POLICE PATROL OPTIMIZATION: A PROFICIENCY-AWARE MODEL FOR RAPID RESPONSE TO INCIDENTS

KABIRU M.  KOKO; PETER  AYUBA; PETER  ANTHONY; SANI  DARI

KABIRU M. KOKO DEPARTMENT OF MATHEMATICS, AIR FORCE INSTITUTE OF TECHNOL- OGY, KADUNA, NIGERIA.
PETER AYUBA DEPARTMENT OF MATHEMATICAL SCIENCES, KADUNA STATE UNIVER- SITY, KADUNA, NIGERIA.
PETER ANTHONY DEPARTMENT OF MATHEMATICAL SCIENCES, KADUNA STATE UNIVER- SITY, KADUNA, NIGERIA.
SANI DARI DEPARTMENT OF MATHEMATICAL SCIENCES, KADUNA STATE UNIVER- SITY, KADUNA, NIGERIA.

Keywords: police patrol deployment, crime neutralization, resource allocation, proficiency-constrained patrol allocation, heterogeneous team utilization, Crime-severity combination

Abstract

This study introduces the Crime Neutralization Model (CNM), an optimization based framework designed to improve the strategic deployment of police patrol teams. The CNM addresses critical limitations in traditional rapid response systems by incorporating three, often neglected operational factors: (1) variation in patrol team proficiencies, (2) crime-type-specific resource demands and (3) scenario-dependent severity levels. A discrete mathematical programming approach is employed to minimize the expected weighted response distance, while ensuring that all incidents are covered by suitably proficient teams within defined response radii. The model is validated using synthetic urban crime data, where results demonstrate that 10 patrol teams operating within a 1.5 km response radius achieve a 45.29% improvement in travel distance efficiency. Sensitivity analysis yields two key insights: first, optimal deployment strategies remain consistent across increasing response distances, indicating robustness; second, performance does not scale linearly with team count, most notably, a deployment of 12 teams unexpectedly results in re- duced efficiency. With computation times ranging from 4 to 12 seconds, the CNM offers a practical and adaptive tool for police departments to enhance resource allocation in alignment with both spatial constraints and operational capabilities.

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