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Optimal Police Enforcement Allocation . Rajan Batta Christopher Rump Shoou -Jiun Wang.

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optimal police enforcement allocation
Optimal Police Enforcement Allocation

Rajan Batta

Christopher Rump

Shoou-Jiun Wang

This research is supported by Grant No. 98-IJ-CX-K008 awarded by the National Institute of Justice, Office of Justice Programs, U.S. Department of Justice. Points of view in this document are those of the authors and do not necessarily represent the official position or policies of the U.S. Department of Justice.

motivation
Motivation

“Our goals are to reduce and prevent crime,… and to direct our limited resources where they can do the most good.”

- U.S. Attorney General Janet Reno

- Crime Mapping Research Conference, Dec. 1998

consider crimes motivated by an economic incentive
Consider Crimes Motivated by an Economic Incentive
  • Auto theft
  • Robbery
  • Burglary
  • Narcotics
literature review
Literature Review
  • Cornish et al. (Criminology,1987):

Criminals seek benefit from their criminal behavior.

  • Freeman et al. (J. of Urban Economics, 1996):

A neighborhood with higher expected monetary return is more attractive to criminals.

  • Greenwood et al. (The Criminal Investigation Process, 1977): A neighborhood with lesser arrest ability has a larger amount of crimes.
literature review1
Literature Review
  • Caulkins (Operations Research, 1993):

Drug dealers’ risk from crackdown enforcement is proportional to “totalenforcement per dealer

raised to an appropriate power”.

  • Gabor (Canadian J. of Criminology, 1990):

A burglary prevention program may decrease local burglary rates, but increase neighboring rates - geographic displacement.

arrest rate p a enforcement e crime incidents n
Arrest Rate (PA), Enforcement (E) & Crime Incidents (n)
  • PA(E,n) = 1- exp(-E/n)

 = arrest ability value (Caulkins)

  • Under constant E,

PA decreases in n (Greenwood et al.)

  • PA increases in E
  • Effect of E is more significant for small n

Crime Level

monetary return r wealth w crime incidents n
Monetary Return (R), Wealth (w) & Crime Incidents (n)
  • R(w,n) = c w exp(-n)

c,  depend on crime type

  • R decreases in n
  • Physical Explanations:
    • Limited by the wealth of the neighborhood
    • Victims become aware and add security

Crime Level

expected monetary return e r crime incidents n
Expected Monetary Return (E[R]) & Crime Incidents (n)
  • E[R]= R(w,n)*(1-PA(E,n)) =c w exp(-E/n-n)

(Freeman)

  • For small n, E[R] is small because of high arrest probability.
  • For large n, E[R] is small due to many incidents.
  • E forces the E[R] down.

Crime Level

crime rate socio economy
Crime Rate & Socio-Economy
  • One area is relatively crime-free (Amherst)
  • Another area is relatively crime-ridden (Buffalo)
  • Expected return for crime, E[R], may equally attract offenders
crime equilibrium
Crime Equilibrium
  • At equilibrium, number of crimes is either 0 or n(2)
    • If n<n(1), high arrest rate; all criminals will leave
    • If n(1)<n<n(2), return>cost; attracts more criminals
    • If n>n(2), over-saturated; some criminals will leave
  • n*: organized crime equilibrium

Opportunity

Cost of crime

m

E[R]

n(1)

n*

n(2)

Crime Level

crime crackdown

m

Opportunity

Cost of crime

E[R]

E

Crime Level

Crime Crackdown
  • Sufficient enforcement, E, can lower expected return curve E[R]
  • If E[R] curve < m, there is no incentive for criminals; crime collapses to 0
minimizing total crime 2 neighborhoods
Minimizing Total Crime (2 Neighborhoods)
  • Objective 1: Minimize total number of crimes
  • Optimal Allocation Policy:
    • one-neighborhood crackdown policy is optimal: place as many resources as necessary into one neighborhood; if resources remain, into the other.
    • Generally, the neighborhood with better arrest ability tends to have higher priority to receive resources.
    • Under equal arrest ability: affluent neighborhood has priority only if both neighborhoods can be collapsed.
minimizing crime disparity 2 neighborhoods
Minimizing Crime Disparity(2 Neighborhoods)
  • Objective 2: Minimize the difference of crime numbers
  • Optimal Allocation Policy:
    • The difference of the crime numbers can be minimized to 0 unless the wealth disparity between them is large.
    • Under equal wealth, allocation of resources is inversely proportional to arrest ability.
    • If the wealth disparity between the two neighborhoods is large, the affluent neighborhood has priority.
a numerical example
A Numerical Example
  • Data:
    • Arrest ability: 1 = .35, 2 = .10
    • Wealth level: w1= $30,000, w2 = $25,000
    •  = .02; c = .01; m = $15.
  • Calculated Values:
    • Enforcement required to collapse crimes in NB1=320 hours
    • Enforcement required to collapse crimes in NB2=990 hours
    • Note: Every day, Buffalo Police Department patrols 300-500 hrs in each of its five districts and the number of call-for-service in each district is about 100-150.
  • Decision Variable: x (proportion of enforcement allocated in NB 1).
total enforcement 1000 hours

------- Neighborhood 1; ------- Neighborhood 2

Total Enforcement = 1000hours

x = .01

n1 = 149; n2 = 0

Total = 149

Difference = 149

(dominated)

x = .265

n1 = 106; n2 =106

Total = 212

Difference = 0

x = .3

n1 = 94; n2 = 108

Total = 202

Difference = 15

(non-dominated)

x = .32

n1 = 0; n2 = 110

Total = 110

Difference = 110

total enforcement 520 hours

x = 0.5

n1 = 107; n2 = 131

Total = 238

Difference = 23

(non-dominated)

------- Neighborhood 1; ------- Neighborhood 2

Total Enforcement = 520 hours

x = 0

n1 = 150; n2 = 119

Total = 269

Difference = 31

(dominated)

x = .32

n1 = 127; n2 = 127

Total = 254

Difference = 0

x = 0.62

n1 = 0; n2 = 133

Total = 133

Difference = 133

total enforcement 300 hours

------- Neighborhood 1; ------- Neighborhood 2

Total Enforcement = 300 hours

x = 0

n1 = 150; n2 = 129

Total = 279

Difference = 21

(dominated)

x = 0.4

n1 = 134; n2 = 134

Total = 268

Difference = 0

x = 0.5

n1 = 130; n2 = 135

Total = 265

Difference = 5

(non-dominated)

x = 1

n1 = 94; n2 = 141

Total = 235

Difference = 47

slide18

Optimal Enforcement Allocation (Multiple Neighborhoods)

  • Objective 1: Minimize total number of crimes
    • The neighborhoods should be either cracked down or given no resources except for one of them.
    • The neighborhoods with higher arrest/wealth value have higher priority.
  • Objective 2: Minimize the difference of crime numbers
    • “Evenly” distribute enforcement to the wealthier neighborhoods such that the wealthier neighborhoods have the same number of crimes.
bpd case study
BPD Case Study

Buffalo Police Department

  • ~42 Square Miles
  • 5 Command Districts
  • ~6700 calls for service/wk
  • ~6400 patrol hours/week
  • ~530 police officers
  • 30-55 patrol cars at any time w/ 2 officers/car
current and future work
Current and Future Work
  • Geographic Information System (GIS) implementation for crime mapping & prediction
  • Dynamic (iterative) model of crime displacement
  • Optimizing transportation model (Deutsch) of geographic criminal displacement
  • Scheduling of BPD Flex Force