. (2018). Variants and Formulations of the Vehicle Routing Problem. In: Pardalos, P., Migdalas, A. (eds) Open Problems in Optimization and Data Analysis. Springer Optimization and Its Applications, vol 141. Springer, Cham. https://doi.org/10.1007/978-3-319-99142-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-99142-9_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-99141-2
Online ISBN: 978-3-319-99142-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)