U(3CTINH BUCfNG CONG STRONG OaANDl/CiNGBOTiNHBINHfilNH
Duong Minh Tin Le Hoai Long
ABSTRACT
Forecasting and controlling cash flow is extremely important to the existence of any bidder (Kaka and Price, 1993). And this issue is the concern of most clients as well.
This research presents a technique which is simple and could be ap- plied rapiply to estimate and pre- dict time of payment of transporta- tion project with the S - curve.
Keywords: Project control, S - Curves, Polynomials, Estimates,
Cash flow. Curve fitting
KS Dirorng Minh Tin Bo mon Xay diTng - Khoa Xay difng va Cd hoc uTng dung Trirdng dai hoc Su Pham Ky
Thuat Tp. Ho Chi Minh Di dong: 0977 977 258 Email: tinduongminh(a)gmail.com TS Le Hoai Long Pho chu nhiem nganh Cong nghe va Quan ly xay dirng -
Khoa Ky thuat xay dirng Trirdng dai hoc Bach Khoa Tp.
HdChiMinh Di dong: 0977 596 268 Email: lehoailong(S)hcmut.edu.vn
Du doan d d n g tien va kiem soat nd la edng viee vd cung quan trpng den sU t d n tai cua bat ky nha thau nao (Kaka va Price, 1993). Va van de nay cung dupe cac chu dau t u het sdc chu y. Nghien cdu trinh bay mpt ky thuat dPn gian va nhanh chdng la sd d u n g dUdng eong S de ddc tinh va d d doan viec chi tra thep thdi gian eua t d n g loai d u a n .
Qua trinh nay bao g d m viec t h u thap sd lieu bang p h u o n g phap tiep can trUe tiep bp so lieu thuc tai Ban quan ly cdng trinh giap t h d n g tinh Binh Ojnh dupe tat ca 81 bd sd lieu; tiep theo la qua trinh Ipc SP lieu thep tieu chuan dupc Jarrah (2007) de xuat dUcJc 63 bd sd lieu; qua trinh phan nhdm sd lieu dda vao Ipai cdng viec, hinh thdc hpp d o n g . Cae bd sd lieu lan lUPt dUpc kiem tra lai vdi cac ham so ma cac nghien cdu cua cac tac gia Chao (2009), Skitmpre (1992), Kenly va Wilson (1986), Tucker (1988), Skitmpre (1992) va Miskawi (1989), Bromilow (1974) da de xuat. Ngoai ra, qua viec phan tich nay tac gia da de xuat hieu chinh ham da thdc bae bon ciia Bromilow.
Ket qua m d hinh hdi quy ddpc danh gia sai so MSE (IVIean Square Error), SDY (Standard Deviation about the estimate of Y) chp thay ham Bromilow hieu chinh cho sai sd be nhat.
1 . Gicri thieu
Oudng cong S la m p t do thj mieu ta qua trinh tich luy cua m p t dU an xay d u n g t d luc khdi dau den luc ket thuc dU an. Trong khi dUdng cong S de kiem soat d u an trong qua trinh xay d u n g can ddpc phan tich Udc t i n h dUa tren m p t tien dp cua cae cdng tae, phUPng phap Udc tinh kinh nghiem bang each sd d u n g da dang cac edng thdc toan hpc da va dang phat trien cho ke hoach ban dau d cac giai doan tien thiet ke, cac d u a n t u o n g t U t r o n g qua k h d t h u d n g dugc s d d u n g lam cPsdcua d u bao (Chao, 2009).
Theo Jarrah (2007), trong ke hoach chi tra cho nha thau, m p t chu dau tU can Udc tinh mdt lupng tien de chi tra cho cac nha thau trong t h d i gian sap tdi (thang tdi).
Nang ldc ke hoaeh eho ngan quy va dam bao day du tai ehinh la viec vo eung quan t r p n g . Trong thUe te, cac du an xay dung khdng cd mdt dudng chi tra dOn gian. Nhieu nghien cdu da sddung so lieu cua cac dU an t d qua khd phat trien mo hinh cd the sd dung cho viec Udc tinh ke hoach chi tra trong tuong lai. Md hinh hoi quy la ddi tupng ddpc dng dung rpng rai trong cac nghien cdu dang nay.
Trong nghien cdu nay tac gia sd dung Micrpspft Excel de ve hinh dang ban dau cua dudng cpng S va Ipe sd lieu; sCf dung SPSS de thdng ke, phan loai va kiem tra, danh gia sd lieu; dung Sigma Plot de ve hinh dang eua cac Ipai dudng cpng S theo cac ham sd de xuat t d nhdng nghien cufu trudc; dung Matlab de tinh sai so cua dddng cong hoi quy. Viec dung nhieu cdng cu giup tim ra ket qua nhanh chdng va chinh xac hPn.
Viec phan tich tap trung vap gia tri ehi tra tuong dng vdi thdi gian chi tra, ve cae dddng cong rieng le tdng gdi thau (hpp ddng) khac nhau. Cac gdi thau khdng dat yeu cau tieu chuan se bj loai trd khi tien hanh phan tich.Vi du: viec gdi thau tre tien dp qua nhieu, bat thudng trong dU an se khdng ddpc dda vao phan tich. SU bien doi qua cao cua gia, viee nay dan den viec chuyen hpp ddng hay nguyen nhan do boi thudng, gdi thau nay cung dupe loai bo (Jarrah, 2007).
Cae bd so lieu lan lupt duoc kiem tra lai vdi eac ham sd ma cac nghien cdu cua cac tae gia Skitmore (1992), Chao (2009), Turker (1988), Kenly va Wilson (1986), Bromilow (1974) da de xuat. Ngoai ra, qua viee phan tich nay tac gia da de xuat hieu chinh ham da thdc bac bon cua Bromilow, sau dd kiem tra cae sai sd va mdc dp dang tin cay cua cac tham sd ham sd nay, thay r\6 phu hPp nhat trpng dieu kien cac sd lieu cac gdi thau eua d d an dddng bp tinh Binh B i n h .
2. Tong quan ngliien ciiTu
DU doan d d n g tien chi tra thudng rat quan trpng tai thdi diem dau thau cdng
66,»BSlli:»iBJ» 1 2 . 2 0 1 0
Bang 1: Tpng hpp cac ham eua nghien cdu trudc ve dddng cong S Stt Tac gia
1
Thdi gian Dang ham sd
Bromilow 1974 T = Co + CiP + CjP^ + C3P^ + C4P'*
Kenly va Wilson 1986
ln[y/(l-y)] = a + b{ln[x/(l-x)l}
ho?c y = F/(1+F)
F = y/(l-y) = e»[x/(l-x)]^
Tucker
Skitmore hieu chinh dUa tren ham sd cua Berny-Howes (1982)
1988 y = X + ax' - ax =(6x' - 9x' + 3x) /b 1992 y = [ l +a(l-x)(x-b)]x
Skitmore hieu ehinh dUa tren ham sd
cua Miskawi (1989) 1992 3 sin[(n / 2)(1 - x)]sin(Tix)log[(x + 0.5) / (a + x)] - 2x^ + 3x^
Chao
2009 y = ax' + bx' + (l-a-b)xBang 2; Phan loai sd lUpng cac gdi thau theo loai cdng viee va hinh thdc hpp ddng
TendiTan, g o i t l i a u So lircing goi tliau Loai edng viec 1: D d d n g
Loai edng viee 1, hinh thdc hdp ddng trpn gdi Loai cdng viec 1, hinh thdc dPn gia dieu ehinh Lpai cdng viee 2: Cau (Hdp ddng don gia dieu ehinh 2) Loai cdng viee 3: Thoat nUdc (Hpp ddng trpn gdi 1)
54 46 8 9 2
Bang 3:Tieu chuan Ipc sd lieu DUan, goi thau Tieu chi Bd sd lieu
Bpsd lieu Bp sd lieu Bdsd lieu
Thdi gian chi tra > 120%
Chi phi tich luy chi tra > 120%
Thieu sd lieu 50%
Cd sUcham tien dp r r ang, tri ho n
Ket luan Loai bd hoan toan Loai bd hoan toan Loai bd hoan toan Loai bd hoan toan
trinh nham de Udc tinh kha nang tai ehinh cho d u a n vadieu nay anh hddng den toan bp kha nang thanh toan cua chu dau tU.
Chinh vi the yeu eau can cd mpt ky thuat don g'\in, nhanh chdng ddpc dung de d d doan ddng tien vdi dp ehinh xac tUPng ddi.
(Kaka va Price 1993).
Theo Navon (1996), viec quan ly ddng tien mat va kha nang thanh toan bang tien mat la chia khda, la yeu t d then chdt cho sU sdng cdn cua nha thau. Phuong phap dPn gi^n nhat dupc dung de kiem soat ddng tien mat nay la dung d u d n g cong S (Turan va cpng sU, 2004). Hinh thdc phd bien nhat cua dudng cong S la da thdc bae ba, bdn, nam (Navon, 1996).
Skitmore (1992) da khao sat ddng tien chi tra dudi sU tac ddng eua eac loai cdng trinh khac nhau t d 27 d u an. Ket qua duoc md hinh hai tham sd. M d hinh t h d nhat cho gia trj tham sd tdt nhat cho moi md hinh eho tdng d d an dupc tim ra bdi phuang phap xap xi lien tuc (successive approximation). M d hinh t h d hai la hdi qui
tuyen tinh da bien dupe dung de phan tich va Udc tinh tham sd md hinh qua gia trj, thdi gian va loai dU an. Cudi cung mpt ky thuat phi tuyen dupe dung de tim ra mpt bp cdng cu d u doan tdt nhat eho moi d u an ben ngoai bd sd lieu.
Jarrah (2007) da tong hpp eac d u an cua TxDoT (Phdng giao thdng cua Texas - My) t d nam 2001 den 2003 de phan tich, tao cae m d hinh tai hien ke hoach chi tra hang thang cho cac dU an khac nhau. Md hinh ham da thdc bae bdn dupc de nghi va chay ket qua, ve dddng eong hdi qui, kiem tra dp mdc dp tin cay ciia xac suat, thu dugc dudng cong d d doan viec chi tra.
Cac nghien cdu trUdc day ve S - Curves va nghien cdu ve dang ham sd lien quan den sd lieu ehi phi, thdi gian eho d u a n :
3. Quy trinh de tim dUdng cong S phu help cho d u a n
3.1. Thu thap sd lieu
Sd lieu dUPc thu thap b^ng phUPng phap tiep can true tiep tai lieu eua dU an.
ket qua gdm 81 bd sd lieu la cac gdi thau cua cae d u an dudng bd tinh Binh Ojnh tU nam 2002 den nam 2009. Sd lieu sau khi thu thap dupe xd ly sp bo bang cac Ipc eac thdi diem chi tra, ket qua cd 65 bp sd lieu phu hpp. Sd lieu dupc dUa vao SPSS de tien hanh loc de chia ra lam 5 nhdm: Loai edng viec 1: Dudng; Loai cdng viee 2: Cau; Loai edng viec 3: Thoat nUdc. Trong loai cdng viec 1 chia ra lam 2 loai nhd: hinh thdc hpp ddng trpn gdi va hpp ddng don gia dieu chinh. Vl sd lupng cua loai cdng viee 3:
Thoat nUdc chi ed 2 gdi thau nen tac gia khdng tien hanh phan tich tren loai cdng viec nay.
Cac bien chinh dupe dung trong nghien cdu: Gia hpp ddng (contract amount); Thdi gian (duration);
Sd lieu cua bien chi phi tich luy va thdi gian chi tra dUOc chuan hda va gia tri n5m trong doan [0% 100%]. Bien thdi gian duoe lay tdng thdi diem 10%, 20%, 30%,... 100%, va gia trj cua bien chi phi tich luy chi tra tai cae thdi diem tUpng dng dd, cac gia tri nay
Bang 4: Thdng ke cac gdi thau theo gia trj hpp ddng
Stt Ten du an, goi thau Gia ho-p dong (Ty VND)
Nho nhat 1.093 1.093 2.983 3.400
Ldn nhat 14.149 14.149 13.404 114.890
Trung binh Lech chuan 4.967
4.611 7.014 42.198
3.197 3.030 3.572 49.985
1 Loai edng viec 1: Oudng
2 Lpai cdng viec 1, hinh thdc hop ddng trpn gdi 3 Loai edng viec 1, hinh thdc dPn gia dieu chinh 4 Loai cdng viec 2: Cau (Hpp dong dPn gia dieu chinh)
Bang 5:Thdng ke cae gdi thau theo thdi gian thuc hien chi tra
Stt Ten du an, goi thau Thcri gian thUc hien chi tra (nam)
Nho n 0.167 0.293 0.167 1.356
hat Ldnnl 6.693 2.781 6.693 5.737
hat Trung 1.751 1.403 3.752 3.882
bii -ih Lech chuan 1.367 0.705 2.364 1.418
1 Loai cdng viec 1: Oudng
2 Loai cdng viec 1, hinh thdc hpp dong trpn gdi 3 Loai cdng viee 1, hinh thdc don gia dieu chinh 4 Loai edng viec 2: Cau (Hpp dpng don gia dieu chinh)
Bang 6: Ket qua eiia sai sd cua 63 gdi thau dupe phan tich rieng le vdi cac dang ham sd dUOc phan tich trong nghien cdu:
Ham Chao (2009), Skitmore (1992), Tucker (1988)
Stt
1 2 3 4
Cia trj
Min Max Mean
SD
Chao
MSE 0.00045 0.02517 0.00823 0.00585
(2009)
SDY 0.02120 0.15866 0.08480 0.03249
SI(itmore(1992)
MSE 0.00045 0.23944 0.01315 0.03067
SDY 0.02121 0.48933 0.09502 0.06474
Tucker (1988)
MSE 0.00045 0.04400 0.01391 0.01030
SDY 0.02120 0.20977 0.10936 0.04448
Bang 7: Ket qua cua sai sd cua 63 gdi thau dupe phan tieh rieng le vdi cac dang ham sd dupc phan tich trpng nghien cdu:
Skitmore (1992) va Miskawi (1989), Bromilow (1974), Bromilow hieu chinh
Stt
1 2 3 4
Gia tri
Min Max Mean
SD
SI<itmore(1992) va Mislcawi (1989)
MSE 0.00145 1.85786 0.09225 0.29626
SDY 0.03809 1.36303 0.21870 0.21246
Bromil
MSE 0.00042 0.01791 0.00502 0.00396
low (1974)
SDY 0.02041 0.13382 0.06588 0.02621
Bromilow h
MSE 0.00043 0.01907 0.00515 0.00410
ieu chinh
SDY 0.02080 0.13809 0.06672 0.02669
duac chuan hda ve phan tram.
Cac bien loai cdng viec, vi tri, hinh thdc hpp ddng, thdi gian chi tra ddng tien cho nha thau, gia trj hpp ddng, la cac bien an, dupe dUng de phan loai cac nhdm duan.
Viec ehi tra hien tai ciia Ban quan ly cho cac du an deu dUa theo khdi luong thanh toan ma nha thau lam dUpc va yeu cau nghiem thu de dUPc quyet toan, viec
nay phu thudc rat nhieu vao ke hoach tai chinh ciia ban, ngudn tien eua ngan sach cap ve hay ngudn tien cua Lly ban nhan dan tinh.
3.2. Phdn logi sd lieu
Theo Jarrah (2007) udc tinh dupe xuat phat td gia djnh rang mdt du an cd trung binh 7 diem sd lieu, va cd 7 bd sd lieu de phan tieh tde la cd tdng cdng 49 diem sd
lieu de phan tich. Jarrah thay rang cac dU an ed mdc dp tin cay khac nhau tuy thudc vao tdng nhdm va gia trj hop ddng (tham chi trong cung mpt nhdm) se ed ke hoaeh ehi tra khac nhau phu thudc vao kich thudc cua du an. Jarrah cho rang cac du an Idn cd nhieu tai nguyen, vj tri thue te va sU chi tra da dang hon eac du an nhd. Tae gia sd dung ket qua nay de phan nhdm nhd bo dd lieu. Ngoai ra trong nghien cdu nay tac
68^<^if'W^V 12.2010
0.10000 0.09000 0.08000 0.07000 0.06000 0.05000 0.04000 0.03000 0 0 2 0 0 0 0.01000 0.00000
• Mean
MSE
^ H
1 0.00823
• . . wm
2 3 0.01315 0.01391
^ 1 ^ ^
4 5 0.09225 0.00515
Hinh 1: Bleu do bieu dien Mean MSE cua 63 goi thau theo cac dang ham so: 1 (Chao, 2009);
2 (Skitmore, 1992); 3 (DHSS (1977) va Tucker (1988)); 4 (Skitmore hieu chinh ham so ciia Miskawi (1989), 1992); 5 (Hieu chinh Bromilow).
SDY
0.25000 0.20000 0.15000
0,10000
0.05000 0.00000
Mean 0.08480 0.09502 0.10936 0.21870 0.06672
Hinh 2: Bieu do bieu dien Mean SDY cua 63 goi thau theo cac dang ham so: 1 (Chao, 2009);
2 (Skitmore, 1992); 3 (DHSS (1977) va Tucker (1988)); 4 (Skitmore hieu chinh ham so cua Miskawi (1989), 1992); 5 (Hieu chinh Bromilow).
gici cdn chia nhd bd sd lieu theo thdi gian thUe hien viee ehi tra cua chu dau t u cho nha thau theo de xuat cua Kaka va Price (1993).
Loc sd lieu va tieu chuan loai bd sd lieu:
Oe tien hanh Ipc sd lieu, nghien cdu da ap dung theo tieu chuan lpai trdcua Jarrah (2007) de xuat:
Cae d u an, gdi thau ed nhieu hon 50%
sd lieu bj thieu deu bj loai bd de tranh viec thieu su chae chan cua eac sd lieu khac nhau.
Vdi nghien cdu nay thi cac d u a n dugc tac gia chpn phan lai moi nhdm cd it nhat la 5 gdi thau, moi gdi thau dupe quy ve tong cpng 11 diem ehi tra: t d 0%, 10%,... den 100%, vi vay cd tdng cdng 55 diem sd lieu tren md hinh, dap dng dupe tieu chuan 49 di^m so lieu ma Jarrah (2007) de xuat.
Ket qua phan loai sd lieu (bang 4) Td ket qua cua bang 2: Sd lupng cac gdi thau phan theo nhdm d u vao loai cdng viec trong hpp ddng la Oudng giao thdng, Cau be tdng cdt thep va hinh thdc hpp ddng la hop ddng trpn gdi, hpp ddng don gia dieu chinh cd sU phan nhdm cac gdi thau khdng ddng deu. Gdi thau loai edng viec 1; dudng giao thdng chiem da sd (85.7%) va gdi thau loai cdng viec 2: cau be tdng cdt thep chiem ti le it hon (14.3%).
Cho thay cac cdng trinh giao thdng trong tinh phan nhieu la xay dUng mdi hay nang cap cae tuyen dudng giao thdng da cd nhdng bj hU hdng do thdi gian sd dung, hay dac biet la do Id lut gay ra.
Td bang 4 ta thay gia tri cua cac gdi thau trong d u an dudng cd gia trj trung binh la 4.967 ty ddng, eho thay hau het eac gdi thau dudng giao thdng nay cd
quy m d tuang ddi nhd so vdi eac gdi thau cdng trinh cau be tdng cdt thep. Qua bang so sanh tren ta cung thay rang do quy md nhd nen hau het cae gdi thau dudng giao thdng trong tinh deu sd dung loai hinh thuc hpp ddng la hpp ddng trpn gdi, khi cac gdi thau cd gia trj hpp ddng Idn hpn, chu dau t u se tien hanh ky vdi hinh thdc hpp ddng don gia dieu ehinh. Cdng trinh dudng giao thdng vdi hinh thdc hpp ddng don gia dieu ehinh cd trj trung binh la 7.014 ty ddng, Idn hon so vdi hinh thdc hpp ddng trpn gdi.
Phan tieh ket qua tU bang 5 ta thay thdi gian thUc hien ehi tra eiia ehii dau tU eho nha thau eung dupe phan nhdm theo loai cdng viec va hinh thdc hop ddng. Viee phan tich nay cho thay loai cdng trinh dudng giao thdng, hinh thdc hpp ddng trpn gdi eho thdi gian chi tra trung binh nhd nhat la 1.403 nam (17 thang), dieu nay cung phii hpp vdi ket qua ciia bang 4 la loai cdng trinh nay cung ed trj trung binh gia hpp ddng nhd nhat 4.611 ty. Dua vao ket qua bang 5, thay rang cdng trinh dudng giao thdng vdi hinh thdc hpp ddng dPn gia dieu chinh ed trj trung binh thdi gian chi tra keo dai hpn hinh thdc hpp ddng trpn gdi hon 150%, va dp lech ehuan cd gia trj tuong ddi Idn: 2.364 nam, dieu nay mdt phan do sd lupng gdi thau it (8 gdi thau), cac gdi thau nay nam trong dU an eau dudng Quy Nhon - Nhon Hdi, hau het eac gdi thau dudng giao thdng va cau be tdng cdt thep trong dU an nay dupc ky ket vdi hinh thdc hop ddng dan gia dieu chinh, chi cd cac d u an cay xanh, chieu sang thi dUpc ky ket vdi hinh thdc hpp ddng trpn gdi. Vi khdi lupng cac gdi thau dudng giao thdng trong d u a n ed suchenh lech nen viec chi tra cua chu dau t u c h o cac gdi thau eung tuy thupe vao cae gdi thau.
Hon nda, dU an nay keo dai hon so vdi cac d u an cdng trinh dudng giao thdng vl eac d u an dudng giao thdng trong tinh chu yeu la lam mdi, nang cap, cai tao cua cac tuyen dudng lien huyen, eac tuyen dudng ven bien.
Ket qua nay eung tUPng tU vdi loai cdng trinh eau. Loai cdng trinh eau be tdng edt thep do cd gia tri hpp ddng Idn hon rat nhieu so vdi cac dudng giao thdng (Idn nhat len tdi 114.89 ty ddng), va loai cdng trinh cau cd thdi gian chi tra trung binh Idn nhat 3.882 nam chinh vi the ma hinh thdc hpp ddng don gia dieu ehinh dUpc ap dung de ky ket cac loai hpp ddng nay nham kiem soat viec bien ddng gia trong mdt khoang thdi gian dai thuc hien hpp ddng.
Oe ed the phan tieh sau sac ket qua eua tdng nhdm gdi thau, tae gia da tien hanh phan loai theo gia tri hop ddng ddi vdi tdng loai cdng viee tren. Cae bd sd lieu tren lan lUpt dUpc md hinh, kiem tra dang dudng cong S vdi cac ham sd ma tac
MSE
0.05000 O.OSDOO 0.04000 0.03000 0.02000 0.01000 0 0 0 0 0 0
• LCVl LCV1_HTHD1
• LCV1_HTHD2
• LCV2_HTHD2
•~ •
-MM^
1 •
1 0.03652 0.03862 0.02387 0.02464
•"
• ~ ~
-IH- II
_ B _ ^ L
0.03652 0.03862 0.02387 0.02464
W' m
\ •" II
^ ^
0.03652 0.03862 0.02387 0.02464
rt w
V ' l ^
T i - l l
^MJ^t^
0.04489 0.04767 0.02888 0.02640
H~ M
-fw 1 1
JL^H_
0.03619 0.03849 0.02064 0.02393
0.25000 0.20000 0,15000 0.10000 0,05000 0,00000
• LCVl
• LCV1_HTHD1
• LCV1_HTHD2
• LCV2_HTHD2
11^ I H
J | ^
1 0,19110 0.19652 0.15450 0.15696
SDY
• ' rti
IH^W^
T I H B ^
T l ^ l ^
J L H „ J L H „
2 3 0.19111
0.19653 0.15450 0.15696
0.19111 0.19653 0.15450 0.15696
#h fl_
TW m H"
4 0.21187 0.21834 0.16994 0.16249
fU • •
Tw im^
5 0.19024 0.19618 0.14366 0.15470
so gan n h u bang nhau trpng nhdm (dp chenh lech tUPng ddi nhd).
Dang ham sd ma Miskawi de xuat nam 1989 sau d d dupc Skitmpre hieu ehinh (1992) cd dang thdc phdc tap (dang ham sieu viet) vi the neu sd lupng mau nhd thi viec hoi quy se cho ket qua kem chi'nh xac.
Td ket qua MSE va SDY tinh toan dUOc ta ve bieu do so sanh gida cac ham so d u n g trpng nghien cdu theo tdng nhdm gdi thau (Hinh 3 va 4).Ket qua chp thay ham Brpmilow hieu chinh cho ket qua tdt nhat neu so sanh trong t d n g nhdm gdi thau.
4. Ket luan
Nghien cdu t i m ra dUPc dang phUPng trinh dUdng cong S chp cac nhdm d u an:
d u an eau, d u an dUdng trong do d u an edng trinh d d d n g giao t h d n g cd hai hinh thdc hpp d d n g la hpp d d n g trpn gdi va hpp d d n g dPn gia dieu ehinh.
Tat ca cac gdi thau rieng le, cac nhdm loai cdng trinh d d d n g giao thdng, edng trinh cau be t d n g cdt thep, cae nhdm phan loai theo hinh thdc hpp ddng dupe kiem tra lai vdi eac dang ham sd trong cac nghien cdu trudc day ve dddng eong S:
Ham Chao (2009), Skitmore (1992),Tucker (1988), Skitmore (1992) va Miskawi (1989), Bromilow (1974) va Bromilow hieu ehinh do tac gia de xuat. Va Ket qua m d h i n h hdi quy dugc danh gia bang sai sd MSE, SDY chp thay ham Bromilow hieu chinh cho ket qua sai sd nhd nhat trong cac ham
dupc de nghi. •
g i i Skitmpre (1992), Chao (2009), Turker (1988), Kenly va Wilson (1986), Bromilow (1974) da de xuat trong cac nghien cUu trude day ve dudng eong S. Ngoai ra, qua viec phan tieh nay tae gia da de xuat hieu ehinh ham da thdc bae bdn cua Bromilow ap dung cho bp sd lieu ma tac gia thu thap, phan loai dupe n h u tren.
3.3. Phdn tich hdi quy
Sau khi Ipc sd lieu, phan loai cac bp sd lieu bang Excel, SPSS, tien hanh dung Sigma Plot de ve cac dudng cong S theo cac ham sd ma cac nghien cdu trUde da de nghj, tiep theo tinh sai sd MSE va SDY tren Matlab. Ket qua dupc trinh bay trong bang 6 va 7. Sau khi phan tich, so sanh va danh gia ket qua cua cae md hinh ciia cac ham sd trudc day vdi ham Bromilow hieu chinh ma tac gia dexuat.
Qua viec phan tich t d n g dU an rieng le, tae gia thay rang ket qua MSE, SDY cua ham bac bdn Bromilow cho ket qua nhd nhat (Mean MSE=0.00502, SD MSE
= 0.00396; Mean SDY=0.06588, SD SDY = 0.02621). Tuy nhien he sd CO eua ham bac bdn nay khdng ed y nghia thdng ke vi mdc y nghia gia trj xac suat P ludn Idn hpn 0.5,
trong khi theo Jarrah (2007) de xuat gia trj nay nhd hon hoac bang 0.2) trong 63 gdi thau dem hdi quy. TU d d tac gia de xuat hieu chinh ham Bromilow nay bang each bd di he sd CO khi do ham Bromilow hieu chinh cd dang:
y = CiX + C2X +C3X (10) Khi do ket qu3~phan tieh vdi ham Bromilow hieu ehinh cho ket qua sai sd MSE va SDY be hon cac dang ham cua cac nghien cdu trudc day nhu Chao (2009), Skitmore (1992), Skitmore (1992) va Miskawi (1989), Tucker (1988).Td bieu d d MSE ta thay gia trj MSE thap nhat la eua ham Bromilow hieu chinh: 0.00515; tiep den la Chao (2009):
0.00823; Skitmore (1992): 0.01315; Tucker (1988): 0.01391 va cao nhat la Skitmore (1992) va Miskawi (1989): 0.09225. Oe de dang quan sat, cac gia trj trung binh ciia MSE va SDY eua tdng dang ham sd dupe the hien trong Hinh 1 va 2.
Vdi ham bae ba ciia Chao (2009), Skitmore (1992), Tucker (1988) tac gia thay rang cae ham nay deu cd dang chung la da thdc bac ba, ehi ed khac la each tim eac he sd cua dang ham, vi the trong cac ket qua cua cac nhdm sau, eac ham nay cd sai
TAI LIEU THAM KHAO
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Manage., 135(3), 169-177.
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3. Kaka, A. R, and Price, A. D. F. (1993)."Modeling standard cost commitment curves for contractors' cash flow forecasting." Constr. Manage. Econom., 11(4), 271-283.
4. Banki and Esmaeili (2009), "The Effects of Variability of the Mathematical Equations and Project Categorizations on Forecasting S-Curves at Construction Industry".
International Joumal of Civil Engineering. 7(4), 258-270.
5. Kenley, P., and Wilson, 0. D. (1986). "A construction projects cash flow model - An idiographic approach."
Constr. Manage. Econom., 4(3), 213-232.
6. Miskawi, Z. (1989). "An S-curve equation for projects control." Constr. Manage. Econom., 7(2), 115-124.
7. Navon, R. (1996). "Cash flow forecasting and updating for building projects." Proj. Manage. J., 27(2), 14-23, 8. Peer, S (1982). "Application of cost-flow forecasting model."]. Constr. Div., 108(2), 226-232.
9. Skitmore, M. (1992). "Parameter prediction for cash flow forecasting model."Constr. Manage. Econom., 10(5), 397413.
10. Tucker, S. N. (1988). "A single alternative formula for Department of Health and social Security S-curves."
Constr. Manage. Econom., 6(1), 13-23.
