RMT Notes

MCA Friday, 11 October 2013

RESOURCE MANAGEMENT TECHNIQUES NOTES MC9242

UNIT

RESOURCE MANAGEMENT TECHNIQUES

I

LIN INEA EAR R

PROG OGR RAMMING

MODEL ELS S

9

Mathemat Mathe matica icall Fom om!la !latio tio" " # Ga Ga$hi $hical cal Sol Sol!ti !tio" o" o% li" li"ea  ea  $o&ammi"& mo'el( ) Sim$le* metho' ) Ati+cial ,aia-le Tech"i.!e(# /aia"t( o% Sim$le* metho' UNIT UNI T II 9

TRANSPO TRA NSPORT RTA ATION AND AS ASSIGN SIGNMENT MENT MOD MODELS ELS

Mathem Math emat atic ical al %o %om m!l !lat atio io" " o% t ta" a"($ ($o ota tati tio" o" $ $oo-le lem# m# Metho'( %o +"'i"& i"itial -a(ic %ea(i-le (ol!tio" ) o$tim!m (ol!tio" # 'e&e"eac0 ) Mathematical %om!latio" o% a((i& a((i&"me" "me"tt mo'e mo'el( l( ) H!"& H!"&aia aia" " Al&o Al&oith ithm m ) /aia aia"t( "t( o%  the A((i&"me"t $o-lem UNIT III 9

INTEGER PROGRAM PROGRAMMING MING MODELS

Fo om! m!la lati tio" o" ) Go Gomo mo0 01( 1( IPP IPP me meth tho' o' ) Go Gomo mo0 01( 1( mi mi*e *e' ' i"te&e metho' ) a"ch a"' -o!"' tech"i.!e3 UNIT I/

SCHEDULING  PERT AND CPM 9

Net5o Net5 o6 6 Co Co"( "(t t!c !cti tio" o" ) C Cit itic ical al Pat ath h Me Meth tho' o' ) P Po7 o7ec ectt E,al E, al!a !ati tio" o" a" a"' ' Re Re,i ,ie5 e5 Tech" ech"i. i.!e !e ) Re(o Re(o! !ce ce A" A"al al0( 0(i( i( i" Net5o6 Sche'!li"&

UNIT

/

QUEUEING

MODELS

9

Chaactei(tic( o% Q!e!i"& Mo'el( ) Poi((o" Q!e!e( # 8M  M Chaactei(tic(  :; < 8FIFO  = =;> 8M  M  :; < 8FIFO  N  =;> 8M  M  C; < 8FIFO  =  =;> 8M  M  C; C; < 8FIFO  N  =; =; mo'el(3 Total No3 o% Peio'( < 4?

RESOURCE MANAGEMENT TECHNIQUES ) MC9242 Pat#A ) Q!e(tio"( a"' A"(5e( UNIT#I :3 @hat i( o$eatio" o$eatio"( ( e(each O$eatio"( e(each i( a (t!'0 o% o$timiBatio" tech"i.!e(3 It i( a$$lie' 'eci(io" theo03 OR i( the a$$licatio" o% (cie"ti+c metho me tho'(> '(> tec tech" h"i.! i.!e( e( a"' too tool( l( to $o $o-le -lem( m( i", i",ol, ol,i"& i"& the o$eatio"( o% (0(tem( (o a( to $o,i'e the(e i" co"tol o%  o$eatio"( 5ith o$tim!m (ol!tio"( to the $o-lem3 23 Li(t (ome a$$licatio"( o% OR3 O$tima mall a((i&"me"t o% ,aio!( 7o-( to 'iee"t machi"e( a"' 'iee"t o$eato(3 To +" +"' ' th the e 5a 5ait iti" i"& & ti time me a" a"' ' "! "!mm-e e o% c! c!(t (tom ome e( (  5aiti"& i" the the .!e!e a"' (0(tem i" .!e!i"& .!e!i"& mo'el To +"' the mimim!m ta"($otatio" co(t a%te  allocati"& &oo'( %om 'iee"t oi&i"( to ,aio!( 'e(ti"atio"( i" ta"($otat ta"($otatio" io" mo'el Deci De ci(i (io" o" th theo eo0 0 $ $oo-le lem( m( i" ma ma6 6et eti" i"&> &>+" +"a" a"ce ce a" a"' ' $o'!ctio" $la""i"& a"' co"tol3 3 @hat ae the ,aio!( t0$e( o% mo'el( i" OR Mo'el( -0 %!"ctio" i; De(ci$ti,e mo'el ii; Pe'icti,e mo'el iii; Nomati,e mo'el Mo'el( -0 (t!ct!e i; Ico"ic mo'el ii; A"alo&!e mo'el iii; Mathematical mo'el

Mo'el( -0 "at!e o% e",io"me"t i; Detemi"i(tic mo'el ii; Po-a-ili(tic mo'el 43 @hat ae mai" chaactei(tic( o% OR E*ami E*a mi"at "atio" io" o% %!" %!"cti ctio" o"al al el elati atio"( o"(hi$ hi$ %o %om m a (0( (0(tem tem o,e,ie53 UtiliBatio" o% $la""e' a$$oach  A'a$tatio" o% o% $la""e' a$$oach a$$oach U"co,ei"& o% "e5 $o-lem( %o (t!'0  ?3 Name (ome chaactei(tic( o% &oo' mo'el3 The "!m-e o% a((!m$tio"( ma'e (ho!l' -e a( %e5 a( $o((i-le It (ho!l' -e ea(0 a( $o((i-le to (ol,e the $o-lem The "! The "!m m-e o% ,ai ia a-l -le e( !(e (e' ' (ho ho! !l' -e a( %e5 a( $o((i-le3 It (ho!l' -e moe e*i-le to !$'ate the cha"&e( o,e a $eio' o% time 5itho!t cha"&e i" it( %ame5o63 3 @hat ae the 'iee"t $ha(e( o% OR Fom!latio" o% the $o-lem Co"(t!ctio" o% mathematical mo'eli"& Dei,i"& the (ol!tio" %om the mo'el  /ali'it0  / ali'it0 o% the the mo'el E(ta-li(hi"& the co"tol o,e the (ol!tio" Im$leme"tatio" Im$leme"ta tio" o% the +"al (ol!tio"3 3 Li(t o!t the a',a"ta&e( o% OR O$tim!m !(e o% ma"a&e( $o'!ctio" %acto( Im$o,e' .!alit0 o% 'eci(io" Pe$a Pe$ aat atio io" " o% %! %!t! t!e e ma ma"a "a&e &e( ( -0 im im$ $o, o,i" i"& & th thei ei    6"o5le'&e a"' (6ill Mo'i+catio" o% mathematical (ol!tio" -e%oe it( !(e3 3 @hat ae the limitatio"( o% OR

Mathematical mo'el 'o "ot ta6e i"to acco!"t the i"ta"&i-le %acto( (!ch a( h!ma" elatio"( etc3 ca" "ot -e .!a"ti+e'3 Mathematical mo'el( ae a$$lica-le to o"l0 ($eci+c cate&oie( o% $o-lem(3 Re.!ie( h!&e calc!latio"(3 All the(e calc!latio"( ca""ot -e ha"'le' ma"!all0 a"' e.!ie com$!te( 5hich -ea hea,0 co(t3 93 @hat i( li"ea $o&ammi"& Li"ea $o&ammi"& i( a tech"i.!e !(e' %o  'etemi"i"& o$tim!m !tiliBatio" o% limite' e(o!ce( to meet o!t the &i,e" o-7ecti,e(3 The o-7ecti,e i( to ma*imiBe the $o+t o mi"imiBe the e(o!ce( 8me"> machi"e> mateial( a"' mo"e0; :3 @ite the &e"eal mathematical %om!latio" o% LPP3 :3 O-7ecti,e %!"ctio" Ma* o Mi" J K C :* :  C2* 2 33 C "* " 23 S!-7ect to the co"(tai"t( a::* :a:2* 2 a:"* " 8K;-: a2:* :a22* 2 a2"* " 8K;-2 33 33

am:* :am2* 2 am"* " 8K;-m 3 No"#"e&ati,e co"(tai"t( * :>* 2>3* m  ::3 @hat ae the chaactei(tic o% LPP Thee m!(t -e a 5ell 'e+"e' o-7ecti,e %!"ctio"3 Thee m!(t -e alte"ati,e co!(e o% actio" to choo(e3 oth the o-7ecti,e %!"ctio"( a"' the co"(tai"t( m!(t -e li"ea e.!atio" o i"e.!alitie(3 :23 @hat ae the chaactei(tic o% (ta"'a' %om o% LPP The o-7ecti,e %!"ctio" i( o% ma*imiBatio" t0$e3  All the co"(tai"t e.!atio" m!(t -e o% e.!al t0$e -0  a''i"& (lac6 o (!$l!( ,aia-le(

RHS o% the co"(tai"t e.!atio" m!(t -e $o(iti,e t0$e  All the 'eci(io" ,aia-le( ae o% $o(iti,e t0$e :3 @hat ae the chaactei(tic( o% ca"o"ical %om o% LPP 8NO/ 1; I" ca"o"ical %om> i% the o-7ecti,e %!"ctio" i( o%  ma*imiBatio" t0$e> the" all co"(tai"t( ae o%  t0$e3 Similal0 i% the o-7ecti,e %!"ctio" i( o% mi"imiBatio" t0$e> the" all co"(tai"t( ae o%  t0$e3 !t "o"#"e&ati,e co"(tai"t( ae t0$e %o -oth ca(e(3 :43 A +m ma"!%act!e( t5o t0$e( o% $o'!ct( A a"'  a"' (ell( them at $o+t o% R( 2 o" t0$e A a"' R(  o" t0$e 3 Each $o'!ct i( $oce((e' o" t5o machi"e( M: a"' M23T0$e  A e.!ie( : mi"!te o% $oce((i"& time o" M: a"' 2 mi"!te( o" M2 T0$e  e.!ie( : mi"!te o% $oce((i"& time o" M: a"' : mi"!te o" M23 Machi"e M: i( a,aila-le %o "ot moe tha"  ho!( 4 mi"!te( 5hile machi"e M2 i( a,aila-le %o  : ho!( '!i"& a"0 5o6i"& 'a03 Fom!late the $o-lem a( a LPP (o a( to ma*imiBe the $o+t3 8MA 1; Ma*imiBe B K2* : * 2 S!-7ect tot the co"(tai"t(< * :  * 2  4 2* :  * 2   * : >* 2  :?3 A com$a"0 (ell( t5o 'iee"t $o'!ct( A a"'  > ma6i"& a $o+t o% R(34 a"' R(3  $e !"it o" them>e($ecti,el03The0 ae $o'!ce' i" a commo" $o'!ctio" $oce(( a"' ae (ol' i" t5o 'iee"t ma6et(> the $o'!ctio" $oce(( ha( a total ca$acit0 o% > ma"#ho!(3 It ta6e( thee ho!( to $o'!ce a !"it o% A a"' o"e ho! to $o'!ce a !"it o% 3 The ma6et ha( -ee" (!,e0e' a"' com$a"0 oicial %eel that the ma*im!m "!m-e o% !"it( o% A  that ca" -e (ol' i( > !"it( a"' that o%  i( :2> !"it(3 S!-7ect to the(e limitatio"(> $o'!ct( ca" -e (ol' i" a"0  com-i"atio"3 Fom!late the $o-lem a( a LPP (o a( to ma*imiBe the $o+t Ma*imiBe B K4* : * 2 S!-7ect tot the co"(tai"t(<

* :  * 2  > * :   * 2  :2 * : >* 2  :3 @hat i( %ea(i-ilit0 e&io" 8MA 1; Collectio"( o% all %ea(i-le (ol!tio"( ae calle' a %ea(i-le (et o e&io" o% a" o$timiBatio" mo'el3O A e&io" i"  5hich all the co"(tai"t( ae (ati(+e' i( calle' %ea(i-le e&io"3 :3 @hat i( %ea(i-ilit0 e&io" i" a" LP $o-lem I( ti "ece((a0 that it (ho!l' al5a0( -e a co",e* (et  A e&io" i" 5hich all the co"(tai"t( ae (ati(+e' i( calle' %ea(i-le e&io"3 The %ea(i-le e&io" o% a" LPP i( al5a0( co",e* (et3 :3 De+"e (ol!tio"  A (et o% ,aia-le( *:>*23*" co"(tai"t( o% LPP i( calle' a (ol!tio"3

5hich

(ati(+e(

the

:93 De+"e %ea(i-le (ol!tio" 8MA 1;  A"0 (ol!tio" to a LPP 5hich (ati(+e( the "o" "e&ati,it0 e(tictio"( o% LPP1( calle' the %ea(i-le (ol!tio" 23 De+"e o$timal (ol!tio" o% LPP3 8MA 19;  A"0 %ea(i-le (ol!tio" 5hich o$timiBe( the o-7ecti,e %!"ctio" o% the LPP1( calle' the o$timal (ol!tio" 2:3 State the a$$licatio"( o% li"ea $o&ammi"&  @o6 (che'!li"& Po'!ctio" $la""i"&  $o'!ctio" $oce(( Ca$ital -!'&eti"& Fi"a"cial $la""i"& le"'i"& Fam $la""i"& Di(ti-!tio"

M!lti#$eio' 'eci(io" $o-lem I",e"to0 mo'el Fi"a"cial mo'el @o6 (che'!li"& 223 State the Limitatio"( o% LP3 LP teat( all %!"ctio"al elatio"( a( li"ea  LP 'oe( "ot ta6e i"to acco!"t the eect o% time a"' !"cetai"t0  No &!aa"tee %o i"te&e (ol!tio"3 Ro!"'i"& o ma0 "ot %ea(i-le o o$timal (ol!tio"3 Deal( 5ith (i"&le o-7ecti,e> 5hile i" eal li%e the (it!atio" ma0 -e 'iic!lt3 23 @hat 'o 0o! !"'e(ta"' -0 e'!"'a"t co"(tai"t( I" a &i,e" LPP a"0 co"(tai"t 'oe( "ot aect the %ea(i-le e&io" o (ol!tio" ($ace the" the co"(tai"t i( (ai' to -e a e'!"'a"t co"(tai"t3 243 De+"e U"-o!"'e' (ol!tio" I% the %ea(i-le (ol!tio" e&io" 'oe( "ot ha,e a -o!"'e' aea the ma*im!m ,al!e o% J occ!( at i"+"it03 He"ce the LPP i( (ai' to ha,e !"-o!"'e' (ol!tio"3 2?3 De+"e M!lti$le O$timal (ol!tio"  A LPP ha,i"& moe tha" o"e o$timal (ol!tio" i( (ai' to ha,e alte"ati,e o m!lti$le o$timal (ol!tio"(3 23 @hat i( (lac6 ,aia-le I% the co"(tai"t a( &e"eal LPP -e K t0$e the" a "o" "e&ati,e ,aia-le i( i"to'!ce' to co",et the i"e.!alitie( i"to e.!alitie( ae calle' (lac6 ,aia-le(3 The ,al!e( o% the(e  ,aia-le( ae i"te$ete'a( the amo!"t o% !"!(e' e(o!ce(3 23 @hat ae (!$l!( ,aia-le( I% the co"(tai"t a( &e"eal LPP -e K t0$e the" a "o" "e&ati,e i( i"to'!ce' to co",et the i"e.!alitie( i"to e.!alitie( ae calle' the (!$l!( ,aia-le(3

23 De+"e a(ic (ol!tio" Gi,e" a (0(tem o% m li"ea e.!atio"( 5ith "  ,aia-le(8m";3The (ol!tio" o-tai"e' -0 (etti"& 8"#m;  ,aia-le( e.!al to Beo a"' (ol,i"& %o the emai"i"& m  ,aia-le( i( calle' a -a(ic (ol!tio"3 293 De+"e "o" De&e"eate a(ic %ea(i-le (ol!tio" The -a(ic (ol!tio" i( (ai' to -e a "o" 'e&e"eate -a(ic (ol!tio" i% No"e o% the -a(ic ,aia-le( i( Beo3 3 De+"e 'e&e"eate -a(ic (ol!tio"  A -a(ic (ol!tio" i( (ai' to -e a 'e&e"eate -a(ic (ol!tio" i% o"e o moe o% the -a(ic ,aia-le( ae Beo3 :3 @hat i( the %!"ctio" o% mi"im!m atio To 'etemi"e the -a(ic ,aia-le to lea,e To 'etemi"e the ma*im!m i"cea(e i" -a(ic ,aia-le To mai"tai" the %ea(i-ilit0 o% %ollo5i"& (ol!tio" 23 Fom the o$tim!m (im$le* ta-le ho5 'o 0o! i'e"ti%0 that LPP ha( !"-o!"'e' (ol!tio" To +"' the lea,i"& ,aia-le( the atio i( com$!te'3 The atio i( K the" thee i( a" !"-o!"'e' (ol!tio" to the &i,e" LPP3 3 Fom the o$tim!m (im$le* ta-le ho5 'o 0o! i'e"ti%0 that the LPP ha( "o (ol!tio" I% atlea(t o"e ati+cial ,aia-le a$$ea( i" the -a(i( at Beo le,el 5ith a ,e ,al!e i" the - col!m" a"' the o$timalit0 co"'itio" i( (ati(+e' the" the oi&i"al $o-lem ha( "o %ea(i-le (ol!tio"3 43 Ho5 'o 0o! i'e"ti%0 that LPP ha( "o (ol!tio" i" a t5o $ha(e metho' I% all J7 ) C7    the" atlea(t o"e ati+cial ,aia-le a$$ea( i" the o$tim!m -a(i( at "o" Beo le,el the LPP 'oe( "ot $o((e(( a"0 (ol!tio"3 ?3 @hat 'o 0o! !"'e(ta"' -0 'e&e"eac0

The co"ce$t o% o-tai"i"& a 'e&e"eate -a(ic %ea(i-le (ol!tio" i" LPP i( 6"o5" a( 'e&e"eac03 Thi( ma0 occ! i" the i"itial (ta&e 5he" atlea(t o"e -a(ic ,aia-le i( Beo i" the i"itial -a(ic %ea(i-le (ol!tio"3 3 @ite the (ta"'a' %om o% LPP i" the mati* "otatio" I" mati* "otatio" the ca"o"ical %om o% LPP ca" -e e*$e((e' a( Ma*imiBe J K C8o-7 %"3; S!- to A K -8co"(tai"t(; a"'  K  8"o" "e&ati,e e(tictio"(; @hee C K 8C:>C2>33C";> *: *2 3 3 *"

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3 De+"e -a(ic ,aia-le a"' "o"#-a(ic ,aia-le i" li"ea  $o&ammi"&3 A -a(ic (ol!tio" to the (et o% co"(tai"t( i( a (ol!tio" o-tai"e' -0 (etti"& a"0 " ,aia-le( e.!al to Beo a"' (ol,i"& %o emai"i"& m ,aia-le( "ot e.!al to Beo3 S!ch m  ,aia-le( ae calle' -a(ic ,aia-le( a"' emai"i"& " Beo  ,aia-le( ae calle' "o"#-a(ic ,aia-le(3 3Sol,e the %ollo5i"& LP $o-lem -0 &a$hical metho'3 8MA 1; Ma*imiBe B K* : 4* 2 S!-7ect tot the co"(tai"t(< * :  * 2  ? * 2  * : >* 2 

93 De+"e !"e(ticte' ,aia-le a"' ati+cial ,aia-le3 8NO/  1; U"e(ticte' /aia-le "e&ati,e o Beo ,al!e(  Ati+cial ,aia-le
UNIT#II :3 De+"e ta"($otatio" $o-lem3 It i( a ($ecial t0$e o% li"ea $o&ammi"& mo'el i"  5hich the &oo'( ae (hi$$e' %om ,aio!( oi&i"( to 'iee"t 'e(ti"atio"(3 The o-7ecti,e i( to +"' the -e(t $o((i-le allocatio" o% &oo'( %om ,aio!( oi&i"( to 'iee"t 'e(ti"atio"( (!ch that the total ta"($otatio" co(t i( mi"im!m3 3 De+"e the %ollo5i"&< Fea(i-le (ol!tio" A (et o% "o"#"e&ati,e 'eci(io" ,al!e( *i7 8iK:>2>3m  7K:>2"; (ati(+e( the co"(tai"t e.!atio"( i( calle' a %ea(i-le (ol!tio"3 43 De+"e the %ollo5i"&< -a(ic %ea(i-le (ol!tio" A -a(ic %ea(i-le (ol!tio" i( (ai' to -e -a(ic i% the "!m-e o% $o(iti,e allocatio"( ae m"#:38 m#oi&i" a"' "# 'e(ti"atio";3I% the "!m-e o% allocatio"( ae le(( tha" 8m"# :; it i( calle' 'e&e"eate -a(ic %ea(i-le (ol!tio"3 ?3 De+"e o$timal (ol!tio" i" ta"($otatio" $o-lem  A %ea(i-le (ol!tio" i( (ai' to -e o$timal> i% it mi"imiBe( the total ta"($otatio" co(t3 3 @hat ae the metho'( !(e' i" ta"($otatio" $o-lem to o-tai" the i"itial -a(ic %ea(i-le (ol!tio"3 Noth#5e(t co"e !le Lo5e(t co(t e"t0 metho' o mati* mi"ima metho'

 /o&el1( a$$o*imatio" metho' 3 @ite 'o5" the -a(ic (te$( i",ol,e' ta"($otatio" $o-lem3 To +"' the i"itial -a(ic %ea(i-le (ol!tio"

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To +"' a" o$timal (ol!tio" -0 ma6i"& (!cce((i,e im$o,eme"t( %om the i"itial -a(ic %ea(i-le (ol!tio"3 3> @hat 'o 0o! !"'e(ta"' -0 'e&e"eac0 i" a ta"($otatio" $o-lem 8NO/ 1; I% the "!m-e o% occ!$ie' cell( i" a m * " ta"($otatio" $o-lem i( le(( tha" 8 m"#:; the" the $o-lem i( (ai' to -e 'e&e"eate3 93 @hat i( -ala"ce' ta"($otatio" $o-lem !"-ala"ce' ta"($otatio" $o-lem  @he" the (!m o% (!$$l0 i( e.!al to 'ema"'(> the" the $o-lem i( (ai' to -e -ala"ce' ta"($otatio" $o-lem3  A ta"($otatio" $o-lem i( (ai' to -e !"-ala"ce' i% the total (!$$l0 i( "ot e.!al to the total 'ema"'3 :3 Ho5 'o 0o! co",et a" !"-ala"ce' ta"($otatio" $o-lem i"to a -ala"ce' o"e The !"-ala"ce' ta"($otatio" $o-lem i( co",ete' i"to a -ala"ce' o"e -0 a''i"& a '!mm0 o5 8(o!ce; o  '!mm0 col!m" 8'e(ti"atio"; 5hiche,e i( "ece((a03 The !"it ta"($otatio" co(t o% the '!mm0 o5 col!m" eleme"t( ae a((i&"e' to Beo3 The" the $o-lem i( (ol,e' -0 the !(!al $oce'!e3 ::3 E*$lai" ho5 the $o+t ma*imiBatio" ta"($otatio" $o-lem ca" -e co",ete' to a" e.!i,ale"t co(t mi"imiBatio" ta"($otatio" $o-lem3 8MA 1; I% the o-7ecti,e i( to ma*imiBe the $o+t o ma*imiBe the e*$ecte' (ale( 5e ha,e to co",et the(e $o-lem( -0  m!lti$l0i"& all cell e"tie( -0 #:3No5 the ma*imiBatio" $o-lem -ecome( a mi"imiBatio" a"' it ca" -e (ol,e' -0 the !(!al al&oithm

:23 Detemi"e -a(ic %ea(i-le (ol!tio" to the %ollo5i"& ta"($otatio" $o-lem !(i"& lea(t co(t metho'3 8MA 19; A  C D SUPPL  P : 2 : 4  Q   2 : ? R 4 2 ? 9 2 Dema"' 2 4  : :3 De+"e ta"((hi$me"t $o-lem(  A $o-lem i" 5hich a,aila-le commo'it0 %e.!e"tl0  mo,e( %om o"e (o!ce to a"othe (o!ce o 'e(ti"atio" -e%oe eachi"& it( act!al 'e(ti"atio" i( calle' ta"((hi$me"t $o-lem(3 :43 @hat i( the 'iee"ce -et5ee" Ta"($otatio" $o-lem  Ta"((hi$me"t Po-lem I" a ta"($otatio" $o-lem thee ae "o i"teme'iate (hi$$i"& $oi"t( 5hile i" ta"((hi$me"t $o-lem thee ae i"teme'iate (hi$$i"& $oi"t( :?3 @hat i( a((i&"me"t $o-lem  A" a((i&"me"t $o-lem i( a $atic!la ca(e o% a ta"($otatio" $o-lem i" 5hich a "!m-e o% o$eatio"( ae a((i&"e' to a" e.!al "!m-e o% o$eato( 5hee each o$eato $e%om( o"l0 o"e o$eatio"> the o,eall o-7ecti,e i( to ma*imiBe the total $o+t o mi"imiBe the o,eall co(t o% the &i,e" a((i&"me"t3 :3 E*$lai" the 'iee"ce a((i&"me"t $o-lem(

-et5ee"

Ta"($otatio" $o-lem( :;

2;

(!$$l0 at a"0 (o!ce ma0 -e a (o!ce 5ill a"0 $o(iti,e .!a"tit03 Dema"' at a"0 'e(ti"atio" ma0 'e(ti"atio" -e a $o(iti,e .!a"tit03

ta"($otatio" a"' A((i&"me"t $o-lem( S!$$l0 at a"0  -e :3 Dema"' at a"0  5ill -e :3

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O"e o moe (o!ce to a"0 "!m-e 'e(ti"atio"3 o% 'e(ti"atio"3

O"e (o!ce o"e

:3 De+"e !"-o!"'e' a((i&"me"t $o-lem a"' 'e(ci-e the (te$( i",ol,e' i" (ol,i"& it I% the "o3 o% o5( i( "ot e.!al to the "o3 o% col!m" i" the &i,e" co(t mati* the $o-lem i( (ai' to -e !"-ala"ce'3 It i( co",ete' to a -ala"ce' o"e -0 a''i"& '!mm0 o5 o '!mm0  col!m" 5ith Beo co(t3 :3 E*$lai" ho5 a ma*imiBatio" $o-lem i( (ol,e' !(i"& a((i&"me"t mo'el The ma*imiBatio" $o-lem( ae co",ete' to a mi"imiBatio" o"e o% the %ollo5i"& metho'3 8i; Si"ce ma* B K mi"8#B; 8ii; S!-tact all the co(t eleme"t( all o% the co(t mati* %om the Hi&he(t co(t eleme"t i" that co(t mati*3 :93 @hat 'o 0o! !"'e(ta"' -0 e(ticte' a((i&"me"t E*$lai" ho5 0o! (ho!l' o,ecome it The a((i&"me"t tech"i.!e> it ma0 "ot -e $o((i-le to a((i&" a $atic!la ta(6 to a $atic!la %acilit0 '!e to tech"ical 'iic!ltie( o othe e(tictio"(3 Thi( ca" -e o,ecome -0 a((i&"i"& a ,e0 hi&h $oce((i"& time o co(t 8it ca" -e =; to the coe($o"'i"& cell3 23 Ho5 'o 0o! i'e"ti%0 alte"ati,e (ol!tio" i" a((i&"me"t $o-lem Sometime( a +"al co(t mati* co"tai"( moe tha" e.!ie' "!m-e o% Beoe( at the i"'e$e"'e"t $o(itio"3 Thi( im$lie( that thee i( moe tha" o"e o$timal (ol!tio" 5ith (ome o$tim!m a((i&"me"t co(t3 2:3 @hat i( a ta,eli"& (ale(ma" $o-lem  A (ale(ma" "omall0 m!(t ,i(it a "!m-e o% citie( (tati"& %om hi( hea' .!ate(3 The 'i(ta"ce -et5ee" e,e0 

$ai o% citie( ae a((!me' to -e 6"o5"3 The $o-lem o%  +"'i"& the (hote(t 'i(ta"ce i% the (ale(ma" (tat( %om hi( hea' .!ate( a"' $a((e( tho!&h each cit0 e*actl0 o"ce a"' et!"( to the hea'.!ate( i( calle' Ta,eli"& Sale(ma" $o-lem3 223 De+"e o!te co"'itio" The (ale(ma" (tat( %om hi( hea'.!ate( a"' $a((e( tho!&h each cit0 e*actl0 o"ce3 23 Gi,e the aea( o% o$eatio"( o% a((i&"me"t $o-lem(  A((i&"i"& 7o-( to machi"e(3  Allocati"& me" to 7o-(machi"e(3 Ro!te (che'!li"& %o a ta,eli"& (ale(ma"3 243 Ho5 'o 0o! co",et the !"-ala"ce' a((i&"me"t $o-lem i"to a -ala"ce' o"e 8MA 1; Si"ce the a((i&"me"t i( o"e to o"e -a(i( > the $o-lem ha,e a (.!ae mati*3 I% the &i,e" $o-lem i( "ot (.!ae mati* a'' a '!mm0 o5 o '!mm0 col!m" a"' the" co",et it i"to a -ala"ce' o"e 8(.!ae mati*;3 A((i&" Beo co(t  ,al!e( %o a"0 '!mm0 o5col!m" a"' (ol,e it -0 !(!al a((i&"me"t metho'3

UNIT#III  :3 De+"e I"te&e Po&ammi"& Po-lem 8IPP; 8DEC 1;  A li"ea $o&ammi"& $o-lem i" 5hich (ome o all o% the  ,aia-le( i" the o$timal (ol!tio" ae e(ticte' to a((!me "o"#"e&ati,e i"te&e ,al!e( i( calle' a" I"te&e  Po&ammi"& Po-lem 8IPP; o I"te&e Li"ea Po&ammi"& 23 E*$lai" the im$ota"ce o% I"te&e $o&ammi"& $o-lem I" LPP the ,al!e( %o the ,aia-le( ae eal i" the o$timal (ol!tio"3 Ho5e,e i" cetai" $o-lem( thi( a((!m$tio" i( !"eali(tic3 Fo e*am$le i% a $o-lem ha( a (ol!tio" o% :2 ca( to -e $o'!ce' i" a ma"!%act!i"& com$a"0 i( mea"i"&le((3 The(e t0$e( o% $o-lem( e.!ie i"te&e ,al!e( %o the 'eci(io" ,aia-le(3 Thee%oe IPP i( "ece((a0 to o!"' o the %actio"al ,al!e(3

3 Li(t o!t (ome o% the a$$licatio"( o% IPP 8MA 19; 8DEC 1; 8MA 1; IPP occ! .!ite %e.!e"tl0 i" -!(i"e(( a"' i"'!(t03  All ta"($otatio"> a((i&"me"t a"' ta,eli"& (ale(ma" $o-lem( ae IPP> (i"ce the 'eci(io" ,aia-le( ae eithe  Jeo o o"e3  All (e.!e"ci"& a"' o!ti"& 'eci(io"( ae IPP a( it e.!ie( the i"te&e ,al!e( o% the 'eci(io" ,aia-le(3 Ca$ital -!'&eti"& a"' $o'!ctio" (che'!li"& $o-lem ae PP3 I" %act> a"0 (it!atio" i",ol,i"& 'eci(io"( o% the t0$e eithe to 'o a 7o- o "ot to 'o ca" -e teate' a( a" IPP3  All allocatio" $o-lem( i",ol,i"& the allocatio" o%  &oo'(> me"> machi"e(> &i,e i(e to IPP (i"ce (!ch commo'itie( ca" -e a((i&"e' o"l0 i"te&e a"' "ot %actio"al  ,al!e(3 43 Li(t the ,aio!( t0$e( o% i"te&e $o&ammi"& 8MA 1; Mi*e' IPP P!e IPP ?3 @hat i( $!e IPP I" a li"ea $o&ammi"& $o-lem> i% all the ,aia-le( i" the o$timal (ol!tio" ae e(ticte' to a((!me "o"#"e&ati,e i"te&e ,al!e(> the" it i( calle' the $!e 8all; IPP3 3 @hat i( Mi*e' IPP I" a li"ea $o&ammi"& $o-lem> i% o"l0 (ome o% the  ,aia-le( i" the o$timal (ol!tio" ae e(ticte' to a((!me "o"#"e&ati,e i"te&e ,al!e(> 5hile the emai"i"& ,aia-le( ae %ee to ta6e a"0 "o"#"e&ati,e ,al!e(> the" it i( calle' A  Mi*e' IPP3 3 @hat i( Jeo#o"e $o-lem I% all the ,aia-le( i" the o$tim!m (ol!tio" ae allo5e' to ta6e ,al!e( eithe  o : a( i" 'o1 o "ot to 'o1 t0$e 'eci(io"(> the" the $o-lem i( calle' Jeo#o"e $o-lem o  (ta"'a' 'i(cete $o&ammi"& $o-lem3

3 @hat i( the 'iee"ce -et5ee" P!e i"te&e $o&ammi"&  mi*e' i"te&e i"te&e $o&ammi"&3  @he" a" o$timiBatio" $o-lem> i% all the 'eci(io"  ,aia-le( ae e(ticte' to ta6e i"te&e ,al!e(> the" it i( e%ee' a( $!e i"te&e $o&ammi"&3 I% (ome o% the  ,aia-le( ae allo5e' to ta6e i"te&e ,al!e(> the" it i( e%ee' a( mi*e' i"te&e i"te&e $o&ammi"&3 93 E*$lai" the im$ota"ce o% I"te&e Po&ammi"& I" li"ea $o&ammi"& $o-lem> all the 'eci(io"  ,aia-le( allo5e' to ta6e a"0 "o"#"e&ati,e eal ,al!e(> a( it i( .!ite $o((i-le a"' a$$o$iate to ha,e %actio"al ,al!e( i" ma"0 (it!atio"(3 Ho5e,e i" ma"0 (it!atio"(> e($eciall0 i" -!(i"e(( a"' i"'!(t0> the(e 'eci(io" ,aia-le( ma6e (e"(e o"l0 i% the0 ha,e i"te&e ,al!e( i" the o$timal (ol!tio"3 He"ce a "e5 $oce'!e ha( -ee" 'e,elo$e' i" thi( 'iectio" %o the ca(e o% LPP (!-7ecte' to a''itio"al e(tictio" that the 'eci(io" ,aia-le( m!(t ha,e i"te&e ,al!e(3 :3 @h0 "ot o!"' o the o$tim!m ,al!e( i" (tea' o%  e(oti"& to IP 8MA 1; Thee i( "o &!aa"tee that the i"te&e ,al!e' (ol!tio" 8o-tai"e' -0 (im$le* metho'; 5ill (ati(%0 the co"(tai"t(3 i3e3 3> it ma0 "ot (ati(%0 o"e o moe co"(tai"t( a"' a( (!ch the "e5 (ol!tio" ma0 "ot %ea(i-le3 So thee i( a "ee' %o  'e,elo$i"& a (0(tematic a"' eicie"t al&oithm %o o-tai"i"& the e*act o$tim!m i"te&e (ol!tio" to a" IPP3 ::3 @hat ae metho'( %o IPP 8MA 1; I"te&e $o&ammi"& ca" -e cate&oiBe' a( 8i; C!tti"& metho'( 8ii; Seach Metho'(3 :23 @hat i( c!tti"& metho' A (0(tematic $oce'!e %o (ol,i"& $!e IPP 5a( +(t 'e,elo$e' -0 R3E3Gomo0 i" :9?3 Late o"> he e*te"'e' the $oce'!e to (ol,e mi*e' IPP> "ame' a( c!tti"& $la"e al&oithm> the metho' co"(i(t( i" +(t (ol,i"& the IPP a( o'i"a0 LPP30 i&"oi"& the i"te&it0 e(tictio" a"' the" i"to'!ci"& a''itio"al co"(tai"t( o"e a%te the othe to c!t

cetai" $at o% the (ol!tio" ($ace !"til a" i"te&al (ol!tio" i( o-tai"e'3 :3 @hat i( (each metho' It i( a" e"!meatio" metho' i" 5hich all %ea(i-le i"te&e $oi"t( ae e"!meate'3 The 5i'el0 !(e' (each metho' i( the a"ch a"' o!"' Tech"i.!e3 It al(o (tat(  5ith the co"ti"!o!( o$tim!m> -!t (0(tematicall0 $atitio"( the (ol!tio" ($ace i"to (!- $o-lem( that elimi"ate $at( that co"tai" "o %ea(i-le i"te&e (ol!tio"3 It 5a( oi&i"all0  'e,elo$e' -0 A3H3La"' a"' A3G3Doi&3 :43 E*$lai" the co"ce$t o% a"ch a"' o!"' Tech"i.!e The 5i'el0 !(e' (each metho' i( the a"ch a"' o!"' Tech"i.!e3 It (tat( 5ith the co"ti"!o!( o$tim!m> -!t (0(tematicall0 $atitio"( the (ol!tio" ($ace i"to (!$o-lem( that elimi"ate $at( that co"tai" "o %ea(i-le i"te&e (ol!tio"3 It 5a( oi&i"all0 'e,elo$e' -0 A3H3La"' a"'  A3G3Doi&3 :?3 Gi,e the &e"eal %omat o% IPP The &e"eal IPP i( &i,e" -0  Ma*imiBe J K C S!-7ect to the co"(tai"t(  A  ->   a"' (ome o all ,aia-le( ae i"te&e3 :3 @ite a" al&oithm %o Gomo01( Factio"al C!t al&oithm :3 Co",et the mi"imiBatio" IPP i"to a" e.!i,ale"t ma*imiBatio" IPP a"' all the coeicie"t( a"' co"(tai"t( (ho!l' -e i"te&e(3 23 Fi"' the o$tim!m (ol!tio" o% the e(!lti"& ma*imiBatio" LPP -0 !(i"& (im$le*    metho'3 3 Te(t the i"te&it0 o% the o$tim!m (ol!tio"3 43 Re5ite each  i ?3 E*$e(( each o% the "e&ati,e %actio"( i% a"0> i" the 6 th o5  o% the o$tim!m (im$le* 

ta-le a( the (!m o% a "e&ati,e i"te&e a"' a "o"#"e&ati,e %actio"3 3 Fi"' the %actio"al c!t co"(tai"t 3 A'' the %actio"al c!t co"(tai"t at the -ottom o%  o$tim!m (im$le* ta-le o-tai"e' i" (te$ 23 3 Go to (te$  a"' e$eat the $oce'!e !"til a" o$tim!m i"te&e (ol!tio" i( o-tai"e'3 :3 @hat i( the $!$o(e o% Factio"al c!t co"(tai"t( I" the c!tti"& $la"e metho'> the %actio"al c!t co"(tai"t( c!t the !"!(e%!l aea o% the %ea(i-le e&io" i" the &a$hical (ol!tio" o% the $o-lem3 i3e3 c!t that aea  5hich ha( "o i"te&e#,al!e' %ea(i-le (ol!tio"3 Th!( the(e co"(tai"t( elimi"ate all the "o"#i"te&al (ol!tio"( 5itho!t loo(i"& a"0 i"te&e#,al!e' (ol!tio"3 :3A ma"!%act!e o% -a-0 'oll( ma6e( t5o t0$e( o% 'oll(> 'oll  a"' 'oll 3 Poce((i"& o% the(e 'oll( i( 'o"e o" t5o machi"e( A a"' 3 Doll  e.!ie( 2 ho!( o" machi"e A a"'  ho!( o" Machi"e 3 Doll  e.!ie( ? ho!( o" machi"e A  a"' ? ho!( o" Machi"e 3 Thee ae : ho!( o% time $e  'a0 a,aila-le o" machi"e A a"'  ho!( o" machi"e 3 The $o+t i( &ai"e' o" -oth the 'oll( i( (ame3 Fomat thi( a( IPP Let the ma"!%act!e 'eci'e to ma"!%act!e * : the "!m-e o% 'oll  a"' * 2 "!m-e o% 'oll  (o a( to ma*imiBe the $o+t3 The com$lete %om!latio" o% the IPP i( &i,e" -0  Ma*imiBe J K * :* 2 S!-7ect to 2 * :  ? * 2 :  * : ? * 2  a"'  a"' ae i"te&e(3 :93 E*$lai" Gomo01( Mi*e' I"te&e Metho' The $o-lem i( +(t (ol,e' -0 co"ti"!o!( LPP -0  i&"oi"& the i"te&it0 co"'itio"3 I% the ,al!e( o% the i"te&e  co"(tai"e' ,aia-le( ae i"te&e(> the" the c!e"t (ol!tio" i( a" o$timal (ol!tio" to the &i,e" mi*e' IPP3 El(e (elect the (o!ce o5 5hich coe($o"'( to the la&e(t %actio"al $at amo"& the(e -a(ic ,aia-le( 5hich ae co"(tai"e' to -e i"te&e(3 The" co"(t!ct the Gomaia" co"(tai"t %om the

(o!ce o53 A'' thi( (eco"'a0 co"(tai"t at the -ottom o%  the o$tim!m (im$le* ta-le a"' !(e '!al (im$le* metho' to o-tai" the "e5 %ea(i-le o$timal (ol!tio"3 Re$eat thi( $oce'!e !"til the ,al!e( o% the i"te&e e(ticte' ,aia-le( ae i"te&e( i" the o$tim!m (ol!tio" o-tai"e'3 23 @hat i( the &eometical mea"i"& o% $otio"e' o  -a"che' the oi&i"al $o-lem Geometicall0 it mea"( that the -a"chi"& $oce(( elimi"ate( $otio" o% the %ea(i-le e&io" that co"tai"( "o %ea(i-le#i"te&e (ol!tio"3 Each o% the (!-#$o-lem( (ol,e' (e$aatel0 a( a LPP3 2:3 @hat i( (ta"'a' 'i(cete $o&ammi"& $o-lem I% all the ,aia-le( i" the o$tim!m (ol!tio" ae allo5e' to ta6e ,al!e( eithe  o : a( i" 'o1 o "ot to 'o1 t0$e 'eci(io"(> the" the $o-lem i( calle' (ta"'a' 'i(cete $o&ammi"& $o-lem3 223 @hat i( the 'i(a',a"ta&e o% -a"che' o $otio"e' metho' It e.!ie( the o$tim!m (ol!tio" o% each (!- $o-lem3 I" la&e $o-lem( thi( co!l' -e ,e0 te'io!( 7o-3 23 Ho5 ca" 0o! im$o,e the eicie"c0 o% $otio"e' metho' The com$!tatio"al eicie"c0 o% $otio"e' metho' i( i"cea(e' -0 !(i"& the co"ce$t o% -o!"'i"&3 0 thi( co"ce$t  5he"e,e the co"ti"!o!( o$tim!m (ol!tio" o% a (!- $o-lem  0iel'( a ,al!e o% the o-7ecti,e %!"ctio" lo5e tha" that o% the -e(t a,aila-le i"te&e (ol!tio" it i( !(ele(( to e*$loe the $o-lem a"0 %!the co"(i'eatio"3 Th!( o"ce a %ea(i-le i"te&e (ol!tio" i( o-tai"e'> it( a((ociati,e o-7ecti,e %!"ctio" ca" -e ta6e" a( a lo5e -o!"' to 'elete i"%eio (!-# $o-lem(3 He"ce eicie"c0 o% a -a"ch a"' -o!"' metho' 'e$e"'( !$o" ho5 (oo" the (!cce((i,e (!-#$o-lem( ae %athome'3

UNIT#I/  :3 @hat 'o 0o! mea" -0 $o7ect

 A $o7ect i( 'e+"e' a( a com-i"atio" o" i"te elate' acti,itie( 5ith limite' e(o!ce( "amel0 me"> machi"e( mateial(> mo"e0 a"' time all o% 5hich m!(t -e e*ec!te' i" a 'e+"e' o'e %o it( com$letio"3 23 @hat ae the thee mai" $ha(e( o% $o7ect Pla""i"&> Sche'!li"& a"' Co"tol 3 @hat ae the t5o -a(ic $la""i"& tech"i.!e( i" a "et5o6 a"al0(i( Citical Path Metho' 8CPM;

a"'

co"tolli"&

Po&amme E,al!atio" a"' Re,ie5 Tech"i.!e 8PERT; 43 @hat ae the a',a"ta&e( o% CPM a"' PERT tech"i.!e( It e"co!a&e( a lo&ical 'i(ci$li"e i" $la""i"&> (che'!li"& a"' co"tol o% $o7ect( It hel$( to eect co"(i'ea-le e'!ctio" o% $o7ect time( a"' the co(t It hel$( -ette !tiliBatio" o% e(o!ce( li6e me">machi"e(>mateial( a"' mo"e0 5ith e%ee"ce to time It mea(!e( the eect o% 'ela0( o" the $o7ect a"' $oce'!al cha"&e( o" the o,eall (che'!le3 ?3 @hat i( the 'iee"ce CPM a"' PERT CPM Net5o6 i( -!ilt o" the -a(i( o% acti,it0  Detemi"i(tic "at!e O"e time e(timatio" PERT  A" e,e"t oie"te' "et5o6  Po-a-ili(tic "at!e Thee time e(timatio" 3 @hat i( "et5o6  A "et5o6 i( a &a$hical e$e(e"tatio" o% a $o7ect1( o$eatio" a"' i( com$o(e' o% all the e,e"t( a"' acti,itie( i"

(e.!e"ce alo"& 5ith thei i"te elatio"(hi$ a"' i"te  'e$e"'e"cie(3 3 @hat i( E,e"t i" a "et5o6 'ia&am  A" e,e"t i( ($eci+c i"(ta"t o% time 5hich ma6( the (tat( a"' e"' o% a" acti,it03 It "eithe co"(!me( time "o  e(o!ce(3 It i( e$e(e"te' -0 a cicle3 3 De+"e acti,it0  A $o7ect co"(i(t( o% a "!m-e o% 7o- o$eatio"( 5hich ae calle' acti,itie(3 It i( the eleme"t o% the $o7ect a"' it ma0 -e a $oce((> mateial ha"'li"&> $oc!eme"t c0cle etc3 93 De+"e Citical Acti,itie( I" a Net5o6 'ia&am citical acti,itie( ae tho(e 5ho(e i% co"(!me moe tha" e(timate' time the $o7ect 5ill -e 'ela0e'3 :3 De+"e "o" citical acti,itie(  Acti,itie( 5hich ha,e a $o,i(io" (!ch that the e,e"t i%  the0 co"(!me a ($eci+e' time o,e a"' a-o,e the e(timate' time the $o7ect 5ill "ot -e 'ela0e' ae teme' a( "o" citical acti,itie(3 ::3 De+"e D!mm0 Acti,itie(  @he" t5o acti,itie( (tat at a (ame time> the hea' e,e"t ae 7oi"e' -0 a 'otte' ao5 6"o5" a( '!mm0 acti,it0 5hich ma0 -e citical o "o" citical3 :23 De+"e '!atio" It i( the e(timate' o the act!al time e.!ie' to com$lete a ta'e o a" acti,it03 :3 De+"e total $o7ect time It i( time ta6e" to com$lete to com$lete a $o7ect a"'  7!(t %o!"' %om the (e.!e"ce o% citical acti,itie(3 I" othe   5o'( it i( the '!atio" o% the citical $ath3 :43 De+"e Citical Path

 It i( the (e.!e"ce o% acti,itie( 5hich 'eci'e( the total $o7ect '!atio"3 It i( %ome' -0 citical acti,itie( a"' co"(!me( ma*im!m e(o!ce( a"' time3 :?3 De+"e oat o (lac6 8MA 1; Slac6 i( 5ith e($ect to a" e,e"t a"' oat i( 5ith e($ect to a" acti,it03 I" othe 5o'(> (lac6 i( !(e' 5ith PERT a"' oat 5ith CPM3 Float o (lac6 mea"( e*ta time o,e a"' a-o,e it( '!atio" 5hich a "o"#citical acti,it0 ca" co"(!me  5itho!t 'ela0i"& the $o7ect3 :3 De+"e total oat 8MA 1; The total oat %o a" acti,it0 i( &i,e" -0 the total time  5hich i( a,aila-le %o $e%oma"ce o% the acti,it0> mi"!( the '!atio" o% the acti,it03 The total time i( a,aila-le %o  e*ec!tio" o% the acti,it0 i( &i,e" -0 the late(t +"i(h time o%  a" acti,it0 mi"!( the ealie(t (tat time %o the acti,it03 Th!( Total oat K Late(t (tat time ) ealie(t (tat time3

:3 De+"e %ee oat 8MA 1; Thi( i( that $at o% the total oat 5hich 'oe( "ot aect the (!-(e.!e"t acti,itie(3 Thi( i( the oat 5hich i( o-tai"e'  5he" all the acti,itie( ae (tate' at the ealie(t3 :3 De+"e I"'e$e"'e"t oat 8MA 1; 8MA 1; I% all the $ece'i"& acti,itie( ae com$lete' at thei  late(t> i" (ome ca(e(> "o oat a,aila-le %o the (!-(e.!e"t acti,itie( 5hich ma0 thee%oe -ecome citical3 I"'e$e"'e"t oat K %ee ) tail (lac63 :93 De+"e I"te%ei"& oat Sometime( oat o% a" acti,it0 i% !tiliBe' 5holl0 o i" $at> ma0 i"!e"ce the (tati"& time o% the (!ccee'i"& acti,itie( i( 6"o5" a( i"te%ei"& oat3 I"te%ei"& oat K late(t e,e"t time o% the hea' # ealie(t e,e"t time o% the e,e"t3

23 De+"e O$timi(tic O$timi(tic time e(timate i( the '!atio" o% a"0 acti,it0   5he" e,e0thi"& &oe( o" ,e0 5ell '!i"& the $o7ect3 2:3 De+"e Pe((imi(tic Pe((imi(tic time e(timate i( the '!atio" o% a"0 acti,it0   5he" almo(t e,e0thi"& &oe( a&ai"(t o! 5ill a"' a lot o%  'iic!ltie( i( %ace' 5hile 'oi"& a $o7ect3 223 De+"e mo(t li6el0 time e(timatio" Mo(t li6el0 time e(timate i( the '!atio" o% a"0 acti,it0   5he" (ometime( thi"& &o o" ,e0 5ell> (ometime( thi"&( &o o" ,e0 -a' 5hile 'oi"& the $o7ect3 243 @hat i( a $aallel citical $ath  @he" citical acti,itie( ae ca(he' a"' the '!atio" i( e'!ce' othe $ath( ma0 al(o -ecome citical (!ch citical $ath( ae calle' $aallel citical $ath3 2?3 @hat i( (ta"'a' 'e,iatio" a"' ,aia"ce i" PERT "et5o6 8NO/ 1; The e*$ecte' time o% a" acti,it0 i" act!al e*ec!tio" i( "ot com$letel0 elia-le a"' i( li6el0 to ,a03 I% the ,aia-ilit0  i( 6"o5" 5e ca" mea(!e the elia-ilit0 o% the e*$ecte' time a( 'etemi"e' %om thee e(timate(3 The mea(!e o% the  ,aia-ilit0 o% $o((i-le acti,it0 time i( &i,e" -0 (ta"'a' 'e,iatio"> thei $o-a-ilit0 'i(ti-!tio"  /aia"ce o% the acti,it0 i( the (.!ae o% the (ta"'a' 'e,iatio" 23 Gi,e the 'iee"ce -et5ee" 'iect co(t a"' i"'iect co(t 8NO/ 1; Diect co(t i( 'iectl0 'e$e"'i"& !$o" the amo!"t o%  e(o!ce( i",ol,e' i" the e*ec!tio" o% all acti,itie( o% the $o7ect3 I"cea(e i" 'iect co(t 5ill 'ecea(e i" $o7ect '!atio"3 I"'iect co(t i( a((ociate' 5ith &e"eal a"' a'mi"i(tati,e e*$e"(e(> i"(!a"ce co(t> ta*e( etc3 I"cea(e i" i"'iect co(t 5ill i"cea(e i" $o7ect '!atio"3

UNIT#/  :3 De+"e Ve"'al1( "otatio" %o e$e(e"ti"& .!e!i"& mo'el(3 A .!e!i"& mo'el i( ($eci+e' a"' e$e(e"te' (0m-olicall0 i" the %om 8a-c; < 8'e;  @hee a# i"te ai,al time -#(e,ice mecha"i(m c#"!m-e o% (e,ice '#the ca$acit0 o% the (0(tem e#the .!e!e 'i(ci$li"e 23 I" a (!$e ma6et> the a,ea&e ai,al ate o% c!(tome i( ? i" e,e0  mi"!te( %ollo5i"& Poi((o" $oce((3 The a,ea&e time i( ta6e" -0 the ca(hie to li(t a"' calc!late the c!(tome1( $!cha(e i( 43? mi"!te( %ollo5i"& e*$o"e"tial 'i(ti-!tio"3 @hat i( the $o-a-ilit0 that the .!e!e le"&th e*cee'( ?  Ai,al ateK ? mi" Se,ice ateK29mi" Po-a-ilit0 that the .!e!e le"&th e*cee'( ? K 8W;  "2 K  83?; K3: 3 E*$lai" Q!e!e 'i(ci$li"e a"' it( ,aio!( %om(3 8i; FIFO o FCFS # Fi(t I" Fi(t O!t o Fi(t Come Fi(t Se,e'3 8ii; LIFO o LCFS # La(t I" Fi(t O!t o La(t Come Fi(t Se,e'3 8iii; SIRO # Selectio" %o (e,ice i" a"'om o'e3 8i,; PIR # Pioit0 i" (electio" 43 Di(ti"&!i(h -et5ee" ta"(ie"t a"' (tea'0 (tate .!e!i"& (0(tem3  A (0(tem i( (ai' to -e i" ta"(ie"t (tate 5he" it( o$eati"& chaactei(tic( ae 'e$e"'e"t o" time3 A (tea'0 (tate (0(tem i( o"e i" 5hich the -eha,io o% the (0(tem i( i"'e$e"'e"t o%  time3 ?3 De+"e (tea'0 (tate

 A (0(tem i( (ai' to -e i" (tea'0 (tate 5he" the -eha,io  o% the (0(tem i"'e$e"'e"t o% time3 Let $ "8t; 'e"ote the $othat thee ae "1 !"it( i" the (0(tem at time t3 the" i" (tea'0 (tateK lim $ "X8 t ;K tY=

3 @ite 'o5" the little %om!la  L(KL.Z[ @hee L(K the a,ea&e "o3 o% c!(tome( i" the (0(tem L.K the a,ea&e "o3 o% c!(tome( i" the .!e!e 3 I% taic i"te"(it0 o% MMI (0(tem i( &i,e" to -e 3>  5hat $ece"t o% time the (0(tem 5o!l' -e i'le Taic i"te"(it0 K 3 8-!(0 time; S0(tem to -e i'le K :#3 K324 3 @hat ae the -a(ic eleme"t( o% .!e!i"& (0(tem S0(tem co"(i(t( o% the ai,al o% c!(tome(> 5aiti"& i" .!e!e> $ic6 !$ %o (e,ice acco'i"& to cetai" 'i(ci$li"e> act!al (e,ice a"' 'e$at!e o% c!(tome3 93 @hat i( mea"t -0 .!e!e 'i(ci$li"e The ma""e i" 5hich (e,ice i( $o,i'e' o a c!(tome  i( (electe' %o (e,ice i( 'e+"e' a( the .!e!e 'i(ci$li"e3 :3 @hat ae the cla((i+catio"( o% .!e!i"& mo'el( m \ m \ I \= m \ m \ I \" m \ m \ c\= m \ m \ c \" ::3 @hat ae the chaactei(tic o% .!e!i"& $oce(( Ai,al $atte" o% c!(tome(> (e,ice $atte" o%  (e,e(> .!e!e 'i(ci$li"e> (0(tem ca$acit0> "o3 o% (e,ice cha""el(> "o3 o% (e,ice (ta&e3 :23 De+"e Poi((o" $oce(( The Poi((o" $oce(( i( a co"ti"!o!( $aamete 'i(cete (tate $oce(( 8ie; a &oo' mo'el %o ma"0 $actical (it!atio"(3 i% 8t;e$e(e"t( the "o3 o% Occ!e"ce( o% a cetai" i" 8> t;

the" the 'i(cete a"'om $oce(( ] 8t;^ i( calle' the Poi((o" $oce((3 i% it (ati(+e( the %ollo5i"& $o(t!late( I3 P_: occ!e"ce i" 8t>t`t; KZ`t  O8`t; II3 P_ occ!e"ce i" 8t>t`t; K:#Z`t  O8`t; III3 P_2 o moe occ!e"ce i" 8t>t`t; KO8`t; I/3 8t; i( i"'e$e"'e"t o% the "!m-e o% occ!e"ce( o% the e,e"t i" a"0 i"te,al $io 8o; a%te the i"te,al8>t;  /3 The $o- that the e,e"t occ!( a ($eci+e' "!m-e o% time( i" 8t > t t; 'e$e"'( o"l0 o" t -!t "ot o" t 3 :3 Gi,e" a"0 t5o e*am$le( o% Poi((o" $oce(( :3 The "!m-e o% i"comi"& tele$ho"e call( ecei,e' i" a $atic!la time 23 The ai,al o% c!(tome at a -a"6 i" a 'a0  :43 @hat ae the $o$etie( o% Poi((o" $oce(( :3 The Poi((o" $oce(( i( a ma6o, $oce((3 23 S!m o% t5o i"'e$e"'e"t $oi((e" $oce((e( i( a $oi((o" $oce((3 3 Diee"ce o% t5o i"'e$e"'e"t $oi((o" $oce((e( i( "ot $oi((o" $oce((3 43 The i"te ai,al time o% a $oi((o" $oce(( ha( a" e*$o"e"tial 'i(ti-!tio" 5ith mea" :Z3 :?3 C!(tome ai,e( at a o"e#ma" -a-e (ho$ acco'i"& to a Poi((o" $oce(( 5ith a" mea" i"te ai,al time o% :2 mi"!te(3 C!(tome( ($e"' a a,ea&e o% : mi"!te( i" the -a-e1( chai"3@hat i( the e*$ecte' "o o% c!(tome( i" the -a-e (ho$ a"' i" the .!e!e Gi,e" mea" ai,al ate :Z K :23 Thee%oe Z K ::2 $e mi"!te3 Mea" (e,ice ate :[ K :3 Thee%oe [ K :: $e mi"!te3 E*$ecte' "!m-e o% c!(tome( i" the (0(tem L( K Z[#Z K ::2::#::2 K ? c!(tome(3 :3 De+"e $!e -ith $oce((

I% the 'eath ate( [6 K  %o all 6 K :> 2 5e ha,e a $!e -ith $oce((3 :3 @ite 'o5" the $o(t!late( o% -ith a"' 'eath $oce(( :; $ _: -ith 8t> t  `t; K Z"8t;`t  8`t; 2; $ _ -ith i" 8t> t  `t; K : # Z"8t;`t  8`t;3 ; $ _: 'eath i" 8t> t  `t; K ["8t;`t  8`t; 4; $ _ 'eath i" 8t> t  `t; K : # ["8t;`t  8`t;3 :3 @hat i( the %om!la %o the $o-lem %o a c!(tome to  5ait i" the .!e!e !"'e  8mm: NFCFS; @ ( K L(Z3 :93 @hat i( the a,ea&e "!m-e o% c!(tome( i" the (0(tem !"'e  8mme< =FCFS; Z[ 8Z[;c  8c#:;b8c[ # Z ;2  Z[3

23 @hat i( the 'iee"ce -et5ee" $o-a-ili(tic 'etemi"i(tic a"' mi*e' mo'el( Po-a-ili(tic< @he" thee i( !"cetai"t0 i" -oth ai,al( ate a"' (e,ice ate ae a((!me' to -e a"'om ,aia-le(3 Detemi"i(tic< oth ai,al ate a"' (e,ice ate ae co"(ta"t(3 Mi*e'< @he" eithe the ai,al ate o the (e,ice ate i( e*actl0 6"o5" a"' the othe i( "ot 6"o5"3 2:3 @hat ae the a((!m$tio"( i" mm: mo'el 8i; E*$o"e"tial 'i(ti-!tio" o% i"te ai,al time( o  $oi((o" 'i(ti-!tio" o% ai,al ate3 8ii; Q!e!e 'i(ci$li"e i( +(t come> +(t (e,e3 8iii; Si"&le 5aiti"& li"e 5ith "o e(tictio" "o le"&th o% .!e!e3 8i,; Si"&le (e,e 5ith e*$o"e"tial 'i(ti-!tio" o% (e,ice time(3

223 Peo$le ai,e at a theate tic6et -ooth i" $oi((o" 'i(ti-!te' ai,al ate o% 2?ho!3 Se,ice time i( co"(ta"t at 2 mi"!te(3 Calc!late the mea" Z K 2?h [ K 8; K  $e ho!3 W K Z[ K 2? K ? K 3 L. K W2  :#W K 83; 2  : # 3 K 43:??2 Mea" 5aiti"& timeKL.Z K 42? K 42? d  K 93 mi"!te(3 RMT Solved Question Posted by Sankaranarayanan C at 07:23 Email This BlogThis! Share to Twitter Share to Faebook 

3 comments :

"

dinesh krish 3 Febr#ary 20$ 07:%&

'(( )*+TS P,-B(E. '*/ S-(+*1 +T S-()T+-* SE*/ .E .'+( S+,  ,e4ly

2" Dharshini ri!a & .arh 20$ 0&:2

5or all #nits im4oratant 6#estions i need sir  ,e4ly

3" An" Nick" 2& '4ril 20$ :23

%th #nit theroy ery rare 4l8 send it to me sir  ,e4ly

 *ewer Post-lder Postome S#bsribe to: Post Comments 9 'tom 

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