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An Upperbound Algorithm for the Single and Multiple Terminal Delivery Problem

Author

Listed:
  • Frank A. Tillman

    (Kansas State University)

  • Thomas M. Cain

    (Electronic Data Systems, Des Moines, Iowa)

Abstract

An upperbound algorithm is presented for solving the multiterminal delivery problem. The method involves determining savings from joining points on routes and making possible assignments as a function of the maximum savings for joining cities on routes. The algorithm permits restrictions to be imposed on the system. If all possibilities are investigated, this approach will lead to an optimal solution using savings as the criterion to be optimized. In practice this may be very time consuming so a limited version is presented where only the most promising nodes are investigated. The methodology developed is applicable to the single terminal problem, since it is a special case of the multiterminal problem. A computer program has been written and a set of problems were solved with the algorithm using an IBM 360/50 computer. The results of a series of single and multi-terminal problems are illustrated in the paper. As is evident from these results the time required to solve a problem increases as a function of the number of demand points and the number of terminals.

Suggested Citation

  • Frank A. Tillman & Thomas M. Cain, 1972. "An Upperbound Algorithm for the Single and Multiple Terminal Delivery Problem," Management Science, INFORMS, vol. 18(11), pages 664-682, July.
    • Handle: RePEc:inm:ormnsc:v:18:y:1972:i:11:p:664-682
    DOI: 10.1287/mnsc.18.11.664
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    Cited by:

    1. Fernández, Elena & Roca-Riu, Mireia & Speranza, M. Grazia, 2018. "The Shared Customer Collaboration Vehicle Routing Problem," European Journal of Operational Research, Elsevier, vol. 265(3), pages 1078-1093.
    2. Ropke, Stefan & Pisinger, David, 2006. "A unified heuristic for a large class of Vehicle Routing Problems with Backhauls," European Journal of Operational Research, Elsevier, vol. 171(3), pages 750-775, June.
    3. Merve Cengiz Toklu, 2023. "A fuzzy multi-criteria approach based on Clarke and Wright savings algorithm for vehicle routing problem in humanitarian aid distribution," Journal of Intelligent Manufacturing, Springer, vol. 34(5), pages 2241-2261, June.
    4. François, Véronique & Arda, Yasemin & Crama, Yves & Laporte, Gilbert, 2016. "Large neighborhood search for multi-trip vehicle routing," European Journal of Operational Research, Elsevier, vol. 255(2), pages 422-441.
    5. B Yu & Z-Z Yang & J-X Xie, 2011. "A parallel improved ant colony optimization for multi-depot vehicle routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 183-188, January.
    6. Menezes, Mozart B.C. & Ruiz-Hernández, Diego & Verter, Vedat, 2016. "A rough-cut approach for evaluating location-routing decisions via approximation algorithms," Transportation Research Part B: Methodological, Elsevier, vol. 87(C), pages 89-106.
    7. Ramos, Tânia Rodrigues Pereira & Gomes, Maria Isabel & Barbosa-Póvoa, Ana Paula, 2014. "Economic and environmental concerns in planning recyclable waste collection systems," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 62(C), pages 34-54.
    8. Lucio Martins, Carlos & Vaz Pato, Margarida, 1998. "Search strategies for the feeder bus network design problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 425-440, April.
    9. Crevier, Benoit & Cordeau, Jean-Francois & Laporte, Gilbert, 2007. "The multi-depot vehicle routing problem with inter-depot routes," European Journal of Operational Research, Elsevier, vol. 176(2), pages 756-773, January.
    10. Salhi, S. & Sari, M., 1997. "A multi-level composite heuristic for the multi-depot vehicle fleet mix problem," European Journal of Operational Research, Elsevier, vol. 103(1), pages 95-112, November.
    11. T R P Ramos & R C Oliveira, 2011. "Delimitation of service areas in reverse logistics networks with multiple depots," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1198-1210, July.

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