UCGIS, Feb 2000 Optimal Police Enforcement Allocation Rajan Batta Christopher Rump Shoou -Jiun Wang...

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UCGIS, Feb 2000 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.

Transcript of UCGIS, Feb 2000 Optimal Police Enforcement Allocation Rajan Batta Christopher Rump Shoou -Jiun Wang...

UCGIS, Feb 2000

Optimal Police Enforcement Allocation

Rajan BattaChristopher 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.

UCGIS, Feb 2000

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

UCGIS, Feb 2000

Consider Crimes Motivated by an Economic Incentive

Auto theftRobberyBurglaryNarcotics

UCGIS, Feb 2000

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.

UCGIS, Feb 2000

Literature Review

Caulkins (Operations Research, 1993):

Drug dealers’ risk from crackdown enforcement is proportional to “total enforcement 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.

UCGIS, Feb 2000

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

Arrest Rate (PA), Enforcement (E) & Crime Incidents (n)

Crime Level

UCGIS, Feb 2000

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

UCGIS, Feb 2000

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

UCGIS, Feb 2000

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

UCGIS, Feb 2000

Crime Equilibrium

n*

Opportunity Cost of crime

n(1) n(2)

m

E[R]

Crime Level

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

UCGIS, Feb 2000

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

Crime Level

E[R]

Opportunity Cost of crime

E

m

UCGIS, Feb 2000

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.

UCGIS, Feb 2000

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.

Minimizing Crime Disparity(2 Neighborhoods)

UCGIS, Feb 2000

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).

UCGIS, Feb 2000

Total Enforcement = 1000 hours

x = .01

n1 = 149; n2 = 0

Total = 149

Difference = 149

(dominated)

x = .265

n1 = 106; n2 =106

Total = 212

Difference = 0

x = .32

n1 = 0; n2 = 110

Total = 110

Difference = 110

x = .3

n1 = 94; n2 = 108

Total = 202

Difference = 15

(non-dominated)

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

UCGIS, Feb 2000

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

x = 0.5

n1 = 107; n2 = 131

Total = 238

Difference = 23

(non-dominated)

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

UCGIS, Feb 2000

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 = 1

n1 = 94; n2 = 141

Total = 235

Difference = 47

x = 0.5

n1 = 130; n2 = 135

Total = 265

Difference = 5

(non-dominated)

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

UCGIS, Feb 2000

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.

Optimal Enforcement Allocation (Multiple Neighborhoods)

UCGIS, Feb 2000

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

UCGIS, Feb 2000

Burglary Data in Buffalo

District Median Household

Income (w)

Weekly Patrol

Hours (E)

Total Burglary

Numbers (n)

Arrest Prob.

(PA)

A $21,250 896.0 187 13.37 %

B $13,750 1485.4 350 23.86 %

C $13,750 1536.0 481 13.72 %

D $21,250 1314.1 373 9.65 %

E $21,250 1183.3 304 16.78 %

Total 6414.8 1695 15.43%

UCGIS, Feb 2000

Minimizing Burglary Disparity in Buffalo

District

Arrest

Ability

()

Opportunity

Cost

(m)

Optimal

Patrol Hours

(E*)

Required Hours

to Collapse

Crime Activity

Number of

Burglaries

(n*)

A .0300 157.0 252.1 (3.9%) 2967.6 329

B .0612 79.0 1475.8 (23.0%) 2663.3 329

C .0462 79.0 1954.9 (30.5%) 3528.0 329

D .0288 138.5 1696.7 (26.5%) 4371.7 329

E .0472 138.5 1035.3 (16.1%) 2667.5 329

Total 6414.8 (100%) 16198.1 1645

UCGIS, Feb 2000

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