Giải thuật tabu cho bài toán cần bằng dây chuyển sản xuất một nghiên cứu so sánh kết hợp thay đổi lời giải ban đầu và điều kiện cải thiện lời giải

G\S\ THIEU sd trgm lam viec tai thiel ke day chuyen ,1 Chiing ta bigt rang bai toan can b i n g san xuat vdi san lugng la cao nhat, hay ndi ji, day chuyen san x u l t dugc phan thanh 2

G I A I T H U ^ T T A B U C H O B A I T O A N

C A N B A N G D A Y C H U Y £ N S A N X U A T :

M o t n g h i e n clhi so sanh k e t h o p t h a y doi l e i giai b a n d a n

va dieu Iden cai thien loi giai

ThS Ehr&ng Vo Himg'

TOM TAT

Nghien cuu ndy tap trung vdo viec so sdnh dieu kiin cdi thien cita thugt lodn TABU, dong thai kit hap vdi vi^c ihay doi ldi gidi ban ddu cung cdp cho gidi ihudt Nghien cdu nhdm hodn thien gidi thugt TABU, thudt lodn gdn diing de gidi bdi todn Ion, du^c irng [ dung de gidi bdi todn cdn bdng ddy chuyen sdn xudt, Ket qud cita nghiin cuu ndy cung [ cdp cho cdc nhd qudn ly, nhd ddn tu ldi gidi nhanh chdng vd hiiu qud cho viec thiil ke

\ ddy chuyen sdn xudt theo nhu cdu cho trudc Kit qud nghien ciru duQC kiem chirng v&i

nliirng bdi todn cdn bdng ddy chuyen sdn xudi dd du^c cong bo tren cdc tgp chi quoc

i te vd thong qua chuang trinh cua phdn mem LINGO Ngodi ra, l&i gidi chi tiet cho mot

• tru&ng hap ung dung thuc ti cOng duoc de cap trong nghien cuu ndy

i Tjj khda: thugt loan Tabu, cSn bang day chuyen san xuat

^ ABSTRACT

IS

This research focuses on comparing improvement proces.<!es (first improvement and

X best improvement), and changing initial solution provided Jor Tabu search algorithm,

that is a heuristic method for solving combinatorial opiimizalion problems Moreover, this research attempts to simplify Tabu search algorithm for practical implemenatiion and provides completed solutions for assembly line balancing problems The research solutions wilt offer the excellent a Iter natives for managers and investors in production lines design Jn term": of validity, all re'iu Its are compared with optimal values proposed

by LINGO programs and previous studies A detailed solution of a case study is also presented in this research

'^ Keywords: Tabu search algorithm, assembly line balancing problems

I G\(S\ THIEU sd trgm lam viec) tai thiel ke day chuyen

,1 Chiing ta bigt rang bai toan can b i n g san xuat vdi san lugng la cao nhat, hay ndi

ji, day chuyen san x u l t dugc phan thanh 2 each khac thdi gian chu ky la nho nhat,

dgng (Mastor 1970, Hung 2011) Dgng bai loan nay hrong iing vdi viec tan dimg 1; vdi thcri gian chu ky cho trudc, thiet ke lgi day chuyen cu sao cho hieu qua nhat day chuyen san xual v d i sd trgm lam viec Trong digu ki$n san x u l t ciia Viet N a m

^ la it nhat, bai toan nay l u o n g iing vdi viec hien nay thigt kg mdi hay tgn dung lai day

thiel kg mdi day chuyen; Dgng 2: dya tten chuyen da d i u tu chua lau v a n thyc sir c i n

^ day chuyen san xuat da cd san (biet Uudc thiet cho cac nha quan ly va dau tu Chiing

s

m

ta biit ring, cac doanh nrfiiep san xuJt ciia (1,994); giai thuat gen (genetic) cho Icn gial VietNamthucnigphiinhapdaychuylnsan gan diing cung dtrgc cong bd ben Suresh, xuit ICr mioc ngoai, gia thanh cong nghe la et al., (1995); trongkhi do, Yasunon et J kha cao trong viec dap tog nhu cau san (1994) da de ngh mpt gia phap mm de xult Hon nua khi da diu tu cong nghe giii quyet bii toan Ita bang each ap dung , xuit, thi cong nghe bj l5i thcri cung la giai thuat mang Hopfield Thoi g.an gan mgt vin dg ldn, tgn dung lgi cung la mgt

thach thiic ddi vdi cac nba diiel kg quan

ly va diu tu (Hiing, 2011), deu nay cSn

them niia nhung nghien cuu cho bai toan

can bang da\' chu>'gn san xuat Tuy nhien,

ban chat ciia bai loan can bSiig day chuyen

san xult la kha phirc tap, id hop ldi giai

day, dg giai quyet rang bugc ve thdi gian

va sijx: chua kho bai, rang bugc ca ban ve nang lyc ho trg cho san xult, Baulisia va Pereira (2007) ap dung thanh cdng giai thuat Ant (Ant algorithm) trong n ^ i e n cuu ciia minh

M|ic dil nhigu thuat toan da dugc Idn, ddi hdi md hinh va thuat loan phii hgp ^dng bd va ung dung dd cung cSp ldi giai (Suresh et al 1994, Bautista and Pereira, cho bai toan can bang day chuygn san xuat, 2007,2009 Hiing, 2004, 2011, ) my nhien nhihig giai thugt nay kha phuc

Dg tim ldi giai cho bai toan can bang lap dg hilu, ddi hdi nhihig ky thugl tinh day chu>-6n san xuk, cac nha nghien cuu toan cao cip Do vay, trong khoang 2 thgp

da bli diu thyc hien tir nhirng nam 50 ciia nien trd lai day, tir khi thugl loin TABU tha ky trudc nhu Mastor (1970) Bowman dugc cdng bd (Glover, 1990) v a u n g dun^ (I960), Tuy nhien, dg cd the giai dugc rgng rai cho nhigu ITnh vyc, djc biel ddi bai toin can'bing day chuyan san xuat, vdi bai loan ma igp ldi giai ldn va phuc chiing ta cin nhiiu giai thuit cd thg giai tap, md ra nhiing hudng nghien cim mdi dugc bai loan ldn va cho ldi giai nhanh Giai diuM nay rlt phu hgp vdi bai loan can chdng, dii dg lin cay can thiet Ngay nay,

cd nhigu phuang phap giai da dugc cdng

bd yen cac tap chi quoc te nhu Patterson

va Albrachi (1975) da thanh cdng khi ap

dyng bai loan quy hoach 0-1 uong nghign

cuu ciia minh; Bowman (1960) da denghi

hai md hinh quy hogch nguyen dung cho

bg do lieu xac dinh Ben canh do, quy

hogch dgng ciing la mgt Uong nhCTng

phuang phap dugc cdng bd va ap dyng

thanh cong nhu cdng uinh ciia Held, et al.,

(1963), va Bautista and Pereira (2009)

Tuy nhien md hinh quy hogch dgng ciia

Held, et al., (1963) thi chi ap dung cho

bai toan nhd; Trong khi dd, Bautista and

Pereira (2009) ap dung dugc cho bai loan

ldn dya Uen nen tang Icri giai gan d6ng dg

phan bd cdng viec Ngoai ra nhung giai

Ihugt h i ^ dgi khac cung lan lugt dugc

cdng bd va ap dung nhu ky thugl SA

(Simulated Annealing) dugc nghign cuu

bdi Suresh va Sahu (1994) va Woodruff

bang day chuyen san xuat, nen ngay cang nhieu cdng trinh nghien cuu ling dung lien quan dgn giai thuat dugc cdng bd treo cac tap chi khoa hgc nhu Chiang (1998), Hung (2004 & 2011), Lapien-e el al (2006) va Ozcan va Toklu (2009),

Trong khi dd theo digu kien nghien cuu ciia Viet Nam hien nay, cac nghi«i cuu ve bai loan can bang day chuygn san xual cung nhu cac ung dung thuat toan Tabu rat higm Day cung la mgt ca hgi de lac gia thyc hien nghien cOru nay Trong

n ^ i e n cuu nay, mgt lan niJa giai thuat Tabu dugc utng dung de giii quygt bai loan can bang dSy chuyen san xuat N ^ i e n ciru nay md rgng nghign cuu cua Hiing (2004, 2011) ap dyng cho bai loan dgng 1 va dang

2 bang each so sanh sy thay ddi ldi giai ban dau cung d p cho giai thugt, va chign luge khao sat tap ldi giai (tuong ty nhu Chiang 1998), ddng thdi nghign cim cung

mdi khdng cai thien dugc ldi giai dg tranh

vi^c giai thugt cho ldi giai tdi uu cue bd

Ket qua ciia nghien cuu dugc kiem tra vdi

nhihig ket qua dugc cdng bd uong cac tgp

chi, ddng Oidi giai thuit cflng cung cap ldi

giai chi liet cho mdl iing dung cu thg

2 BAI TOAN CAN BANG DAY

CHUYAN SAN X U A T

Theo Mastor (1970), Hung (2011)

bai toan can bang day chuygn san xual dugc

chia thanh 2 dang, va dugc nghien cuu rai

nhieu uong khoang 1-2 thap nign trudc chiJ yeu tap trung vao bai loan dgng 1 Bai toan dgng I dugc hieu la bai loan thigl kg mdi day chuyen san xuat vdi yeu cau vg san lugng cho trudc Ham muc tieu ciia bai toan 1 (theo Mastor 1970 Bowman

1960, Chiang 1998, Hiing 2 004, ) la tdi tliieu hda sd trgm lam viec hay Min Z = n, vdi n la sd tram lam vi?c Tuy nhien, phan ldn nhfltig nghien cuu ve bai toan I deu dung ham muc tieu tuong duong khac de tiet giam sd trgm lam vide nhu sau:

vdi k^: sd cdng vi?c dugc phan bd

vao tram thii i

Trong khi do, bai toan dang 2 dugc

higu la bai toan tan dung dSy chuyen san

xuat da cd de san xult san pham khac

Trong dieu ki?n cdng nghe thay ddi

nhanh nhu hi^n nay, bai loan dang 2 ft

dugc nghign ciin han Tuy nhien, vdi dieu

ki^n san xuat ciia Vi?t Nam, thi bai toan

dang 2 vin cd nhihig i^g dyng nhlt dinh

(Hiing 2011)

Ham muc tieu cua bai toan nay la tdi thigu hda thdi gian chu ky C (hay tdi

da hda san lugng san xuat trong ciing dan

vi thdi gian), ham mye tieu cd the bieu dien nhu sau: Min Z = C

Tuong ty nhu bai toan dgng 1, ham muc tieu ctia bai loan dgng 2 cung dugc viet lai dudi dgng khac vdi yeu cau dam bao giam thigu thdi gian chu

ky nhu sau;

Min.Z = ^\c~Y.t\ = n.C-Y.Y.(.i (2) Trong do:

C: thdi gian chu ky

k\ so cdng viec dugc phan bd vao

ugm thii i

n: sd tram lam v i ^

t • thdi gian gia cdng cua cdng viecy

phan bd vao iram thd" i

Tucmg ty nhu nhirng nghien cuu

trudc, trong nghien cdu nay, ham muc lieu

su dung da giai quy^ bai toan chii yeu la

cac ham muc Iigu tuong duang (l)va (2)

3 THU^T TOAN TABU CHO BAI

TOAN CAN BANG DAY CHUYEN

Thugt toan Tabu da dugc nghign cim tu thap nign 80, 90 ciia the ky Irudc

va dugc Glover (1990) xay dyng khung hudng dan va iing dung cho nhieu ITnh vyc khac nhau Tuy dugc ung dung cho nhieu llnh vyc khac nhung ung dung trong viec giai quylt bai toan can bang day chuyen san xuat dac bict la bai loan dgng 1 ihi rat thanh cdng nhu Chiang (1998), Hung (2004), Lapierre et al., (2006) va Ozcan

va Toklu (2009),., Ddi vdi bai toan dang

2 thi Hung (2011) cung da nghien ciiu thanh cong md ra huong tan dung lai nhiing day chuygn cu cho digu kien san

Thuat loan Tabu da dugc de cap

trong nhigu nghien cuu da dugc cdng bd,

tuy nhien, nghien cuu na) ciing tdm luge

ngi dung chinh ciia thugl loan Tabu va md

rgng not dung tim hieu ciia nghien ciiu nay

3.1 Ldi giai ban dSu: Chiing ta bigt

ring Tabu la giai thuat can loi giai ban dau,

tir dd giai thuat se lim viing lan can tim ldi

giai ldt hem dg cai thien ldi giai hienco Tuy

nhign, giai thuit Tabu khdng ty xay dyng

liti giai diu tjgn cho minh, do vay, chiing

ta phai cung d p liri ban dau Theo nhiing

nghien cim tnrdc day (Chiang 1998, Himg

2004&2011, ) thudng sii dyng nguyen

tic cdng viec theo sau nhieu nhat, neu cd

nhieu cdng viec thda man nguj'en tac nay

thi chgn cdng vige cd thdi gian gia cdng

dai nhat, trong nghign cihi nay dugc ggi

\ii phuang phdp 1 Ngoai ra dg so sanh va

danh gia, nghien cuu diing each xay dyng

Icri giai dau don gian hon bSng each phan

bd moi cdng viec vao mgt tram lam viec

each niy dugc ggi \i phuong phdp 2 Cach

niy dan gian hoa vice cap ldi giai dau cho

giai thual don gian hda linh loan ciia giai

thugl igo ra ldi ^ai kha thi tryc tiep K.et

qua cua nghien ciiu dugc so sanh va trinh

bay trong phan 5

3.2 B$ nhd: Ddi vdi thuat toan

Tabu bg nhd dung de kiem sodt tdi uu

cue bg cua Idi giai, trong hau het cac

nghien cuu dung mang 2 chigu Tabu dg

kigm soat di chuygn qua lgi cua cac cdng

vifc giiJa cac tram

3.3 Tieu chuan chap nhan thay

ddi: Diy la mdt tieu chuan quan trgng de

chap nhan mdl ldi giai mdi tdt hon Idi

giai tot nhat dang lira trong bg nhd, tigu

chuan nay giup ldi giai dugc cai ihien

lien tyc cho den khi dgt dieu kien dimg

3.4 f>a d^ng hoa tap ldi gi&i: Da dgng hda la mgt phan quan trgng ciia giai thuat trong viec Uanh tdi uu cue bd, bang each chip nhan liri giai tdt nhlt ciia tap ldi giai hien tai (mac dii Idi giai nay cd the khdng tdt hem Icri giai hien lai trong bg nhd) Trong trudng hgp nay giai thuat se

bi lap vi khdng cd ldi giai nao cai thien ldi giai trong bd nhd, chiing ta diJng bd nhd tam thdi nay dg chip nhgn di chuyen nhlm lao lip ldi giai mdi

3.5 Tieu chuan cai thien ldi giai: Tucmg ty nhu nhinig cdng trinh nghien cuu trudc, nghign ciiu nay cung dung 2 hinh ihuc cai thien dd la: i) chip nhgn di chuyen dgn tap Idi giai mdi khi lim dugc

I di giai cai thien diu tien {first improvement

- nguyen tSc 1), nguyen tic nay khdng

tim het tap ldi giai hien tgi; ii) chap nhgn

di chuygn khi loan bg tap ldi giai hien tgi dugc khao sat het va Idi glai cai thien nhat

se dugc chgn dl thay thg ldi giai tdt nhlt

{best improvement-ngnyen tac 2) Cahai

nguygn tic dgu dugc khao sat va so sanh ket qua

3.6 Tieu chuan chdng toi un cue bd: Trong trudng hgp tdp ldi giai hign tgi khdng cho bat ky ldi giai nao tdt hon ldi

giai hien tgi (non-improvement), theo tieu

chuan da dang hda, giai thuat van chap nhan di chuyen va cap nhgt ldi giai hien tai Dieu nay din din ldi giai hien tai sg bj

thay ddi {co the gidm) do dd, nghien cuu

nay cd dung them mdt bg nhd de luu giir ldi giai tdt nhat cho den hien tai Ldi giai nay chi dugc cap nhgt khi gia tri ldi giai dugc chap nhan tdt hem ldi giai tdt nhlt nay Tieu chuan nay cua nghien ciru dam bdo kill dat digu kien thoat, ldi giai tdt nhlt

se dugc dim bao dd la ldi giii dugc xuJt

Baag 4.\ Ket qua nghien cthi theo nguyen tac I

Bai

toan

Bowman

8 cong viec

Hopfield

8 cong viec

Wooden car toy

22 c6ng vi?c

Jaclcson

11 cong viec

Dar-el

11 cong viec

Kenneth - Ramsing

16 cong viec

Thai gian

chu ley

(giay)

20

36

11

7

9

10

13

14

21

48

62

94

27

28

29

30

31

32

33

34

Giatrj ch|n duoi

4

4

5

7

6

5

4

4

3

4

3

2

5

5

5

5

5

5

5

4

Gia tri toi uu

a i N G O )

5

4

S

8

6

5

4

4

3

4

3

2

6

5

5

5

5

5

5

4

Kit P.l

5

4

5

8

6

5

4

4

3

4

3

2

5

5

5

5

s

5

qua P2

5

4

5

8

6

5

4

4

3

4

3

2

5

5

5

5

5

s

5

4

Bai

toan

HofEtnan

9 cdng vi?c

Kilbridge - Wester

12 cdng vice

Author's Case

Thdi gian

chuky

(giay)

14

100

552

Gia ui Gia tri

Chan dudi ^^^^^^^

3

4

5

3

5

N/A

KJt qua

P I j P.2

3 i 3

5

5

5

5

Kilbridge - Wester

45 cong viec

Mitchell

21 cong viec

Tonge

70 cong viec

57

79

92

UO

138

184

14

15

21

25

35

39

176

364

410

468

527

10

7

6

5

4

3

8

7

5

5

3

3

21

11

9

8

7

10

7 1

3

8

8

5

5

3

3

21

11

9

8

7

10

7

6

6

4

3

8

8

5

5

3

3

21

11

10

8

7

10

7

6

6

4

3

8

8

5

5

3

3

21

11

10

8

7

Vdi viec ap dung thugt toan Tabu vdi gia Ui cban dudi (lower bound) cua so cung sy thay ddi digu kien diu cung nhu tram lam viec be nhat, va kgt qua cd dugc

tigu chuin tim va chgn Icri giai tigp theo, iir LINGO Kgl qua cy thg dugc trinh bay

nghien cuu ciing cho nhiing kgt qua nhat Irong cac bang 4.1 va 4.2

dinh Kgt qua cua nghien cuu dugc so sanh

Bang 4.2 Ket qua nghien cvu theo nguyen tac 2

Bai

toan

Bowman

8 cong viec

Hopfield

8 cong viec

Wooden car toy

22 cong viec

Thoi gian

chuky

(giay)

20

Gia tri ch^n dudi

4

Gia tri , KSt qua (LINGO) P I

5 5

36 j 4 4 4

11 5 5 ! 5

7 7 8 ! 8

9 6 6 6

11 congvi^c 13 4 4 4

14 4 4 4

P.2

5

4

5

8

6

5

4

4

Dar-el

11 cong viec

Kenneth - Ramsing

16 cong viec

62

94

27

28

29

30

31

32

33

34

3

2

5

5

5

5

5

5

5

4

3

2

6

5

5

5

5

5

5

4

3

2

5

S

5

5

5

5

5

4

3

2

5

5

5

5

5

5

5

4

Bai

toan

Thdi gian

chuky

(giay)

Hoffitian ,

9 cong viec

Kilbridge-Wester 1

12c6ngvi?c

Author's Case

study 41 cong viec

Kilbridge - Wester

45 cong vi?c

Mitchell

21 cong viec

Tonge

70 cong viec

552

57

79

92

110

138

184

14

15

21

26

35

39

176

364

410

468

Gia tri

c h ^ dudi

3

4

5

10

7

6

5

4

3

8

7

5

5

3

3

21

II

9

8

Giatrj toiuu (LINGO)

3

5 N/A

10

7

6

6

4

3

8

8

5

5

3

3

21

11

9

8

Ketqua P.l

3 P.2

3

:

5 ' 5

5 5

10

7

6

6

4

3

8

8

5

5

3

3

21

11

10

8

10

7

6

6

5

3

8

8

5

5

3

3

21

11

10

8

Ghi chii:

Gia tri tdi uu (LINGO): gia tri tdi uu

cd dugc tCr chuang trinh cua phan mem

LINGO

Gia tri ehan dudi: gia tri nguyen nhd

nhat (ldn han hoac bing tdng thdi glan

cdng viec thanh phin chia cho thdi gian

chu

k>')-P.I va P.2: phuong phap 1 va phuong

phap 2 tuong ung vdi sy thay ddi Idi giai

ban dau

Bt minh hga fligm cho giai thuat,

nghien cuu trinh bay ldi giai chi tiet cua bai toan lirng dung tuong img vdi nguygn tic 1 cho ca 2 phuang phap va dugc the hi?n irong bang 4.3 va 4.4 Bai toan ung dung la quy trinh l i p rap dgng co xe gin may ciia ddng xe Yamaha, trong bjgu dd quan he tien quyet cua 41 cdng doan dugc gidi thieu trong so do 5

Bang 43 Ket qua cong vi^c diryc phan bl chi tiet theo phiromg phap 1

S6 tram Cong viec tirtmg ung vdi tram

1 1 , 2 , 4 , 5 , 6 , 7 , 8 , 12,15, 16, 17,27,28

ThM gian moi tram

552

2 ' 1 1 , 1 8 2 2 , 2 3 2 4 , 3 1 , 3 4 , 3 8 1 552

3

4

5

9, 14.20.21,30,32.33,35.36

3 , 1 0 , 1 3 , 1 9 , 2 5 , 2 6 , 2 9 , 3 7 3 9 , 4 1

40

552

550

100

Bang 4.4 Ket qua cdng vifc duyc phan b l chi tiet tbeo phmmg ph^p 2

1 1

So tr^m Cong vi£c tvomg ^ g voi tr^m Thai gian moi tram

1

2

3

4

5

1 , 2 , 4 5 , 6 7 , 8 , 9 , 1 1 , 12,15,16,27

3,14,17, 18,19,20.21,37,38

23, 24, 25, 28, 29, 30, 31, 32, 33, 34, 35

10, 13.26,36.39,40,41

22

552

535

552

552

115

(cd 2 phuamg phdp cho kit qud luang S KET LUAN VA K I £ N NGHI duong vi sd tram ldm vi$c vd thdi gian pi qua cua nghien cuu c6 Ihl du?c

Bang 5.1 Tom t&t va dinh gia k£t qua

So bai toan kiem tra

So bai toan dat toi uu

Ty le phin tram dat toi uu

Nguyen tac 1 Phuong phap I

39

38

9744 %

Phuong phap 2

39

38 97.44 %

nghien cuu Nguyen tac 2 Phuong phap 1

39

37 94.87 %

Phuong phap 2

39

36

92.31 % Til bang tdm tit, chung ta thay rang

ca 04 nhdm ket qua dgu cho ty' le dgt tdi uu

kha cao trong dd nhdm nguyen lie 2 cd

nhieu han hai trudng hgp khdng dgt tdi uu

(Kilbridge - Wester vdi thdi gian chu Vy la

138 va Tonge vdi thdi gian chu ky la 527;

trong khi nguyen tac 1 chi cd mdt trudng

hgp duy nhat la Tonge vdi thdi gian chu ky

la 410) Tuy nhien, ty le tdi uu tren 90% la

kha cao, va chiing ta cd the thay rang dg

tin egy ciia nguyen tac I ciia nghien ciiu

cao hon Nghien cuu cung dimg nguyen

lac nay dg cung cap liri giai chi tiet cho bai

toan ung dung Uong bang 4.3 va 4,4

Vdi ty le dgt tdi uu cua giai thugt kha

cao, nghign cim cd the cung cap thuat loan

Tabu hoan chinh, hoan toan cd the ung

dung de thiet ke cac day chuyen san xuat

Nghign cuu nay cd the cung cip ldi giai

dO dg tin c^y, va hieu qua can thiet cho

cac nha thiet kg va cac nlia dau tu de giai

quygt bai loan thigt ke day chuyen san xuat, giam chi phf thigt kg, giam gia thanh cac day chuyen mdi Dac bi|t Uong digu kien san xuat cua Vi^t Nam, cac nha dau tu phai nhap nhilu day chuygn san xuSt do dieu kien thiet ke cua chung ta khdng dii

do tin cay va hieu qua

Hi?n giai thugt dugc thyc hi?n vdi gia thiet lal ca cac thdng sd then gian gia cdng la xac dinh dieu nay thudng phu hgp vdi cac thiet bi lip dat cho day chuyen la

tu ddng, thdi gian gia cdng la chinh xac, phil hgp vdi xu hudng gia tang ty ddng hda trong san xuai ciia chiing ta Ket qua cd the sai lech vdi cac day chuyen thii cdng, ban

tu ddng, do vay, nghien cuu nay nen dugc

md rgng dieo hudng su dgng md hinh ma cac thdng sd thdi gian cd the thay ddi

6 M0T.S6 SO £)6 KHOI THAM KHAO CUA GIAI THUAT