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Approximation Algorithms for Cumulative VRP with Stochastic Demands

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Algorithms and Discrete Applied Mathematics (CALDAM 2016)

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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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Acknowledgements

This work was supported in part by an NSERC Discovery Grant. AM was supported in part by ISIRD grant from IIT Ropar. Part of the work was done while DRG was visiting IIT (BHU) Varanasi and RRS was at IIT Ropar. Authors would like to thank K. K. Shukla for his inputs on the split version of the problem on trees that is noted as a corollary in the paper.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive, Lethbridge, AB, Canada

    Daya Ram Gaur

  2. Department of Computer Science and Engineering, Indian Institute of Technology Ropar, Nangal Road, Rupnagar, 140001, Punjab, India

    Apurva Mudgal

  3. Department of Information Technology, Indian Institute of Information Technology Allahabad, Jhalwa, Allahabad, 211012, Uttar Pradesh, India

    Rishi Ranjan Singh

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  1. Daya Ram Gaur
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  2. Apurva Mudgal
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  3. Rishi Ranjan Singh
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Correspondence to Rishi Ranjan Singh .

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Editors and Affiliations

  1. Indian Institute of Science, Bangalore, India

    Sathish Govindarajan

  2. Carleton University, Ottawa, ON, Canada

    Anil Maheshwari

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Gaur, D.R., Mudgal, A., Singh, R.R. (2016). Approximation Algorithms for Cumulative VRP with Stochastic Demands. In: Govindarajan, S., Maheshwari, A. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2016. Lecture Notes in Computer Science(), vol 9602. Springer, Cham. https://doi.org/10.1007/978-3-319-29221-2_15

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  • DOI: https://doi.org/10.1007/978-3-319-29221-2_15

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-29220-5

  • Online ISBN: 978-3-319-29221-2

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