Ranking Police Administration Units on the Basis of Crime Prevention Measures using Data Envelopment Analysis and Clustering

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1 Rankng Polce Admnstaton Unts on the Bass of Cme Peventon Measues usng Data Envelopment Analyss and Clusteng Mansh Gupta 1, B. Chanda 2 * and M. P. Gupta 3 ABSTRACT In ths pape, a novel appoach has been poposed to ank polce admnstaton unts on the bass of the effectve enfocement of cme peventon measues usng Data Envelopment Analyss (DEA) and Clusteng. The poposed appoach wll offe an effectve mechansm not only to ank polce admnstaton unts but also povde an evaluaton tool to monto the mplementaton of cme peventon measues at vaous levels of polce admnstaton. The pape dscusses two majo phases of the poposed appoach. In the fst phase, clusteng s used to dentfy the cme zones and to fom homogeneous goups n cme data. In the second phase, polce admnstaton unts n a patcula cme zone ae anked usng DEA. The effectveness of the poposed appoach has been llustated on Indan cme data. The compaatve esults of DEA wth clusteng and DEA wthout clusteng ae also gven to hghlght mpotance of lnkng DEA wth clusteng. Keywods: Data Envelopment Analyss, Clusteng, Pefomance Measuement, Polce Admnstaton. 1. Intoducton In the pesent scenao, cme deteence has become an upheaval task wth an enomous ncease n the cme. Seveal cme peventon measues such as e-govenance ntatves, CCTV vglance, polce patollng, specal task foce (STF) etc ae undetaken by vaous polce admnstaton unts.e. state, dstct and polce staton. Thee s a need to monto these cme peventon measues on egula bass so that shotcomngs of these measues and mplementaton elated ssues could be hghlghted. In ths pape, Data Envelopment Analyss (DEA) (Andeson & Petesen, 1993; Banke et al., 1984; Chanes et al., 1978; Kao & Hung, 2005; Sexton & Slkman, 1986) has been appled n combnaton wth clusteng technque to ank polce admnstaton unts on the bass of the effectve enfocement of cme peventon measues. The appoach wll offe a compute-based envonment not only to ank polce admnstaton unts but also povde an evaluaton tool to monto the mplementaton of cme peventon measues at vaous levels of polce admnstaton. DEA has been poposed by Chanes, Coope & Rhodes (1978) as a technque fo measung effcences of vaous decson-makng unts (DMUs). DEA s a mathematcal model that measues the elatve effcency of DMUs wth multple nputs and outputs wthout poducton functon. The esults of DEA detemne 1 Insttute fo Systems Studes and Analyses, Metcalfe House, Delh, Inda 2 Depatment of Industal Engneeng and Management, Indan Insttute of Technology, Kanpu, Inda 3 Depatment of Management Studes, Indan Insttute of Technology, Delh, Inda * Coespondng Autho: (E-mal : bchanda104@yahoo.co.n, Telephone: ) 40

2 Mansh Gupta et al. / Rankng Polce Admnstaton Unts on the Bass of Cme Peventon Measues Paeto Fonte whch s attaned & maked by specfc DMUs on the bounday envelope of nput/output vaable space f DMU le on the envelope than effcent othewse neffcent. Instead of usng fxed weghts fo all DMUs unde evaluaton, DEA computes a sepaate set of weghts fo each DMU. Each DMU wll choose weghts so as to maxmze self-effcency wth the constants that the effcency of no DMU exceeds 1 when usng the same weghts. DEA also povde easons fo neffcency by compang neffcent unts wth the pee goup of effcent unts. It also sets taget levels fo the neffcent unts to become effcent one. In the past, DEA has been wdely appled fo elatve pefomance measuement n soco-economc secto (Banke et al., 2007; Bege & Humphey, 1997) and publc sevces (Chanes et al., 1994; Coope et al., 2007). Banke, Chang, Nataajan (2007) has used DEA techncal neffcency measue to estmate allocatve neffcency n the publc accountng ndusty usng evenue and pesonnel data fo the top U.S. publc accountng fms ove Bege & Humphey (1997) has evewed 130 studes on DEA appled to fnancal nsttutons n 21 countes. Chanes, Coope & Rhodes (1978) povdes a collectons of vaous papes on applcatons of DEA n publc sevces such as health, educatons etc. Begendahl & Lndblom (2008) has appled DEA to evaluate the pefomance of Swedsh savngs banks based on sevce effcency. DEA has also been used fo measung effcences of polce foces (Butle & Johnson, 1997; Cangton et al., 1997; Dake & Smpe, 2000, 2003; Thanassouls, 1995; Vema & Gavnen, 2006). But the esults of stand-alone usage of DEA may not be satsfactoy snce cme locatons on whch DEA s appled ae heteogeneous n context of cme densty, aea and sze of the populaton. The majo dawbacks of usng DEA n standalone mode.e. DEA wthout clusteng fo measung effcences of polce admnstaton unts as DMUs s the ceaton of nsgnfcant pee goups fo neffcent unt. A DMU should not have a pee goup consstng of DMUs fom dffeent cme zones snce two DMUs fom dffeent cme zones cannot be benchmak fo each othe n DEA models. To ovecome these lmtatons, clusteng s used to dentfy the homogeneous goups of smla cme densty, aea and populaton. Clusteng (Jan et al., 1999) as unsupevsed technque s the pocess of oganzng objects nto goups such that smlaty wthn the same cluste s maxmzed and smlates among dffeent clustes ae mnmzed. Clusteng technques have been appled n vaous aeas such as nfomaton eteval, patten ecognton etc. In ths pape, clusteng technque s appled to Indan cme data to cluste the cme locatons and to fnd cme zones n Inda, as the densty of cme ncdents wll be contnuous ove an aea, beng hghe n some pats and lowe n othes. The pape descbes two majo phases of the poposed appoach. The fst phase uses clusteng to dentfy the cme zones and to fom homogeneous goups n the aea of nteest. In the second phase, polce admnstaton unts as DMUs n a patcula cme zone ae anked usng DEA based on the effcency scoe. The poposed appoach has been effectvely appled on Indan cme data. Compaatve esults of constant etun to scale (CRS) model (Chanes et al., 1978) and vaable etun to scale (VRS) model (Banke et al., 1984) fo DEA wth clusteng and DEA wthout clusteng ae also shown n the pape. Secton 2 hghlghts some of the eale wok done n measung effcences of polce foces usng DEA as well as the lmtatons of those appoaches. The two-phase methodology has been descbed along wth bef detals of clusteng and DEA technque n secton 3. Secton 4 shows the esults of clusteng and DEA on Indan cme data fo yea 2006 unde vaous cme heads such as mude, ape kdnappng etc. The Compaatve evaluaton of both the appoaches.e. DEA wth clusteng and DEA wthout clusteng fo CRS model and VRS model ae shown n secton 5. Concludng emaks s gven n the last secton of the pape. 41

3 Emegng Technologes n E-Govenment 2. Related Wok Thanassouls (1995) has appled DEA to measue elatve polce foce effcency of Englsh and Welsh polce foce. It focuses solely on the clea up ates fo volent cme, buglay and othe cmes, whle also ncludng the total numbes of each cme as nputs n the DEA analyss alongsde the numbe of offces. It does not consde the majo nput measue.e. total expendtue cost snce all the effot and cme peventon measues ae dectly depend upon the money nvested fo the pupose. The lmtaton of the pape s n constuctng weght estcton fo measung effcences snce t s subjectve n natue. Dake & Smpe (2000) measued the sze effcency of Englsh and Welsh polce foces usng DEA and multple dscmnant analyss. In ths pape, nfeences about the optmal sze and stuctue of the Englsh and Welsh polce foces ae made usng DEA effcency esults and the ssue of the statstcal sgnfcance of the dffeences n effcency scoes acoss staff sze goups s ectfed usng analyss of vaance (ANOVA) and dscmnant analyss technques. It deals only wth the poblem of sze and stuctue n Englsh and Welsh polcng and not wth the oveall effcency of polce foces. Dake & Smpe (2003) compae fou dffeent dstance functon models.e. DEA, fee dsposal hull (FDH) (Tulkens, 1993), supe-effcency DEA (Andeson & Petesen, 1993) and stochastc fonte analyss (Banke, 1993; Banke et al., 1992) n ode to assess polce foce effcency of Englsh and Welsh polce foce. It does not hghlght lmtatons of paametc and non-paametc appoaches n case of dffeent cme zones whch s pesent n the data. Vema & Gavnen (2006) measued polce effcency n Inda as an applcaton of data envelopment analyss. Ths wok povdes a atonale fo dentfyng good pefomance pactces. It helps n geneatng tagets of pefomance, the optmum levels of opeatons, ole models that neffcent depatments can emulate and the extent to whch mpovements can be made ove a peod of tme. The pape measues the pefomances of state polce unts n Inda and the esults suggest ways n whch some State polce depatments can mpove the oveall effcency. But ths pape dd not consde the aspects of heteogeneous natue of state polces pesents n Inda snce some states has lage aea and populaton as compae to othe states. The pape dffes fom the eale studes due to the use of DEA n combnaton of clusteng and caes out analyss on the homogeneous goups of polce admnstaton unts not on all unts as eale done. 3. Methodology The pape dscusses two majo phases of the poposed appoach. In the fst phase, clusteng s used to dentfy the cme zones and to fom homogeneous goups n the aea of nteest. In the second phase, polce admnstaton unts as DMUs n a patcula cme zone ae anked usng DEA. The bef descptons of clusteng wth some of ts popula algothms and DEA along wth ts models ae gven n the subsequent sectons. 3.1 Clusteng Technques In ths secton, some of the wdely known clusteng algothms lke K-means clusteng, Heachcal clusteng and Self Oganzng Map (SOM) have been descbed n bef. K-means (McQueen, 1967) s one of the most popula clusteng algothms. K-means s a pattonng method, whch ceates ntal pattonng and then uses teatve elocaton technque that attempts to mpove the pattonng by movng objects fom one goup to anothe. The algothm s used to classfy a gven data set nto fxed numbe of clustes (K). K-means uses the concept of centod, whee a centod epesents the cente of a cluste. In the pocess, K centods, one fo each cluste s defned apo. Then 42

4 Mansh Gupta et al. / Rankng Polce Admnstaton Unts on the Bass of Cme Peventon Measues each object of the data set s assgned a goup wth the closest centod. The postons of k centods ae ecomputed when all objects have been assgned to any of the clustes. The pocess s epeated untl the centods ae no longe move. Heachcal clusteng (Johnson, 1967) goups the data objects by ceatng a cluste tee called dendogam. Goups ae then fomed by ethe agglomeatve appoach o dvsve appoach. The agglomeatve appoach s also called the bottom-up appoach. It stats wth each object fomng a sepaate goup. Goups, whch ae close to each othe, ae then gadually meged untl fnally all objects ae n a sngle goup. The dvsve appoach s also called as top-down appoach. It begns wth a sngle goup contanng all data objects. Sngle goup s then splt nto two goups, whch ae futhe splt and so on untl all data objects ae n goups of the own. The dawback of Heachcal clusteng s that once a step of mege o splt s done t can neve be undone. SOM (Kohenen, 1990) s a neual netwok based unsupevsed clusteng. It maps hgh dmensonal data nto a dscete one o two-dmensonal space. SOM pefoms clusteng though a compettve leanng mechansm. In the pocess, seveal unts compete fo the cuent object and the unt whose weght vecto s closest to the cuent object becomes the wnnng o actve unt. Only the wnnng unt and ts neaest neghbous patcpate n the leanng pocess usng Mexcan Hat functon. 3.2 Data Envelopment Analyss Data envelopment analyss (DEA) was fst put fowad by Chanes et al. n DEA s used fo evaluatng the elatve effcency of decson makng unts (DMUs) whch poduce multple outputs and multple nputs, va weghts attached to nput-output measues. DEA uses lnea pogammng poblems to evaluate the elatve effcences and neffcences of pee decson-makng unts. DEA s a nonpaametc appoach that does not eque any assumptons about the functonal fom of the poducton functon. In the smplest case, whee a unt has a sngle nput (X) and output (Y), effcency s defned as the output to nput ato: Y/X. DEA usually deals wth unt k havng multple nputs X k whee =1,2,,m and multple outputs Y k, whee =1,2,,s whch can be ncopoated nto an effcency measue. Effcency measue fo DMU k s gven by h k 1 = Max m= u, v s = 1 u v Y X k k 43 (1) whee the weghts, u and v, ae non-negatve. A second set of constants eques that the same weghts, when appled to all DMUs, do not povde any unt wth effcency geate than one. Ths condton appeas n the followng set of constants: s = m = 1 uyj 1 1 fo j = 1, K, n. v X j (2) Each unt k s assgned the hghest possble effcency scoe (h k 1) that the constants allow fom the avalable data, by choosng the optmal weghts fo the outputs and nputs. If unt k eceves the maxmal value h k = 1, then t s effcent, but f h k < 1, t s neffcent. Bascally, the model dvdes the unts nto two goups, effcent (h k = 1) and neffcent (h k < 1) by dentfyng the effcent fonte of the data. Once the effcent fonte s detemned, neffcent DMU s can mpove the pefomance to each the effcent

5 Emegng Technologes n E-Govenment fonte by ethe nceasng the cuent output levels o deceasng the cuent nput levels. Cook & Sefod (2009) has evewed vaous DEA models developed dung last thee decades whch ncludes basc DEA models such as constant etun to scale (CRS) model (Chanes et al., 1978), vaable etun to scale (VRS) model (Banke et al., 1984) and specfc models lke fee dsposal hull (FDH) model (Tulkens, 1993), coss evaluaton (Sexton & Slkman, 1986) and mnmum dstance models (Fe & Hake, 1999). The two most commonly used models.e. CRS and VRS ae descbed n bef n the next subsecton. Constant Retun to Scale (CRS) Model CRS model (Chanes et al., 1978) s often efeed to as the CCR model based on ts founde s name.e. Chanes, Coope and Rhodes. The model assumes that the poducton functon exhbts constant etuns-toscale.e. an ncease n nputs leads to a popotonate ncease n ts outputs. The model can be wtten nto a lnea pogam, whch can be solved elatvely easly and a complete DEA solves n lnea pogams, one fo each DMU. h k subject m = 1 m = 1 u v = v v Max X X 0 0 j k to = s = 1 = 1 1 fo fo s u u Y Y k j 0 = 1, K, s. = 1, K, m. fo j = 1, K, n. (3) It should be noted that the esults of the CRS nput-mnmzed o output-maxmzed fomulatons ae the same. Vaable Retun to Scale (VRS) Model VRS model (Banke et al., 1984) s often called on the name of ts ognato BCC.e. Banke, Chanes and Coope. VRS model adds an addtonal constant vaable, c k, n ode to pemt vaable etuns-to-scale.e. an ncease n nputs does not poduce a popotonal change n ts outputs. It should be noted that the esults of the VRS nput-mnmzed o output-maxmzed fomulatons ae dffeent, whch s not the case n the CRS model. Thus, n the output-oented VRS model, the fomulaton maxmzes the outputs gven the nputs and vce vesa. h k subject m = 1 m = 1 u v = v v Max X X 0 0 j k to s = 1 = 1 = 1 fo fo s u u Y Y k j + c c = 1, K, s. = 1, K, m. k k 0 fo j = 1, K, n. (4) DEA does not use common weghts, as do multple ctea decson theoy models, whch usually ank the elements based on the multple ctea (nputs and outputs), and usually povde common weghts. The weghts vay among the unts and ths vaablty s the essence of DEA. 44

6 Mansh Gupta et al. / Rankng Polce Admnstaton Unts on the Bass of Cme Peventon Measues 4. Results and Dscussons The two-phase methodology has been appled on cme elated data of Indan state polce foces. It s needed to descbe befly the Indan polce system to undestand natue of cme data. Indan consttuton assgns esponsblty fo mantanng law and ode to the states and unon tetoes (UT), and almost all outne polcng, ncludng appehenson of cmnals, s caed out by state-level polce foces. Inda s dvded nto 28 states and 7 unon tetoes (UT). Measung effcences of state polce foces has emaned a constant aea of govenmental concen snce these states and UT ae havng dvestes n aea, populaton and cme densty. So, fst phase of the methodology s to dentfy cme zones of states wth smla cme densty usng clusteng technques. 4.1 Identfcaton of Cme Zones Usng Clusteng Technques Clusteng technque has been employed to Indan cme data to cluste the cme locatons as the densty of cme ncdents dffes fom one state to anothe. Snce the numbe of cme zones s known apo, K means clusteng has been used fo clusteng the cme locatons. Cme data contans the cme ecods of all 28 states and 7 unon tetoes of Inda fo yea 2006 unde 12 cme heads.e. Mude, Attempt to mude, Culpable Homcde (C.H.) Not Amountng To Mude, Kdnappng & Abducton, Rape, Cuelty by husband, Dowy Deaths, Dacoty, Pepaaton And Assembly Fo Dacoty, Robbey, Rots and Ason. The states have been gouped nto thee cme zones such as Hgh Cme Zone (H), Modeate Cme Zone (M) and Low Cme Zone (L) based on the denstes of vaous cmes. Table-1 shows the cme denstes and cme zones of 28 states & 7 UTs of Inda fo yea Clusteng esults ae shown n the last column of Table-1 as cme zones. Bha, Kanataka, Keala, Madhya Padesh, Mahaashta and Utta Padesh ae gouped nto hgh cme zone snce cme densty of all cme heads of these states ae much hghe than any othe states wheeas, Andha Padesh, Gujaat, Rajasthan and West Bengal wth lesse cme densty than hgh cme zone states ae clusteed nto modeate cme zones. The est of the 25 states and UTs come nto the low cme zone categoy. These homogeneous goups.e. cme zones ae used to measue the effcences of polce admnstaton unts.e. states and UTs by applyng DEA. 4.2 Rankng Polce Admnstaton Unts usng DEA In the second phase, DEA technque has been used to measue the effcences of polce admnstaton unts as DMUs ove the espectve cme zone as dentfed n the fst phase. Futhemoe, polce admnstaton unts ae anked based on the effcency scoes. The selecton of ctea fo analyss.e. nput and output measues play a cucal ole n DEA esults. The next subsecton descbes the nput and output measues consdeed fo measung effcences of polce admnstaton unts fo effectve mplementaton of cme peventon measues. Selecton of Input /Output Measues We have dentfed only the elevant nput and output measues fom cme peventon measues befoe applyng DEA. The selected nput measues fo analyss ae cvl and amed polce foce stengths and total polce expendtue. A polce admnstaton unt has hgh effcency f t s utlzng ts esouces well both pesonnel and fnancal esouces to acheve the desed objectves. Total polce expendtue conssts of all the money nvested fo mplementng all cme peventon measues. Outputs ae selected by consdeng the fact that DEA model tes to maxmze the output measues to make DMUs as effcent. Theefoe, appehenson of cmnals.e. numbe of peson aest s consdeed as the fst output measues fo analyss. The second output measue s the output functon of cme ate defned by Output Functon of Cme Rate = 1/Cme Rate (5) Hee, cme ate s obtaned by dvdng total cme densty of the state/ut wth total populaton of that state/ut snce the polce of a state/ut s called effcent f ts cme ate s low.e. the output functon of cme ate s hgh. 45

7 Emegng Technologes n E-Govenment State/UT Table 1: Cme denstes & Cme Zones of 28 states & 7 UTs of Inda fo yea 2006 Mude Attempt To Commt Mude C.H. Not Amountng To Mude Kdnappng & Abducton Rape Cuelty By Husband And Relatves Andha Padesh M Aunachal Padesh L Assam L Bha H Chhattsgah L Goa L Gujaat M Hayana L H P L J & K L Jhakhand L Kanataka H Keala H Madhya Padesh H Mahaashta H Manpu L Meghalaya L Mzoam L Nagaland L Ossa L Punjab L Rajasthan M Skkm L Taml Nadu L Tpua L Utta Padesh H Uttaanchal L West Bengal M A & N Islands L Chandgah L D & N Havel L Daman & Du L Delh L Lakshadweep L Pondchey L Dowy Death Dacoty Pepaaton And Assembly Fo Dacoty Robbey Rots Ason Cme Zone STATE/UT Table2: Data of all Indan states/uts fo yea 2006 unde selected I/O measues Amed Total Polce Cvl Polce Aested Polce Expendtue Stength Peson Stength (Rs. In Coes) 46 Output Functon of Cme Rate Andha Padesh Aunachal Padesh

8 Mansh Gupta et al. / Rankng Polce Admnstaton Unts on the Bass of Cme Peventon Measues Assam Bha Chhattsgah Goa Gujaat Hayana Hmachal Padesh Jammu & Kashm Jhakhand Kanataka Keala Madhya Padesh Mahaashta Manpu Meghalaya Mzoam Nagaland Ossa Punjab Rajasthan Skkm Taml Nadu Tpua Utta Padesh Uttaanchal West Bengal A & N Islands Chandgah D & N Havel Daman & Du Delh Lakshadweep Pondchey Table 2 shows the data of all Indan states/uts fo yea 2006 unde selected nput/output measues fo measung effcences of polce foces of all states/uts as DMUs fo DEA model. Constant etun to scale (CRS) model and vaable etun to scale (VRS) model of DEA have been appled on the data gven n Table-2. The effcency scoes of CRS model and VRS model of DEA wth clusteng and DEA wthout clusteng ae gven n the next secton of the pape. Effcency Scoes The effcency scoes povde the man summay of compaatve effcency. Table-3 shows the effcency scoes of all states/uts usng CRS model and VRS model of DEA wth clusteng and DEA wthout clusteng. 47

9 Emegng Technologes n E-Govenment Table 3: Effcency Scoes STATE/UT Effcency Scoe wth Clusteng Effcency Scoe wthout Clusteng CRS VRS CRS VRS Andha Padesh Aunachal Padesh Assam Bha Chhattsgah Goa Gujaat Hayana Hmachal Padesh Jammu & Kashm Jhakhand Kanataka Keala Madhya Padesh Mahaashta Manpu Meghalaya Mzoam Nagaland Ossa Punjab Rajasthan Skkm Taml Nadu Tpua Utta Padesh Uttaanchal West Bengal A & N Islands Chandgah D & N Havel Daman & Du Delh Lakshadweep Pondchey All the analyzed states/uts ae gven an effcency scoe. Ths scoe s between 0 and 1. A state/ut wth a scoe of 1 s elatvely effcent. Any state/ut wth a scoe of less than 1 s elatvely neffcent. States/UTs can also be anked based on the effcency scoe. The effcency scoes of CRS model s less than the effcency scoes of VRS model fo both DEA wth clusteng and DEA wthout clusteng. The esults of DEA wth clusteng appoach ae bette than the DEA wthout clusteng. The compaatve evaluaton of both the appoaches s gven n the next secton to demonstate ths fact. 48

10 Mansh Gupta et al. / Rankng Polce Admnstaton Unts on the Bass of Cme Peventon Measues 5. Compaatve Evaluaton The compaatve evaluaton of both the appoaches.e. DEA wth clusteng and DEA wthout clusteng s gven to judge, whch one s the bette appoach. Compaatve effcency scoes and pee goups of both the appoaches ae shown n ths secton. 5.1 Compaatve Effcency Scoe Fgue 1: Compaatve Effcency Scoes fo CRS Model The mean effcency scoe of DEA-CRS model wth clusteng and wthout clusteng ae and espectvely. Futhemoe, mean effcency scoe of DEA-VRS model wth clusteng and wthout clusteng ae and espectvely. We have appled a paed samples t-test fo 5% level of sgnfcance level to check that the effcency scoes obtaned fom both the appoaches ae statstcally same o dstnct. Accodng to estmate, t-statstc fo DEA-CRS model and DEA-VRS model ae and espectvely. Theefoe, we conclude that both the appoaches ae dstnct wth 100% confdence level. Fgue-1 and Fgue-2 shows that the effcency scoe of DEA wthout clusteng s always less than the effcency scoe of DEA wth clusteng fo both DEA-CRS model and DEA-VRS model. It means, DEA wthout clusteng technques undeestmates the states/uts n measung the effcences and does not poduce satsfactoy esults. Futhemoe, DEA wth clusteng technques poduces the satsfactoy esults by estmatng the DMUs coectly based on the espectve cme zones. 49

11 Emegng Technologes n E-Govenment Fgue 2: Compaatve Effcency Scoes fo VRS Model 5.2 Compaatve Pee Goups Table-4 shows the pee goups of DEA-VRS model wth clusteng and DEA-VRS model wthout clusteng. In Table 4, t s seen that fo states lke Andha Padesh, Kanataka, Keala, Kanataka etc, pee goups wth DEA and clusteng have the same states as shown n column 3 of Table 4 snce these states ae themselves effcent unts and thee s no need of benchmakng. Howeve fo states lke Aunachal Padesh, Assam whch ae neffcent unts, the benchmakng s done wth the states (Nagaland, Ossa, Lakshadweep) and (Ossa, Taml Nadu, Nagaland) whch fom the pee goups obtaned wth DEA and clusteng. It s also seen fom the Table-4 that both appoaches have dffeent pee goups fo neffcent unts. It s mpotant to note that a state/ut should not have a pee goup of states/uts fom dffeent cme zones snce a state/ut cannot be benchmak wth states/uts fom othe cme zones. It s seen fom Table-4 that many states/uts ae havng pee membes fom dffeent cme zones wth the case of applyng DEA wthout usng clusteng technques. Fo example, Assam s n the low cme zones but havng pee membes of hgh cme zone state.e. Madhya Padesh and Utta Padesh. Smlaly, Gujaat s n the modeate cme zone but havng pee membes fom low cme zone state.e. Nagaland and hgh cme zone states.e. Mahaashta, Bha, Madhya Padesh. Thus, DEA wthout clusteng fals to ecognze 50

12 Mansh Gupta et al. / Rankng Polce Admnstaton Unts on the Bass of Cme Peventon Measues sutable pee goups and DEA wth clusteng appoach povdes the sutable pee goups n benchmakng the neffcent unts to effcent unts. Table 4: Pee Goups State/UT Cme Pee Goup of DEA-VRS Pee Goup Of DEA-VRS Zone Wth Clusteng Wthout Clusteng Andha Padesh M Andha Padesh Mahaashta, M P, Bha, Kanataka Aunachal Padesh L Nagaland, Ossa, Lakshadweep Nagaland, Lakshadweep, M P Assam L Ossa, Taml Nadu, Nagaland Nagaland, M P, U P Bha H Bha Bha Chhattsgah L Chhattsgah Lakshadweep, M P, Nagaland Goa L Taml Nadu, Lakshadweep, Nagaland, Jhakhand Lakshadweep, Nagaland, Kanataka Gujaat M Gujaat Mahaashta, Bha, Nagaland, M P Hayana L Jhakhand, Taml Nadu, D & N Havel Lakshadweep, Kanataka, Bha, D & N Havel Hmachal Padesh L Pondchey, Lakshadweep, Taml Nadu, M P, Bha, Nagaland, Lakshadweep Ossa Jammu & Kashm L Nagaland, Taml Nadu M P, U P, Nagaland Jhakhand L Jhakhand Lakshadweep, Nagaland, Kanataka Kanataka H Kanataka Kanataka Keala H Keala D & N Havel, Bha, M P Madhya Padesh H M P M P Mahaashta H Mahaashta Mahaashta Manpu L Ossa, Nagaland, Lakshadweep Nagaland, Lakshadweep, M P Meghalaya L Ossa, Nagaland, Lakshadweep Lakshadweep, Nagaland, M P Mzoam L Lakshadweep, Ossa, Nagaland Lakshadweep, M P, Nagaland Nagaland L Nagaland Nagaland Ossa L Ossa Nagaland, M P, Lakshadweep Punjab L Nagaland, Taml Nadu M P, U P, Nagaland Rajasthan M Rajasthan Bha, M P, D & N Havel Skkm L Ossa, Lakshadweep, Nagaland Lakshadweep, M P, Nagaland Taml Nadu L Taml Nadu U P, Mahaashta, M P, Bha Tpua L Nagaland, Lakshadweep, Ossa Nagaland, Lakshadweep, M P Utta Padesh H U P U P Uttaanchal L Taml Nadu, Lakshadweep, Nagaland, Jhakhand Lakshadweep, Nagaland, Kanataka, Bha West Bengal M West Bengal M P, U P, Nagaland A & N Islands L Jhakand, Lakshadwep, Nagaland Kanataka, Lakshadweep, Nagaland Chandgah L Lakshadweep, Taml Nadu, Jhakhand, D Kanataka, Nagaland, Lakshadweep & N Havel D & N Havel L D & N Havel D & N Havel Daman & Du L Daman & Du Daman & Du Delh L Ossa, Lakshadweep, Nagaland, Taml Nadu Nagaland, U P, M P, Bha Lakshadweep L Lakshadweep Lakshadweep Pondchey L Pondchey D & N Havel, M P Theefoe, t can be concluded fom ths compaatve evaluaton that DEA n combnaton of clusteng technques povdes bette esults than DEA n stand-alone mode n measung effcences of polce foces. 51

13 Emegng Technologes n E-Govenment 6. Concludng Remaks In ths pape, the technques of clusteng and Data Envelopment Analyss (DEA) have been appled to measue effcences and subsequently to ank polce admnstaton unts on the bass of the pefomance n cme peventon measues. These polce admnstaton unts mght be at any level of polce admnstaton system.e. states, dstct and polce staton. Ths pape also llustates how the concept of clusteng s used fo effectve applcaton of DEA methodology n measung effcences of polce foces. The effectveness of the appoach has also been demonstated fo data of Inda polce foces. It can be concluded fom the esults and dscussons that DEA n combnaton wth clusteng poduces bette esults than DEA wthout clusteng appoach. The poposed appoach of measung effcences of polce foces s potentally useful to monto the mplementaton of cme peventon measues at vaous levels of polce admnstaton on egula bass. Acknowledgement: We ae hghly ndebted to Sh Sudh Awasth, Decto, Natonal Cme Recods Bueau (NCRB) fo fundng a poject on cme data mnng. Refeences 1. Andeson, P., Petesen, N.C.(1993). A pocedue fo ankng effcent unts n data envelopment analyss. Management Scence, 39 (10), Banke, R.D. (1993). Maxmum lkelhood, consstency and data envelopment analyss: A statstcal foundaton. Management Scence, 39 (10), Banke R. D., Chang H., Nataajan R. (2007). Estmatng DEA techncal and allocatve neffcency usng aggegate cost o evenue data. Jounal of Poductvty Analyss, 27(2), Banke, R.D., Chanes, A., Coope, W.W. (1984). Some models fo estmatng techncal and scale effcences n data envelopment analyss. Management Scence, 30, Banke, R.D., Mandatta, A. (1992). Maxmum lkelhood estmaton of monotone and concave poducton fontes. Jounal of Poductvty Analyss 3, Begendahl G., Lndblom T. (2008). Evaluatng the pefomance of Swedsh savngs banks accodng to sevce effcency. Euopean Jounal of Opeatonal Reseach, 185, Bege, A. N., Humphey, D.B. (1997). Effcency of fnancal nsttutons: Intenatonal suvey and dectons fo futue eseach. Euopean Jounal of Opeatons Reseach, 98, Butle T. W., Johnson W. W. (1997). Effcency Evaluaton of Mchgan Psons Usng Data Envelopment Analyss Cmnal Justce Revew, 22(1) Cangton, R., Puthucheay, N., Rose, D., Yasawang, S. (1997). Pefomance measuement n govenment sevce povson: The case of polce sevces n New South Wales. Jounal of Poductvty Analyss, 8, Chanes A., Coope W. W., Lewn A., Sefod L. M. (1994) Data Envelopment Analyss: Theoy, Methodology and Applcatons. Boston, Kluwe Academc Publshes. 11. Chanes, A., Coope, W.W., Rhodes, E. (1978). Measung the effcency of decson makng unts. Euopean Jounal of Opeatonal Reseach, 2, Cook W. D., Sefod L. M. (2009). Data envelopment analyss (DEA) Thty yeas on. Euopean Jounal of Opeatonal Reseach, 192, Coope W. W., Sefod L. M., Tone K., Zhu J. (2007). Some models and measues fo evaluatng pefomances wth DEA: past accomplshments and futue pospects. Jounal of Poductvty Analyss, 28(3), Dake, L., Smpe, R. (2000). Poductvty estmaton and the sze-effcency elatonshp n Englsh and Welsh polce foces: An applcaton of DEA and multple dscmnant analyss. Intenatonal Revew of Law and Economcs, 20, Dake, L., Smpe, R. (2003). The measuement of Englsh and Welsh polce foce effcency: A compason of dstance functon models. Euopean Jounal of Opeatonal Reseach, 147, Fe, F., Hake, P. (1999). Pojectons onto effcent fontes: Theoetcal and computatonal extensons to DEA. Jounal of Poductvty Analyss 11, Jan A. K., Muty M. N., Flynn P. J. (1999). Data clusteng: a evew, ACM Computng Suveys, 31(3),

14 Mansh Gupta et al. / Rankng Polce Admnstaton Unts on the Bass of Cme Peventon Measues 18. Johnson S.C. (1967). Heachcal clusteng schemes, Psychometka, 32(3), Kao C., Hung H.T. (2005). Data envelopment analyss wth common weghts: the compomse soluton appoach. Jounal of Opeatonal Reseach Socety, 56, Kohenen T. (1990). The Self Oganzng Map. Poc. IEEE, 78, McQueen J. (1967). Some methods fo classfcaton and analyss of multvaate obsevatons, Poc. Symp. Math. Statst. And Pobablty, 5th, Bekeley, 1, Sexton, T. R., Slkman R. H. (1986). Data envelopment analyss: ctque and extensons. Measung Effcency: An Assessment of Data Envlelopment Analyss. San Fancsco, Amecan Evaluaton Assocaton, Jossey Bass, Inc Thanassouls, E. (1995). Assessng polce foces n England and Wales usng data envelopment analyss. Euopean Jounal of Opeatonal Reseach, 87, Tulkens, H. (1993). On FDH effcency analyss: Some methodologcal ssues and applcatons to etal bankng, couts and uban tanst. Jounal of Poductvty Analyss 4, Vema, A., Gavnen, S. (2006). Measung polce effcency n Inda: an applcaton of data envelopment analyss Polcng: An Intenatonal Jounal of Polce Stateges and Management, 29(1) About the Authos Mansh Gupta s a Scentst n Insttute fo Systems Studes and Analyses and a doctoal student n the Depatment of Mathematcs, Indan Insttute of Technology, Delh (IIT Delh). He has pevously woked as a Juno Reseach Fellow (JRF) at Depatment of Management Studes, IIT Delh. He has been awaded Juno Reseach Fellowshp unde Councl of Scentfc and Industal Reseach (CSIR) schemes n Hs eseach nteests nclude Intellgent Decson Suppot System, Data Mnng, Clusteng and Atfcal Neual Netwok. B. Chanda s a Pofesso n the Depatment of Mathematcs, Indan Insttute of Technology, Delh. She belongs to the computng goup of the Depatment. She has publshed a numbe of eseach papes n eputed Intenatonal jounals n the aea of Neual Netwoks, Classfcaton, Clusteng and Assocaton ule mnng..she has been a vstng Pofesso fo a yea at the Gaduate School of Busness, Unvesty of Pttsbugh, USA and woked at Wold Bank at Washngton D.C. Dung she has been a vstng Pofesso Penn State Unvesty, USA. She has also been a vstng Scentst at INRIA, Fance. She has been Chaman n the sesson on Neual Netwoks at vaous Intenatonal confeences held n USA, UK, Canada, Fance and Sngapoe. She has gven nvted lectues at vaous unvestes n USA: Unvesty of Mayland, Unvesty of Hawa, Unvesty of Pttsbugh, Pennsylvana State Unvesty Kast,Koea, Unvesty of Uttecht, Nethelands, Ecole de Mnes Pas and unvesty of Bango U.K. She has been a pncpal nvestgato of many eseach and consultancy eseach pojects n the of Neual Netwoks and Machne leanng. Among the ecent ones ae Identfcaton of Cme Hotspots usng clusteng funded by NCRB and Clusteng fo developng effcent tadng stateges fo stock maket data She s also the autho of thee books. M. P. Gupta s Cha-Infomaton Systems Goup & Coodnato-Cente fo Excellence n E-gov at the Depatment of Management Studes, Indan Insttute of Technology (IIT Delh). Hs eseach nteests les n the aeas of IS/ IT plannng and E-govenment. Pof. Gupta has authoed acclamed book Govenment Onlne and edted two othes enttled Towads E-Govenment and Pomse of E-Govenment, publshed by McGaw Hll, Hs eseach papes have appeaed n Natonal and Intenatonal Jounals/Confeence Poceedngs. He was the ecpent of the pestgous Humantes & Socal Scences (HSS) fellowshp of Shast Indo Canadan Insttute, Calgay (Canada) and a Vstng Fellow at the Unvesty of Mantoba. He supevsed e-govenment potal Gam Pabhat whch won the IBM Geat Mnd Challenge Awad fo the yea He has steeed seveal semnas and also founded the Intenatonal Confeence on E-govenance (ICEG) n 2003 whch unnng nto ffth yea. He s on the juy of Compute Socety of Inda (CSI) E-gov Awads and also a membe of Pogam Commttee of seveal Intenatonal Confeences. He s lfe membe of Global Insttute of Flexble Systems Management (GIFT) and Systems Socety of Inda. 53