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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. 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 theft Robbery Burglary Narcotics 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 Arrest Rate (PA), Enforcement (E) & Crime Incidents (n) PA(E,n) = 1- exp(-E/n) = arrest ability value (Caulkins) Crime Level Under constant E, PA decreases in n (Greenwood et al.) PA increases in E Effect of E is more significant for small n UCGIS, Feb 2000 Monetary Return (R), Wealth (w) & Crime Incidents (n) R(w,n) = c w exp(-n) c, depend on crime type Crime Level R decreases in n Physical Explanations: Limited by the wealth of the neighborhood Victims become aware and add security 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) Crime Level 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. 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 At equilibrium, number of crimes is either 0 or n(2) Opportunity Cost of crime m E[R] 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(1) n* n(2) n*: organized crime equilibrium Crime Level UCGIS, Feb 2000 Crime Crackdown m Opportunity Cost of crime Sufficient enforcement, E, can lower expected return curve E[R] E[R] E If E[R] curve < m, there is no incentive for criminals; crime collapses to 0 Crime Level 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 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. 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-forservice 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 x = .265 x = .3 x = .32 n1 = 149; n2 = 0 n1 = 106; n2 =106 n1 = 94; n2 = 108 n1 = 0; n2 = 110 Total = 149 Total = 212 Total = 202 Total = 110 Difference = 149 Difference = 0 Difference = 15 Difference = 110 (dominated) (non-dominated) ------- Neighborhood 1; ------- Neighborhood 2 UCGIS, Feb 2000 Total Enforcement = 520 hours x=0 x = .32 x = 0.5 x = 0.62 n1 = 150; n2 = 119 n1 = 127; n2 = 127 n1 = 107; n2 = 131 n1 = 0; n2 = 133 Total = 269 Total = 254 Total = 238 Total = 133 Difference = 31 Difference = 0 Difference = 23 Difference = 133 (dominated) (non-dominated) ------- Neighborhood 1; ------- Neighborhood 2 UCGIS, Feb 2000 Total Enforcement = 300 hours x=0 x = 0.4 x = 0.5 x=1 n1 = 150; n2 = 129 n1 = 134; n2 = 134 n1 = 130; n2 = 135 n1 = 94; n2 = 141 Total = 279 Total = 268 Total = 265 Total = 235 Difference = 21 Difference = 0 Difference = 5 Difference = 47 (dominated) (non-dominated) ------- Neighborhood 1; ------- Neighborhood 2 UCGIS, Feb 2000 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. 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 Weekly Patrol Total Burglary Arrest Prob. Income (w) Hours (E) Numbers (n) (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 % 6414.8 1695 15.43% Total UCGIS, Feb 2000 Minimizing Burglary Disparity in Buffalo Arrest Opportunity Optimal Required Hours Number of Ability Cost Patrol Hours to Collapse Burglaries () (m) (E*) Crime Activity (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 6414.8 (100%) 16198.1 1645 District Total 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 UCGIS, Feb 2000