1. 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.

2. 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

3. UCGIS, Feb 2000 Consider Crimes Motivated by an Economic Incentive zAuto theft zRobbery zBurglary zNarcotics

4. UCGIS, Feb 2000 Literature Review zCornish et al. (Criminology, 1987): Criminals seek benefit from their criminal behavior. zFreeman et al. (J. of Urban Economics, 1996): A neighborhood with higher expected monetary return is more attractive to criminals. zGreenwood et al. (The Criminal Investigation Process, 1977): A neighborhood with lesser arrest ability has a larger amount of crimes.

5. UCGIS, Feb 2000 Literature Review zCaulkins (Operations Research, 1993): Drug dealers’ risk from crackdown enforcement is proportional to “total enforcement per dealer raised to an appropriate power”. zGabor (Canadian J. of Criminology, 1990): A burglary prevention program may decrease local burglary rates, but increase neighboring rates - geographic displacement.

6. UCGIS, Feb 2000 z P A (E,n) = 1- exp(-  E/n)  = arrest ability value (Caulkins) z Under constant E, P A decreases in n (Greenwood et al.) z P A increases in E z Effect of E is more significant for small n Arrest Rate (P A ), Enforcement (E) & Crime Incidents (n) Crime Level

7. UCGIS, Feb 2000 Monetary Return (R), Wealth (w) & Crime Incidents (n) z R(w,n) = c w exp(-  n) c,  depend on crime type z R decreases in n z Physical Explanations: zLimited by the wealth of the neighborhood zVictims become aware and add security Crime Level

8. UCGIS, Feb 2000 Expected Monetary Return (E[R]) & Crime Incidents (n) z E[R]= R(w,n)*(1-P A (E,n)) =c w exp(-  E/n-  n) (Freeman) z For small n, E[R] is small because of high arrest probability. z For large n, E[R] is small due to many incidents. z E forces the E[R] down. Crime Level

9. UCGIS, Feb 2000 Crime Rate & Socio-Economy z One area is relatively crime- free (Amherst) z Another area is relatively crime-ridden (Buffalo) z Expected return for crime, E[R], may equally attract offenders

10. UCGIS, Feb 2000 Crime Equilibrium n*n* Opportunity Cost of crime n (1) n (2) m E[R] Crime Level z At equilibrium, number of crimes is either 0 or n (2) yIf n<n (1), high arrest rate; all criminals will leave yIf n (1) cost; attracts more criminals yIf n>n (2), over-saturated; some criminals will leave z n*: organized crime equilibrium

11. UCGIS, Feb 2000 Crime Crackdown z Sufficient enforcement, E, can lower expected return curve E[R] z 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

12. UCGIS, Feb 2000 Minimizing Total Crime (2 Neighborhoods) zObjective 1: Minimize total number of crimes zOptimal Allocation Policy: yone-neighborhood crackdown policy is optimal: place as many resources as necessary into one neighborhood; if resources remain, into the other. yGenerally, the neighborhood with better arrest ability tends to have higher priority to receive resources. yUnder equal arrest ability: affluent neighborhood has priority only if both neighborhoods can be collapsed.

13. UCGIS, Feb 2000 zObjective 2: Minimize the difference of crime numbers zOptimal Allocation Policy: yThe difference of the crime numbers can be minimized to 0 unless the wealth disparity between them is large. yUnder equal wealth, allocation of resources is inversely proportional to arrest ability. yIf the wealth disparity between the two neighborhoods is large, the affluent neighborhood has priority. Minimizing Crime Disparity (2 Neighborhoods)

14. UCGIS, Feb 2000 A Numerical Example zData: yArrest ability:  1 =.35,  2 =.10 yWealth level: w 1 = $30,000, w 2 = $25,000 y  =.02; c =.01; m = $15. zCalculated Values: yEnforcement required to collapse crimes in NB1=320 hours yEnforcement required to collapse crimes in NB2=990 hours yNote: 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. zDecision Variable: x (proportion of enforcement allocated in NB 1).

15. UCGIS, Feb 2000 Total Enforcement = 1000 hours x =.01 n 1 = 149; n 2 = 0 Total = 149 Difference = 149 (dominated) x =.265 n 1 = 106; n 2 =106 Total = 212 Difference = 0 x =.32 n 1 = 0; n 2 = 110 Total = 110 Difference = 110 x =.3 n 1 = 94; n 2 = 108 Total = 202 Difference = 15 (non-dominated) ------- Neighborhood 1; ------- Neighborhood 2

16. UCGIS, Feb 2000 Total Enforcement = 520 hours x = 0 n 1 = 150; n 2 = 119 Total = 269 Difference = 31 (dominated) x =.32 n 1 = 127; n 2 = 127 Total = 254 Difference = 0 x = 0.62 n 1 = 0; n 2 = 133 Total = 133 Difference = 133 x = 0.5 n 1 = 107; n 2 = 131 Total = 238 Difference = 23 (non-dominated) ------- Neighborhood 1; ------- Neighborhood 2

17. UCGIS, Feb 2000 Total Enforcement = 300 hours x = 0 n 1 = 150; n 2 = 129 Total = 279 Difference = 21 (dominated) x = 0.4 n 1 = 134; n2 = 134 Total = 268 Difference = 0 x = 1 n 1 = 94; n2 = 141 Total = 235 Difference = 47 x = 0.5 n 1 = 130; n 2 = 135 Total = 265 Difference = 5 (non-dominated) ------- Neighborhood 1; ------- Neighborhood 2

18. UCGIS, Feb 2000 zObjective 1: Minimize total number of crimes yThe neighborhoods should be either cracked down or given no resources except for one of them. yThe neighborhoods with higher arrest/wealth value have higher priority. zObjective 2: Minimize the difference of crime numbers y“Evenly” distribute enforcement to the wealthier neighborhoods such that the wealthier neighborhoods have the same number of crimes. Optimal Enforcement Allocation (Multiple Neighborhoods)

19. UCGIS, Feb 2000 BPD Case Study Buffalo Police Department z ~42 Square Miles z 5 Command Districts z ~6700 calls for service/wk z ~6400 patrol hours/week z ~530 police officers z 30-55 patrol cars at any time w/ 2 officers/car

20. UCGIS, Feb 2000 Burglary Data in Buffalo

21. UCGIS, Feb 2000 Minimizing Burglary Disparity in Buffalo

22. UCGIS, Feb 2000 Current and Future Work zGeographic Information System (GIS) implementation for crime mapping & prediction zDynamic (iterative) model of crime displacement zOptimizing transportation model (Deutsch) of geographic criminal displacement zScheduling of BPD Flex Force