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The Stochastic Team Orienteering Problem with Position-Dependent Rewards

Author

Listed:
  • Javier Panadero

    (Department of Management, Universitat Politècnica de Catalunya—BarcelonaTech, 08028 Barcelona, Spain)

  • Eva Barrena

    (Department of Economics, Quantitative Methods and Economic History, Universidad Pablo de Olavide, 41013 Seville, Spain)

  • Angel A. Juan

    (Department of Applied Statistics and Operations Research, Universitat Politècnica de València, 03801 Alcoy, Spain)

  • David Canca

    (Department of Industrial Engineering and Management Science, Universidad de Sevilla, 41092 Seville, Spain)

Abstract

In this paper, we analyze both the deterministic and stochastic versions of a team orienteering problem (TOP) in which rewards from customers are dynamic. The typical goal of the TOP is to select a set of customers to visit in order to maximize the total reward gathered by a fixed fleet of vehicles. To better reflect some real-life scenarios, we consider a version in which rewards associated with each customer might depend upon the order in which the customer is visited within a route, bonusing the first clients and penalizing the last ones. In addition, travel times are modeled as random variables. Two mixed-integer programming models are proposed for the deterministic version, which is then solved using a well-known commercial solver. Furthermore, a biased-randomized iterated local search algorithm is employed to solve this deterministic version. Overall, the proposed metaheuristic algorithm shows an outstanding performance when compared with the optimal or near-optimal solutions provided by the commercial solver, both in terms of solution quality as well as in computational times. Then, the metaheuristic algorithm is extended into a full simheuristic in order to solve the stochastic version of the problem. A series of numerical experiments allows us to show that the solutions provided by the simheuristic outperform the near-optimal solutions obtained for the deterministic version of the problem when the latter are used in a scenario under conditions of uncertainty. In addition, the solutions provided by our simheuristic algorithm for the stochastic version of the problem offer a higher reliability level than the ones obtained with the commercial solver.

Suggested Citation

  • Javier Panadero & Eva Barrena & Angel A. Juan & David Canca, 2022. "The Stochastic Team Orienteering Problem with Position-Dependent Rewards," Mathematics, MDPI, vol. 10(16), pages 1-25, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2856-:d:885036
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    References listed on IDEAS

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    1. Morteza Keshtkaran & Koorush Ziarati & Andrea Bettinelli & Daniele Vigo, 2016. "Enhanced exact solution methods for the Team Orienteering Problem," International Journal of Production Research, Taylor & Francis Journals, vol. 54(2), pages 591-601, January.
    2. Chao, I-Ming & Golden, Bruce L. & Wasil, Edward A., 1996. "The team orienteering problem," European Journal of Operational Research, Elsevier, vol. 88(3), pages 464-474, February.
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    4. Bian, Zheyong & Liu, Xiang, 2018. "A real-time adjustment strategy for the operational level stochastic orienteering problem: A simulation-aided optimization approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 115(C), pages 246-266.
    5. Arnau, Quim & Barrena, Eva & Panadero, Javier & de la Torre, Rocio & Juan, Angel A., 2022. "A biased-randomized discrete-event heuristic for coordinated multi-vehicle container transport across interconnected networks," European Journal of Operational Research, Elsevier, vol. 302(1), pages 348-362.
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