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Design of multiple-vehicle delivery tours--I a ring-radial network

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  • Newell, Gordon F.
  • Daganzo, Carlos F.

Abstract

Certain aspects of what is commonly described as the "Vehicle Routing Problem" are discussed. We wish to deliver items to a large number of points randomly distributed over some region by means of vehicles, each of which can deliver to only C points. The key to any detailed routing to minimize the cost of delivery (by hand or computer) is first to partition the region into zones in which individual vehicles make deliveries. We assume here that there are many such zones, an average density of points [delta], that the "unit of length" [delta]-1/2 is large compared with the spacing between roads, and C >> 1. To minimize the delivery cost, zones should be approximately rectangular in shape with a width comparable with [delta]-1/2 and length comparable with C[delta]-1/2. In order to illustrate some numerical methods of approximation, we will first analyze, in considerable detail, the routing of vehicles on an idealized ring-radial network including how one would distort the shape of the zones near the origin and at boundaries. In Part II we will generalize this to other network geometries, and in Part III consider modifications in strategy if the items (people, for example) are valuable. In contrast with presently available computer programs for which the accuracy may decrease with increasing number of points in the region, the methods described here are essentially asymptotic approximations; the more points there are in the region, the more accurate are the results.

Suggested Citation

  • Newell, Gordon F. & Daganzo, Carlos F., 1986. "Design of multiple-vehicle delivery tours--I a ring-radial network," Transportation Research Part B: Methodological, Elsevier, vol. 20(5), pages 345-363, October.
  • Handle: RePEc:eee:transb:v:20:y:1986:i:5:p:345-363
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    Cited by:

    1. Jabali, Ola & Gendreau, Michel & Laporte, Gilbert, 2012. "A continuous approximation model for the fleet composition problem," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1591-1606.
    2. repec:eee:transe:v:104:y:2017:i:c:p:165-188 is not listed on IDEAS
    3. Bard, Jonathan F. & Jarrah, Ahmad I. & Zan, Jing, 2010. "Validating vehicle routing zone construction using Monte Carlo simulation," European Journal of Operational Research, Elsevier, vol. 206(1), pages 73-85, October.
    4. repec:eee:transb:v:107:y:2018:i:c:p:229-252 is not listed on IDEAS
    5. Daganzo, Carlos F. & Smilowitz, Karen R., 2000. "Asymptotic Approximations for the Transportation LP and Other Scalable Network Problems," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt3dn2j66w, Institute of Transportation Studies, UC Berkeley.
    6. Diana, Marco & Dessouky, Maged M. & Xia, Nan, 2006. "A model for the fleet sizing of demand responsive transportation services with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 40(8), pages 651-666, September.
    7. del Castillo, Jose M., 1998. "A heuristic for the traveling salesman problem based on a continuous approximation," Transportation Research Part B: Methodological, Elsevier, vol. 33(2), pages 123-152, April.
    8. Novaes, Antonio G. N. & Graciolli, Odacir D., 1999. "Designing multi-vehicle delivery tours in a grid-cell format," European Journal of Operational Research, Elsevier, vol. 119(3), pages 613-634, December.
    9. Ouyang, Yanfeng, 2007. "Design of vehicle routing zones for large-scale distribution systems," Transportation Research Part B: Methodological, Elsevier, vol. 41(10), pages 1079-1093, December.
    10. Qi, Mingyao & Lin, Wei-Hua & Li, Nan & Miao, Lixin, 2012. "A spatiotemporal partitioning approach for large-scale vehicle routing problems with time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(1), pages 248-257.
    11. repec:eee:transb:v:106:y:2017:i:c:p:375-392 is not listed on IDEAS
    12. Daganzo, Carlos F & Smilowitz, Karen R, 2000. "Asymptotic Approximations for the Transportation LP and Other Scalable Network Problems," University of California Transportation Center, Working Papers qt7wb1g4z7, University of California Transportation Center.
    13. Koç, Çağrı & Bektaş, Tolga & Jabali, Ola & Laporte, Gilbert, 2016. "Thirty years of heterogeneous vehicle routing," European Journal of Operational Research, Elsevier, vol. 249(1), pages 1-21.
    14. Bertazzi, Luca & Speranza, Maria Grazia & Ukovich, Walter, 1997. "Minimization of logistic costs with given frequencies," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 327-340, August.
    15. Campbell, James F., 1995. "Using small trucks to circumvent large truck restrictions: Impacts on truck emissions and performance measures," Transportation Research Part A: Policy and Practice, Elsevier, vol. 29(6), pages 445-458, November.
    16. Franceschetti, Anna & Honhon, Dorothée & Laporte, Gilbert & Woensel, Tom Van & Fransoo, Jan C., 2017. "Strategic fleet planning for city logistics," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 19-40.
    17. Langevin, André & Mbaraga, Pontien & Campbell, James F., 1996. "Continuous approximation models in freight distribution: An overview," Transportation Research Part B: Methodological, Elsevier, vol. 30(3), pages 163-188, June.

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