Phương pháp điều chỉnh tối ưu giải bài toán tối ưu đa mục tiêu ứng dụng trong kinh tế

VAN DE HOM NAY ( So 1(66) - 2009^

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Phirong phap dieu chinh toi iru giai bai toan

TOI (fU n NUC TIEU iim DUNG TRONG KINH TE

Trong boat ddng kinh te, phdn ldn cdc bai toan

tdi uru md chiing ta thudng gap Id bai toan quy

hoach tuyen tinh. Ci mdi bdi toan ndy chiing ta can

tim cue trj tuyet ddi ciia mdt ham muc tieu ( phdn

anh muc tieu kinh te cdn dat ) tren tap hgp cdc

nghiem khdng dm ciia mdt he cdc rang budc tuyen

tinh. Viec gidi cdc bai todn nay cd the dung cdc

phuong phdp thdng thudng ciia quy hoach tuyen

tinh. Tuy nhien trong thuc tl khi xdy dung cdc

phuong dn san xudt kinh doanh ciia mdt doanh

nghiep (ddc biet ddi vdi cac doanh nghiep Idn )

thudng phdi ddt ra nhieu muc tieu khdc nhau

(chang ban ddm bdo Igi nhuan thu dugc tdi da khi

ban cac sdn phdm, dat tdi da tdng gia trj sdn phdm

sdn xudt ra, dat nang sudt tdi da cac thilt bj, dat

tdng chi phi san xudt thdp nhdt, dam bdo tinh dn

djnh cao nhdt trong sdn xudt kinh doanh). Trong

nhu'ng trudng hgp nhu vay, chiing ta gap bai todn

quy hoach vdi nhieu hdm muc tieu, bieu thj cdc

muc tieu kinh te ma doanh nghiep cho la quan

trgng cdn phdi quan tdm. Neu chiing ta giai tirng

bai toan vdi tiing ham muc tieu rieng biet thi khd

chgn ra dugc mdt Idi gidi dap img dugc tat ca cdc

yeu cdu ddi vdi cdc muc tieu da ddt ra.

Trong nhQng nam gdn day, cdc bdi todn tdi uu

da muc tieu tuyen tinh va phi tuyen da dugc nbilu

tac gid quan tdm nghien ciru vd da dl xudt nbilu

phuang phdp giai khdc nhau img vdi cac Idp bdi

todn rieng biet. Ci ddy chiing ta trinh bay ca sd ly

ludn ciia mdt phuang phdp tdi uu md sau ndy ta ggi

Id phuong phdp dieu chinh tdi uu giai bdi toan tdi

uu da muc tieu irng dung trong kinh tl.

Thir nhat, Md hinh todn hgc

Gid sir cho he hdm muc tieu tuyin tinh:

(2)

TS.Pham Dinh Phung

(I) (p'*'(A') = C<*'A' -^ Max(Min)(k = 'lS)

O ddy vdi mdi ham muc tieu, chiing ta cdn tim cue

trj tuyet ddi ciia nd tren tap hgp cdc rdng huge

tuyen tinh.

• A.\ = B ' ' '•'

.Y > 0

Trong dd ta ky hieu A la ma trdn cap m.n

C'" =(q|,Cj., ,Cj„) la vec ta thir k khdng dm

n chieu, B la vec ta cdt khdng dm m chieu (cung

cd the coi la ma trdn khdng dm cdp m.I)

Gid sir chiing ta ldn lugt giai tat cd s bdi toan

quy hoach tuyen tinh tren ( chdng ban bdng thudt

todn dan hinh), chung ta cd dugc ddy cac diem

cue trj tren da dien loi (2) tao nen tap con toi uu

(S) n = {XI'\X'," Xl,'>} Vdi ndthod

(4) M c K= {X: AX = B\ X>0 }

man

(5a)

Max {<P'*'(^)} = C'"X*' P"> C"X. I«) v""!

X

ih)

0

Hoac (5. b)

Min {p""{X)} ^ CXl" = F"" < CX,

X

Vdi k,h G (1,2, ,sy, k^h "''''-'

Tir md hinh tuyen tinh tren, chiing ta dua ra

djnh nghTa bai toan quy hoach tuyin tinh da muc

tieu:

Tim cue tieu tuyet ddi ciia ham phi tuyin

I I /'

(6.a)G{X) = Max I < * < .v ^"'^\--Jl^:,

62)> Tap chf nghien cdu Tdi chfnh ke'todn