ر # "م(' &. (()% - + /0 صص) 33-0 ترد ن لد 00٥3-50)٦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hamed_ouralikhani@aut.ac.ir : " ) W
O "ر % K L M N و Hر;ن IJ Dل EFG B " C "د?@A > =>;ر و 89 ر c ; V_"` یa V]^GV_"` \ ;] Zم % K VW VXY و; STU R ز Pن %&<8& % <D(<VD ]D @P aw ; (`# ( &S.D.&/ D&[ 7 -/ '; %V8 <' < @ <R ]V<4 (<' " &2 %I 5. @.7]D I : - '; <&3 <' @< " ; </ </ N< (</ / < a '; %V8 ; :D %/ / & 9< :< < (< <K -<_ 5 ' / @ -/ /./ 7 / (\b @8 - '; " % J &W %& ( ( \/ A& ( '; %V8 D1 ` %/ c %</@< =H ;@ 4 9&MK ( D'; -. #- '; %V8 (\ < < 4 (/ d&/ (VD%&8& X % D(VD / "6O D'; -(@8-; A=D &[/ <'; <&/ (< D@ ; `.& (VD J.K " R ; / )& (/ ' ( &8" V % <Dg<K N<D " <D < N<D MMf (8& & &.DA. ed.d & (/ -. @ &/ " c= % <D@< &<. h <K) <. I&<S (/ < - < <'; ( < %&<8&% <D 9 /.@< (<4# 7 -K(8& &. (_ F L& (/%2#@.7"%&8&" )& %V( / <& &<S(</ <([3W (/. #j3 J) (/( Q&R& L / ; D]f/ ik - 7" <<)& L& (/ - -4# G ; @=(/ I &/ 4:; O / L&<S (</@< (<-<-4<# G 2).)&%V( / "%2#@.7 %&8& % D@ 5 b " (<)(<. G (/%"RA/ 7" % ; ( % D9((/ :.(_ F " << 4 % <DI ND <` J < Q&<R& L </ 5" ]<f/.@< < D ; ; L& (/ </ &< < < 4 % <DI %</ < `<<)&% <D9< / " " g %&8& % D9 ]<f/.< (<[3() <= % D@"K " L R4 4 () = Y (/ 5& ]f/. (4#7 ; J< H X <.@< < Y (/ JH N&)N'3 ]f/ " #()& 9 5 _ N<]f/ 9 % D 3 %" J @ =HV) W / 9 P: %/ N&) %# (/ " 9 %8.@ (W L K %/ 3 " ik %#(' N`D @ " # J\K (/ 5&\O " G ch &.".(/ 9&. % 12 7:9 ;" #; 4 567 56<7[1] e< %&<D%" L <)?(</(<8& </. Jk 4567 %/ ` G l ` : 9&<S I < 1;@<4D <# " < >&= f U[ &3 567; 4 (<((/.O L &M[ / & 23 =4 567 %&8&% D9.& Q 8 ; 2. %/( ; </ c 9"; ( %&8& % D9 " 4 M.O / %&8& % D9 @/ a.o / %&8& % D9 </ & (#8 D(- ; 5 D.& I %/ " V4 ]D oo / %&8&
تردن () (3(/0) 33-0( I <<_ J</ I : % D9:& N= % \f % D( (/ @`O %/N= J</ <[ %&<3 <_ J</ %&<3 :< = T % R ).H J/?7 % R.[2]T > J/ 9"; @/ a > ; ' &. J/ ; 'b &. 9&MK )& 4567 %"( ()?[3] #" "-" g& /-)" 4567 %&8&() = CM ( d &[ %()? [4] " 7. 7 / & %" % 567 %&8& 9 DW di ( t ) + θ I ( t ) = f ( t ) dt t <; <R >< f ( t ) EF< " t. %"3 ; (/ @= `. ;& / ; q = 4 567 ; %&8& Y? : 3; L& (/ 4 I ( t ) 567 4 > θ / - \ L / "[5] "[2] LI./ ;&H - (/ L )? %&8& 9 -./. / 4 567 %(; 56<7 4 @D ( / 4567 %&8&()?. & 4 4 > 9" J<H.<D %" `\f gan (GH6 567 4 > 7". & [4] LI < <.<< (<4# <G @</ a L&< (</ < < 4 % <D>< c<\b (<)?-< <Mf / < L&< (</(<@<@< %&<8&; T @/ a @= 9"; > D9 -.[9-6] < 9< <.D" < </ -<)" < v J7 ( &S.D.& ()"V %&) &. ; () =JH @/ a > ( ) H A(9"; @/ a > / % M7 1 ` g< <[ L <K <; L <GH6 / 4 > -/ / AD U ; / 47" g (</ [11"10] <; ; <?[ / < L&< (</ < < 4 ><.@< "W &8" (/ " ` % D& >< "[15]% <3 (< 9&<" ;& L& (/ 4 > [14-12] % 3 " 9&" ;& L& >< <=/" ( / ;&H - & I (\.8;[16] ; ;% /& L& (/ 4 % <M7 1 `< 9< " < (& 9 y\4 " L"&. x? ; (/ 4.[17]"W @ (/ 3 " / 9&" ;& / z4 / 9"; T > %/.<. (<GH6 <)& @< %&<8& @<= /< #<# N.M 4 567 )& %/ ;% <=/.[18]@< < (<4# <D@< %2<3@/ 7 ]V4@8 )& %&8& N.M 3 >< " <)& >< R > z4 /.[23-19].&. ()? ;&H - %=# L& (/ K (<?< @<K < 456<7 %/ )& %&8& 9[2524] LI @/ a L& (/ 4 56<7 %/(/ )& 1 ` 9[26] %().. ~ 1"4[ %/%' O - E< @</ a < < 4 >< " %&8& Y? " 1"4 @.7 (/ (=/" R > ( ) H 4 (/ R " )& > ()-.&. %; =) 4567 %/ )& %&8& e " e.# 13
O "ر % K L M N و Hر;ن IJ Dل EFG B " C "د?@A > =>;ر و 89 ر c ; V_"` یa V]^GV_"` \ ;] Zم % K VW VXY و; STU R ز Pن 1"<4 % D ; L" ` % D ` @8 D@4 )& @.[27] (4# G @/ a L& <\ N< %<@<%"W&< &/ @8 4567 %/ 3 4T8 % D; /-/ \M4 L" <` 1"<49&<M4 "%;/ _ L GH6 / 4567 )& %&8& 9 &" e&.&.[28] &. ()? % DI %/ )& %V( / "()" & %/(/%; 3; / ; c= %/ :@ ([3)&() =%; 9@8 L R"` " 7;< 3 D. Y (/ ( > 1-3. 1 ` J&K ; / 5i " % %&8& Qi. ; [ t. ; H" )& > M. 4 ;& / θ ( t ). 9&" ;& / @/ a % D 3 α. 1"4[ 1 ` ( ; q. )& " D %; @/ a (VD A. 9 D 1"4[ %/ I 9 @/ a (VD As. ; H" I H" D %(VD ch. )& %/ I H" : )& (VD c. 5 i " t ; - %&8& Y? I ( t ) i. ; S J&K n t. / (.[ )& ( ; % ; ; L t n. P P b t t = n T + t N )&( ; L.( λ ) 1"4[ %/ 1 ` 1 ` : L Tb. )& J " : T. N )& " N CM ( ; L td. N T = t + t )& LI N b d. " D 9 "%; (VD J TCA. " D %(VDJ TCH. " D 9&MK )& (VD J T CP. " D 1"4 ; J H W J Revenue 14
تردن () (3(/0) 33-0(. " D 1"4 ; J H & J rofit 7;< 2-3 -<; <f/ ( & (4#G Dz4A &8" %&8& 9 (; ( D9. ; %#&<\8 " L < K %; < < %</ </ (< < %&< (8 f/ " =D 7" L R4 θ ( t ) :@ W ( \ L& (/ D9 (4# G L R4.#( <# (< % (&# (/ %"3 % 3 " 9&" ;& ; " ; (/ (=/" 4 > < < 4> " ( t ) t 1. θ = α ; < α < 1 > A / ; H" I 4 > R > Q&.' ;. /. ; ' 4 567. " &. -V#% 8./. ;' )& %/ &../ "K %; 3; / > " ` ~ ;.& z4 "K L& (/ ; i4 V/ )& > " / M // " "K )& > D9 #j3.@ 9 < @< " J< Q6<S " % <M7 1 `< < " 1"<4<[ " ; <)&.@ )& " 9&S %" = % D()&.K 9 L& (/ )&.& ].(/:. L& (/() =)&%; =) " R ND -1-2 -3-4 -5-6 -7 $; "# 4 ` / ~ @8 <# z<4.@< < <2J < <)& g<& <)& %I < %&<8& Y? A<D< 1 `< 1"<4<[ (< ; A&. )& (/ Q" % 1 `; J7 ; )&.. 9 I I I ( ) t Q n +1 Q n Q n +1 Q 1 Q 2 Tb T t t )& %&8& N= 4# ]..1 @5% 15
O "ر % K L M N و Hر;ن IJ Dل EFG B " C "د?@A > =>;ر و 89 ر c ; V_"` یa V]^GV_"` \ ;] Zم % K VW VXY و; STU R ز Pن (</ <)& %&<8& ; H" q B ; &3 9"@.<=7.@< <W@<(</ @.<=7(< 5 i T b D " ;3 )& (/ %( L& (/ )& " %/ %&8& Y?.& J 1"4[ %</ 5&< @.<=7" & 7& W S )& (%" 5" @.=7. &8" )& (% D" 1"<4 <[%" % < < R - @8 %&8& ; " )& 9&MK DW ( % D" A(<4 ]V<4 M t λ i n 1.& ` @) H )& % D" :9" @.=7 <)& >< </ %&<8&.&< )& " )& LI&MK @) H - " > % <D 3 </ θ( t ) = α t <; L&< (</ i di ( t ) = M θ ( t ) I ( t ) dt I ( ) Q i = i 1 1 9&<" <;& / < ; ( ; (/ (=/" > / J[ %&8& " %</ <; (\< 4 - )& %&8& - /.& 4< α <1 t α y ( ) = ( + i 1 ) I t M e dy Q e α ( ) = M e dy + Q e t y t i 1 " α 2 :N y T T " I ( ) P i = Qi 1 :&/ D&[ (1) d / l&4 J=` () JH / % <D&< < z4 /" &\ / g=/ ; ` / #ok/ 1"4[ %/(&S.D :W@(/ ; L& (/ I + 1 αt I i ( t ) = M t Qi 1 e + 1 ( t ) i (2) / " N. %; 9 %&8& 9 I / (3) (/ I J&K ; / (1 i n ) 5i &3 % %&8& Y? A (GH6 ( &S.D./ 5i +1" %/ ()" Y? &O (/ - ( Q = I ( λ) q i P i B / &/ D&[ // % :@& & -/ / A I )& %"%/ ( z4-_nd Q = Q1 = I P 1( λ) -qb Q2 = I P 2( λ) qb Q = I ( λ) q np P np B (4) :# (' Q i %&8& l&4 % L a /"(4)"(3)%(?/; ` / 16
تردن () (3(/0) 33-0( + 1 + 1 αλ αλ Qi = M ( λ ) + M ( λ )( 1+ ( e ( 1+ e... = + 1 + 1 + 1 + 1 j = i 1 αλ αt 1 αt 2 αt αλ jαt M ( λ )( e + e + e +...) = M ( λ ) ( e ) + 1 + 1 T <; < ( n +1 ") D&[ 7& W S )& ( )& " -[W :5" @.=7 1"<4<[ ; < &< %I 5. ( / ( 8 j = n P +1 (5) " )& ( z4 <; < ( )& -/ /./ t ; - N z4. - )& ( / &/ " t t -</ t W (< ) <H () <=.<W<@<(</ <; L&<(</ 5 n &<3 t P +1 :@ / / t λ i = n +1 " 0 t t t t λ.d %&8& () A@ )& 9 H 9&MK " N I J[ ; / - ( 8W ; + 1 αt I i ( t ) = M t Qi 1 e + 1 ().W@(/(3)() A&<. `<(6) (<) ;@ 4 A@ )& %&8& Y? -I/.D( Q n +1 -@8 :N.%2#% 8 i = n P +1" t W + 1 α ( t ) Q n I ( ) P i t + M t 1 = = Qn e + 1 α ( t ) (6) (7) t λ i = n +1 " t t λ (U (' ; J=` LI A& 4 I g4 " N )& ; ; /- ( W (/(8& / di ( t ) + 1 = α t I ( t ) dt I ( t = λ) = Q i n + 1 :D (8) :@ JH ; L& (/ J=` () ()" g / l&4 J=` () JH / (( ) t ) I ( t ) e α λ = Q n + 1 Q I t e Q ( ( ) ) = ( )= α λ t n + 1 P i n + 1 ( N :N(9)() %() (9) t = t %;(/ (10) n +2 ") )&; E3 " :5& @.=7 17
O "ر % K L M N و Hر;ن IJ Dل EFG B " C "د?@A > =>;ر و 89 ر c ; V_"` یa V]^GV_"` \ ;] Zم % K VW VXY و; STU R ز Pن (< %&8&%/ " &8" )& )& %&8& " % " -;( W (/(8& / di ( t ) + 1 = α t I ( t ) dt I ( t = ) = Q i i 1 I ( t ) e Q. &8" 4 :@ JH ; L& (/ J=` () ()" g / l&4 J=`() JH / = i 1 %&8& N" 3 (-(/(8& / D" % %&8&%/()& "/ ") @.=7- Q = I ( λ) q Q n = I ( ) - P n λ q + 3 + 3 B Q N 1 = I P N 1( λ) qb Q N = n + 2 P n + 2 B :# (' Q i : @ ND&[ 2 3 Qi = qb e + qb e + qb e +... = qb e Q N = (11) (12) D&[ ` (/ )& (13) %&8& l&4 % L a /"(13)"(12)%(?/; ` / N i αt αt αt jαt j = i (14) :#( K N= W" % D(VD V ( 9 "%;(VD().9 / N" %; /:(VD Q&.' / &/ D&[ // " : 9 "%;(VD TCAP = AP + N AS (15) %&8&%(VD(U @< ) H 9" @.=7 A# N= \f@.=7 ((/%&8&%%(VD )& @.=7 <7& &<[ <)& )& (@ 8W ; ; ; / 5" @.=7.@ )& 9 H )& ( % < <; ; 5& @.=7%/-_ND" @4 1"4 [ CS ;( ` -)" (t ) : ' 9&S (/ )& " % )& 7& ; E3 1 ` -)" 18
تردن () (3(/0) 33-0( n + 1 t + 1 αt TCH 1 + TCH 2 + TCH 3 = ch ( M t Qi 1 e dt i = 1 + 1 Tb t N Tb α (( t ) t ) n + 1 i 1 t np + 2 + e Q dt + e Q dt ) TCP = C t M = Cost n T + t M P P ( P b ) Revenue = Pr ice N q P P T = N T = N λ b B (16) :": 9&MK )& (VD( (17) :" 1"4 ; J H W( (18) :)& " 9&S(<D (19) :" )& 1"4 ; J H & J(" :@ ND&[ )& J & %/ AW 1"4[ J (VD-@.=7( KR& / rofit P = Revenue P TCAP TCH P TCPP N.<M <<)& (< ) < < " T P q B (20) 1"4[ 1 ` V ;@ / )& & 7" <[ <D1 `< % <D@< (</ <<)& W V ( 8W ;./( 1" #.@ (4# G & N.V CD )& 9 /(=/" 1"4 @. CD 4 < L <O6S 1"4[ % M7 1 ` " " ;@=/ )& (() = (/(8& / (</ <<)& <W V< (< <8W ;.<#< <3 < )&N&)( 2) /( <D 1"4[ (/ 1 ` J&K ; E3 )& %&8& V " 1"4[ D1 ` % D@ /%O 9 P @.=7. &8" %#i L& (/%& %; (/ L a 2) =/ " &</ <4 (</ <MK " </ (/ )& &@ =H J\K " \K (/ (? %/ &'=8 ; ` 5.N;3 (/ U&8 (& t ( K %/% D %</ N... 1 = i %</ Q i n P -; E3.@ ( 19 n P @. CD -@8 ; N&) @/ a N%; (/ (5)(<?/; `< </ " <<)& %&8&().@ ]. Q L i Q =. (/(8& /.1 / ( & - D".
O "ر % K L M N و Hر;ن IJ Dل EFG B " C "د?@A > =>;ر و 89 ر c ; V_"` یa V]^GV_"` \ ;] Zم % K VW VXY و; STU R ز Pن Q R j </ (N 1 N 2 N j ) @#;/ L& (/. / np. Q Q j Q R j L i (14)(?/; ` /" Q (/(8& /.2 N = ( & ( K ; " = i 1. l l&4 (?/ ( i -/ /.3 I I ( ) t Q L i.#( K Q n P +1 3%(\H ; W @(/.&( K t (10) "(7) n P JH N&) 4# ]..2 @5% "(7)"(5)%() ; ` /.4 % D() 7 // ; ` /.5 %</&'<=8; `< </ (.@< < L a \f LI ) @ YK O N (W z4 /.6 </ " < -< <)& %&8&(VDq 7 " Tb T rice t Q n P+ 1 t n P Q R j (\H D ND %;(/ \K (/ T.& (/ N &#. @+1 F 6.&< J\K "(V' X 9 % D 3 %"@ =H J\K "(V' /" () P @.=7- <)& %</ 9< % <D <3 < -< </.@# f L / ;(/ & () = % D 3 :/ ; x (/ 20
تردن () (3(/0) 33-0( M λ =T b ch c 9 800 0/08561 30 80 A A s α 1000 800 0/05 2/2 )& % D 3 " DT.1 @< =H J\K "(V'"(/ X (JH N&) " )& %&8& 9 % D 3 / t =0/ 20953 d :@ W ( W % D&. " 9"8 ( 5 ' MATLAB V45 g& rice =196 / 225 t =0/ 21852 n =2 t =0/ 0473 N =5.@ W @(/ rofit = 66598 / 87 (<<<<<<</ <<<<<<< " T =0/ 42805 (<?/ &< </ D (VD. / (/./ ]D & A/ ]V4 D(VD ( 7" &<S <.D" D %I/@ =H [ @.7(/@= & ( W (8& J/ 7 (. & &< [ (VD%50]V4" D 3 / @/ a / A@ D J/ 7 ; J ( (TP) 150000 100000 50000 0-50% -25% 25% 50% A As Ch C.# ` -50000 D(VD T / & @ =H V) W.3 @5% %-50]D < </ (<@< 8W @<.D V<H ( " / ]D )& & V )& > ]V4 / &< "W</ ; < <)& 9 &. & ;' z4 /" & &. _ )& )& >.@ G C W 21
O "ر % K L M N و Hر;ن IJ Dل EFG B " C "د?@A > =>;ر و 89 ر c ; V_"` یa V]^GV_"` \ ;] Zم % K VW VXY و; STU R ز Pن (TP) 90000 80000 70000 60000 50000 40000 30000 20000-25% 25% 50% )&>T / & @ =H V) W.4 @5% $I 7JK- H < < 4 %I < </ %< <)& %/%&8& 9 (L R4 (/(8& / / R H ik &'<=8% DN&) ; ` / 9 (/% D U&8 - W ik -((&#.D. (& 9<.W@(/ 9 (/ U&8A ` %O 9 P ; 9 X @8.@(4# L& D<W " <D(<VD.-= 7" J.O. (/ & &. N.V CD / )& %&8&.< 3 \.O / (8 " ; l&4 ik 2) A / -. b " & E/ % I / %/ -<A<< <3 J< L <O6S 1"4 [ D 1 ` " " V ; )& ( W (/(8& / qi" @<8(</(<@ c "4[ %/ q a. 3 %I/@.D e\d % D '; %/ ik.. G & %I )& (/ N.M &[ " " R @R" ; Q6S " I ; / &/ c &<.@<1 ` J&K ; &. " A23 5 '() -( & ( K; <W L )?%/ O&R& &O (/ & (@D@[3 [ -_ND" L ``f &. " 5" M 7.&( [1] Wee H. M. (1993). Economic roduction lot size model for deteriorating items with artial back-ordering. Comuters & Industrial Engineering 24 449-458. [2] Raafat F. (1991). Survey of literature on continuously deteriorating inventory models. Journal of the Oerational Research Society 27-37. [3] Wagner H.M. and Whitin T.M. (1958). Dynamic version of the economic lot size model. Management science 5 89-96. [4] Ghare P. and Schrader G. (1963). A model for exonentially decaying inventory. Journal of Industrial Engineering 14 238-243. [5] Goyal S. Giri B. (2001). Recent trends in modeling of deteriorating inventory. Euroean Journal of oerational research 134 1-16. [6] Shah Y. Jaiswal M. (1977). An order-level inventory model for a system with constant rate of deterioration. Osearch 14 174-184. [7] Aggarwal S. (1978). A note on an order-level inventory model for a system with constant rate of deterioration. Osearch 15 184-187. L 22
تردن () (3(/0) 33-0( [8] Padmanabhan G. Vrat P. (1995). EOQ models for erishable items under stock deendent selling rate. Euroean Journal of Oerational Research 86 281-292. [9] Bhunia A. and Maiti M. (1999). An inventory model of deteriorating items with lot-size deendent relenishment cost and a linear trend in demand. Alied Mathematical Modelling 23 301-308. [10] Bhunia A. Maiti M. (1998). Deterministic inventory model for deteriorating items with finite rate of relenishment deendent on inventory level. Comuters & oerations research 25 997-1006. [11] Mukhoadhyay S. Mukherjee R. Chaudhuri K. (2004). Joint ricing and ordering olicy for a deteriorating inventory. Comuters & Industrial Engineering 47 339-349. [12] Wee H. M. (1999). Deteriorating inventory model with quantity discount ricing and artial backordering. International Journal of Production Economics 59 511-518. [13] Mahaatra N. Maiti M. (2005). Decision rocess for multiobjective multi-item roduction-inventory system via interactive fuzzy satisficing technique. Comuters & Mathematics with Alications 49 805-821. [14] Triathy C. Mishra U. (2010). An inventory model for Weibull deteriorating items with rice deendent demand and time-varying holding cost. Alied Mathematical Sciences 44 2171-2179. [15] Chakrabarty T. Giri B. Chaudhuri K. (1998). An EOQ model for items with Weibull distribution deterioration shortages and trended demand: an extension of Phili's model. Comuters & Oerations Research 25 649-657. [16] Abad P. L. (2001). Otimal rice and order size for a reseller under artial backordering. Comuters & Oerations Research 28 53-65. [17] Covert R. P. Phili G. C. (1973). An EOQ model for items with Weibull distribution deterioration. AIIE transactions 5 323-326. [18] Wen X. Zuo L. (2007). A review of develoment of deteriorating inventory theory research [J]. Journal of South China Agricultural University: Social Science Edition 6 46-52. [19] Goyal S. Gunasekaran A. (1995). An integrated roduction-inventory-marketing model for deteriorating items. Comuters & Industrial Engineering 28 755-762. [20] Jiang D. Du W. (1998). A study on two-stage roduction systems of erishable goods [J]. Journal of Southwest Jiaotong University 33 430-435. [21] Chen S. Chen S. Liu X. (2002). A roduction-inventory model for deteriorating items [J]. Journal of Zhaoqing University 23 66-68. [22] Gontg Z. and Wang C. (2005). A roduction-inventory arrangement model for deteriorating items in a linear increasing market [J]. Logistics Technology 6-8. [23] Maity A. Maity K. Mondal S. Maiti M. (2007). A Chebyshev aroximation for solving the otimal roduction inventory roblem of deteriorating multi-item. Mathematical and Comuter Modelling 45 149-161. [24] Liao J. J. (2007). On an EPQ model for deteriorating items under ermissible delay in ayments. Alied Mathematical Modelling 31 393-403. [25] Liao J. J. (2008). An EOQ model with noninstantaneous receit and exonentially deteriorating items under two-level trade credit. International Journal of Production Economics 113 852-861. [26] Teng J. T. Chang C. T. (2005). Economic roduction quantity models for deteriorating items with rice-and stock-deendent demand. Comuters & Oerations Research 32 297-308. [27] Yang P. C. Wee H. M. (2003). An integrated multi-lot-size roduction inventory model for deteriorating item. Comuters & Oerations Research 30 671-682. [28] He Y. Wang S. Y. Lai K. (2010). An otimal roduction-inventory model for deteriorating items with multile-market demand. Euroean Journal of Oerational Research 203 593-600. 23