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A Hybrid Mathematical Model for Flying Sidekick Travelling Salesman Problem with Time Windows

Author

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  • Gerçek Budak

    (Southern Illinois University)

  • Xin Chen

    (Southern Illinois University)

Abstract

Unmanned aerial vehicles (UAVs) are advanced technologies being implemented in diverse fields such as military operations, weather forecasting, supply chain logistics, and personal entertainment. UAVs have the potential of performing many pickup and delivery tasks in the near future as logistics companies keep investing in research and development of UAV technologies. Government and research agencies are catching up with UAV technologies through legislation and enabling technologies such as routing algorithms for UAVs. This article develops a hybrid mathematical model for flying sidekick travelling salesman problem with time windows (FS-TSP-TW). In the FS-TSP-TW, a truck pairs with a UAV (flying sidekick) to deliver packages to customers within predetermined time windows. The objective of the mathematical model is to minimize the total time (tour duration) for deliveries. Two models developed in previous research aimed to solve the flying sidekick travelling salesman problem without time windows and the travelling salesman problem (without flying sidekick) with time windows. This article integrates these two models (hence hybrid) into the FS-TSP-TW model by eliminating redundant constraints and incorporating an innovative sub-tour elimination routine. The new model effectively computes optimal routes for both the truck and UAV that meet delivery time windows. In addition, the FS-TSP-TW model identifies optimal routes for more customers with less computation time compared to previous models. The computational study validates the newly developed hybrid FS-TSP-TW model.

Suggested Citation

  • Gerçek Budak & Xin Chen, 2023. "A Hybrid Mathematical Model for Flying Sidekick Travelling Salesman Problem with Time Windows," SN Operations Research Forum, Springer, vol. 4(4), pages 1-21, December.
    • Handle: RePEc:spr:snopef:v:4:y:2023:i:4:d:10.1007_s43069-023-00280-x
    DOI: 10.1007/s43069-023-00280-x
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    References listed on IDEAS

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    1. Olli Bräysy & Michel Gendreau, 2005. "Vehicle Routing Problem with Time Windows, Part I: Route Construction and Local Search Algorithms," Transportation Science, INFORMS, vol. 39(1), pages 104-118, February.
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    3. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
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