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The Hot Spot Coverage Patrol Problem: Formulations and Solution Approaches

Author

Listed:
  • Yuchen Luo

    (Advanced Analytics Group, Bain & Company, Boston, Massachusetts 02116)

  • Bruce Golden

    (Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742)

  • Rui Zhang

    (Leeds School of Business, University of Colorado Boulder, Boulder, Colorado 80309)

Abstract

When designing a patrol route, it is often necessary to pay more attention to locations with high crime rates. In this paper, we study a patrol routing problem for a fleet of patrol cars patrolling a region with a high-crime neighborhood (HCN) consisting of multiple hot spots. Considering the disorder and chaos in the HCN, at least one patrol car is required in the HCN at any given time during the patrol. We call this routing problem the hot spot coverage patrol problem (HSCPP). In the HSCPP, the importance of a patrol location is quantified by a prize, and the prize is collected if a patrol car visits the location. Our objective is to maximize the sum of prizes collected by the patrol cars, obeying all operational requirements. We propose mathematical formulations and develop several solution approaches for the HSCPP. The global approach consists of finding the routing solution for all patrol cars with a single integer programming (IP) formulation. The partition approach involves first partitioning the region geographically and solving the routing problem in each subregion with two IP formulations. Next, we strengthen the partition approach by developing a column generation (CG) approach in which the initial columns of the CG approach are the solutions generated from the partition approach. We conduct a detailed computational case study using instances based on real crime data from Montgomery County, Maryland. To further understand the computational tractability of our solution approaches, we also perform a sensitivity analysis using synthetic instances under various scenarios.

Suggested Citation

  • Yuchen Luo & Bruce Golden & Rui Zhang, 2023. "The Hot Spot Coverage Patrol Problem: Formulations and Solution Approaches," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1286-1307, November.
    • Handle: RePEc:inm:orijoc:v:35:y:2023:i:6:p:1286-1307
    DOI: 10.1287/ijoc.2022.0192
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    References listed on IDEAS

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