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2016 | OriginalPaper | Buchkapitel

Approximation Algorithms for Cumulative VRP with Stochastic Demands

verfasst von : Daya Ram Gaur, Apurva Mudgal, Rishi Ranjan Singh

Erschienen in: Algorithms and Discrete Applied Mathematics

Verlag: Springer International Publishing

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Abstract

In this paper we give randomized approximation algorithms for stochastic cumulative VRPs for split and unsplit deliveries. The approximation ratios are \(2(1+\alpha )\) and 7 respectively, where \(\alpha \) is the approximation ratio for the metric TSP. The approximation factor is further reduced for trees and paths. These results extend the results in [Technical note - approximation algorithms for VRP with stochastic demands. Operations Research, 2012] and [Routing vehicles to minimize fuel consumption. Operations Research Letters, 2013].

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Literatur
1.
Zurück zum Zitat 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.
Zurück zum Zitat Archetti, C., Feillet, D., Gendreau, M., Speranza, M.G.: Complexity of the VRP and SDVRP. Transp. Res. Part C. 19(5), 741–750 (2011)CrossRef Archetti, C., Feillet, D., Gendreau, M., Speranza, M.G.: Complexity of the VRP and SDVRP. Transp. Res. Part C. 19(5), 741–750 (2011)CrossRef
3.
Zurück zum Zitat Arora, S.: Polynomial time approximation schemes for euclidean traveling salesman and other geometric problems. J. ACM (JACM) 45(5), 753–782 (1998)MathSciNetCrossRefMATH Arora, S.: Polynomial time approximation schemes for euclidean traveling salesman and other geometric problems. J. ACM (JACM) 45(5), 753–782 (1998)MathSciNetCrossRefMATH
4.
Zurück zum Zitat 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)
6.
Zurück zum Zitat 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
7.
Zurück zum Zitat 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)
9.
Zurück zum Zitat 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
10.
11.
Zurück zum Zitat Gaur, D.R., Singh, R.R.: Cumulative vehicle routing problem: a column generation approach. In: Ganguly, S., Krishnamurti, R. (eds.) CALDAM 2015. LNCS, vol. 8959, pp. 262–274. Springer, Heidelberg (2015) Gaur, D.R., Singh, R.R.: Cumulative vehicle routing problem: a column generation approach. In: Ganguly, S., Krishnamurti, R. (eds.) CALDAM 2015. LNCS, vol. 8959, pp. 262–274. Springer, Heidelberg (2015)
12.
Zurück zum Zitat 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
14.
Zurück zum Zitat 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
15.
Zurück zum Zitat Haimovich, M., Rinnooy Kan, A.H.G.: Bounds and heuristics for capacitated routing problems. Math. Oper. Res. 10(4), 527–542 (1985)MathSciNetCrossRefMATH Haimovich, M., Rinnooy Kan, A.H.G.: Bounds and heuristics for capacitated routing problems. Math. Oper. Res. 10(4), 527–542 (1985)MathSciNetCrossRefMATH
16.
Zurück zum Zitat Kara, I., Kara, B.Y., Yetis, M.K.: Energy minimizing vehicle routing problem. In: Dress, A.W.M., Xu, Y., Zhu, B. (eds.) COCOA 2007. LNCS, vol. 4616, pp. 62–71. Springer, Heidelberg (2007)CrossRef Kara, I., Kara, B.Y., Yetis, M.K.: Energy minimizing vehicle routing problem. In: Dress, A.W.M., Xu, Y., Zhu, B. (eds.) COCOA 2007. LNCS, vol. 4616, pp. 62–71. Springer, Heidelberg (2007)CrossRef
17.
Zurück zum Zitat Kara, I., Kara, B.Y., Yetis, M.K.: Cumulative vehicle routing problems. In: Vehicle Routing Problem, pp. 85–98 (2008) Kara, I., Kara, B.Y., Yetis, M.K.: Cumulative vehicle routing problems. In: Vehicle Routing Problem, pp. 85–98 (2008)
18.
Zurück zum Zitat Labbé, M., Laporte, G., Mercure, H.: Capacitated vehicle routing on trees. Oper. Res. 39(4), 616–622 (1991)CrossRefMATH Labbé, M., Laporte, G., Mercure, H.: Capacitated vehicle routing on trees. Oper. Res. 39(4), 616–622 (1991)CrossRefMATH
19.
Zurück zum Zitat Mitchell, J.S.B.: Guillotine subdivisions approximate polygonal subdivisions: a simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems. SIAM J. Comput. 28(4), 1298–1309 (1999)MathSciNetCrossRefMATH Mitchell, J.S.B.: Guillotine subdivisions approximate polygonal subdivisions: a simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems. SIAM J. Comput. 28(4), 1298–1309 (1999)MathSciNetCrossRefMATH
20.
Zurück zum Zitat 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
21.
Zurück zum Zitat Xiao, Y., Zhao, Q., Kaku, I., Yuchun, X.: 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., Yuchun, X.: Development of a fuel consumption optimization model for the capacitated vehicle routing problem. Comput. Oper. Res. 39(7), 1419–1431 (2012)MathSciNetCrossRefMATH
Metadaten
Titel
Approximation Algorithms for Cumulative VRP with Stochastic Demands
verfasst von
Daya Ram Gaur
Apurva Mudgal
Rishi Ranjan Singh
Copyright-Jahr
2016
Verlag
Springer International Publishing
DOI
https://doi.org/10.1007/978-3-319-29221-2_15