chuong 7-so do mang (cpm & pert)

TR NG CAO TON KINH T K THU T SI GN NG KINH T Chng 6: S m ng (PERT) Khoa Kinh t & Qu n tr Kinh doanh

TON KINH T Chng 6: S m ng (PERT)

TON KINH T

Gi ng vin: PGS. TS. NGUY N TH NG E-mail: [email protected] or [email protected] Web: http://www4.hcmut.edu.vn/~nguyenthong/PGS. TS. Nguy n Th ng1

N I DUNG MN H C Chng 1: Gi tr ti n t theo th i gian Chng 2: Chu i dng ti n & Ch tiu nh gi Chng 3: Cc ki n th c m u v phng php t i u Chng 4: Quy ho ch tuy n tnh (QHTT) Chng 5: Cc d ng c bi t pp. QHTT Chng 6: Bi ton v n t i. Chng 7: S m ng (CPM & PERT).2

Tl. (08) 38 640 979 - 098 99 66 719

PGS. TS. Nguy n Th ng


TON KINH T


TI LI U THAM KH O 1. Ton kinh t . PGS. TS Nguy n Qu ng & TS. Nguy n Th ng Thi. 2. Cc phng php ton kinh t . PGS. TS. Nguy n H i Thanh. 1. Download ti li u gi ng t i:

http:// www4.hcmut.edu.vn/~nguyenthong Th m c: Bi gi ng39/19/2011

S M NG (CPM & PERT)4


PGS. Dr. Nguy n Th ng



S M NG G m c 2 phng php - Phng php ng gng CPM (Critical Path Method) Phng php ny s d ng m hnh t t nh, th i gian hon thnh m i h ng m c cng vi c c b n l h ng s .5

- Phng php PERT (Project Evaluation and Review Techniques) Phng php ny s d ng m hnh xc su t theo th i gian hon thnh cng vi c c cho d i d ng hm phn ph i xc su t (phn ph i bta).6





HAM MAT O XAC SUAT PHAN PHOI BETAp

Hm m t xc su t btaXc su t x y ra a l 1% Xc su t x y ra b l 1%

PHNG PHP CPM M t vi nh ngha qui c: i S ki n iS ki n xu t pht i i A t S ki n k t thc j

j Th i gian hon thnh c/tc A

Thu n l i aPGS. TS. Nguy n Th ng

Bnh th ng m

B t l i Th i gian hon b thnh7

Cng tc A(t)8




Thi t l p m t s m ng c 2 phng php : Phng php 1 : Thi t l p theo s trong m t cng tc c b n bi u th b ng 1 vect (trong m t s ti li u ng i ta g i y l phng php AOA - Activity On Arrow). jB(10) iPGS. TS. Nguy n Th ng

Phng php 2 : Thi t l p theo s trong m t cng tc c b n bi u th b ng 1 nt (trong m t s ti li u ng i ta g i y l phng php AON Activity On Node).A (5) B (10)

A (5)

k9 10




V nguyn t c ta c th chuy n i t s m ng d ng AON thnh d ng AOA v ng c l i. Xem cc v d sau : Xt cc cng tc a, b, c,.., f v k hi u cc s ki n 1, 2,, 6.a Start bStart

Cong tac ao (Dummy)3 a 4 oi thanh 3 a b 5 ung a b 3 c d e cPGS. TS. Nguy n Th ng

4 Ao

b Sai v a=34 va b=34

a

1

a b

3 Ao 4 e

d

b

211

A-O-NPGS. TS. Nguy n Th ng

A-O-A

d khong oi hoi sau cong tac c

12



Phng phap lap s o mang: 3 2 1 3 4 Khng nnPGS. TS. Nguy n Th ng

V d : L p s m ng c a cng tc sau:Cng tc A B C D E Cng tc i tr c Khng c Khng c A C B, C

4

1

2

Nn13 14




Ket qua:A 1 2 C

Bi t p: V s mng A-O-A cho d n c m t bi cc cng vic sau:Cng vic 3 D E 5 A B C D E F G15

Cong tac ao

B 4

Cng vic trc A A B, C B, C D, E

Thi gian ho n th nh (tun) 4 2 5 4 6 1 616





L i gi iAB t u

1 C

D

Bi t p: L p s m ng c a cng tc sau: (Xem l i gi i trong Bi t p PERT)3 E GK t thc Cng vi c A B C D E F G H I J PGS. TS. Nguy n Th ng Cng tc i tr c sau A sau A sau B, C sau B, C sau D, E sau D, E sau H, F Sau G, I

B

2

F

17

18




CC THNG S C A S M NG Th i i m s m nh t cng tc b t u ES ES (Earliest Start) l th i i m s m nh t cng tc c th b t u. Th i i m s m nh t cng tc k t thc EF EF (Earliest Final) l th i i m s m nh t cng tc c th k t thc.19

Th i i m mu n nh t cng tc b t u LS LS (Latest Start) l th i i m mu n nh t m cng tc ph i b t u. Th i i m mu n nh t cng tc k t thc LF LF (Latest Final) l th i i m mu n nh t m cng tc ph i k t thc.20





PHNG PHP CPM

M HNH CPM PHNG PHP XC NH NG GNG nh ngha: ng gng l t p h p cc cng vi c c b n (thnh chu i lin t c) t kh i u n k t thc d n v i tnh ch t l b t k m t s ko di th i gian hon thnh c a b t k cng vi c c b n no trn ng gng cng ko theo s ko di th i gian hon thnh d n.22

9/19/2011

21





c s li u xc nh ng gng cho s m ng th c hi n 2 b c: B c 1: Gi i bi ton xui dng v i kh i hnh s m. B c 2: Gi i bi ton ng c dng v i k t thc tr . T cc k t qu trong B c 1 & 2 s xc nh ng gng.23

V d : Xt m t d n xy d ng X v i cc h ng m c cng vi c v th i gian han thnh c trnh by trong b ng sau:Cng vi cA B C D E F G HPGS. TS. Nguy n Th ng

Th i gian k v ng hon thnh cng tc (tu n)2 3 2 4 4 3 5 2 25 tu n

24




B c 1 : Gi i xui dng v i kh i hnh s m ESi : th i i m kh i hnh cng vi c i s m nh t. EFi : th i i m k t thc cng vi c i s m nh t. G i cng vi c i c th i gian hon thnh l t. Ta c quan h sau: EFi = ESi + t T i b t k m t nt s ki n i no ta c tnh ch t : ESi =Max(EFi) 25PGS. TS. Nguy n Th ng

Earliest Start Time (ES) 1 0

2 (ES) B t=2 Earliest Start t=5 7 3 Time (ES) Earliest Final XUI DNG Time (EF) KHI HANH SM26

A

2

2

Earliest Final Time (EF)



TON KINH T Chng 6: S m ng (PERT)Gi i xui dngEF=2 A (t=2) Start ES=0 2 ES=2 ES=4 E (t=4) D (t=4) EF=3 3 ES=3 EF=8 5 EF=7 C (t=2) EF=4 4

Earliest Start Time (ES) i 0

A t=2

2 5

k

Earliest Final Time (EF) 5 =Max(2,5)

KH I HNH S MES=4

Earliest Start B t=3 Time (ES) j 2

t=4 C 9 m Earliest Start Earliest Final Time (ES) Time (EF) XUI DNG27

F (t=3) EF=7 H (t=2) 6 ES=13 EF=13 G (t=5) End EF=15

B (t=3)

ES=828

KHI HANH SMPGS. TS. Nguy n Th ng


Thi gian can thiet hoan thanh d an



GHI CH Khi gi i xui dng c n ch cc i m nt c s h i t c a t nh t 2 cng vi c (v d nt 5, nt 6). T i s ki n 5, ES =8 v G ch c th b t u s m nh t khi c 2 cng vi c E v D u k t thc. Trong khi D k t thc thc s m nh t l EF=7 tu n v E k t thc s m nh t l EF=8 tu n, do G ch c th b t u s m nh t sau 8 tu n m thi.29

Tng t t i s ki n 6, cng vi c ch c th b t u s m nh t ES=13 tu n v k t thc s m nh t c a G l EF=13 tu n, m c d k t thc s m nh t c a F l EF=7 tu n. Theo k t qu bi ton xui dng ta c th i gian c n thi t hon thnh d n l 15 tu n.

30





B c 2: Gi i ng c dng v i k t thc tr LSi : th i i m kh i hnh cng vi c i tr nh t. LFi : th i i m k t thc cng vi c i tr nh t. G i cng vi c i c th i gian hon thnh l t. Ta c quan h sau: LSi = LFi - t T i b t k m t nt s ki n i no ta c tnh ch t : LFi =Min(LSi)31

Latest Start Time (LS) 1 4

A

6

6 t=2 Latest Start Time (LS)

2

Latest Final Time (LF) B t=4 10 3 Latest Final Time (LF)32

NGC DONG KET THUC MUONPGS. TS. Nguy n Th ng



TON KINH T Chng 6: S m ng (PERT)Gi i ng c dngLF=2 C (t=2) LF=4 2 LS=2 LS=4 E (t=4) LS=1 B (t=3) D (t=4) 3 LS=4 LF=8 LF=8 5 4

1

LF=6 [Min(6,8)] A C

Ng c dng 2 LS=6 B 3LS=0 A(t=2)

K T THC TRLS=10 F (t=3) LF=13 H (t=2) 6 LS=13 LF=13 G (t=5) LS=8 End LF=15

LS=8

Start

4

KET THUC MUON33

LF=4

Gia tr t li giai xuoi dong34





Ghi ch: Khi gi i ng c dng c n ch cc i m nt c s xu t pht c a t nh t 2 cng vi c (v d nt 4). T i s ki n 4, th i gian tr nh t ph i c l LF=4 v th i gian kh i hnh tr nh t t i nt 4 ph i l min(LS=4, LS=10).35

XC NH NG GNGLF LS Cng tc A EF

ES Cng tc A l gng (hay LF =EF)PGS. TS. Nguy n Th ng

LS = ES36




Cng vi c A B C D E F G H

ES 0 0 2 3 4 4 8 13

LS 0 1 2 4 4 10 8 13

(LS-ES) T/ ng gng ? 0 1 0 1 0 6 0 0 C Khng C Khng C Khng C C37

KET QUA XAC NH NG GANG T CPM A-C-E-G-H NG GNGC (t=2)2 4 F (t=3) H (t=2)

A (t=2) Start

E (t=4)

6

End

B (t=3) D (t=4) 3 538

G (t=5)





Th i gian t i thi u hon thnh d n L th i i m s m nh t s ki n cu i cng c a d n x y ra va k t thc. Th i gian t i thi u hon thnh v d trn l 15 tu n. d n ng gng A-C-E-G-H39

PHN TCH K T QU CPM Qua vi c tnh ton thng s s m ng ta c th xc nh c: Th i gian t i thi u hon thnh d n. Th i gian d tr c a cc cng tc. ng gng v cc cng tc gng.40





NGHA C A NG GNG M i s m ng c t nh t m t ng gng. T ng th i gian c a t t c cc cng tc n m trn ng gng chnh l th i gian CAN THIET t i thi u hon thnh d n.41

N u 1 cng tc trn ng gng b tr th th i gian c n thi t hon thnh ton b d n s b tr theo. Do v y mu n rt ng n th i gian hon thnh d n th nh qu n l ph i t p trung cc gi i php lm gi m th i gian cc cng tc trn ng gng.42





i v i cc cng tc khng gng ta c th x d ch th i gian th c hi n nhng v i i u ki n khng c v t qu th i gian d tr tng ng. V i v du trn ta c: Cng tc B c 1 tu n d tr. Cng tc F c 6 tu n d tr.43

MOT DANG TRNH BAY KHAC KHI GIAI XUOI & NGC DONG NG GANG

EF LF A 1 ES LSPGS. TS. Nguy n Th ng

ES LS 2 B C ES LS

EF LF 3 444




Bi t p (CPM): Cho d n c s m ng sau. Xac nh ng gng, th i gian hon thnh d n. C (t=5)A (t=10) Start 2 4 F (t=3) H (t=2)

Bi t p (CPM): Cho d n c s m ng sau. Xac nh ng gng, th i gian hon thnh d n.2 A=5 D=7 5 H=5 I=8 J=8 646

E=6 B=4 4 F=5 3

K=10 7 L=12 M=4 8

D (t=7)

6

End

1B (t=7) 3 E (t=11) 5 G (t=5)

C=6

G=745





PHNG PHAP PERT(Program Evaluation and Review Technique)

V i phng php CPM th i gian hon thnh 1 cng tc c b n l H NG S . Phng php PERT th i gian hon thnh 1 cng tc c b n c nh ngha b i 3 gia tr tng ng v i: - i u ki n lm vi c B T L I - i u ki n lm vi c BNH TH NG - i u ki n lm vi c THU N L I48

9/19/2011

47





CC NH NGHA C B N Th i gian hon thnh 1 cng tc c b n trong pp. PERT c m t bng m t quy lu t xc su t bta v i 3 tham s : a, b, m: Th i gian l c quan a: (Optimistic time): l l2 th i gian hon thnh cng tc ny trong /k thu n l i.49

Th i gian bi quan b: (Pessimistic time): l th i gian hon thnh cng tc trong i u ki n x u nh t (th i gian di nh t). Th i gian bnh th ng m: l th i gian hon thnh cng tc trong i u ki n bnh th ng.

50





NH N XT S khc bi t c b n gi a phng php CPM & phng php PERT: ti (th i gian hon thnh cc cng tc c b n th i) trong CPM l t t nh. ti dng trong PERT l theo quy lu t xc su t (). 51

HAM MAT O XAC SUAT PHAN PHOI BETAp

Phn ph i xc su t btaXc su t x y ra a l 1% Xc su t x y ra b l 1%

Thu n l i aPGS. TS. Nguy n Th ng

Bnh th ng m

B t l i Th i gian hon b thnh52




G i T l th i gian hon thnh d n. V ti l bi n xc su t T l bi n xc su t. PERT gi thi t T tun theo phn ph i chu n N(T0,T) v i T0 th i gian hon thnh d n tnh t CPM &

CC B C TH C HI N C A PHNG PHP PERT

B c 1: Tnh te & e cho t ng cng tc c b n:

te =

=2 T

[ ]2 e i

a + 4m + b e = 6

(b a )26

i

i

cng tc trn

ng gng t

CPM

53

B c 2: Dng te v p d ng phng php CPM xc nh NG GNG Th i gian hon thnh d n T0 theo p/p CPM. 54PGS. TS. Nguy n Th ng




T k t qu phng php CPM C T0 th i gian hon thnh d n. Trn ng gng tnh: 2 V = T = i2i

HAI D NG BI TON C A PERT Lo i 1: n nh tr c th i gian hon thnh d n, TNH XC SU T tng ng Lo i 2: Cho xc su t hon thnh tr c, TNH TH I GIAN c n thi t.


V i i ch cc cng tc trn ng gng.55

56




B c 3:Bi ton lo i 1: Cho Tx , tnh xc su t p:p = Pr(T Tx ) = Pr( = Pr( t a o ) T T0 T Tx T0 ) T

C Tx c a0 tra b ng phn ph i chu n N(0,1) p

with t =

T T0 T

& a0 =

Tx T0 T57 58





CH T tun theo phn ph i N(T0,T) bi n it t tun theo phn ph i chu n N(0,1)

ti =

Ti T0 T

Tnh ch t bi n t Gi tr trung bnh b ng 0. l ch chu n c a t l 1. Bin t KHNG co n v .

g i l php bi n i trung tm v chu n ha bi n T.59 60





B c 3: Bi ton lo i 2: Cho p, tnh Tx:p = Pr(T Tx ) = Pr( = Pr( t a o ) T T0 T Tx T0 ) T

C p

tra b ng N(0,1)

a061

V du: Xet mot d an xay dng gom cac cong viec c ban A, B,.H. Cac thi gian hoan thanh cac cong tac c ban trong cac ieu kien thi cong khac nhau nh trong b ng sau:

Tx = a 0 T + T0PGS. TS. Nguy n Th ng

62


TON KINH T Chng 6: S m ng (PERT)Cng Th i hon thnh cng tc (tu n) Th i gian k v ng hon thnh d vi cn (tu n) Phng sai V

TON KINH T Chng 6: S m ng (PERT)Rng bu c v th t cng vi c nh sau: A Chu n b m t b ng ; B B tr ng thi cng ; C sau A ; D sau B ; E sau C ; F sau C ; G sau D, E ; H Sau F, G.C (t=2) 2 A (t=2) 4 F (t=3) H (t=2) E (t=4) 6

/k thu n /k bnh l i th ng (a) (m) A B C D E F G H 1 2 1 2 1 1 3 1 2 3 2 4 4 2 4 2

/k b t l i (b) 3 4 3 6 7 9 11 3

a + 4m + b 6

b a 6

2

2 GI 3 TR 2 DNG 4 4 TRONG 3 5 CPM 225 tu n

4/36 4/36 4/36 16/36 36/36 64/36 64/36 4/36 63

Start

End

B (t=3) D (t=4) 3PGS. TS. Nguy n Th ng

G (t=5) 564




a. Xc nh ng gng v th i gian hon thnh d n v i phng php CPM. b. Xc nh xc su t d n han thnh trong 16 tu n. c. Xc nh th i gian han thnh d n v i xc su t 90%.65


GI I: a. Dng phng php gi i xui v i kh i hnh s m v l i gi i ng c dng v i k t thc tr trong l thuy t c a phng php CPM Xc nh ng gng v th i gian hon thnh d n v i cc gi tr th i gian k v ng hon thnh cc cng vi c c b n nh trn. PGS. TS. Nguy n Th ng66



Th i gian hon thnh d n: 15 tu n (t CPM). ng gng: A-C-E-G-H (t CPM). b. Xc nh xc su t p% d n han thnh trong 16 tu n. Gi tr phng sai trn ng gng: V = 4/36 + 4/36 + 36/36 + 64/36 + 4/36 = 112/36 =3.11 l ch chu n:PGS. TS. Nguy n Th ng

T = V = 3.11 = 1.76 ( tuan) 67

Thi gian hoan thanh cong viec T tuan theo Phan phoi chuan : N(T0=15, T=1.76) Theo l thuy t c a phng php PERT, th i gian hon thnh d n s tun theo phn ph i chu n c : Gi tr trung bnh l T0=15 tu n l ch chu n T=1.76 tu n.68



TON KINH T Chng 6: S m ng (PERT)p

Th i gian han thnh d n gi thi t tun theo phn ph i chu n. Xc su t hon thnh d n trong 16 tu n c m t nh th sau:

p16 : F=Xc su t T 0.57) = 1 0.2843 = 0.715669


t tun theo phn ph i chu n N(0,1) , dng b ng tra phn ph i 70 chu n N(0,1): p16 =71,56%. (xem b ng tra N(0,1) cu i)PGS. TS. Nguy n Th ng


TON KINH T Chng 6: S m ng (PERT)c. Xc nh th i gian han thnh Tx d n v i xc su t 90%.

K T LU N Xa c su t hon thnh d n ni trn t hn 16 tu n l p=71,56%.

px =0,9: Xc su t th i gian hon thnh d n sau Tx tu n

pPhn ph i chu n N (T0=15,T=1.76)

T0=15

Tx=?

T (tu n)

V i px=0,9 dng b ng tra phn ph i chu n ta c a0=1,28 t :71

Tx = a 0 T + T0 = 17.25 weeksPGS. TS. Nguy n Th ng

72




K t k lu n: xc su t hon thnh d n p=0.9, ta c n th i gian l 17.25 tu n. Ghi ch: Th i gian gon thnh v i xc su t p=50% l T0=15 tu n.

Bai tap (PERT). Gia thiet rang phng sai cua tat ca cong tac c ban trong bai tap trc la V=6. a. Xac nh xac suat e hoan thanh d an toi a trong 2 t/hp: 14 tuan & 17 tuan. b. Tnh thi gian t nhat can co e d an c hoan thanh vi xac suat la 95%. pT(tuan)73


PGS. TS. Nguy n Th ng14

15 tuan

17

74



H ng d np14 = Pr(T 14) = Pr( = Pr( t = 0.34

Bi n t: chu n & trung tm ha

T T0 14 T0 ) T T

Bi t p PERT

14 15 ) = Pr( t 0.408) = Pr( t > 0.408) 2.45 Tnh /x ng hm m t x/su t chu n759/19/2011 76

Xc su t d n hon thnh d i 14 tu n l 0.34PGS. TS. Nguy n Th ng



TON KINH T Chng 6: S m ng (PERT)Cng vic Cng tc i trc Phng sai Th i gian hon thnh trong /k (tu n) Thun li Binh thng Bt li Trung(a)

M t d n c th i gian c tnh hon thnh cc cng tc c b n va s m ng c trnh by sau. a. Dng p/p CPM xc nh ng gng & th i gian hon thnh d n. b. Tm xc su t hon thnh d n t i a l 40 tu n. c. Tnh th i gian t i thi u xc su t hon thnh d n p=95%.77

V=(b-a)2/36

(m)

(b)

A B C D E F G H I J

sau A sau A sau B, C sau B, C sau D, E sau D, E sau H, F Sau G, I

4 3 2 1 2 5 8 5 6 4

5 4 4 2 4 6 10 7 8 5

12 11 6 9 12 13 24 15 16 12

bnh 6 5 4 3 5 7 12 8 9 6

1,78 1,78 0,44 1,78 2,78 1,78 7,11 2,78 2,78 78 1,78





HD: T

SA

LI U C B N2 D 4

S G

M NG SAU

Start

C B 3

E

J H 6End

GIAI XUOI DONG GIA DO NG VI KHI HANH SM (ES) V KH HA NH S

F

I 5799/19/2011 80


T=38 tuan (?)


TON KINH T Chng 6: S m ng (PERT)EF=6 ES=0 Start B (5) EF=5 A (6) C (4) EF=10 3 ES=10 F (7) 2 ES=6 EF=9 4 G (12) D (3) EF=27 EF=15 ES=15 H (8) EF=23 5 6


ES=6

J (6) Final EF=38

E (5)

ES=32

EF=32 I (9) ES=23

TIEP TUC GIAI NGC DONG VI KET THUC TRE (LF) ng gang A-C-E-H-I-J ?

EF=17 Ghi ch: Ti nt 4 c : - cng tc D kt thc sm nht ch sau 9 tun. - cng tc E kt thc sm nht ch sau 15 tun. Do , khi h nh sm nht (ES) ca cng tc G v cng tc H ch c th bt u sau 15 tun. 81PGS. TS. Nguy n Th ng PGS. TS. Nguy n Th ng

82



Phn ph i Chu n N(0,1)

HM PHN PH I CHU N N(, )

p

Hm m t xc su t Di n tch==Pr(X>t)

09/19/2011 83

t

xSAU)84

(XEM B NG TRAPGS. TS. Nguy n Th ng

TON KINH T Chng 6: S m ng (PERT)t0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 0 5000 4602 4207 3821 3446 3085 2743 2420 2119 1841 1587 1357 1151 968 1 4960 4562 4168 3873 3409 3050 2709 2389 2090 1814 1562 1335 1131 951 2 4920 4522 4129 3745 3372 3015 2676 2358 2061 1788 1539 1314 1112 934 3 4880 4483 4090 3707 3336 2981 2643 2327 2033 1762 1515 1292 1093 918 4 4840 4443 4052 3669 3300 2946 2611 2296 2005 1736 1492 1271 1075 901 5 4801 4404 4013 3632 3264 2912 2578 2266 1977 1711 1469 1251 1056 885 6 4761 4364 3974 3594 3228 2877 2546 2236 1949 1685 1446 1230 1038 869 7 4721 4325 3936 3557 3192 2843 2514 2206 1922 1660 1423 1210 1020 853 8 4681 4686 3897 3520 3156 2810 2483 2217 1894 1635 1401 1190 1003 838 9 4641 4247 3859 3483 3121 2776 2451 2148 1867 1611 1379 1170 985 82385

TON KINH T Chng 6: S m ng (PERT)0 1 808 793 668 655 548 537 446 436 359 351 1.9 287 281 2 228 222 2.1 179 174 2.2 139 136 2.3 107 104 2.4 82 80 2.5 62 60 2.6 47 45 2.7 35 34 2.8 26 25 2.9 19 18 3 13 13 PGS. TS. Nguy n Th ng t 1.4 1.5 1.6 1.7 1.8 2 778 643 526 427 344 274 217 170 132 102 78 59 44 33 24 18 13 3 764 630 516 418 366 268 212 166 129 99 75 57 43 32 23 17 12 4 749 618 505 409 329 262 207 162 125 96 73 55 41 31 23 16 12 5 735 606 495 401 322 256 202 158 122 94 71 54 40 30 22 16 11

6721 594 485 392 314

250197 154 119 91 69 52 39 29 21 15 11


t=0.57

= p= 2843/10000

7 708 582 475 384 307 244 192 150 116 89 68 51 38 28 20 15 10

8 694 571 465 375 301 239 188 146 113 87 66 49 37 27 20 14 11

9 681 559 455 367 294 233 183 143 110 84 64 48 36 26 19 14 10

86


H T CHNG

9/19/2011

87

chuong 7-so do mang (cpm & pert)

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