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Approximation Algorithms for the Multi-Vehicle Scheduling Problem

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Algorithms and Computation (ISAAC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6507))

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Abstract

In this paper we investigate approximation algorithms for the multi-vehicle scheduling problem (MVSP). In MVSP we are given a graph G = (V,E), where each vertex u of V is associated with a job j(u), and each edge e has a non-negative weight w(e). There are m identical vehicles available to service the jobs. Each job j(u) has its own release time r(u) and handling time h(u). A job j(u) can only be serviced by one vehicle after its release time r(u), and the handling time h(u) represents the time needed to finish processing j(u). The objective is to find a schedule in which the maximum completion time of the jobs, i.e. the makespan, is minimized. In this paper we present a 3-approximation algorithm for MVSP on trees, and a (\(5-\frac{2}{m}\))-approximation algorithm for MVSP on general graphs.

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References

  1. Augustine, J.E., Seiden, S.: Linear time approximation schemes for vehicle scheduling problems. Theoretical Computer Science 324(2-3), 147–160 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bansal, N., Blum, A., Chawla, S., Meyerson, A.: Approximation algorithms for deadline-TSP and vehicle routing with time-windows. In: Proceedings of the 36th Annual ACM Symposium on Theory of Computing, pp. 166–174 (2004)

    Google Scholar 

  3. Bar-Yehuda, R., Even, G., Shahar, S.: On approximating a geometric prize-collecting traveling salesman problem with time windows. In: Proceedings of the 11th Annual European Symposium on Algorithms, pp. 55–66 (2003)

    Google Scholar 

  4. Bhattacharya, B.K., Carmi, P., Hu, Y., Shi, Q.: Single Vehicle Scheduling Problems on Path/Tree/Cycle Networks with Release and Handling Times. In: Proceedings of the 19th International Symposium on Algorithms and Computation, pp. 800–811 (2008)

    Google Scholar 

  5. Dantzig, G.B., Ramser, R.H.: The truck dispatching problem. Management Science 6, 80–91 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  6. Even, G., Garg, N., Konemann, J., Ravi, R., Sinha, A.: Min-max tree covers of graphs. Operations Research Letters 32(4), 309–315 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  7. Karuno, Y., Nagamochi, H.: Better approximation ratios for the single-vehicle scheduling problems on line-shaped networks. Networks 39(4), 203–209 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Karuno, Y., Nagamochi, H.: A polynomial time approximation scheme for the multi-vehicle scheduling problem on a path with release and handling times. In: Proceedings of the 12th International Symposium on Algorithms and Computation, pp. 36–47 (2001)

    Google Scholar 

  9. Karuno, Y., Nagamochi, H.: A 2-Approximation Algorithm for the Multi-vehicle Scheduling Problem on a Path with Release and Handling Times. In: Proceedings of the 9th Annual European Symposium on Algorithms, pp. 218–229 (2001)

    Google Scholar 

  10. Korula, N., Chekuri, C.: Approximation algorithms for orienteering with timewindows (September 2007) (manuscript)

    Google Scholar 

  11. Megiddo, N.: Combinatorial optimization with rational objective functions. Math. Oper. Res. 4, 414–424 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  12. Megiddo, N.: Applying parallel computation algorithms in the design of serial algorithms. Journal of ACM 30(4), 852–865 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  13. Menger, K.: Reminiscences of the vienna circle and the mathematical colloquium. Dortmund (1994)

    Google Scholar 

  14. Nagamochi, H., Mochizuki, K., Ibaraki, T.: Complexity of the Single Vehicle Scheduling Problem on Graphs. Inform. Systems Oper. Res. 35(4), 256–276 (1997)

    Article  MATH  Google Scholar 

  15. Nagamochi, H., Okada, K.: A faster 2-approximationalgorithm for the minmax p-traveling salesmenproblem on a tree. Discrete Applied Mathematics 140(1-3), 103–114 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  16. Nagamochi, H., Okada, K.: Polynomial time 2-approximation algorithms for the minmax subtree cover problem. In: Ibaraki, T., Katoh, N., Ono, H. (eds.) ISAAC 2003. LNCS, vol. 2906, pp. 138–147. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  17. Toth, P., Vigo, D. (eds.): The vehicle routing problem. SIAM Monographs on Discrete Mathematics and Applications, vol. 9. SIAM, Phaladelphia (2002)

    MATH  Google Scholar 

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Authors and Affiliations

  1. School of Computing Science, Simon Fraser University, Burnaby, Canada, V5A 1S6

    Binay Bhattacharya & Yuzhuang Hu

Authors
  1. Binay Bhattacharya
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  2. Yuzhuang Hu
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Editor information

Editors and Affiliations

  1. Department of Computer Science, KAIST, Gwahangno 335, Yuseong-gu, 305-701, Daejeon, Korea

    Otfried Cheong  & Kyung-Yong Chwa  & 

  2. School of Computer Science and Engineering, Seoul National University, 151-742, Seoul, Korea

    Kunsoo Park

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Bhattacharya, B., Hu, Y. (2010). Approximation Algorithms for the Multi-Vehicle Scheduling Problem. In: Cheong, O., Chwa, KY., Park, K. (eds) Algorithms and Computation. ISAAC 2010. Lecture Notes in Computer Science, vol 6507. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17514-5_17

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  • DOI: https://doi.org/10.1007/978-3-642-17514-5_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17513-8

  • Online ISBN: 978-3-642-17514-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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