Abstract
The capacitated vehicle routing problem with time windows (CVRPTW) is a variant of the classical vehicle routing problem. In a category of CVRPTW, each customer has same unit-demand and must be served within a time window from a finite set of consecutive time windows. This paper gives a quasi-polynomial time approximation scheme (Q-PTAS) for this category of CVRPTW under the Euclidean setting. With a reasonable vehicle speed requirement, our algorithm could generate a set of routes of the length of \((1 + O(\epsilon ))OPT\) on expectation.
Hejiao Huang: This work was financially supported by National Natural Science Foundation of China with Grants No. 11071271, No. 11371004, No. 61100191 and No. 61370216, and Shenzhen Strategic Emerging Industries Program with Grants No. ZDSY20120613125016389, No. JCYJ20120613151201451 and No. JCYJ20130329153215152.
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References
Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Manag. Sci. 6, 80–91 (1959)
Toth, P., Vigo, D.: The Vehicle Routing Problem. Society for Industrial and Applied Mathematics, Philadelphia (2001)
Bao, X., Liu, Z.: Approximation algorithms for single vehicle scheduling problems with release and service times on a tree or cycle. Theor. Comput. Sci. 434, 1–10 (2012)
Nagamochi, H., Ohnishi, T.: Approximating a vehicle scheduling problem with time windows and handling times. Theor. Comput. Sci. 393, 133–146 (2008)
Karuno, Y., Nagamochi, H.: An approximability result of the multi-vehicle scheduling problem on a path with release and handling times. Theor. Comput. Sci. 312, 267–280 (2004)
Lacomme, P., Prins, C., Ramdane-Chérif, W.: Competitive memetic algorithms for arc routing problems. Ann. Oper. Res. 131, 159–185 (2004)
Toklu, N.E., Gambardella, L.M., Montemanni, R.: A multiple ant colony system for a vehicle routing problem with time windows and uncertain travel times. J. Traffic Logist. Eng. 2, 52–58 (2014)
Baldacci, R., Mingozzi, A., Roberti, R., Calvo, R.W.: An exact algorithm for the two-echelon capacitated vehicle routing problem. Oper. Res. 61, 298–314 (2013)
Baldacci, R., Mingozzi, A., Roberti, R.: New route relaxation and pricing strategies for the vehicle routing problem. Oper. Res. 59, 1269–1283 (2011)
Sousaa, J.C., Biswasa, H.A., Britob, R., Silveirab, A.: A multi objective approach to solve capacitated vehicle routing problems with time windows using mixed integer linear programming. Int. J. Adv. Sci. Technol. 28, 1–8 (2011)
Arora, S.: Approximation schemes for NP-hard geometric optimization problems: a survey. Math. Program. 97, 43–69 (2003)
Arora, S.: Polynomial time approximation schemes for euclidean traveling salesman and other geometric problems. J. ACM 45, 753–782 (1998)
Das, A., Mathieu, C.: A quasi-polynomial time approximation scheme for Euclidean capacitated vehicle routing. In: The Twenty First Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics, Philadelphia (2009)
Das, A.: Approximation schemes for euclidean vehicle routing problems. Dissertation, Brown University, Providence, Rhode Island, USA (2011)
Haimovich, M., Rinnooy Kan, A.H.G.: Bounds and heuristic for capacitated routing problems. Math. Oper. Res. 10, 527–542 (1985)
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Song, L., Huang, H., Du, H. (2014). A Quasi-polynomial Time Approximation Scheme for Euclidean CVRPTW. In: Zhang, Z., Wu, L., Xu, W., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2014. Lecture Notes in Computer Science(), vol 8881. Springer, Cham. https://doi.org/10.1007/978-3-319-12691-3_6
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DOI: https://doi.org/10.1007/978-3-319-12691-3_6
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