Tài liệu Luận văn thạc sĩ những mô hình dự trữ với dòng cầu ngẫu nhiên

BQ GIAO Dl)C & DAO T~O D~I HOC QUOC GIA TP. HO CHi MINH TRUONG D~I HOC KINH TE --·-- HOANG NGQC QUANG NHU'NG M0 HiNH Du'• TRU' ' vOI nONa c.Au NGA.u NHIEN ,. ~ ~ CHUYEN NGANH : TOAN E>IEU KHIEN MA s6 : s.o2.2o LO!N AN TH~C Sl f{HOA HOC f{INHTl NGUOI HUONG DAN KHOA HQC: PGS- PTS: LEVAN HOT - TP. HO CHI MINH 1998- CONG TRiNH E>A E>U'QC HOAN THANH T~l TRUONG E>AI . HOC . KINH TE THUOC . E>AI . HOC . QUOC GIA THANH PHO HO CHI MINH ---...---- NGU'OI HU'ONG DAN KHOA HOC: PGS- PTS: LEVAN HOT .. - .. - PHAN BII;N 1: .............................................................................. PHAN BII;N 2: .............................................................................. Lu~n an se du<;jc bao v$ t9i H(>i dong cham Lu~n an Nha nude hop t9i Truong E>9i hoc Kinh te vao hoi .......... gio ....... ngay ............. thang ........... nam 1998. MUCLUC . . Trang LOI NOI £>AU···················································································· Chu'ong I r-{ Md £>AU- CAC KHAI NI~M Cv BAN ........................................ . ? ~ / / ? A - So lu'<;5c lich sll' ly thuye't quan ly dt! tn1' ................................... . - Cac khai ni~m co ban ............................................................... . - Cac loc;ti chi phi ......................................................................... . - Cach xay dtfng mo hlnh ............................................................. . Chu'ong II MO HINH QUAN L Y Dl)' TRU TRONG TRUONG HC)P cAc £>AI Lu'C)NG xAc E>JNH ................................................................. . A. Mo hlnh don gian xac dinh muc d() b6 sung voi gia thie't dtf tril' khong dtt<;1c thie'u ............................................................................... . - M~nh d€ I ................................................................................... - M~nh d€ II ................................................................................. . B. Tru'ongh<;1p yeu c~u xua't hi~n khi thie'u hang dt! tn1' thl cho ........ . C. Truong h<;1p ma't yeu c~u khi yeu c~u khong du'<;jc dap ung ......... . Chu'ong III MO HINH QUAN LY Dl)' TRU VOl YEU CAU NGAU NHIEN ... . A. Md d~u ..................................................................................... . B. Mieu ta xa'p xi - Mo hlnh tru'ong h<;1p yeu c~u khong 1 3 3 3 4 7 9 9 12 13 15 20 23 23 du'QC dap ung ngay se cho ....................................................... . C. Mieu ta xa'p xi - Mo hlnh bi ma't nhung nhu c~u khong 25 du'QC dap ung ngay ................................................................... . D. Phan tich mo hlnh va thi d1..1 tinh toan ..................................... . Chu'ong IV. ~ ~ E>IEU KI~N TON TAl NGHI~M VA Sl)' ON E>JNH CUA NGHI~M ............................................................................................ . 1 . st! ton ~ tc;tl d uy n h~ at cua ng h•H~m ................................................ . 2. Stj 6n dinh nghi~m .................................................................... . 3. St! phl.l thu()c cua nghi~m (Q*, r*) vao 'A, TI, I, C .................... . 30 A A ' 0 ? A ---·--- "" 32 ? 38 38 40 43 ***** Quan ly Dv tru la m()t va'n d€ c'lln thie't trong m9i thanh phlin kinh te': trong san xua't kinh doanh, trong dich Vl;l cling nhu' trong qu6c phong .. Ly thuye't quan ly dl,i tru ra doi vao d§u the' ky 20 voi cong thuc Wilson d~ xac dinh kh6i lu'<;lng hang h6a b6 sung cho tung d<;lt. Nhung ly thuye't quan ly dl,i tru voi cac d~i lu'<;lng ng~u nhien chi du'QC phat tri~n m~nh me sau the' chie'n II. Be'n nay cung voi slf phat tri~n cua ky thu~t vi tinh, quan ly dl,i tru du'<;lc phat tri~n m~nh me v€ ly thuye't cling nhu' trong ung dl,ing. Nhung ly thuye't toan hQc hi<$n d~i nhu' giai tich, quy ho~ch phi tuye'n, ly thuye't t6i u'u, ly thuye't t6i u'u toan eve, ly thuye't cac qua trlnh ng~u nhien dtt<;lc sll' dl;lng r()ng rai trong nghien cilu quan ly dl! tru. Ly thuye't nay ngay cang du'QC nhi€u nha toan hQC ung dl;lng Ion tren the' gioi quan tiim nhu' Hadley, Whitin, Kovalurko ... Ban lu~n van gom 4 chuong: Chu'ong I: Chung tOi lu'<;lc qua lich sll' ly thuye't quan ly dl,i tru va cac khai ni<$m co ban, phan tich cac chi phi va each xay dl,ing mo hlnh. Chu'ong II : Trinh bay m()t s6 mo hlnh quan ly dlf tru voi cac d~i lu'<;lng xac dinh. - Mo hlnh don gian (cong thuc Wilson) - Mo hlnh voi yeu CllU se cho khi thie'u hang dl,i tru. - Mo hlnh voi yeu eli u bi m1t khi thie'u hang dl,i tru. Chu'ong III: Xet mo hlnh voi dong cliu Ia d~i lu'<;lng ng~u nhien m6 hlnh trong hai tru'ong h<;lp: Truong h<;lp yeu cliu se cho va tru'ong h<;lp yeu cliu hi ma"t khi thie'u hl;lt hang dl,i tru. Chu'ong IV: Xet sv t5n t~i, duy nha't nghi<$m cling nhu' tinh 6n dinh cua mo hlnh xet d chu'ong III. Trong 3 chu'ong d'au chung toi t6m t~t nhii'ng ke't qua v'e ly thuye't quan ly dlf trii' duqc trinh bay trong cac tai lil$u (vi dv nhu trong sach chuyen khao cua Hadley-Whitin (Analysis of Inventory System9 mot s6 chung minh rieng cua chung toi. B6ng g6p chinh cua chung toi d chuang IV. Nhii'ng ke't qua chung toi trinh bay d chuang IV theo ch6 chung toi duqc bie't la hoan toan moi. Nhii'ng ke't qua d6 giup chung ta bie't duqc hi$: Q= 2A.(A + TI11(r) IC H(r) = QIC TIA. Khi nao c6 nghil$m, khi nao thl c6 nghil$m duy nhfft va cho bie't nghil$m cua hi$ tren kha vi theo cac tham s6 A., TI, I, C. Nhii'ng ke't qua d6 giup chung ta ra'"t nhi'eu khi giai quye't nhii'ng bai toan tht;t'c te'. ***** Trang 2 ... CtiiJ()~(3 I ~ .. , ~ ... M() 1),:\U - C:AC: 1\tiAI ~I~M . f:(} 13A~ ***** van d~ quan ly dv tn1 thie't hi Ia m(lt van d~ rna mQi thanh ph'an kinh te', mQi n~n kinh te' d~u quan tam. Dt! tn1 rat c'an thie't trong n~n kinh te' qu6c dan, trong san xua't cong nghi~p, trong dich vv thu'dng m~i cling nhu' trong qu6c phong. C6 ra't nhi~u nguyen nhan dfin de'n vi~c t6 chile dt! tn1 nguyen v~t li~u hang h6a. Tren thvc te' khong th€ ho~c khong kinh te' ne'u nhu' m6i khi xuat hi~n yeu c'au v~ m(lt lo~i hang h6a nao d6 ta moi di kie'm d€ thoa man yeu c'au d6. Ne'u ta khong c6 hang h6a dt! tru thl khach hang mat thoi gian cho d<;1i, doi khi khach hang khong mu6n ho~c khong th€ cho. Nhu' v~y chung ta se mat m(lt ph'an 1<;1i nhu~n va uy tin cua ta d6i voi khach hang hi giam di, anh hu'dng de'n vi~c kinh doanh lau dai con nhung nguyen nhan khac nua cling khong kern ph'an quan trQng. Thi dv nhu' gia nguyen v~t li~u nao d6 thay d6i dang k€ theo mua, khi gia nguyen v~t li~u d6 tha'p, tat nhien ta c6 1<;1i ne'u mua dt! tru cho vi~c san xuat cho nhung thoi di€m gia nguyen li~u len cao. So qua m(lt vai nguyen nhan, ta thay vi~c dt! tru nguyen v~t li~u la c'an thie't. Trong cong vi~c quan ly dt! tru chung ta phai tra loi hai cau hoi sau: 1, Thoi di€m h6 sung dv tru. 2, Kh6i lu<;1ng hang h6a h6 sung dv tru la hao nhieu. Trong chu'ong nay chung ta se c6 ga:ng tra loi hai cau hoi tren trong m(lt s6 tinh hu6ng khac nhau. Nhung h~ th6ng quan ly dv tru ra't khac nhau theo tinh chat cua chung. Vi dv vi~c dt! tru nu'oc d h6 chua nu'oc ch~ng h~n khong chi phv thu(lc vao y mu6n cua ta, rna chu ye'u con phv thu(lc vao lu'<;1ng nu'oc mu'a cua khu vvc d6 trong thoi gian d6. d day chung ta se khong xet nhung va'n d~ nhu' v~y. Chung ta se chi xet va'n d~ quan ly dv tru trong tru'ong h<;1p ta c6 dQ tv do nha't djnh, d€ quye't dinh v'e thoi di€m va kh6i lu'<;1ng hang h6a (thie't hi) c'an h6 sung. Stl' dvng cac phu'dng phap toan hQC ta se chi ra cac quy lu~t quan ly dv tru, ta phai mieu ta h~ th6ng quan ly dlj tru h~ng ngon ngu toan hQC. Vi~c mo Trang 3 ta m9t h~ thO'ng b~ng ngon ngu tmin h9c thu'ong du'cjc g9i la mo hlnh h6a toan h9c cua h~ thO'ng d6. Nhu'ng the' gioi th\l'c khong th€ rnieu ta b~ng ngon ngu toan h9c rn9t each chinh sach tuy~t d6i. Vl v~y khi tie'n h~mh mo hlnh h6a chung ta chi c6 th€ xa'p xi rna thoi. Ne'u ta rno ta th€ gioi thvc cang chinh xac thl rno hlnh toan cang phuc t(;lp. Cong vi~c phan tich cac mo hlnh phuc t';lp nhu' v~y se g;Jp nhi"eu kh6 khan khong din thie't. Do d6 tuy theo rnuc d9 yeu c'au chung ta phai ddn gian h6a the' gioi thvc. Vi~c nghien cliu quan ly dt! tru da xua't hi~n tu lau. Nhung cong thuc chinh thuc du'cjc xac l~p l'an d'au do Ford Harros rut ra vao narn 1915 thu'ong du'cjc g9i la cong thuc ddn gian xac djnh kh6i lu'cjng b6 sung hay cong Wilson. Quy€n sach d'au tien vie't v"e va'n d"e quan ly dv tru la do rn9t c9ng tac vien cua H9c vi~n Massachuset F.F Raymond vie't vao narn 1931. Nhu'ng chi vao cu6i nhung narn cua The' chi€n II, khi vi~c nghien cliu chie'n lu'cjc phat tri€n r'arn r9 thl cong vi~c nghien cliu quan ly dlf tru rnoi du'cjc chu y. Quy€n sach cua Whitin vie't narn 1953 la quy€n sach vie't b~ng tie'ng Anh xem xet rn9t each c;Jn ke rno hlnh quan ly dt! tru ng~u nhien. De'n nay vi~c nghien CUu quan ly d\1' trfi' dang phat tri€n va da thu du'cjc ra't nhi"eu thanh qua trong ly thuy€t ciing nhu' trong ling dl;lng. Cac nha nghien cliu da sii' dl;lng kha nhi'eu nhung cong Cl;l toan h9c hi~n d';li nhu' giai tich, quy ho(;lch phi tuy€n, quy ho~ch ng~u nhien. Bay gio chung toi xin lu'cjc qua rn9t sO' khai ni~rn cd ban. Tru'oc he't d6 1a nhung chi phi. Trong dt! tru san ph§rn c6 ra't nhi"eu lo~i chi phi. C6 nhung lo~i chi phi khong thay d6i du ta thay d6i each thuc quan ly. Nhung chi phi d6 ta se khong d"e c~p toi. Chung ta chi d"e c~p toi nhung chi phi thay d6i khi ta thay d6i cung each di"eu hanh. Cl;l th€ c6 5 lo~i chi phi sau: 1. Chi phi lien quan d€n nh~n hang (chi phi ti€p li~u). 2. Chi phi lien quan de'n bao quan san ph§rn (con g9i lu~t chi phi htu kho). 3. Chi phi lien quan de'n vi~c giao hang (chi phi giao hang). 4. Chi phi xua't hi~n khi san ph§rn (hang h6a) dt! trii' bj thie'u hl;lt. 5. Chi phi lien quan de'n vi~c thu th~p va xU' ly du li~u (chi phi thong tin). 1/ Chi phi tie'p li~u: Tru'oc he't d6 la chi phi cho ngu'oi di tie'p li~u va phu'dng ti~n tie'p li~u (giao thong). Sau de'n chi phi cho nhung van ban gia'y Trang 4 tO d~t hang, chi phi gia'y to bi~u bao van ban, h6a ddn, gio ch(;ly may, phi bu'u di~n. Nhung chi phi tren ta chia lam hai lo<;1i: rn9t lo<;1i ph1;1 thu9c vao khO'i ht<;1ng hang h6a (san phffrn) tie'p li~u va rn9t lo(;li khong phl;l thu9c vao khO'i lu'<;1ng hang h6a tie'p li~u. Nhung chi phi ph1;1 thu9c vao khO'i lu'<;1ng hang h6a tiSp li~U thu'ong du'QC tinh gQp VaO gia hang h6a. Ta ky hi~u chi phi tiSp li~u ph1;1 thu9c vao khO'i lu'<;1ng san phffrn tiSp li~u Ia C (Q) trong d6 Q la khO'i lu<;1ng san phfirn tie'p li~u. Gia tie"p li~u trung . "" 1"1eu 1'a C(Q) b'mh cua ddn v1.. tlep . Q- . ? A Ta d~c bi~t lu'u y de"n tru'ong h<;1p gia tie"p li~u trung blnh cua rn9t san phfirn khong d6i va ky hi~u C. Trong tru'ong h<;1p d6 C(Q) = C.Q. Khong rna'y khi xay ra tru'ong h<;1p tren, nhu'ng trong th~c t€ thong thu'ong ta c6 th~ xa'p xi nhu'v~y. Nay ta xet chi phi khong phl;l thUQC vao khO'i lu'<;1ng tie"p li~u. D6 Ia nhung chi phi cho gia'y tO, bi~u rn~u. thu' tin, di~n tho(;li... va ca nhung chi phi tie"p li~u. quan ly rna khong phl;l thu9c vao kich co cua hang h6a tie"p li~u. Nhung chi phi d6 xua't hi~n rn6i fan ta d~t hang. Ta gQi n6 la chi phi d~t hang. Gia d~t hang ta ky hi~u la A. Nhu' v~y t6ng chi phi cho rn9t l'an b6 sung Ia A+ C(Q). Trong chung rn~c nao d6 ta c6 th~ gia thie"t gia d~t hang trong cac l'an d~t hang la khong d6i. Gia d~t hang choN l'an d~t hang Ia NA. 21 Chi phi hiu kho: Bao g'Orn nhung chi phi thue kho, thue cac thie"t bi bao quan ... trong rn9t sO' tru'ong h<;1p n6 g'Orn ca nhung chi phi lien quan de"n hao h1;1t rna khong phai lUc nao cling th~ hi~n tren gia'y to. Nhung rna't mat d6 xua't hi~n do s~ hao h1;1t v~ khO'i lu'<;1ng do bi rna't dip, nhii'ng thi~t h<;1i do vO'n bi t'On dQng, ti~n d6ng quy bao hi~rn. thu€. Khong phai ta't ca cac chi phi lu'u kho d~u thay d6i giO'ng nhau khi ta thay d6i rnuc dQ va each d~ tru. Ra't kh6 tinh du'<;jc ta't ca nhii'ng chi phi d6 rn9t each chinh xac. Ta ddn gian h6a b~ngcach tinh xa'p xi. Ta se coi chi phi lu'u kho ty 1~ thu~n voi gia thanh san phffrn lu'u kho t<;1i thoi di~rn d6. H~ sO' ty 1~ se ky hi~u la Iva ta coi n6 khong thay d6i theo thoi gian va gQi la h~ sO' chi phi lu'u kho. Ta't nhien 0 < I < 1. Nhu' v~y chi phi lu'u kho x san phfirn voi gia thanh C trong rn9t ddn vi thoi gian (vi d1;1 1 narn) la ICx. Nhu' ta tha'y chi phi lu'u kho rn9t ddn vi san phfirn con ty 1~ thu~n voi thoi gian lu'u kho. Ne"u Trang 5 x(t) la lu'm nhung chi phi cho may m6c dS xi't ly thong tin, b() ph~n thu th~p thong tin dS thu'ong xuyen thong bao v~ gia ca san phfim va dv doan nhii'ng yeu c'au trong thoi gian toi. Nhu'ng trong m()t sO' tru'ong hcJp ta coi chi phi nay khong ph\1 thu()c vao phu'ong phap di~u hanh h~ thO'ng. Tie'p theo chung ta se ban de'n phu'ong phap chQn chie'n lu'cjc di~u hanh h~ thO'ng. Ml;lc tieu cua xlt ly mo hlnh quan ly dv trii' b~ng phu'dng phap toan hQC la nho n6 ta chQn du'cjc chie'n lu'cjc thich hcjp dS di~u hanh sao cho lcji nhu~n thu du'cjc la cao nha't ho~c chi phi be nha't. N6i va:n dt Ia chQn phu'ong phap di~u hanh t6i ttu. Ta't nhien ta chi c6 thS chQn du'cjc phu'ong an t6i u'u ne'u lcji nhu~n ho~c chi phi la hii'u h<;1n. Theo tieu chufin nay ta chQn chie'n lu'cjc lam eve d<;1i h6a lcJi nhu~n blnh quan hang nam ho~c eve tiSu h6a chi phi blnh quan hang nam. Ne'u nhu' lcji nhu~n trong khoang thoi gian t la B(t) va chi phi trong khoang thoi giant Ia Z(t) thllcJi nhu~n blnh quan hang nam B va chi phi blnh quan hang nam Z du'cjc dinh nghia nhu' sau: B =lim B(t) · Z =lim B(t) t ' t t->+oo t->+oo Vi~c chQn phu'ong an theo tieu chufin sau thu'ong la thich hcjp hon. Ta't nhien se khong hay, ne'u nhu' vi~c t6i ttu h6a lcji nhu~n blnh quan hang nam ho~c eve tiSu h6a chi phi blnh quan hang nam d~n de'n nhung phuong an chie'n lu'cjc khac h£n chie'n lu'cjc t6i u'u h6a lcji nhu~n ho~c chi phi trong khoang thoi gian sa:p toi. Nhu'ng ra't may sv vi~c l<;1i xay ra khong hoan toan nhu' v~ y. Trong ling dl;lng thvc te' ca hai tieu chufin d~u d~n ta de'n hoac la cung m()t phuong an hay 1a 2 phuong an khac nhau khong dang kS. Ph'an con l<;1i ta se lam r6 vi~c xac dinh cac ye'u tO' ng~u nhien. DS xac dinh lcji nhu~n blnh quan hang nam ho~c chi phi blnh quan hang nam trong Trang 7 di'eu ki~n nhung ye'u t6 ng~u nhien anh hu'dng thvc den qua trinh quan ly' chung ta se sli' dvng cac phu'ong phap cua ly thuyet xac sua't. Chung ta se thay the' l···, t0 , Qo, ... , Qn) sao cho: /'. Qi-I = 1:' /':'. A.~ti- ti-I) . Vt = 1, 2, ... , n Va chi phi z(t0 ) ung voi phu'ong an sau nho hon hoi;ic b~ng chi phi z(tn) ung voi phu'dng an tru'oc. Chang minh: 11 U'ng voi phuong an (to. t1, ... , tm Qo. QJ, ... , Qn) Voi: Si = Qi-1 + Si-1 -A.Ti z(t") ~ 0 Vi= 1, 2, ... , n ta c6: IC " IC " = A(n + 1) + -L Q ;_ 1t; + -:L (S;_ 1 + S;)T; 2 2 i=l i=l Khi d6 hien nhien: si = 'Qi-1 - ~-. Ti = o Chi phi z(t0 ) ung voi phu'ong an sau ta"t nhien se la: n JC n 2 i=l n z (t") = A(n + 1) + -:L (Q i-l t;) V~y 11 da du'qc chung minh. 2/ Gia sti' (to. t, ... ' t; Qo, Q I' ... ' Qn) Ia 1 phu'dng an voi: Vi = 1, 2, ... , n. n Thl: Q = L i=l n Q i-1 = LA. n=l n Ti =A. L Ti i=l Trang 11 La 1 s6khong d6i va theo bat d~ng thuc Bunhiacovski ta c6: Q~-~ ) ~ (t.1 )(~1 Q~-~) ~ n(~ Q~-~) 2 (t. V~y: z (t.) = A (n + 1) + ~ A (n + 1) + IC' 2 I~ I ( (I Q ;_, ) ~ Q )' n II. A (n + 1) + 2IC' L Q ;_, II. dday: n Q = 0 Khi d6 chi Q \fi, i =1, ... , n va ta d~t T" = tn- to n n = t" 0 < t" I = 1 .T < ... < t" = nT II phi~tn) ling voi phu'dng an~' ... :t"' '{Jo, ... ,Qn) se 1a: Tu ke't lu~n tren ta suy ra d€ tlm phu'dng an sao cho chi phi blnh quan hang nam nho nhat ta chi c'an xet nhfi'ng phu'dng an c6 cac thai di€m b6 sung hang dl)' trfi' each d~u nhau, va khong thai gian gifi'a hai d\ft b6 sung hang dl)' trfi' ta se g<;>i la chu ky. D'ong thai ta chi c'an xet nhfi'ng phu'dng an sao cho t~i thai di€m b6 sung hang thl kh6i lu'\fng hang t'on kho Ia b~ng khong. Chu ky ta se ky hi~u laT. Lu'\fng hang b6 sung m6i l'an ta ky hi~u la Q thl hi€n nhien Q ='AT. S6 chu ky blnh quan cua 1 nam se la: 1/T = 'A/Q. Menh tfe 1: Chi phi blnh quan hang nam b~ng t6ng chi phi cua 1 chu ky nhan voi s6 chu ky blnh quan m<)t nam. Chung minh: tn ~ t ~ tn+I \it Ta c6: IC z(l) = A(n + 1)+-nQT + IC 2 D~t: n(t) = IC l Q-'A(t -t )]dt T n IC r (Q- A.(t- t )]dt < -.Q.T 2 T n Trang 12 V~y: . z(t) A . n + 1 JC Q T . n 1l i D - - = 1l i D - - + - . . 1liDt 1-'>+00 2 t 1-++00 1-'>+00 t Hon nua: t = nT + (t - nT). = !!_T l V~y: + (t- nT ) t t = 1 lim I -'> Nen: = t +co (Vl 0 ::;; t - nT < T) t +OO t - nT lim I~ n 0 Nhttthe': 1 n = T t lim t-+ +oo Dodo: z ( t) z = lim I~ = = t +«> ~ (A ~ (A 2 T + IC 2 + A = - + IC .Q = ( AQA + I~ .Q J -~J A IC -2-.Q .T ) Trong d6 A/Q la s6 chu ky trung blnh mot nam. A+ (IC/2).QT la tdng chi phi trong mot chu V~y m<$nh ky. d'e tren du'Qc chung minh. Menh i!e 2: Chi phi blnh quan hang nam dt;tt gi£1 Q* Khi: tii nho nha't. ~ ~ v oi gia tri d6: Z op = .J 2 AIC (Cong thuc Wilson) A Chung minh: Z = A'A + Q ~Q ~ 2~A'A. ICQ ~ 2 Q .J2AIC 'A 2 Trang 13 Va chi c6 da'u b~ng khi: A A = IC A .Q 2 Q* Vi Q ~ * <=> Q 2 * = 2A A IC 0 nen: Q*= {2AT \j~ Xet thai diem d~t hang: Ta't nhH~n cac thai diem d~t hang cfing each d~u nhau va khoang each giii'a hai thai diem li~n nhau cfing b~ng T = Q*l/... Ta gia sli' thoi diem t: tn:::;; t :::;; tn+I• ta d~t hang va ta't nhien ta se nh~n du'QC lu'<;jng hang h6a d6 tl;li thoi diem b6 sung tn+l + m = (n + 1 + m)T voi m ~ 0 nao d6. Hien nhien: t + 't = (n + 1 + m)T. 't = (n + 1)T- t + mT voi (n + 1)T- t >0 Va (n + l)T - t :::;; T. a) Truong h<;ip 't ga'p 1 s6 nguyen fan T thi hien nhien (n + 1)T- t = T => t = nT = t 0 • Do d6 t(;li nhii'ng diem b6 sung ta ding d~t hang. b) Truong h<;ip -r/T khong nguyen: 't = (n + l)T- t + mT. 't (n+l)T-t T T -= Nen m =['tiT]. +m Vi O<(n+I)T-t e= (m + 1)T- 't. Trang 14 T£:li thoi diSm t, ht<_jng hang dlf tru trong kho se la: r= Q- A.e= Q- A[(m + 1)T- 't] = A't- mAT = A't- mQ B~t: ~='A't la 1 d(;li ht<;5ng khong d6i. V~y chung ta se d~t hang r6i thl diSm hang trong kho con 1lu'<;5ng la: r= ~- mQ trong d6: ~=A 't; m = ['t/T]. Ta se xet 1 tieu chu§'n khac. T£:li thoi diSm d~t hang t, ta con c6 nhfi'ng hang da du<;5c d~t dS b6 sung vao cac thoi diSm tn+h ... tn+m· V~y ta't ca c6 m d<;5t, nen t6ng s6 hang da d~t chua nh~n du'<;5c la mQ. Do d6 t6ng s6 hang t6n kho va s6hang da d~t chua nh~n la: r + mQ = ~· Ta di de'n ke't lu~n sau: Chung ta se d~t hang vao cac thoi diSm rna t6ng s6 hang da d~t chua nh~n va s6 hang con htu kho la ~ = A.'t. B. TRUONG HOP YEU CAU XUAT HIEN KHI TRIEU HANG Du' TRU THI CHO: Trong ph'an A m9i yeu c'au xufft hi~n d~u du<_jc thoa man tuc la khong khi nao thie'u hang dlf trfi'. Bay gid ta xet tru'ong h<_jp t6ng quat hon: Cu6i cung ffiQi yeu c'fiu xufft hi~n d~U du'QC dap ung d'fiy du. d day ta se xet tru'ong h 0 thi hi~n nhien f(Q) = + oo. Khi Q = + V~y d~ z(E,Q) nho nhfft khi E = +oo, Q = +oo thi oo fi = 0. Va ham s6 f(Q) la ham s6khong tang, tuc la: 2 2 2AA.IC- II A- ~ 0 <=> rr ?. ~ 2 A;c = 5 Khi d6: Zmin = ITA.. Tom l~i z chi d~t gia tri nho nhfft voi E = +OO khi va chi khi: f:r = 0, IT ~ 8. Trong tru'ong hqp: E = +oo thi ta khong c'an he$ th6ng dlf tn1. Ta cu cho cho kh6i luqng yeu c'au du IOn (nhu'ng thoi gian cho khong th~ qua dai c6 th~ anh hu'dng de'n ban chfft cua he$ th6ng) ta moi b6 sung m()t lu'<;Jng hang dung b~ng kh6i lu'qng cua nhii'ng yeu c'au d6. Trong nhii'ng tru'ong h<;Jp COn l~i Z chi d~t gia tri nho nhfft t~i CllC di~m (E*, Q*) 0::;; E* < +OO, 0 < Q* < +OO