28 TAP CHI KHOA HOC TRUpNG BAI HQC MO TP.HCM - SO 1 (34) 2014
MO HiNH TOAN THIET KE CHUOI CUNG mVG: XEM XET
C 6 N G SUAT VAN HANH CUA CAC DON VI KINH DOANH Ngay nhan bai: 24/09/2013 Budng Vo Hiing' Ngay nhan iai: 21/10/2013 Bid Nguyen HUng' Ngay duyet dSng: 30/12/2013TOM TAT
Trong nghien cuu ndy, chung tdi xdy dung mdhinh thiet ke chuoi cung ung don sdn phdm, theo th&i gian, trong do cdc nhd mdy sdn xudt vd cdc tong kho diroc quyel dinh md hay khdng tgi nhung vi tri lua chon trudc. V&i mdi don vi kinh doanh duoc m& chimg ta se kiem sodt cdng sudt van hdnh. Neu dan vi kinh doanh ndo van hdnh du&i mitc yeu cdu thi dan vi do phdi trd chi phi (chi phi phgt), vd chi phi ndy se ldm gia tdng tong chi ciia hdm muc tieu. Neu nhu cdu cd xu hu&ng gidm hogc thay ddi thi tdng phi se tdng do phi ddu tu vd phi van hdnh tdng. Thdng tin ndy se giup cdc nhd ddu tu vd nhd qudn ly ddnh gid hieu qud vdn hdnh cua chudi cung img cita ho hogc cd the xem xet chinh sdch thue ngodi. Md hinh duac xdy dung theo bdi todn quy hogch nguyen hdn hop, Irong do hdm muc tieu Id cue tieu tdng phi bao gdm phi van chuyen, phi tdn kho, phi ddu tu cdc dem vi kinh doanh vd chi phi van hdnh du&i muc van hdnh cho phep. Dua tren cdu true cua md hinh, chiing toi phdi dua them mot sd rdng buoc phu truac khi dp dung gidi thugt Lagrange de gidi. Ket qud tinh todn vd gidi thudt cug de nghi cua md hinh duac so sdnh vai loi gidi tdi uu tie phan mim LINGO.
Ttr khda: chudi cung ung, cdng suit van hanh, quy hoach nguyen hdn hpp, giai thuat Lagrange, thiet kl mang.
ABSTRACT
In Ihis paper, we deal with a single-item, multi-period capgcitatedfacility location problemwheremanufacturingplantsanddistributioncentersaredecidedtobeopenedor not at the pre-determined potential sites. At each opened facility, we control operational level. If the opened facility operates at a lower minimum requirement volume then penalty cost will occur and add to objective value. If the demand is decreased or fiuctuated then the total cost is increased because of opened facilities and operational costs This information helps the investors and managers to evaluate performance of their SC network system or use outsourcing facilities. The problem isformulgted gs a mixed integer linear programming (MLP) model with the objective is to minimize the total cost, including transportation cost, inventory holding cost, fixed costs for opening facilities, and penalty costs. Based on the specific structure of the developed model, we need one additional constraint set before using Lagrange relaxation algorithm lor solving tlie problem. Numerical experiments are then conducted to compare the solution ofthe proposed approach as opposing to the optimal solution obtained by the commercial Lingo solver
Keywords: supply cham, operational capacity, mixed integer linear programming, Lagrange relaxation, network design.
• Tnrang Dai hoc Bach Khoa Dai har: Qude Gia TP.HCM.
29
1. Gidl THIEU
Trong hoat dong kinh doanh hien dai.
chiing ta biet rang chuoi cung ung tich hgp va ket noi tat ca cac chuc nang kinh doanh trong doanh nghiep nhu cung ung, nguyen vat lieu, ke hoach san xuat. san xuat san pham, van chuyen va ban hang (Chan va cong s\r, 2003, va Stadtler, 2005). Bihu nay nhan manh vai tro cua chuoi cung ung trong cac hoat dpng kinh doanh. Trong thi truong canh tranh loan cau ngay nay, nhiing nha dau tu va nha quan ty co nhieu quan tam den chuoi cung iing ciia hp (Simchi- Levi va cpng su, 2000, Blackhurst va cpng su, 2005). Do do, van hanh chu6i cung iing dong vai tro xo cimg quan trong trong hoat dpng kinh doanh. Theo Chan va Qi (2003), xay dung chu6i cung iing ho^t dong hieu qua la moi quan tam cua cac nha quan ly va cac nha dau tu, do vay, bai loan lien quan den Iinh vuc nay ngay cang pho bien.
Tuy nhien, do tich hap cac thanh phan va chiic nang van hanh Iam cho chuoi cung ling tra nen phiic tap, vi vay, nghien ciiu ve luih vuc nay hien nay van con gia tri va hap d§n cac nha nghien ciiu va dku tu.
Mac du vay. theo Lan va cpng su (2013) thi nghien ciiu v^ linh vuc nay a Viet Nam ciong con nhieu han che.
De ho tra cho chudi cung ung trong cac hoat dpng va nhiing chien lupc dai han mpt each hieu qua. bai loan thiel ke chuoi cung ling phai duoc quan tam nghien ciiu lien quan den cac bai toan thuc te, dac biet dfii vai loan lira chon va phan bo nguon luc khi xay dimg chuoi cung iing. Mpt trong nhiing cong trinh tien phong doi voi bai loan lua chpn va phan bo nguon luc duoc Geoffrion va Graves cdng bo vao nam 1974. Trong nghien ciiu ciia minh, Geoffrion \'a Graves da thanh eong vai mo hinh quy hoach nguyen hon hgp de thiet kd mang luai p h ^ phoi cho bai toan da san ph3m, umg vai timg thai doan. Ham muc tieu cua nghidn ciiu nay la cue tieu hoa long chi phi ciia he thdng bao gdm phi van chuyen, phi diu tu cac tdng kho. Giai thuat Benders decomposition duac dung
de giai qu)et md hinh toan va cung cap loi giai. Tiep tuc vai quan diem nghien ciiu nay, Pirkul va Jayai^aman (1998), Mazzota vaNeebe (1999) ciing nghien ciiu bai loan thiet ke cho mang cung iing da san pham, tin^ thai doan, tuy nhien, nhung nghien Cliu nay dung giai thuat Lagrange de giai.
trong do, bai loan gdc dugc phan thanh n bai loan nhd iing vai mdi tdng tcho va nha may bang each bo di mpt sd bp rang budc.
Trong quan ly va van hanh chudi cung ling hien dai, nhiing nha quan ly, nha dau tu, va nhung nha nghien cuu ludn phai ddi dku vdi nhiing bai loan thuc te. Hien nay co rat nhieu md hinh toan dupc cdng bd nham dap ling nhiing yeu cau thuc te. Nhieu nha ngtiien ciiu tap trung vao giai quyet cac bai toan thue te. Dien hinh nhu nghien ciiu cua Melachrinoudis va Min (2007), cac tac gia da xay dung md hinh tai cau tnic mang luoi phan phdi bang each xem xet thdng sd thdi gian phan phdi nhu la mgt yeu td chinh trong viec ra quyet djnh. Ket qua ciia md hinh cho phep ddng mdt sd tdng kho hien hiiu nhung kem hi$u qua, ddng thai ciing cho phep md mdt sd tdng kho mdi Idii can thiet. Tuang tu nhu vay, nhieu van dd cu thd trong ITnh vuc chudi cung iing da dupc nghidn ciiu nhu: Rezaei va Davoodi (2008) xem xet ly le phan tram phd p h ^ nhu la mdt ydu Id mdi trong md tiinh, hoac Bitgen va Ozkarahan (2007) phat tridn md hinh quy ho^ch nguyen hdn hap cho bai loan san xuat san pham ngii cdc va bai loan van chuydn hang hda vai sd tupng tdn. Gan day, Dondo va cdng su (2011) cue lieu hda ldng ctii phi van chuyen b5ng each xem xet bai loan ve dudng di theo cross-docking trong nghien ciiu cua minh.
Lee va cdng su (2010) ciing xem xet quydt dinh ve Id trinh trong md hinh quy hoach nguyen hon hgp ddi vdfi bai loan phan bd cac don vj kinh doanh. md hinh nay r4t huu ich vdi cac dan vi kinh doanh la ddi tac thii ba trong hoat ddng logistics (third party logistics - 3PL). Ben canh dd, mot hudrng nghien ciiu khae ciing thuc dung, giai quyet nhiing tinh hudng thuc te nhu
TAP CHi KHOA HQC TRUONG DAI HOC M 6 TP.HCM-SO 1(34)2014 Eksioglu va cdng sy (2006) xera xet miic
tdn kho cung nhu chi phi tdn kho trong van hanh tai cudi mdi thdi doan ttong md hinh thi6t ke chudi cung ung. Hinojosa va cdng sy (2000, 2008) cfing xay dung md hinh quy hoach nguyen hdn hpp cho bai toan thiet ke mang cung ling cho bai toan da san phim, nhiju giai doan, va cac miic tdn kho tai mdi thdi doan. Them mdt ySu td thyc ti nhu dSc tinh chSt lupng san pham dupc xet dJn ttong nghien ciiu cfia Das (2011), md hinh nay cung cap mdt thu tuc can thiet ttong quy trinh giam sat chit luang. Ngoai ra, miic cdng suat cfia don vi kinh doanh khi dau tu cfing la yeu td thyc te khi xem xet thanh lap chudi cung ling. Dilu nay dupc th6 hien trong nghien ciiu cfia Amiri (2006), nghien ciiu nay thanh cdng ttong viec xay dyng md hinh quy hoach nguyen hdn hpp, ttong dd ddi vdi mot dan vi kinh doanh dupc xem xet vdi nhieu miic cdng suat khac nhau, nhung md hinh nay chi xem xet chpn mdt miic de d£iu tu khi don vi kinh doanh dd dupc xem xet thanh lap ttong h$ thdng.
Theo nhung phan tich va nhan dinh nhu tten, chung ta biet rang hien nay nhilu yeu td thyc te da dupc xem xet khi xay dyng md hinh nhu nhieu thdi doan, miic tdn kho cfia cac don vi kinh doanh khi van hanh t^i mdi thdi doan, thdi gian giao hang, lp trinh giao hang, d}c tinh chit lupng, cung nhu thdi gian xem xet md cac don vj kinh doanh tai thdi diim thich hpp,...
tuy theo nhiing bai toan cu thi. Trong thyc te, chiing ta thiy ring, cac nha diu tu va cac nha quan ly cd ging kiSm soat miic van hanh taimdi don vi kmh doanh dang v|n hanh. NSu mdt don vj kinh doanh van hJnh dudi miic van hanh yeu ciu thi he thdng se kem hieu qua. Vdi nhiing dang nhu cau giam, nhung md hinh da cdng bd thi nhihig don vj kinh doanh sS dupc md ngay tii dau, nhu vay. khi nhu ciu giam nhQng don vi kmh doanh nay se kem hieu qua. Diju nay se lam ling phi diu tu va v|n hinh. Do do, nghien ciiu nay s5 nhan dien va giai quylt van dl nay, dem lai hi$u qua kinh doanh cho cac nha diu tu.
Trong nghien ciiu nay, chfing t d i x ^ dung md hinh toan quy hoach nguyen hdn hop cho bai toan thiet kl cbudi cung ting, ttong dd mdt sd yeu td thyc te van hanh se dupc xem xet de md hinh thyc t l han. Md hinh giup ho ttp cho cac nha quan ly va diu tu ra quyet djnh frong viec: (1) Dan vi kinh doanh nao nen dupc md trong nhimg dja dilm tilm nang xac djnh trudc; (2) tai mdi thdi diem van hanh, mdt dan vj kinh doanh da dupc md, he thdng se kiem soat don vi kinh doanh nay van hanh hieu qua hay khdng. Ham muc tieu cua md hinh cyc tieu hda tdng chi phi, ttong do bao gdm chi phi van chuyen, phi tdn kho, phi dSu tu cac dan vi kmh doanh, chi phi phat neu dan vj kinh doanh nao van hanh dudi miic yeu cau. Chfing ta de nhan thay dilu nay khi dang nhu cau giam theo thdi gian, khi dd chi phi van hanh va chi phi dau tu se gia tang. Md hinh nay se gifip cac nha diu tu va quan ly nhan dien vin dl nay va cd the dua ra quyet djnh hpp ly, hieu qua ve mat kinh te, ttong mdt sd trudng hpp thus ngoai cd the la mpt giai phap giup giam chi phi diu hi cho cac dan vj kinh doanh ttong he thdng. Dilu nay lam cho md hinh chung tdi khac biet so vdi nhihig md hinh da dupc cdng bd nhu Hinojosa va cpng sy (2000,2008), Eksioglu va cdng sy (2006), Amiri, (2006), ... Dl cd dupc Idi giai nhanh chdng va hieu qua chung tdi sii dung thuat toan Lagrangian, thuat toan nay dya tten viec tiet giam cac rang budc de cd the phan md hinh ban diu thanh 2 bai toan nhd va chung ta cd thi giai mdt each dl dang, tu kit qua cfia cac bai toan nhd chfing ta cfing dl dang cd dupe Idi giai cho bai to4n ban diu dya tren giai thuat dl nghj.
2. MO HINH TOAN
De thuan tien hem ttong viec xay dyng md hinh va giai thuat nhung phin tiep theo trong nghien ciiu nay, chung tdi su dung nhung nhiing bd biln, tham so va chi sd nhy sau:
2.1. Nhom cac chi sd:
KINHTE 31
/ tap chi sd cac nha may san xual liem nang J = 1,2,..,/
j tap ctii sd cac tdng kho tiem nang j = \.2,...J
r tap chi sd cac dai ly r = \.2,...R ft tap chisd cac san pham k = \,2...,K / t a p c h i s d thdi doan / = t.2....7"
2.2. N h o m cac t h a m sd:
T thdi gian van hanh (thd hien true thai gian)
/ djnh phi khi m d nha may thii / trong he thdng
/ ' " dinh phi m d tdng kho j trong h^ thdng
c,j^ chi phi van chuyen 1 don vi san p h i m k tii nha may / ddn ldng kho j trong mdt thdi doan
cj^ chi phi van chuyen 1 don vi san pham k tir tdng Ithoy den dai ly r trong mdt thdi doan
p,^ ctii phi san xuat dan vj ciia san pham k tai nha may /
ft,^ chi phi tdn trii don vj ciia san pham k tai nha may / trong mpt thdi doan /i]i' chi phi tdn trii dan vj ciia san pham k tai tdng kho j trong mdt thdi doan h'^^ chi phi tdn trii d a n vj cua san pham k tai dai ly r trong mdt thdi doan
d^ nhu cau san pham k ddi vdi dai ly r tai thdi diem t
w,^ miic cdng suat van hanh ciia san pham k tai nh^ may /
wJJ' miic cdng suit van hanh (siic chiia) cua san pham k tai tdng kho j
2.3. N h o m cac b i l n quyet d i n h : X,j^, tdng san p h i m k chuyen t u nha ma>' / den tdng kho j trong thdi doan t
T,^ tdng san pham k chuyen t u tdng kho j den dai ly r trong thdi doan /
Z„ bidn [ 0 , 1 ] (binary) the hien hoac nha may / v ^ hanh tai thdi diem t hoac khdng
Zj," bidn [0, 1] the hien hoac tdng kho j van hanh tai thai diem / hoac khdng V^i^ tdng san tugng san p h ^ k san xuat tai nha may / trong thdi d o ^ /
Q,^, tdng san tupng san pham k tdn Idio tai nha may / trong thdi doan /
Q^|^, tong san lugng san pham k tdn kho tai tdng kho j trong thdi doan /
^)^' tdng san luong san pham k tdn kho tai dai ly r trong thdi do£in t
Trong ngtiien ciiu nay, md hinh loan cho bai loan thiet ke he thdng chudi cung ling dua h-en mgt sd gia thilt nhu sau:
i) Neu mdt nha may hoac tdng kho tchi dupc m d tai thdi didm nao dd thi nd se khdng bj ddng sau do;
ii) Tat ca cac loai cht phi ap dung cho md tiinh deu dupc xac djnh trudc, nghia la chi phi m d nha may hoac tdng kho, chi phi san x u l t d a n vi, chi phi bao quan va chi phi phat sinh deu dugc khao sal va bidt trudc;
iii) Tat ca cac mtic ton Idio ban d i u tai cac dan vi kinh doanh (nha may, tdng kho va d^i Iy) deu bang khdng;
iv) Siic chiia hang hoa tai cac dai ly dii tdn de cd thd dap iing cac d a n h ^ g (nhu cau).
Dua tren cac gia thiel, cac chi sd, cac tham sd ciing nhu cac bien quyet djnh, md hmh toan chi tidt dupc xay dung va trinh bay nhu sau:
32 TAP CHI KHOA HOC TRL/ONG DAI HOC M 6 TP.HCM - SO 1 (34) 2014 Ham muc lieu:
' • I M I=\ -=l ' - I . - I .=1 <=l J=\ <=\ r=1 ,=l
Cdc rang buoc:
Ql'U+T^jtt^dr, "^reR.VteT. ...
V„<wpl,N„+.MU„ V ; g / , V r € r , (3a) V„>wp2,N„ Viel.VteT,
V„ < wp2,U„ + SD:,, Vt eI,Vl€T,
Y.^,„^K*Q,.-„ Visl.yieT,
T.^,,, +0'!.',.,, < wd\,Z',',' VjeJ.Visr,
Z»;»s2;jr„+e;;;_„ VJSJ,\/IET.
2 > - „ < M'rfl,N'/,' + AA"," Vy E y, Vr e T.
'Zy,„i:wd2^N<;,' VJeJ.yteT,
H
Y.y„ <wd2^U';,'*MN';< VjsJ,VteT,
Sa'= 'ty,„+Q';,l„-d„ VrsR,'VtsT,
a = K +S„_„ - 2 ; X „ V/e /. V^ e T,
(3b) (3c)
(4)
(5)
(6)
(7a)
(Vb)
(7c)
(8)
(9)
a"=i;-^,+o;;;-..-i;j'„ vye/,vrer,
2„SZ,„_,, V / € / . V r e r .
•V,+t/„=Z„ V / e / . V r e ? - .
^»"-2;i.'-i, y / € j , V r s r . -V;,"-i-£/;," = Z;;' VjeJ.VieT,
^„-K.Q.iO Viel.VjeJ.yieT, '•,.-O;,".O;,">0 yjsJ,VrsR,yii,T,
^..••V,L„=O.I ViBl.VleT,
^ ; " . n " - C ' ; . " = 0 . 1 VjeJ.MieT ^"'' (18)
(10) (11) (12) (13) (14) (15) (16)
Trong md hinh trinh bay d tren, ham muc lieu (1) la cue tieu hda tdng chi phi van hanh trong dd bao gom tdng chi phi van chuyen tii nha may ddn tdng kho; tu tdng kho ddn dai ly; tdng dinh phi tdii md nha may; tdng djnh phi dd md tdng kho;
tdng chi phi san xuat tai cac nha may duac md; va tdng chi phi bao quan hang hoa tai cac nha may; tdng kho va dai ty.
Cac t « rang budc duac didn giai nhu sau:
+ bd rang budc (2) dam bao nhu clu san ph&n tudn duac dap iing tir cac dai iy tuong ling,
+ bd rang budc (3) thd hien rang budc vd cdng suit van hanh tuong iing vdi tung loai san pham eiia nhiing nha may ktii duoc md,
+ bp rang bugc (4) dam bao long san Iupng hang hda chuyen di tii nha may den cac tdng kho Ididng dugc vupt qua tdng san luang san pham dang cd tai nha may do (not exceed the on-hand inventory),
+ bd rang huge (5) dam bao tdng san lupng hang hda luu trii tai tdng kho tdidng duac vupt qua miic cdng suat tdi da cua tdng kho do tai bit ky thdi diem nao,
+ bd rang budc (6) dam bao tdng san luong hang hoa chuyen di tii tdng Idio den cac dai ty tdidng dupe vuot qua tdng san pham dang cd tai tdng kho do,
+ bd rang budc (7), (8), va (9) ta nhung rang budc ve can bang ciia ddng san pham den va di lai dai ly, tdng kho va nha may,
+ bd rang budc (10), va (11) dam bao ring nhung nha may hoac tdng kho khi da duoc md thi se khdng bi ddng sau dd,
+ cact>d rang budc cdn tai (12), (13), (14), (15) la nhiing bd rang budc ve bien ciia bai toan quy hoach tuyen tinh.
Th^t ra, ddi vdi bai toan ban dau da trinh bay d tren dang tdn tai mdt sd bd rang budc long (redundant constraints), nhimg rang budc nay phai dupc loai khdi md hinh de giai thuat nhanh va tiieu qua.
Xet bd rang budc (8), (9), va (10) thd hien ham cSn bang miic tdn tdio tai dai ly.
nha may va tdng kho tuang iing:
Qir='Z^jr,-^QllL^-d. ^reR,VteT,
2,=P^,+e,„_„-J]Xy, \fieI,\/tsT. va Q'" = i ^,, + eJIL, - i y,„ vy eJ,Vte T,
(-1 r . l
Nhimg phuang ttinh nay cd the dupc viet lai nhu sau:
t,y,r,+Q'r;!-,,-Q'n'=d„ V r £ 5 , W g T , J=l
S'f,,=^;,-^a„-„-e„ v/g/.v/gr, va
'Lj,r,='t^,„ + e ; | l „ - e i " vyeJ,VteT,
Chung ta biet ring 2n',8„,S„ la nhung gia tti duong, va nhu vay, nhiing phuang ttinh nay dupc vilt lai dudi dang bat phuang ttinh nhu sau:
Q»!-»+'ty,n^'l„ VrsR,Vt,ET,
'Zx,^,<V„+Q,^,_„ \/isI,\/tsT, va
y=i
(-=] ,=1
Nhiing bat phuang ttinh nay chinh la nhiing bp rang budc (2), (4), va (6) tucmg ling. Do vay, bd rang budc (2), (4), va (6) frd thanh bd rang budc Idng, va duac loai bd khdi md hinh ban diu. Dilu nay lam cho md hinh ban dau trd nen dan gian hem, va hoan toan cd thi ap dung giai thuat Lagrange de xac dinh Idi giai dac biet cho cac bai toan ldn, va dupc de cap trong phin tiep theo ttong nghien ciiu nay.
3. GIAI THUAT LAGRANGE CHO MO HINH
Chung ta bilt rang md hinh nay la dang bai toan quy hoach nguyen hdn hpp.
va mat nhilu thdi gian de tim Idi giai, dac
mar
TAP CHi KHOA HOC TI^UONG DAI HOC M 6 TP.HCM - SO 1 (34) 2014 biet ddi vdi nhung bai toan Idn. Do dd, Trudc khi ap dung giai thuat Lagrange giai thuat Lagrange se dupc sii dung ttong md hinh ttong nghien ciiu nay se duac thay nghien ciiu nay de xac dinh ldi giai. Chung ddi de dl dang xac dinh ldi giai hon ta hoan toan cd thi tham khao them vl p „ ^ , tig„ .^fing ta xem xet bd rang giaiUiuat nay ttong nghien cm. cua Fisher budc (10), nhusau: ' ^ (1981).
Q'"=t^,,^0%-tKn ^jeJ.VtsT,
Luu y rang ^Ji' = 0, va nhu vay, bd rang budc (10) cd thi dupc vilt lai nhu sau:
0^'Q>p. -ty,r. ^ p, -p,,,^±x„,-p„, 'ti^-iiKrr
Mpt each tdng quat ta dupc,
^"'tp„-tpr, yj^J,V,sT, (19)
Chitag ta thiy ring bp rang budc (19) dam bao ring tai mdi tdng kho / miic tdn san xuat ttu cho tong san pham tich luy phan phdi tu tdng kho / dindaily " " " ^ " " ^
Tu phuong ttinh (19), chung ta cfing cd them:
P"--t[tp..'tp„] ^J.J
Vay.
P"-p.~p.,
P'^P&^^^-tp.]
36
p"'=t[ip,r-±iy,rr)
Mpt each tdng quat ta dupe,
tQ'>t(T-'^i){tx.,-h,n] •^J^J (20)
'=1 '=1 V,.=! r-1 J
Dung phuang trinh (20), thanh phan chi phi lien quan den tdng phi tdn trii tai tdng trong tdng chi phi cd the dupc diln la nhu sau:
thr&:.'=ti'Tt(T->^dtx,,-ty\
; . l - I / . I . . 1 1^ ,.1 ™i )
=ttpT-'*m'x,-tth-r-'^^)>'Ty,r. (21)
Chiing ta lim y ring bd rang bupe (5) cd the dupc vigt Iai thdng qua bifiu thiic (19) sau:
p„*&;i-. —rfi.z;,"=t^„ - wi,z;' *{tp,r -tpr.)
±p,,-wdl,Z'«-±Z
(22)
Dya tten nhimg phan tich tten day, rang budc (10) se dupc loai bd trudc khi ap chiing ta nhan thay ring, bp rang budc dung giai thuat Lagrange.
(10) cd thi dupc chuyin ddi thanh phuang QQ ^jy_ ^hi su dung bd nhan tu ttmh (19). Them vao do, chung ta su dung Lagrange X cho bd rang budc (5), ham phuang frinh nay cho phuang ttinh (21) ^^^ jieu cfia md hhih se duac vilt lai dudi va (22), bd phuang ttinh nay da dupc thay j ^ g ^ ^ ,^, Lagrange (L) 'nhu sau:
the ttong ham muc tieu ban dau. Do dd. bp
4pP'^' 4P'''"'' -^IIs^' 4P& ^tpT-'^iWX,
-ttpT-'*^Ky.4peQi''4p,[tp.,,-wdi,z^^<-f^^^^
>ZQ 1 (Mmp:
TAP CHI KHOA HOC TRUONG DAI HQC M 6 TP.HCM-S6 1 (34) 2014
I I
IT f ¥ i-\ \ J t ^ f S.. \
(23) Ba toan (i) cd thi dl dang dupc phin lach thanh 2 bai toan nhd ( i / ) va (i2) nhu sau;
Bai toan i ( i / ) : -,
M«z„=itik•^i/-,-^(^-<+l)'.;"k
..1 M r.l L — -I
*tt.f{z-z,.-.ytpp.v.4P'''-4P'^'
Cac rang budc (3a, 3b, 3c), (9), (11), (12), (15), va (17).
Bai toan 2 (12):
W'"Z,,=gi[c;r-iA,-(7--.+i)*;']i',„-ii;^.,,wrfi,z;;'
^ltf:{zi-rt,).ticdp';;*itK"Q'r;'
(24)
Cac rang budc (7a, 7b, 7c), (8), (13), ham muc tieu ban diu cd the dupe xac (14) (16) va (18) dinh thdng qua ldi giai cfia 2 bm toan (Ll) ' Vdi'viec chpn gia ttj cua nhan tu ™ C^^) • * " ^^" Z = Zl + 22, ttong dd:
Lagrange X,, chung ta thiy rang gia tri cua
z\'ppc,HT-,^i)h';qx,,4p{z,,-z,,,_,,y±pp,u,,4p,v.4p.Q.
224tp--{T-.i.i)h';%.tp:^z[:,'-z::_,yit^^
Do \'a\. gia trj ciia ham muc tieu ban diu dupc chap nhan khi va chi khi chung la cd dupc ldi giai kha thi eua 2 bai loan nhd. Tuy nhien, vdi cau tnic ciia 2 bai toan nhd thi tdi giai ktia ttii tdidng duoc dam bao, dieu nay se dupc de cap d phan liep theo.
Xem xet bai loan 1 (Ll), chiing ta dd dang nhan thay khdng cd bd rang budc nao dam bao cho bd bien Z^ nhan gia tri duong.
Dieu na>' dan den tit ca cac gia trj cua bp bien Z^^ se bang khdng (zeros) Idii bai toan
1 dupc giai. Khi dd tat ca cac bd bien cdn lai deu bang khdng, va nhu vay, gia trj ham muc tieu ludn ludn bang khdng. De ddi phd vdi van de nay, ddi vdi bai toan 1 yeu cau cd them nhung bd rang huge mdi de dam bao bai loan I ludn ludn kha thi.
Bd rang bugc nay dupc xac djnh nhu sau:
Bd rang budc them:
tit^.i.>-ti''r. ^'^T,
(25) Bd rang budc nay se dupc them vao
37 bd rang budc trong bai loan 1 (LI), vdi
rang budc nay dam bao ring, tai bit ky thdi diem t iiao. tdng san phim s ^ xult tich luy chuydn di tir nha may ddn cac tdng kho ludn ludn ton han tdng nhu clu tich liiy tai cac dai ty.
4. THUAT TOAN CHO MO HINH Giai thuat Lagrange dupc ap dung nhu sau:
Bu&c 0: gia trj ban diu
Gan gia trj ban diu cua bd nhan tut Lagrange (A^^ bing khdng,
Gan gia tri ban diu ciia nhan tu step size S = 2,
Gan gia trj ban dau ciia tham sd MaxNon - gia trj ton nhat ciia buac tap lien tidp ma gia tri ham muc lieu khdng duoc cai thien {MaxNon = 5),
Gan gia trj ciia tham sd Maxlter - sd budc lap ldn nhat ciia giai thuat {Maxlter = 20Q),
Gan gia trj ban dau ciia chl sd budc tap bang 1 {Iter = I),
Gan gia tri ban dSu ciia tham sd budc tap khdng cai thien bang khdng (7\^o« = 0),
Gan gia tri ban dau cho ham muc tieu Z{Best) - gia trj tdt nhat ciia ham muc lieu ma giai thuat nhan duac.
Buac 1: Giai bai loan / va 2 Xac djnh Idi giai ciia ca hai bai loan {LI) va {L2).
Birac 2: Xac ffinh va cap nhat gia trj ham muc tieu
Xac dinh gia tri ham muc lieu hien tai ciia bai loan ban diu [Z = Zl + Z2], va gta tri ham muc tieu ciia giai thuat Lagrange [Z(i) = Z(Zl) + Z(Z2)],
IF [Z<Z{Best)] THEN (assign Non=0, and IF the relaxed constraint sets (5) is satisfied THEN [Z{Best) = Z], goto step 3; ELSE goto step 3} ELSE (Non = Non +1), goto step 3.
Bu&c 3: Cap nhat gia tri nhan tu Lagrange
If Non = MaxNon Then {S = S/2) and {Non = 0),
C^p nhat gia tri cua step size hien tai {Stepsize,,^^) theo cdng thiic
Stepsize,,^^ =Sx [Z{L)-Z(Best)]
J Tfl
zz sz^„-''i4"-i:si'.
^=1 r=l V ,=1 r=l r=\ r=l
Cap nhat nhan tii Lagrange
^,)(/«..i, = i^Xr HStepsize,JYY.^.,r -"'^1,2;;' - 1 Xr^,
^ (=1 r=1 r-1 r=l
Bir&c 4: Kiem tra dieu kien dimg if Iter = Maxlter then slop; else Iter = Iter +1. goto step I.
5. KET QUA TINH TOAN Trong phan nay, chiing tdi Iddm chiing giai thuat thdng qua mot sd bai toan ling dung nhu trong bang 5.1, ben canh do.
chiing tdi ciing dung phan mem LINGO dd giai va so sanh ket qua. Chiing tdi kidm tra 3 nhdm mdi nhdm 5 bai loan, tuang iing vdi gia trj ciia cac chi sd I, J, R, va T: va sd bidn cung nhu trong bang 5.1. Trong dd:
(i) tu Sl den S5 la nhdm bai loan nhd; (ii) tu Ml den M5 ta nhdm bai toan vtra; (iii) tii BI den B5 la nhdm bai loan ldn .
TAP CHi KHOA HOC TRUONG DAI HQC M d TP.HCM - S6 1 (34)2014
3iiiig 5.1. Mot sd bai toan ung Bai toan
Sl S2 S3 S4 S5 Ml M2 M3 M4 M5 Bl B2 3 3 B4 B5
dung So lUVDg Biln*
144(54) 168(63) 288(96) 500(150) 792(216) 1664(384) 2080(480) 2340 (540) 2780(600) 3000 (600) 4500(900) 9000(1350) 13425(1800) 26850(2700) 34950(3150)
Rang buoc 121 138 216 340 492 880 1104 1222 1360 1380 2080 3120 4086 6090 7130
•
3 4 4 5 6 8 8 10 10 10 10 15 20 30 30
J 3 3 4 5 6 8 8 8 10 10 10 15 20 30 40
R 3 3 4 5 6 8 8 8 8 10 10 15 15 20 20
T 3 3 4 5 6 8 10 10 10 10 15 15 15 15 15 C- Gia tri ben ngoai la tong so bien, gia trj trong ngogc la so biin nguyen)
Tat ca cac bai toan deu dugc giai bing phan mem LINGO \ a giai thuat de nghj ciia chiing lot, viec giai nay dupc thuc hien tren may linh cd thdng sd sau:
eore'^'2 CPU. IGB RAM, va phin mgm LINGO9.0. Ddi vdi tdi giai cd dupc theo chuang trinh LINGO thi tdi giai cd dupc la Idi giai tdi uu. trong klii dd, giai thuat dd nghj trong nghien ciiu nay khdng dam bao tinh ldi uu. do vay chiing tdi phai so sanh kel qua giiia 2 phuang phap.
Ket qua tinh loan chi lidl vd gia trj ldng phi ciia ham muc tieu va thdi gian
chuang trinh may tinh ciia ca phan mem LINGO va giai thuat de nghi dupc tdm tit trong bang 5.2. Trong bang 5.2, cdt (2) va (3) trinh bay gia tri ciia ham muc tieu tu LINGO va lu giai thuat tuong iing; cdt (4) trinh b^y ty te phin tram chenh Idch giiia 2 gia tri ham muc lieu trong cdt (2) va (3);
cgl (5) va (6) thd hien thdi gian tinh loan (thai gian chay chuang trinh) ciia LINCJO va giai thuat tuang iing. Vdi kdl qua trong bang na> thi gia trj ham muc tieu tir pliln mem LINGO (cdt 2) ndu cd la gia tri tdi tm.
Bang 5.2. Bang torn tat ket qua tinh toan
Bai toan (1) S I C ) S2 S3 S4 S5 Ml M2 M3 M4 M5 Bl B2 B3 B4 B5
Gia tri ham mue tieu
(LINGO) (2) 753690 1031250 1255230 1609860 2450400 4752980 9322340 10261028 11221804 8207840 9547450 18859176 18155338 N/A N/A
Gia tri ham muc tieu
(giai tbu^t) (3) 761370 1048640 1264440 1625700 2478350 4146610 9424740 10362600 11322610 8273485 9607135 18998250 18212230 20390220 290565420
Chenh lech
( % ) •
(4) 1.01 1.69 0.73 0.98 1.14 1.40 1.10 1.00 0.90 0.80 0.63 0.74 0.31 N/A N/A
Thdi gian L I N G O (hh:mm:ss)
(5) 00:00:02 00:00:02 00:00:03 00:00:25 00:02:15 00:04:36 00:10:55 00:13:33 00:17:45 00:22:11 03:52:12 12:03:56 24:37:23 N/A(**) N/A(**)
Thdl gian Giai thuat (hh:mni:$s)
(6) 00:00:03 00:00:03 00:00:05 00:00:15 00:01:03 00:01:14 00:02:24 00:03:02 00:03:33 00:04:25 00:09:35 00:12:43 00:18:17 00:23:36 00:29:53 f^*.- Thai gian chgy chucmg trinh LINGO han 120 gia)
Vdi ket qua ciia nghien ciiu trong bang 5.2, chiing tdi cd the ket luan rang thu^t toan de nghj ciia chiing tdi so sanh vdi kdt qua cd dupc tu LINGO la dat yeu cau ve tiieu qua chat lupng ciia tdi giai trong hau het cac bai toan (Sl den B3).
Ngoai trii nhGng bai loan nhd, giai thu|t ciia chiing tdi hieu qua hon LfNGO ddi vdi nhQng bai loan cdn tai ve kha nang cd dupc tdi giai \'a thdi gian chay chuang trinh. Dac biet ddi vdi 2 bai loan cudi cung, giai thuSt cua chiing tdi cd thd cung cap ldi giai chip nhan duac, trong khi phan mdm LINGO chay han 120 gid vin chua cho kdt qua cu the. Xet bai toan St (*) trong bang 5.2, neu dang ciia nhu cau la giam trong tuong lai, ddng thdi gia trj chi phi phat cao, chung ta dl dang nhpi thay rang gia trj ham muc tieu tang den 1300290.
Bdi vi ldi giai tdii dd, chiing ta md nhung dan vj kinh doanh ngay tu diu, va sau khi tra nhieu chi phi phat, long chi phi chung se cao. Thong tm nay rlt huu ich ddi vdi ngudi dau tu va ngudi quan ly trong quyet
djnh md cac don vj kinh doanh hay dung ctiinh sach thue ngoai Idii can thiet de mang lai hieu qua kinh te, day ciing la diem khac biet ldn ciia md hinh nay vdi nhihig mo hinh da duac cdng bd trudc day.
6. KET LUAN
Trong nghien ciiu nay, chiing tdi da xay dimg md hinh ty thuyet quy hoach nguyen hdn hpp cho bai loan thiet ke chudi cung ling, md hinh tich hop ke hoach phan phdi va quyet dinh van hanh. Md hinh giai quyet cho bai toan dan san pham trong dd quyet djnh md nha may hoac tdng kho tuy vao thdi diem can thidt. Diem khac biet Idn nhat ciia md tiinh nay vdi nhiing md hinh khac dd la md hinh cd xem xet miic van hanh tdi thieu ciia nhiing dan vi kinh doanh duac md. Thdng tin nay cho phep nhiing nha quan ty va diu tu danh gia hieu qua van hanh ciia chudi cung iing Idii thidt kd, ndu cin thidt cd thd diing chidn lupc thue ngoai. Clu tnic bai toan cua md hinh kha phiic tap vi sd tupng Idn bidn thudng
40 TAPCHIKHOAHOCTRU0NGP^2!g£!^!gi^'^"^°' ^^'^'^°^'' va biln nguyen frong md hmh (nhu trong , M6 hinh co thi tag dyng cho vi?c bang 5.1). Do dd. chfing tdi da xax dung thiet ke cac chuoi cung ung hang vat heu giai thuat Lagrange dl tim Idi giai cho xay dung (sat, thep. xi-mang) xang dau.
bai toan'thilt kl chudi cung ung thyc tl. nhdt.... hoac cac san pham chuyen dung Theo kit qua tmh toan. chung tdi khing Tuy nhien, de mo hmh co the co nhung ung dinh ring giai thuat ma chung tdi dl nghj dung hon nua trong thyc te, bai torn da la hieu qua va dang tm cay, kit qua dupc san pham can dupc xem xet frong nhihig kilm chfing vdi phin mlm LINGO, dac nghien ciiu tiep theo.
biet ddi vdi bai toan Idn.
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