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The maximum collection problem with time‐dependent rewards

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  • E. Erkut
  • J. Zhang

Abstract

We consider a routing problem where the objective is to maximize the sum of the rewards collected at the nodes visited. Node rewards are decreasing linear functions of time. Time is spent when traveling between pairs of nodes, and while visiting the nodes. We propose a penalty‐based greedy (heuristic) algorithm and a branch‐and‐bound (optimal) algorithm for this problem. The heuristic is very effective in obtaining good solutions. We can solve problems with up to 20 nodes optimally on a microcomputer using the branch‐and‐bound algorithm. We report our computational experience with this problem. © 1996 John Wiley & Sons, Inc.

Suggested Citation

  • E. Erkut & J. Zhang, 1996. "The maximum collection problem with time‐dependent rewards," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(5), pages 749-763, August.
    • Handle: RePEc:wly:navres:v:43:y:1996:i:5:p:749-763
    DOI: 10.1002/(SICI)1520-6750(199608)43:53.0.CO;2-J
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    References listed on IDEAS

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    1. B. L. Golden & Qiwen Wang & Li Liu, 1988. "A multifaceted heuristic for the orienteering problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(3), pages 359-366, June.
    2. Fred Glover, 1989. "Tabu Search---Part I," INFORMS Journal on Computing, INFORMS, vol. 1(3), pages 190-206, August.
    3. R. Ramesh & Yong-Seok Yoon & Mark H. Karwan, 1992. "An Optimal Algorithm for the Orienteering Tour Problem," INFORMS Journal on Computing, INFORMS, vol. 4(2), pages 155-165, May.
    4. Bruce L. Golden & Larry Levy & Rakesh Vohra, 1987. "The orienteering problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 307-318, June.
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    Cited by:

    1. Yu, Qinxiao & Fang, Kan & Zhu, Ning & Ma, Shoufeng, 2019. "A matheuristic approach to the orienteering problem with service time dependent profits," European Journal of Operational Research, Elsevier, vol. 273(2), pages 488-503.
    2. Qinxiao Yu & Yossiri Adulyasak & Louis-Martin Rousseau & Ning Zhu & Shoufeng Ma, 2022. "Team Orienteering with Time-Varying Profit," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 262-280, January.

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