NGHIEN CtJU TRAO 5
e c ? r . ^ 3 7,(0-io
VAM DIJIVG PHlfOf^G P H A P BAO Dtf LIEU (DEA) TROMG KIEM TOA]\ HOAT DOMG
DANG ANH TUAN *
Phddng p h i p bao dfl lieu (Data Envelopment Analysis) vilt tat DEA dflde Chames & cong sd phat t r i l n nam 1978 tiT vile ap dyng y tfldng dfldng gidi hgji k h i nang s i n xuat (Production Possibility Frontier) lam tilu chi danh gia h i l u qua (tfldng doi) gifla cac ddn vi trong cung m^t nganh hoac linh vdc cua Farrell (1957). Den nam 1984, Banker & edng sd cai t i l n md hinh t r l n bang cich b o sung yeu td sinh Idi n h d quy md (returns to scale) vao tinh toan, mang lai cai nhin cu the h d n ve tinh hieu qua cua cae e i c don vi hoat d^ng (DMU) dflpc p h i n tich. Tfl dd den nay, md hinh DEA la phfldng p h i p phan U'ch dflpc ap dung phd bien trong kha n h i l u linh vtfc k h i e nhau
*Kiem todn Nhd nUdc khu vUc IV
n g i n hang, bao h i l m , giao due, y te,.. .Mpt so Cd quan K i l m t o i n tdi eac (SAIs) tren t h i gidi cung sii dung cdng cu n i y trong k i l m t o i n hoat ddng de do Ifldng v i d i n h gia tinh hieu q u i (Dan Manh, My...). Bii vilt nay n h a m m u c dich gidi t h i l u p h d d n g p h i p DEA va ling d u n g cua p h d d n g p h a p nay trong vile do Ifldng hieu qua trong kiem toan hoat dpng.
D a n h gia h i l u q u i bang phfldng phap bao dfl lieu (DEA)
Phfldng p h i p DEA dflpc xay dflng trln quan dilm cho ring, n l u cd the fldc Iflong dflde dfldng gidi han kha nang san xuat cua mdt ddn vj hoat dpng (DMU) khi bilt cae y l u to dau v i o cho trddc, cd the x i c djnh dflpc hilu
26 I Sfl 83+84 - (hing 9+10/2014 j N G H I E N CL^• KHOA HOC KIEM T O A N
q u i sfl dyng eic yeu to dau v i o theo ty sd gifla kit q u i dat dflpc thflc t l / k i t q u i ly thuyet (khi nang sin xuat).
Farrell (1957) x i y dflng md hinh do Ifldng hieu q u i dau tien cua mpt ddn vi dfla t r l n nhieu yeu td dau vio. Ong chia mflc dp h i l u q u i gdm hai thinh phan (i) h i l u q u i ky thuit p h i n anh k h i n i n g tdi da hda k i t q u i dau ra vdi dau vao cho trfldc v i (ii) hilu qua phan bd phan i n h k h i nang ddn vi phan bd cic y l u td dau vao khi gii ca tddng flng cfla chflng da bilt, Tdng hdp h i | u q u i cua hai t h i n h phan n i y ddpe gpi l i h i | u qua kinh t l ( h i | u qua tdng hpp), minh hpa md hinh dinh hfldng kit qua d i u ra
Hinh 1: Md hinh DEA dinh hfldng k i t qua dau ra
Md hinh n i y cd I y l u td dau v i o v i hai y l u td dau ra.
Diem A the h i | n k i t q u i dau ra (thflc te) eua mdt DMU, d i l m B l i kit q u i d i u ra v l mat ly thuylt, DD' dfldng ddng Iflpng (dfldng gidi h?n hilu qui). Trfldng hpp, n l u cd t h i xac dmh dflde mflc gia tfldng flng thi ZZ' chinh la dddng gidi han k h i nang sin xuat (PPF),
Md hinh do Iddng h i | u q u i dau ra cua Farrell ddpe xac dinh nhfl sau. Trong Hinh 1, khoing each AB chi mflc do thilu h i l u q u i ky thuat (cd t h i tang kit q u i d i u ra m i khdng can t h i m dau vao). Vi viy, h i l u qua ky thuit (TEo) ddpe tinh blng cdng thflc:
TEo = OA/OB
N l u cd t h i xic djnh mflc gii tddng flng cua tflng yeu to, ed t h i ve dflpc dddng ddng Idpng DD' va xac djnh h i l u q u i p h i n bo theo cdng thflc:
Hilu qua kinh t l ddpe xic dinh tdng hpp tfl hai thflde do tren:
EEo = (OA/OC) - (OA/OB) x (OB/OC) = TEo x AEo
Md hinh tren cung cd the dflpc bilu dien thdng qua cdng thflc t o i n hpc sau:
EEo =: Z umym/Svkxk
Trong dd, u: trpng sd cua bi&i dau ra y, do do 0 < um < 1;
V trpng so biln d i u v i o x, do dd 0 < vk < 1;
N l u ed n don vi hoat ddng khie nhau (trong cung mpt llnh vflc) thi cd the xac dinh dflde hieu qua DMU thflj ( 0 < J < 1) theo edng thflc: EEo - S umymj/Zvkxkj.
D i n n i m 1984, Banker va cdng sfl cai tiln md hinh tren bang each bo sung ylu td sinh lpi nhd quy md (returns to scale) vao md hinh tinh t o i n (dflpc gpi l i md hinh DEA bien ddi theo quy md-VRS) va cho p h i p loai trfl anh hfldng din tfl v i | c thay ddi quy md. Theo md hinh niy, hieu qua ky thuit (TEo) tfl md hinh DEA trong trfldng hdp khdng ddi theo quy md (CRS) dddc chia t h i n h hai phan, mdt la hieu qua theo quy md v i hai l i h i | u q u i ky thuit thuan.
Sau niy, md hinh trln dflpc phit trien tiep bdi Fare 8c cpng sfl (1985,1994) nham do Ifldng hieu q u i kinh t l eua mpt doanh nghi|p hay mdt dpn vi ra quylt dinh dfla tren sfl thay ddi ning suit tdng hpp (TFP).
De giai bai toin hieu q u i n i y mdt each tdng quit, Coelli (1996) d i xay dflng phan mem DEAR 2.1. P h i n m I m nay cd t h i giup tinh toan cac diem h i | u q u i tdi flu (max EFj) dfla trln t i p hdp sd lieu gom cac biln sd dau v i o v i d i u ra cho trddc.
Van d u n g DEA trong Idem t o i n tinh h i l u q u i . Co hai phdong phap p h i n tich dfl lieu de do Ifldng h i | y q u i hosit ddng eua mdt ddn vj Ii p h i n tich dfl lieu cheo va phan tich dfl lieu theo chudi thdi gian:
Phan tich dfl li|u cheo: Phfldng p h i p n i y tinh toan hilu q u i tfldng doi cfla nhilu ddn vi cd hoat dpng tdOng td, theo dd, ddn vj nao cd mflc h i l u qua cao nhat t r l n
NGHlfiN e c u KHOA HQC K I £ M TOAN I So 83+84 - ihdng 9+10/2014 | :
NGHlfiN Giro TRAO B61 _
thflc t l dflpc coi l i mflc hieu qua 100% (hoac hilu q u i tflong ddi bing 1). don vi nao dat mflc hilu qua thip hon ching ban 90%. thi k h i nang cii t h i | n h i | u q u i la 10%. D l xic dinh ddpe nguyin n h i n hoac yeu to n i o i n h hfldng d i n h i | u q u i thap cua mdt dOn vi nao dd, cd t h i chia hilu qua tfldng doi thanh hai lo^i la hilu q u i theo quy md va hieu q u i quin ly (hilu q u i ky thuit thuan). H i | u q u i theo quy md do Ifldng xem mdt ddn vi hogt dpng n i o dd dat ddpe thinh tich cao do quy md qua Idn hoie khdng h o i n thinh chflc nang, nhilm vy do quy md q u i nhd. H i | u q u i quan ly la viec do Iddng mflc dp h i | u qua ma mdi ddn vi boat dpng sfl dyng ngudn lflc mpt each tdi flu nhat.
H'mh 1: H i l u qua tflong ddi cua mpt ddn vi.
Diem A minh hoa mflc dp h i | u q u i cfla mpt dOn vi.
Dfldng gidi han mflc dd hieu q u i ddpe xic dinh tren ed Y
nhat {nim t r l n dfldng gidi h^n h i l u q u i ) v i sfl thay doi eua nhdm ddn vi cd mflc h i | u qua t h i p hdn. Vi viy, tfldng flng, cd the chia v i | c thay doi h i l u q u i thinh hai thanh phan (i) sfl thay ddi h i | u q u i v l m^t edng n g h | do Ifldng sfl diiay doi h i | u q u i cfla c i c ddn vi cd mflc hi|u q u i cao nhat theo thdi gian v i (ii) sfl thay doi hilu qua tflOng ddi (bao gdm h i | u q u i theo quy md v i hilu qua q u i n ly) phin anh toe dp thay ddi h i l u q u i cua cic don vj cd mflc hilu q u i thap hdn theo thdi gian ching hgn ning cao h i l u qua theo quy md va h i l u qua ky thu^t so vdi cic don vi da dgt dflpc h i l u qua tfldng ddi (hi|u qua cao nhit)
Hinh 2: Sd thay ddi h i l u qua theo thdi gian
Hinh 2 minh hpa ddn vi hoat ddng (DMU) dat mile
sd nhflng ddn vj cd mflc dp hieu qua cao nhit (hieu qua tfldng ddi bang 100%). Hilu qua tflOng ddi bing khoing cac tfl diem A tdi dfldng gidi ban mflc dp hilu q u i tflOng ddi, trong khi do, h i | u q u i quan ly bang khoang each tfl diem A tdi dfldng gidi han h i | u q u i quin ly. Hilu q u i theo quy md bang hilu qua tfldng ddi trfl hilu qua quin ly.
Phin tich dfl lieu theo chuoi thdi gian PhflOng p h i p niy n h i m muc dich dinh gii mflc dd hilu q u i ting len theo thdi gian cfla tflng don vi v i mflc dp thay doi hieu qua theo thdi gian ddi vdi nhdm don vi cd h i | u qua cao
hilu q u i tai diem A trong giai doan 1 v i diem B trong giai doan 2, Hilu q u i t i n g lln theo thdi gian dfldc bilu d i l n bing sfl thay ddi dp ddc gifla hai cap eic dfldng trln. Dp doc thay ddi mdt phan do thay ddi dfldng gidi han hieu q u i tfldng ddi (LE) gifla hai thdi k^. mdt phan thay ddi dflpc xac dinh bang c h i n h lech gifla khoing each A-B so vdi khoang each thay doi cua hai dfldng LE1-LE2.
Khi dp ddc dfldng LE ddc hdn, d i l u nay phan anh kha nang cd the cai t h i l n h i l u q u i tfldng ddi d mflc cao hdn vdi cung mflc ehi phi. Bdi vi, h i l u qua tfldng d6i co the dfldc tinh toan dfla tren c i e ddn vi cd h i | u qua nhat, sfl thay doi ky t h u i t thuan md ta h i l u qua tang lln cua cie don vi cd mflc h i l u qua cao nhat. Thay doi khoang
53+84 - thing 9+10/2014 I NGHItN CCX^ KHOA HQC K I I M T O A N
each AA' t h i n h BB' gifla hai thdi ky trong Hinh 2 t h i h i | n sfl thay ddi h i | u q u i gifla cac ddn vi cd mflc dat h i | u qua thip so vdi nhdm cie don vi cd mflc h i l u q u i cao nhat (hi|u qua tddng ddi).
Di minh hpa cho hai phddng p h i p p h i n tich dfl Ii|u trln, ta xem xet mpt vi dy ve hoat dpng pho biln cua cac cd quan n h i nddc theo vi du sau:
Vi dy, kilm toin viln thu t h i p dflde so lieu kit q u i
S I T A
1 2 1
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9 in 11
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SO 60 JE S6 31 62 41 68 57 BO 6S 73
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2 - 3 + 4 + 5
64 5S2 66 266 65.930 65 713 57 145 61.047 7 5 706 57,889 57 549 65 650 6 1 7 1 9 73 616
GFXD 3
12 231 10 513 10 857 1 1 0 7 7 5 634 7,895 1 1 2 3 4 9 889
6 373 12 321 I3 34S 113G9
G C N 4
20 321 2 1 6 9 7 2 1 4 2 2
13 029 19.383 21.020 13.040 2 1 3 2 4 18 373 1S9E2 men
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32 030 34.056 33 651 33 391
34 018 4 0 1 2 3 45 089 26 980 37 936 32 005 30 001 43 245
q n i 6=2/1
I J ! 9 2 1 104 1.137 1.173
1.120 98S 1 8 4 6 BSl 1 0 1 0 321 950 lOOB
thflc h i | n edng vi|c cfla bdn q u i n trong mdt thanh phd tfl nam 2011 d i n nam 2013. Trong dd, ylu t6 d i u v i o la sd Iflpng edng chflc thflc thi nhilm vu lien quan tdi eic n h i | m vu ehinh cap giay phep xiy dflng (GPXD), cip giay chflng nhan quyen sfl dyng dat (GCN), cap hp khau thfldng trfl (HKTT) theo tflng nam v i dau ra la sd Iflpng GPXD, GCN, HKTT dflpc cap tflng nam Bang 1.
Bang 1 : Tdng hdp so Iddng n h i n v i l n v i khdi Ifldng cdng v i | c h o i n t h i n h .
Tinh todn hieu qua tren phdm mem Deap 2.1, ta cd
s„
1 2 3 4
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1 1,000 0.804 0,837 0,711 D , » S
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1,000 0.996 1,000 0,958 0,988
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1,000 0 807 0,837 0.743 0,84"
ket qud sau:
Bang 2: H i | u q u i t d d n g doi theo md hinh DEA d | n h h d d n g d i u ra n i m 2013
Bing 2 cho k i t qua thdng k l md ta cie chi tilu h i l u q u i trong ho?t dpng cung cap djch vy cdng (cap GPXD,
GCN, HKTT) eho ngddi dan cua tflng quan. H i | u q u i tflOng ddi cua bdn quan chpn mau la 0,838 nhd hon 1, eho thay ket qua cung cap dich vu edng trong nam 2013 thap h d n kha nang l i 16,2%. Trong sd 04 quan, chi cd quan 1 dat dflpc h i l u qua tfldng ddi, quan 2 va qugn 4 d i u chfla dflpc h i l u qua ve mat quan ly (hieu qua ky thuat thuan) v i h i l u qua theo quy md, quan 3 dat hieu qua q u i n ly nhflng khdng d^t hieu qua ve mat quy md.
Dieu n i y eho thiy, ca 3 quan chfla khai thae het thdi gian l i m viec cua n h i n viln sfl dyng cho viec thflc hien cac thu tyc hanh chinh do bo tri thfla n h i n sfl thflc h i | n cac n h i l m vy tren (quan 2 ed the giim 9 n h i n vien, q u i n 4 cd t h i giim 18 nhan vien). Ket q u i chay md hinh cung chi ra so vdi q u i n 1 cd cung sd nhan viln, quin 2 cd the cap them dflpc 790 GPXD ma khdng can them thdi gian va nhan vien, q u i n 4 cd t h i cap t h i m dflpc 1.304 GPXD v i 340 HKTT eho ngfldi dan m i khdng can t h i m thdi gian v i nhan vien.
Bang 3: Chi s6 Malmquist binh quan thdi ky 2011-2013.
Bang 3 cho t h i y sfl thay ddi nang suit n h i n td tdng
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2 0 . , . . .
2 0 . - 2 0 1 3
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1 140 0 813 0.916 0 84T
0 878 0.941
0 982 0 928 0.846
hdp trong thdi ky nghiln cflu nhd hon 1 hay ehi dat 0,942 nguyin nhan chu yeu do hieu qua tfldng ddi ehi dat 0,94 mac du cac q u i n d i cai tiln v i flng dung cdng nghe mdi trong thflc thi n h i l m vu cua minh nhflng do k h i u quan ly kem va khdng khai thae h i t thdi gian kha nang cua nhan vien. Trong giai doan 2 0 I I -2013, chi ed quan 4 cd mflc hilu q u i quan ly tang tfl 0,819 len 0,869 (5,0%) trong khi dd q u i n 2, 3 d i u ed xu hfldng giam d i l u nay cho thay viec tang sd Iflpng dau v i o (nhan viln) m i khdng eii thien dfloe kit qua dau ra (sd Iflpng giay td cap cho ngfldi din) tai hai q u i n nay So vdi qua,n 1, trong
NGHIENCtmKHOAHpCKlfiMTOAN I S583+84 - thing9+10/2014 j 29
NGHIEN ClfU T?AO DOl
giai doan 2011 -2013, quin 4 cd mflc ting nar^ suit nhin td tdng hdp 6,3% cao hon 5,3% so vdi mflc ting nang suit nhin td tdng hdp 1% cua quan 1 do hai nguyin nhin:
Thfl nhat, mflc thay ddi cdng nghe quin 4 tang 1,5% cao hon quin 1 tang 1% l i 0,5% trong giai doan 2011 -2013.
Dilu nay eho thiy quin 4 da flng dung cdng nghe hilu q u i hdn quin 1 trong hoat dpng cua minh.
Thfl hai, do quan 1 da dat mflc hilu q u i tfldng ddi (hilu qua cao nhat so vdi eac quin cdn lai), quin 4, tgi thdi diem cudi nam 2011 thap hon quin 1 l i 18,1% vi sau hai nam ting thim 6%;
Vdi lpi the nay, trong dai han neu quin 1 khdng i p dung eac bi|n phip ddi mdi edng nghi de tang ning suat lao dpng, thi mflc hilu qua se thap hdn qu^n 4 do nhflng thay ddi trong quin ly va nhflng thay ddi trong ddi mdi d n g nghe cua quan 4 mang lai h i | u q u i cao hdn. Tuy nhiln, xu hddng thay doi mflc dp hieu q u i cfla quin 4 lai trai ngflpc vdi quan 2 v i quan 3.
Kit l u i n
Vile ap dung md hinh DEA trong kiem toan hoat ddng khdng nhflng giup xae dinh dfloe nhflng hoat dpng kem h i | u qua m i cdn do Ifldng ddpe mflc dd kem hieu q u i cfla tflng boat ddng va cac nguyen nhan ylu kem can khac phyc. Cd hai phfldng p h i p phan tich dfl lieu d l do Ifldng tinh hilu q u i khi van dung md hinh DEA cd t h i dflpc i p dyng trong kilm toin hoat ddng (i) phan tich dfl lilu cheo vi (ii) phan tich dfl lieu theo thdi gian.
Phin tich dfl lieu cheo cung cap thdng tin ve mflc dp hilu q u i tflong ddi dat dflde cua eic ddn vi trong cung mdt nginh hole linh vflc. Kit qua p h i n tich p h i n anh hilu qui quan ly (hilu qui ky thuit thuan) va sfl phu hdp v l quy md (hi|u q u i theo quy md) cua tflng don vi.
Phan tich dfl li|u theo thdi gian ngoii vile phan i n h sfl
thay doi hieu q u i tfldng ddi theo thdi gian cua tflng ddn vi, khi v|.n dung md hinh DEA cdn cho bilt dflpc nhflng tiln bd trong viec ddi mdi cdng n g h | eua nhdm ddn vi dat dflpc mflc hieu q u i cao nhat va sfl thay doi hilu qui tflong doi cua nhdm don vi chfla dat dflpc mflc hi?u qua tflong ddi. Mflc do thay doi h i l u qua tflOng doi eua nhdm ddn vi nay phan i n h kha nang theo kip eac ddn vi nhdm tren hay khdng theo thdi gian. Ngoii ra, md hinh DEA cdn dflpc flng dung de do Ifldng hieu q u i trong phan bd ngudn lflc (dau vio) khi x i c dinh dflpc mflc gii tflong flng hoac trong pham vi rdng hon do Iddng hilu q u i trong trddng h p p cd n h i l u y l u td dau vao v i dau ra.
TA! LIEU THAM KHAO
1. Banker, R.D.. A. Charnes and W.W. Cooper.]
(19S4), Some models for estimating technical and scale inefficiencies in data envelopment analysis.
Management Science 30:1078-1092.
2. Charnes, A., Cooper, W. W. andRhodes, E. (1978), Measuring The Efficiency Of Decision Making Units, European Journal of Operational Research, 2: 429-444.
3. Farrell, M.J. (1957), The measurement of productive efficiency, Journal of the Royal Statistical Society 120(3): 253-290.
B I Sfl83+84-lhing9+10/2014 I N G H I E N CflU KHOAHpC KIEM T O A N
