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2017 | OriginalPaper | Chapter

Cumulative VRP: A Simplified Model of Green Vehicle Routing

Authors : Rishi Ranjan Singh, Daya Ram Gaur

Published in: Sustainable Logistics and Transportation

Publisher: Springer International Publishing

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Abstract

There has been a recent resurge of interest in vehicle routing problems, especially in the context of green vehicle routing. One popular and simplified model is that of the cumulative vehicle routing problem. In this chapter, we examine the motivation, the definition, and the mixed integer linear program for the cumulative VRP. We review some of the recent results on approximation algorithms for the cumulative VRP. A column generation-based procedure for solving the cumulative VRP is also described. We also review approximation algorithms for a stochastic version of the cumulative VRP.

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Literature
1.
go back to reference Altinkemer, K., Gavish, B.: Heuristics for unequal weight delivery problems with a fixed error guarantee. Oper. Res. Lett. 6(4), 149–158 (1987)MathSciNetCrossRefMATH Altinkemer, K., Gavish, B.: Heuristics for unequal weight delivery problems with a fixed error guarantee. Oper. Res. Lett. 6(4), 149–158 (1987)MathSciNetCrossRefMATH
2.
go back to reference Archetti, C., Feillet, D., Gendreau, M., Speranza, M.G.: Complexity of the VRP and SDVRP. Transp. Res. C Emerg. Technol. 19(5), 741–750 (2011)CrossRef Archetti, C., Feillet, D., Gendreau, M., Speranza, M.G.: Complexity of the VRP and SDVRP. Transp. Res. C Emerg. Technol. 19(5), 741–750 (2011)CrossRef
3.
go back to reference Baldacci, R., Christofides, N., Mingozzi, A.: An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts. Math. Program. 115(2), 351–385 (2008)MathSciNetCrossRefMATH Baldacci, R., Christofides, N., Mingozzi, A.: An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts. Math. Program. 115(2), 351–385 (2008)MathSciNetCrossRefMATH
4.
go back to reference Beasley, J.E.: Route firstcluster second methods for vehicle routing. Omega 11(4), 403–408 (1983)CrossRef Beasley, J.E.: Route firstcluster second methods for vehicle routing. Omega 11(4), 403–408 (1983)CrossRef
5.
go back to reference Bektaş, T., Demir, E., Laporte, G.: Green vehicle routing. In: Psaraftis, H.N. (ed.) Green Transportation Logistics, pp. 243–265. Springer, Cham (2016)CrossRef Bektaş, T., Demir, E., Laporte, G.: Green vehicle routing. In: Psaraftis, H.N. (ed.) Green Transportation Logistics, pp. 243–265. Springer, Cham (2016)CrossRef
6.
go back to reference Bell, J.E., McMullen, P.R.: Ant colony optimization techniques for the vehicle routing problem. Adv. Eng. Inform. 18(1), 41–48 (2004)CrossRef Bell, J.E., McMullen, P.R.: Ant colony optimization techniques for the vehicle routing problem. Adv. Eng. Inform. 18(1), 41–48 (2004)CrossRef
7.
go back to reference Bertsimas, D.: Probabilistic combinatorial optimization problems. Ph.D. thesis, Massachusetts Institute of Technology (1988) Bertsimas, D.: Probabilistic combinatorial optimization problems. Ph.D. thesis, Massachusetts Institute of Technology (1988)
9.
go back to reference Bertsimas, D.J., Simchi-Levi, D.: A new generation of vehicle routing research: robust algorithms, addressing uncertainty. Oper. Res. 44(2), 286–304 (1996)CrossRefMATH Bertsimas, D.J., Simchi-Levi, D.: A new generation of vehicle routing research: robust algorithms, addressing uncertainty. Oper. Res. 44(2), 286–304 (1996)CrossRefMATH
10.
go back to reference Bjarnadóttir, Á.S.: Solving the vehicle routing problem with genetic algorithms. Ph.D. thesis, Technical University of Denmark (DTU), Lyngby (2004) Bjarnadóttir, Á.S.: Solving the vehicle routing problem with genetic algorithms. Ph.D. thesis, Technical University of Denmark (DTU), Lyngby (2004)
11.
go back to reference Blum, A., Chalasani, P., Coppersmith, D., Pulleyblank, B., Raghavan, P., Sudan, M.: The minimum latency problem. In: Proceedings of the Twenty-Sixth Annual ACM Symposium on Theory of Computing, pp. 163–171. ACM (1994) Blum, A., Chalasani, P., Coppersmith, D., Pulleyblank, B., Raghavan, P., Sudan, M.: The minimum latency problem. In: Proceedings of the Twenty-Sixth Annual ACM Symposium on Theory of Computing, pp. 163–171. ACM (1994)
12.
13.
go back to reference Bramel, J., Simchi-Levi, D.: Probabilistic analyses and practical algorithms for the vehicle routing problem with time windows. Oper. Res. 44(3), 501–509 (1996)CrossRefMATH Bramel, J., Simchi-Levi, D.: Probabilistic analyses and practical algorithms for the vehicle routing problem with time windows. Oper. Res. 44(3), 501–509 (1996)CrossRefMATH
14.
go back to reference Chaudhuri, K., Godfrey, B., Rao, S., Talwar, K.: Paths, trees, and minimum latency tours. In: Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, pp. 36–45. IEEE, Los Alamitos (2003) Chaudhuri, K., Godfrey, B., Rao, S., Talwar, K.: Paths, trees, and minimum latency tours. In: Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, pp. 36–45. IEEE, Los Alamitos (2003)
15.
go back to reference Chiang, W.C., Russell, R.A.: Simulated annealing metaheuristics for the vehicle routing problem with time windows. Ann. Oper. Res. 63(1), 3–27 (1996)CrossRefMATH Chiang, W.C., Russell, R.A.: Simulated annealing metaheuristics for the vehicle routing problem with time windows. Ann. Oper. Res. 63(1), 3–27 (1996)CrossRefMATH
16.
go back to reference Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Technical report, DTIC Document (1976) Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Technical report, DTIC Document (1976)
17.
go back to reference Christofides, N., Mingozzi, A., Toth, P.: State-space relaxation procedures for the computation of bounds to routing problems. Networks 11(2), 145–164 (1981)MathSciNetCrossRefMATH Christofides, N., Mingozzi, A., Toth, P.: State-space relaxation procedures for the computation of bounds to routing problems. Networks 11(2), 145–164 (1981)MathSciNetCrossRefMATH
18.
go back to reference Cinar, D., Gakis, K., Pardalos, P.M.: Reduction of CO2 emissions in cumulative multi-trip vehicle routing problems with limited duration. Environ. Model. Assess. 20(4), 273–284 (2015)CrossRef Cinar, D., Gakis, K., Pardalos, P.M.: Reduction of CO2 emissions in cumulative multi-trip vehicle routing problems with limited duration. Environ. Model. Assess. 20(4), 273–284 (2015)CrossRef
19.
go back to reference Cinar, D., Gakis, K., Pardalos, P.M.: A 2-phase constructive algorithm for cumulative vehicle routing problems with limited duration. Expert Syst. Appl. 56, 48–58 (2016)CrossRef Cinar, D., Gakis, K., Pardalos, P.M.: A 2-phase constructive algorithm for cumulative vehicle routing problems with limited duration. Expert Syst. Appl. 56, 48–58 (2016)CrossRef
20.
go back to reference Clarke, G., Wright, J.W.: Scheduling of vehicles from a central depot to a number of delivery points. Oper. Res. 12(4), 568–581 (1964)CrossRef Clarke, G., Wright, J.W.: Scheduling of vehicles from a central depot to a number of delivery points. Oper. Res. 12(4), 568–581 (1964)CrossRef
21.
go back to reference Cordeau, J.F., Laporte, G.: Tabu search heuristics for the vehicle routing problem. In: Sharda, R., Alidaee, B., Rego, C., Voß, S. (eds.) Metaheuristic Optimization via Memory and Evolution, pp. 145–163. Springer, Boston (2005)CrossRef Cordeau, J.F., Laporte, G.: Tabu search heuristics for the vehicle routing problem. In: Sharda, R., Alidaee, B., Rego, C., Voß, S. (eds.) Metaheuristic Optimization via Memory and Evolution, pp. 145–163. Springer, Boston (2005)CrossRef
23.
go back to reference Demir, E., Bektaş, T., Laporte, G.: A comparative analysis of several vehicle emission models for road freight transportation. Transp. Res. Part D: Transp. Environ. 16(5), 347–357 (2011)CrossRef Demir, E., Bektaş, T., Laporte, G.: A comparative analysis of several vehicle emission models for road freight transportation. Transp. Res. Part D: Transp. Environ. 16(5), 347–357 (2011)CrossRef
24.
go back to reference Demir, E., Bektaş, T., Laporte, G.: An adaptive large neighborhood search heuristic for the pollution-routing problem. Eur. J. Oper. Res. 223(2), 346–359 (2012)MathSciNetCrossRefMATH Demir, E., Bektaş, T., Laporte, G.: An adaptive large neighborhood search heuristic for the pollution-routing problem. Eur. J. Oper. Res. 223(2), 346–359 (2012)MathSciNetCrossRefMATH
25.
go back to reference Demir, E., Bektaş, T., Laporte, G.: A review of recent research on green road freight transportation. Eur. J. Oper. Res. 237(3), 775–793 (2014)CrossRefMATH Demir, E., Bektaş, T., Laporte, G.: A review of recent research on green road freight transportation. Eur. J. Oper. Res. 237(3), 775–793 (2014)CrossRefMATH
26.
go back to reference Erdoğan, S., Miller-Hooks, E.: A green vehicle routing problem. Transp. Res. Part E: Logist. Transp. Rev. 48(1), 100–114 (2012)CrossRef Erdoğan, S., Miller-Hooks, E.: A green vehicle routing problem. Transp. Res. Part E: Logist. Transp. Rev. 48(1), 100–114 (2012)CrossRef
27.
go back to reference Fakcharoenphol, J., Harrelson, C., Rao, S.: The k-traveling repairman problem. In: Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 655–664. Society for Industrial and Applied Mathematics (2003) Fakcharoenphol, J., Harrelson, C., Rao, S.: The k-traveling repairman problem. In: Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 655–664. Society for Industrial and Applied Mathematics (2003)
29.
go back to reference Fukasawa, R., Longo, H., Lysgaard, J., de Aragão, M.P., Reis, M., Uchoa, E., Werneck, R.F.: Robust branch-and-cut-and-price for the capacitated vehicle routing problem. Math. Program. 106(3), 491–511 (2006)MathSciNetCrossRefMATH Fukasawa, R., Longo, H., Lysgaard, J., de Aragão, M.P., Reis, M., Uchoa, E., Werneck, R.F.: Robust branch-and-cut-and-price for the capacitated vehicle routing problem. Math. Program. 106(3), 491–511 (2006)MathSciNetCrossRefMATH
30.
go back to reference Fukasawa, R., He, Q., Song, Y.: A branch-cut-and-price algorithm for the energy minimization vehicle routing problem. Transp. Sci. 50(1), 23–34 (2015)CrossRef Fukasawa, R., He, Q., Song, Y.: A branch-cut-and-price algorithm for the energy minimization vehicle routing problem. Transp. Sci. 50(1), 23–34 (2015)CrossRef
31.
go back to reference Gaur, D.R., Singh, R.R.: Cumulative vehicle routing problem: a column generation approach. In: Ganguly, S., Krishnamurti R. (eds.) Algorithms and Discrete Applied Mathematics, pp. 262–274. Springer, Cham (2015) Gaur, D.R., Singh, R.R.: Cumulative vehicle routing problem: a column generation approach. In: Ganguly, S., Krishnamurti R. (eds.) Algorithms and Discrete Applied Mathematics, pp. 262–274. Springer, Cham (2015)
32.
go back to reference Gaur, D.R., Singh, R.R.: A heuristic for cumulative vehicle routing using column generation. Discret. Appl. Math. 228, 140-157 (2016)MathSciNetCrossRefMATH Gaur, D.R., Singh, R.R.: A heuristic for cumulative vehicle routing using column generation. Discret. Appl. Math. 228, 140-157 (2016)MathSciNetCrossRefMATH
33.
34.
go back to reference Gaur, D.R., Mudgal, A., Singh, R.R.: Approximation algorithms for cumulative VRP with stochastic demands. In: Govindarajan, S., Maheshwari A. (eds.) Algorithms and Discrete Applied Mathematics, pp. 176–189. Springer, Cham (2016)CrossRef Gaur, D.R., Mudgal, A., Singh, R.R.: Approximation algorithms for cumulative VRP with stochastic demands. In: Govindarajan, S., Maheshwari A. (eds.) Algorithms and Discrete Applied Mathematics, pp. 176–189. Springer, Cham (2016)CrossRef
35.
36.
go back to reference Gendreau, M., Laporte, G., Séguin, R.: Stochastic vehicle routing. Eur. J. Oper. Res. 88(1), 3–12 (1996)CrossRefMATH Gendreau, M., Laporte, G., Séguin, R.: Stochastic vehicle routing. Eur. J. Oper. Res. 88(1), 3–12 (1996)CrossRefMATH
37.
go back to reference Gendreau, M., Potvin, J.Y., Bräumlaysy, O., Hasle, G., Løkketangen, A.: Metaheuristics for the vehicle routing problem and its extensions: a categorized bibliography. In: Golden, B.L., Raghavan, S. (eds.) The Vehicle Routing Problem: Latest Advances and New Challenges, pp. 143–169. Springer, New York (2008)CrossRef Gendreau, M., Potvin, J.Y., Bräumlaysy, O., Hasle, G., Løkketangen, A.: Metaheuristics for the vehicle routing problem and its extensions: a categorized bibliography. In: Golden, B.L., Raghavan, S. (eds.) The Vehicle Routing Problem: Latest Advances and New Challenges, pp. 143–169. Springer, New York (2008)CrossRef
38.
go back to reference Glover, F.W., Kochenberger, G.A.: Handbook of Metaheuristics, vol. 57. Springer Science & Business Media, New York (2006)MATH Glover, F.W., Kochenberger, G.A.: Handbook of Metaheuristics, vol. 57. Springer Science & Business Media, New York (2006)MATH
39.
go back to reference Gupta, A., Nagarajan, V., Ravi, R.: Technical note – approximation algorithms for VRP with stochastic demands. Oper. Res. 60(1), 123–127 (2012)MathSciNetCrossRefMATH Gupta, A., Nagarajan, V., Ravi, R.: Technical note – approximation algorithms for VRP with stochastic demands. Oper. Res. 60(1), 123–127 (2012)MathSciNetCrossRefMATH
40.
41.
go back to reference Jabir, E., Panicker, V.V., Sridharan, R.: Multi-objective optimization model for a green vehicle routing problem. Procedia. Soc. Behav. Sci. 189, 33–39 (2015)CrossRef Jabir, E., Panicker, V.V., Sridharan, R.: Multi-objective optimization model for a green vehicle routing problem. Procedia. Soc. Behav. Sci. 189, 33–39 (2015)CrossRef
42.
go back to reference Jemai, J., Zekri, M., Mellouli, K.: An NSGA-II algorithm for the green vehicle routing problem. In: European Conference on Evolutionary Computation in Combinatorial Optimization, pp. 37–48. Springer, Berlin/Heidelberg (2012) Jemai, J., Zekri, M., Mellouli, K.: An NSGA-II algorithm for the green vehicle routing problem. In: European Conference on Evolutionary Computation in Combinatorial Optimization, pp. 37–48. Springer, Berlin/Heidelberg (2012)
43.
go back to reference Jin, M., Liu, K., Eksioglu, B.: A column generation approach for the split delivery vehicle routing problem. Oper. Res. Lett. 36(2), 265–270 (2008)MathSciNetCrossRefMATH Jin, M., Liu, K., Eksioglu, B.: A column generation approach for the split delivery vehicle routing problem. Oper. Res. Lett. 36(2), 265–270 (2008)MathSciNetCrossRefMATH
44.
go back to reference Kara, I., Kara, B.Y., Yetis, M.K.: Energy minimizing vehicle routing problem. In: Combinatorial Optimization and Applications, pp. 62–71. Springer, Norwell (2007) Kara, I., Kara, B.Y., Yetis, M.K.: Energy minimizing vehicle routing problem. In: Combinatorial Optimization and Applications, pp. 62–71. Springer, Norwell (2007)
45.
go back to reference Kara, İ., Kara, B.Y., Yetis, M.K.: Cumulative vehicle routing problems. In: Caric, T., Gold, H. (eds.) Vehicle Routing Problem, I-Tech, pp. 85–98 (2008) Kara, İ., Kara, B.Y., Yetis, M.K.: Cumulative vehicle routing problems. In: Caric, T., Gold, H. (eds.) Vehicle Routing Problem, I-Tech, pp. 85–98 (2008)
46.
go back to reference Kytöjoki, J., Nuortio, T., Bräysy, O., Gendreau, M.: An efficient variable neighborhood search heuristic for very large scale vehicle routing problems. Comput. Oper. Res. 34(9), 2743–2757 (2007)CrossRefMATH Kytöjoki, J., Nuortio, T., Bräysy, O., Gendreau, M.: An efficient variable neighborhood search heuristic for very large scale vehicle routing problems. Comput. Oper. Res. 34(9), 2743–2757 (2007)CrossRefMATH
47.
go back to reference Laporte, G., Nobert, Y., Desrochers, M.: Optimal routing under capacity and distance restrictions. Oper. Res. 33(5), 1050–1073 (1985)MathSciNetCrossRefMATH Laporte, G., Nobert, Y., Desrochers, M.: Optimal routing under capacity and distance restrictions. Oper. Res. 33(5), 1050–1073 (1985)MathSciNetCrossRefMATH
48.
go back to reference Li, H., Lv, T., Li, Y.: The tractor and semitrailer routing problem with many-to-many demand considering carbon dioxide emissions. Transp. Res. Part D: Transp. Environ. 34, 68–82 (2015)CrossRef Li, H., Lv, T., Li, Y.: The tractor and semitrailer routing problem with many-to-many demand considering carbon dioxide emissions. Transp. Res. Part D: Transp. Environ. 34, 68–82 (2015)CrossRef
49.
go back to reference Liberatore, F., Righini, G., Salani, M.: A column generation algorithm for the vehicle routing problem with soft time windows. 4OR 9(1), 49–82 (2011) Liberatore, F., Righini, G., Salani, M.: A column generation algorithm for the vehicle routing problem with soft time windows. 4OR 9(1), 49–82 (2011)
50.
go back to reference Lin, C., Choy, K.L., Ho, G.T., Chung, S., Lam, H.: Survey of green vehicle routing problem: past and future trends. Expert Syst. Appl. 41(4), 1118–1138 (2014)CrossRef Lin, C., Choy, K.L., Ho, G.T., Chung, S., Lam, H.: Survey of green vehicle routing problem: past and future trends. Expert Syst. Appl. 41(4), 1118–1138 (2014)CrossRef
51.
go back to reference Lysgaard, J., Wøhlk, S.: A branch-and-cut-and-price algorithm for the cumulative capacitated vehicle routing problem. Eur. J. Oper. Res. 236(3), 800–810 (2014)MathSciNetCrossRefMATH Lysgaard, J., Wøhlk, S.: A branch-and-cut-and-price algorithm for the cumulative capacitated vehicle routing problem. Eur. J. Oper. Res. 236(3), 800–810 (2014)MathSciNetCrossRefMATH
52.
go back to reference MirHassani, S., Mohammadyari, S.: Reduction of carbon emissions in VRP by gravitational search algorithm. Manag. Environ. Qual. Int. J. 25(6), 766–782 (2014)CrossRef MirHassani, S., Mohammadyari, S.: Reduction of carbon emissions in VRP by gravitational search algorithm. Manag. Environ. Qual. Int. J. 25(6), 766–782 (2014)CrossRef
53.
go back to reference Newman, P., Alimoradian, B., Lyons, T.: Estimating fleet fuel consumption for vans and small trucks. Transp. Sci. 23(1), 46–50 (1989)CrossRef Newman, P., Alimoradian, B., Lyons, T.: Estimating fleet fuel consumption for vans and small trucks. Transp. Sci. 23(1), 46–50 (1989)CrossRef
54.
go back to reference Ocheni, S.I.: Impact of fuel price increaseon the Nigerian economy. Mediterr. J. Soc. Sci. 6(1 S1), 560 (2015) Ocheni, S.I.: Impact of fuel price increaseon the Nigerian economy. Mediterr. J. Soc. Sci. 6(1 S1), 560 (2015)
55.
go back to reference Park, Y., Chae, J.: A review of the solution approaches used in recent g-VRP (green vehicle routing problem). Int. J. Adv. Logist. 3(1-2), 27–37 (2014)CrossRef Park, Y., Chae, J.: A review of the solution approaches used in recent g-VRP (green vehicle routing problem). Int. J. Adv. Logist. 3(1-2), 27–37 (2014)CrossRef
56.
go back to reference Potvin, J.Y.: Evolutionary Algorithms for Vehicle Routing. CIRRELT, Montreal (2007) Potvin, J.Y.: Evolutionary Algorithms for Vehicle Routing. CIRRELT, Montreal (2007)
57.
go back to reference Prins, C.: A simple and effective evolutionary algorithm for the vehicle routing problem. Comput. Oper. Res. 31(12), 1985–2002 (2004)MathSciNetCrossRefMATH Prins, C.: A simple and effective evolutionary algorithm for the vehicle routing problem. Comput. Oper. Res. 31(12), 1985–2002 (2004)MathSciNetCrossRefMATH
58.
go back to reference Qureshi, A.G., Taniguchi, E., Yamada, T.: Column generation-based heuristics for vehicle routing problem with soft time windows. In: Proceedings of the Eastern Asia Society for Transportation Studies, vol. 2009, pp. 151–151. Eastern Asia Society for Transportation Studies (2009) Qureshi, A.G., Taniguchi, E., Yamada, T.: Column generation-based heuristics for vehicle routing problem with soft time windows. In: Proceedings of the Eastern Asia Society for Transportation Studies, vol. 2009, pp. 151–151. Eastern Asia Society for Transportation Studies (2009)
59.
go back to reference Sahin, B., Yilmaz, H., Ust, Y., Guneri, A.F., Gulsun, B.: An approach for analysing transportation costs and a case study. Eur. J. Oper. Res. 193(1), 1–11 (2009)CrossRefMATH Sahin, B., Yilmaz, H., Ust, Y., Guneri, A.F., Gulsun, B.: An approach for analysing transportation costs and a case study. Eur. J. Oper. Res. 193(1), 1–11 (2009)CrossRefMATH
60.
go back to reference Santos, G.T., Cantao, L.A.P., Cantao, R.F.: Vehicle routing problem with fuel consumption minimization: a case study. In: Proceedings of the XVIII Latin-Iberoamerican Conference on Operations Research, CLAIO, pp. 802–809. IEEE (2016) Santos, G.T., Cantao, L.A.P., Cantao, R.F.: Vehicle routing problem with fuel consumption minimization: a case study. In: Proceedings of the XVIII Latin-Iberoamerican Conference on Operations Research, CLAIO, pp. 802–809. IEEE (2016)
61.
go back to reference Stewart, W.R., Golden, B.L.: Stochastic vehicle routing: a comprehensive approach. Eur. J. Oper. Res. 14(4), 371–385 (1983)CrossRefMATH Stewart, W.R., Golden, B.L.: Stochastic vehicle routing: a comprehensive approach. Eur. J. Oper. Res. 14(4), 371–385 (1983)CrossRefMATH
62.
go back to reference Toro, E.M., Escobar, A.H., Granada, M.: Literature review on the vehicle routing problem in the green transportation context. revista. luna. azúl 42, 362–387 (2016) Toro, E.M., Escobar, A.H., Granada, M.: Literature review on the vehicle routing problem in the green transportation context. revista. luna. azúl 42, 362–387 (2016)
63.
go back to reference Toth, P., Vigo, D.: Branch-and-bound algorithms for the capacitated VRP. In: Toth, P., Vigo, D. (eds.) The Vehicle Routing Problem, pp. 29–51. Society for Industrial and Applied Mathematics, Philadelphia (2001) Toth, P., Vigo, D.: Branch-and-bound algorithms for the capacitated VRP. In: Toth, P., Vigo, D. (eds.) The Vehicle Routing Problem, pp. 29–51. Society for Industrial and Applied Mathematics, Philadelphia (2001)
64.
go back to reference Vaira, G., Dzemyda, G., Augutis, J., Barauskas, R., Kaklauskas, A., žilinskas, J., Bareiša, E., Marcinkevičius, V., Kurasova, O.: Genetic algorithm for vehicle routing problem. Ph.D. thesis, Vilniaus Universitetas (2014) Vaira, G., Dzemyda, G., Augutis, J., Barauskas, R., Kaklauskas, A., žilinskas, J., Bareiša, E., Marcinkevičius, V., Kurasova, O.: Genetic algorithm for vehicle routing problem. Ph.D. thesis, Vilniaus Universitetas (2014)
65.
go back to reference Xiao, Y., Konak, A.: Green vehicle routing problem with time-varying traffic congestion. In: Proceedings of the 14th INFORMS Computing Society Conference, pp. 134–148 (2015) Xiao, Y., Konak, A.: Green vehicle routing problem with time-varying traffic congestion. In: Proceedings of the 14th INFORMS Computing Society Conference, pp. 134–148 (2015)
66.
go back to reference Xiao, Y., Konak, A.: A simulating annealing algorithm to solve the green vehicle routing & scheduling problem with hierarchical objectives and weighted tardiness. Appl. Soft Comput. 34, 372–388 (2015)CrossRef Xiao, Y., Konak, A.: A simulating annealing algorithm to solve the green vehicle routing & scheduling problem with hierarchical objectives and weighted tardiness. Appl. Soft Comput. 34, 372–388 (2015)CrossRef
67.
go back to reference Xiao, Y., Konak, A.: The heterogeneous green vehicle routing and scheduling problem with time-varying traffic congestion. Transp. Res. Part E: Logist. Transp. Rev. 88, 146–166 (2016)CrossRef Xiao, Y., Konak, A.: The heterogeneous green vehicle routing and scheduling problem with time-varying traffic congestion. Transp. Res. Part E: Logist. Transp. Rev. 88, 146–166 (2016)CrossRef
68.
go back to reference 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)MathSciNetCrossRefMATH 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)MathSciNetCrossRefMATH
Metadata
Title
Cumulative VRP: A Simplified Model of Green Vehicle Routing
Authors
Rishi Ranjan Singh
Daya Ram Gaur
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-69215-9_3

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