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Distributionally robust optimization for fire station location under uncertainties.

Jinke Ming1, Jean-Philippe P Richard2, Rongshui Qin1

  • 1State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, 230026, China.

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This study introduces a robust model for optimizing emergency fire service (EFS) systems, enhancing resource allocation and minimizing costs. The developed heuristic method effectively solves large-scale EFS planning problems.

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Area of Science:

  • Operations Research
  • Public Safety Systems
  • Optimization Modeling

Background:

  • Emergency Fire Service (EFS) systems are critical for minimizing property loss and mortality during emergencies.
  • Effective EFS design requires strategic planning of station locations, vehicle allocation, and demand assignment.
  • Existing models may not adequately address uncertainties in demand and travel times.

Purpose of the Study:

  • To propose a distributionally robust model (DRM) for optimizing long-term EFS planning.
  • To minimize worst-case expected total costs, including construction, vehicle purchase, transportation, and penalties.
  • To address ambiguity in demand and travel duration distributions using moment information and mean absolute deviation.

Main Methods:

  • Development of a distributionally robust model (DRM) for EFS optimization.
  • Application of a cutting plane method for solving the DRM.
  • Introduction of two approximate methods: linear decision rules (LDRs) and three-point approximations for computational efficiency.

Main Results:

  • The DRM effectively optimizes fire station location, fire truck numbers, and demand assignment.
  • Approximate methods, particularly the heuristic approach, demonstrate significant utility for large-scale EFS problems.
  • Numerical experiments validate the model's performance across various parameters.

Conclusions:

  • The proposed DRM provides a valuable framework for robust EFS system design.
  • The heuristic method offers a computationally efficient solution for practical, large-scale EFS planning.
  • Case study in Hefei, China, confirms the model's applicability in metropolitan settings.