INSTITUTO TECNOLOGICO SUPERIOR DE FELIPE CARRILLO PUERTO EXTENSION TULUM ORGANISMO PÚBLICO DESCENTRALIAZADO DEL ESTADO DE QUINTANA ROO
INGENIERIA EN GESTÓN EMPRESARIAL
INVESTIGACION DE OPERACIONES UNIDAD 6 REDES
DOCENTE: ING. GERARDO CHI CAHUICH
INTEGRANTES: MALDONADO CRUZ GEMALY SARAI
4º SEMESTRE GRUPO A
! DE FEBRERO DE "#4
INDICE
INTRODUCCION.......................................................................................................3 UNIDAD 6 REDES.....................................................................................................4 6.1 DIAGRAMA DE GANTT.......................................................................................4 6.2-MÉTODO DE LA RUTA CRÍTICA........................................................................6 6.2.1 TERMINOLOGÍA............. TERMINOLOGÍA...................... .................. .................. ................. ................. .................. .....................................8 ............................8 6.2.2 COMPRESIÓN DE REDES................... REDES........................... ................. .................. .................. .................. ......................10 .............10 6.2.3 DETERMINACIÓN DE LA RUTA CRÍTICA.....................................................11 6.2.4 COMPRENSIÓN DE REDES.................. REDES.......................... ................. .................. .................. .............................14 ....................14 6.2.5 ANÁLISIS DE UNA RED PERT.. PERT........... .................. .................. ................... .........................................16 ...............................16 6.3 PROGRAMACIÓN Y CONTROL DE PROYECTOS ASADOS EN COSTOS. .................................................................................................................................1! CONCLUSIÓN.........................................................................................................20
INTRODUCCION L" #"$%&%" '( )('(* '( &+* ,)+&($"* '( +,%$%/"% %&( &+* *%%((* ,)++%,+* '( $+'(&+* P)+&($"* '( "*%"%7 "$%+ )%+7 #&9+ $:;%$+7 "$%+ $:* +)+7 )"*,+)( +*+ $%$+ '( #&9+*. L+* ,)+&($"* *+ (*"&(%'+* #:%&$(( $('%"( (& *+ '( ")+* '( )('(* '( &+* +'+*.
UNIDAD 6 REDES 6.# DIAGRAMA DE GANTT
E* $<+'+ ):#%+ '( ,&"("% +)+& ( &" =( ,)+(+ *( '%>%'( ( '%*%"* "%>%'"'(* *( )("&%/" (*%$"%+(* "()" '( :+ %($,+ )(=%()( "'" " '( (&&"*7 "* +$+ (& +"& '( %($,+ ((*")%+ ,")" ()$%") (& ,)+(+ +"&$((. E +)"* ,"&")"*7 (*" ):#%" $(*)" &"* )(&"%+(* '( %($,+ ()( &+* (>(+* '( ,)+)"$" #( '(*"))+&&"'" ,+) ?()
L.
G".
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
L" ):#%" +*" '( '+* +&$"* :*%"* '( "%>%'"'(* %($,+ $('%'+ ( '"*7 *($""* + $(*(* *(B )(=()%$%(+* '(& *")%+.
L" )(,)(*("% ):#%" '( &"* "%>%'"'(* ,)+)"$" *( @"( " )"><* '( &"* *%%((* "))"* L" &+%' '( &" "))" (* ,)+,+)%+"& "& %($,+ '( ')"% '( &" "%>%'"' ,)+)"$"'". PASOS EN LA APLICACIÓN DE LA TÉCNICA L" (&"+)"% '( G" +$,)('( &+* *%%((* ,"*+*
1. I'(%#%") (& ,)+)"$"7 ,)+(+ ** +9(%>+*. 2. E*"&(() "%>%'"'(* '(& ,)+)"$"7 &+* *,(*+* &%$%"%+(* '( )()*+*. 3. D(*)%%) =%( (9("): "'" "%>%'"'7 $+7 + =< )()*+* ( =< +$(+. A%>%'"'(* *((%". 4. D(()$%") (& %($,+ '( ')"% '( "'" "%>%'"'. 5. R(,)(*(") &"* "%>%'"'(* *((%"&$(( $('%"( &" %&%/"% '( "))"* '( "$"+ ,)+,+)%+"& " * ')"%. 6. D(*,<* '( (&"+)") (& ):#%+ '( G"7 *( ,)+('( " (9(") (& ,)+)"$" +)+&") &"* "%>%'"'(* ,)+)"$"'"* + )(&"% "& $,&%$%(+ '( &"* "%>%'"'(* (9("'"*.
6."$M%TODO DE LA RUTA CR&TICA E& M<+'+ '( &" )" )%" + '(& "$%+ )%+ "$%< ++%'+ ,+) ** *%&"* ( %&<* CPM C)%%"& P"@ M(@+'7 #( '(*"))+&&"'+ ( 15! ( &+* E*"'+* U%'+* '( A$<)%"7 ,+) ()+ '( %>(*%"% '( +,()"%+(* ,")" &"* #%)$"*
D,+ R($%+ R"'7 *"'+ (& +)+& &" +,%$%/"% '( &+* +*+* $('%"( &" ,&"("% ,)+)"$"% "'("'"* '( &"* "%>%'"'(* +$,+((* '(& ,)+(+. E "'$%%*)"% (*% '( ,)+(+*7 " )" )%" (* &" *((%" '( &+* (&($(+* ()$%"&(* '( &" )(' '( ,)+(+* + &" $"+) ')"% ()( (&&+*7 '(()$%"'+ (& %($,+ $:* +)+ ( (& =( (* ,+*%&( +$,&(") (& ,)+(+. L" ')"% '( &" )" )%" '(()$%" &" ')"% '(& ,)+(+ (()+. C"&=%() )()"*+ ( (&($(+ '( &" )" )%" "#(" " &" #(@" '( <)$%+ ,&"("'" '(& ,)+(+7 *( '%( =( + @" @+&)" (
&"
)"
)%".
U ,)+(+ ,('( (() >")%"* )"* )%"* ,")"&(&"*. U" )" ,")"&(&" "'%%+"& " )"><* '( &" )(' + &"* ')"%+(* +"&(* $(+* +)"* =( &" )" )%" (* &&"$"'" " *-)" )%". O)%%"&$((7 (& $<+'+ '( &" )" )%" +*%'() *+&"$(( '(,('(%"* ()( &+* (&($(+* ()$%"&(*. U +(,+ )(&"%+"'+ (* &" "'(" )%"7 &" "& ")(" '(,('(%"* '( )()*+*. C"'" )()*+ '(,('( '(& $"(9"'+) ( (& $+$(+ '+'( &" )" )%" *( ,)(*((. A '%#()(%" '( &" <%" '( )(>%*% (>"&"% '( ,)+)"$"* PERT7 (& $<+'+ '( &" )" )%" *" %($,+* %()+* )("&(* + '(()$%*%+*. S% ($")+7 &" (&"+)"% '( ,)+(+ "*:'+*( ( )('(* CPM PERT *+ *%$%&")(* +*%*( ( F I'(%#%") +'"* &"* "%>%'"'(* =( %>+&)" (& ,)+(+7 &+ =( *%%#%"7 '(()$%") )(&"%+(* '( ,)(('(%"7 %($,+* <%+* ,")" "'" " '( &"* "%>%'"'(*. F C+*)%) " )(' + "*( ( +'+* "%>%'"'(* + ")+*7 *(B (& $<+'+ $:* *"'+7 =( %$,&%" (& ,)+(+. F A"&%/") &+* :&&+* (*,(#%+*7 %'(%#%"'+ &" )" )%" &"* @+&)"* '( &"* "%>%'"'(* =( +$,+( (& ,)+(+.
E <)$%+* ,):%+*7 &" )" )%" *( %(),)(" +$+ &" '%$(*% $:;%$" =( ,('( ')") (& ,)+(+ &"* '%#()(%"* + &"* +)"* )"* =( + *(" &" )%"7 *( '(+$%" %($,+* '( @+&)". MÉTODOS CPM Y PERT L+* $<+'+* CPM $<+'+ '( &" )" )%" + '(& "$%+ )%+7 )%%"I ,"@ $(@+' PERT <%" '( (>"&"% )(>%*% '( ,)+)"$"7 ,)+)"$ (>"&"%+ "' )(>%(H (@%- =( *( "*" ( )('(*7 %(( ,+) +9(+ ";%&%") ( &" ,&"("%7 ,)+)"$"% +)+& '( ,)+(+*. S( '(#%( ,)+(+ +$+ +9+ '( "%>%'"'(* %())(&"%+"'"*7 ( &" =( "'" "%>%'"' +*$( %($,+ )()*+*. E& +9(%>+ '(& CPM '(& PERT (* +") + $<+'+ ""&%+ ,")" ,)+)"$") &"* "%>%'"'(*. E &" #%)" 6.50 *( )(*$( &+* ,"*+* '( (*"* <%"*. P)%$()+ *( '(#%( &"* "%>%'"'(* '(& ,)+(+7 ** )(&"%+(* '( ,)(('(%". D)"( &" (9(% '(& ,)+(+7 ,+')" + $,&%)*( (& ,)+)"$" =( (*"" ,&"("'+7 "*"'+ =( "&"* '( &"* "%>%'"'(* *( "'(&"( + *( ")"*(. E (*( "*+ *(): ((*")%+ ""&%/") (& ,)+)"$" ,")" =( )(#&(9( &" )("&%'"'. É*" (* &" )"/ '( %&%) &(7 &"/+ + %&+ '( )()+"&%$("% ()( &" #"*( '( ,)+)"$" &" #"*( '( )('7 +$+ *( >( ( &" #%)" 6.50.
L"* '+* <%"*7 CPM PERT7 =( *( '(*"))+&&")+ ( #+)$" %'(,('%((7 '%#%()( ( =( ( (& CPM *( *,+( ')"%+(* '(()$%*%"* '( "%>%'"'7 $%()"* =( ( PERT *( *,+( ')"%+(* ,)+"%&*%"*. E*" ,)(*("% +$(/"): + (& CPM '(*,<* *( ,)(*("): &+* '("&&(* '(& PERT.
6.".# TERMINOLOG&A L+* $+'(&+* $:* (;('%'+* ( "+ " * ",&%"% ( (*)+ $('%+ ** ,)%%,"&(* '%#()(%"* *+
PERT 1. 2. 3. 4.
P)+"%&*%+. S( "*" ( (>(+*. O)%("'+ " =%( +)+&" S( ,('( %&%/") ( ,)+(+* '( %>(*%"%.
CPM 1. 2. 3. 4.
D(()$%*%+. S( "*" ( "%>%'"'(* O)%("'+ " =%( (9(" S( ,('( %&%/") ,")" +'+ %,+ '( ,)+(+
E (*( $+$(+ (* %$,+)"( "'>()%) &"* >("9"* '( &+* *%*($"* '( )"(+)%" )%" PERT CPM LPU ROY RAMPS *+)( (& *%*($" )"'%%+"& '( "))"* G):#%" '( G" 1. S( ,('( ++() (;""$(( &" *((%" '( &"* "%>%'"'(*. 2. P+'($+* ""&%/") (& (#(+ '( "&=%() ")"*+ + "'(&"+ '( " "%>%'"' ( )(&"% "& ,)+(+. 2. S( ,('( (*'%") ):,%'"$((
'%#()((*
"&()"%>"*.
4. P+'($+* ""&%/") +'"* &"* >")%"&(* %($,+7 +*+*7 )()*+*. 5. S( ,('( ++() :&(* *+ &"* "%>%'"'(* =( *#)%('+ )()"*+* + $+'%#%" (& ,)+(+. 3. L" (#(%>%'"' '(& *%*($" (* '%)("$(( ,)+,+)%+"& "& B$()+ '( "%>%'"'(*J ""* $:* "%>%'"'(* (;%*" $:* '("&&(* $:* ++%$%(+* '(& ,)+(+ (($+*. 4. P+'($+* >%*"&%/") +'+* &+* ,)+&($"* *%"%+(* ( (& ,",(&7 "(* =( (&&+* +))" ( &" )("&%'"'. R" C)%" K( *( '(*(( (& +*+ '( +,()"% '( ,)+(+ $:* "9+ ,+*%&( '()+ '( %($,+ &$%( '%*,+%&(.K SUS APLICACIONES
E9($,&+* F I>(*%"% '(*"))+&&+ '( (>+* ,)+'+*. F C+*)% '( ,&""*7 ('%#%%+* "))(()"*. F D%*(+ ( %*"&"% '( *%*($"* (>+*. C:&(* *+ &"* ,)("* =( (& PERTCPM +(*" " &+* +$"'+)(* '( '(%*%+(* F C:& (* (& %($,+ +"& ,")" ()$%") (& ,)+(+ F C:&(* *+ &"* #(@"* ,)+)"$"'"* '( %%%+ '( ()$%"% ,")" "'" " '( &"* "%>%'"'(* (*,(#%"* F < "%>%'"'(* *+ K)%"*K '(( ()$%")*( (;""$(( +$+ *( ,)+)"$")+ ,")" $"(() (& ,)+(+ " %($,+ F C:+ *( ,('( )(")'") &"* "%>%'"'(* K+ )%"*K "(* '( %)($(") (& %($,+ '( ()$%"% '(& ,)+(+
P)+('%$%(+ ,")" &&(>") " "+ (& PERTCPM
L" )"(+)%" $:* &")" '(()$%" (& %($,+ +"& )(=()%'+ ,")" &" #%"&%/"% '(& ,)+(+. S% *( )(")'" &"* "%>%'"'(* '( &" )"(+)%" $:* &")"7 &" +"&%'"' '(& ,)+(+ "$%< *( )(")'"):7 ,+) &+ =( &" $:* &")" (* &" K)" )%"K.
6."." COMPRESIÓN DE REDES C"'" "%>%'"' '(& ,)+(+ *( )(,)(*(" + ")+ =( "," ( &" '%)(% '( ">"( '(& ,)+(+. L+* +'+* '( &" )(' (*"&(( &"* )(&"%+(* '( ,)(('(%" ()( &"* '%#()((* "%>%'"'(* '(& ,)+(+. P")" +#%)") &" )(' *( '%*,+( '( '+* )(&"* R(&"
1. C"'"
"%>%'"'
*(
)(,)(*("
+
")+7
+
*&+.
R(&" 2. C"'" "%>%'"' *( '(( %'(%#%") + '+* +'+* '%*%+*. R(&" 3. P")" $"(() &"* )(&"%+(* '( ,)(('(%" +))("*7 *( '(( +(*") &"* *%%((* ,)("* "'+ *( ")(" " &" )(' "'" "%>%'"' " < "%>%'"'(* '(( "(('() %$('%""$(( " &" "%>%'"' ""& < "%>%'"'(* '(( *(%) %$('%""$(( " &" "%>%'"' ""&
< "%>%'"'(* '(( (#(")*( ( #+)$" +))(( + *%$&:(" + &"
"%>%'"' ""&
6.".' DETERMINACIÓN DE LA RUTA CR&TICA D+* *+ &+* +)((* '( <*" <%" + $<+'+ E& $<+'+ P() P)+)"$ E>"&"%+ "' R(>%(HT(@%=( '(*"))+&&"'+ ,+) &" ")$"'" '( &+* E*"'+* U%'+* '( A$<)%" ( 15!7 ,")" +)+&") &+* %($,+* '( (9(% '( &"* '%>()*"* "%>%'"'(* %()"(* '( &+* ,)+(+* (*,"%"&(*7 ,+) &" ((*%'"' '( ()$%") "'" " '( (&&"* '()+ '( &+* %()>"&+* '( %($,+ '%*,+%&(*. ( %&%/"'+ +)%%"&$(( ,+) (& +)+& '( %($,+* '(& ,)+(+
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
$(9+) "&"("'+ =( ,+'): *() (9("'+ '( $"()" $:* (#%%(( +)$"&$((7 ( $(+) %($,+. U ((#%%+ ,)%$+)'%"& =( +* )%'" (& $<+'+ '( &" )" )%" (* =( )(*$( ( *&+ '+$(+ &" %$"( (()"& '( +'+ (& ,)+(+7 &+ =( +* "'" " (>%") +$%*%+(*7 %'(%#%") ):,%'"$(( +)"'%%+(* ( &" ,&"("% '( "%>%'"'(*7 #"%&%"'+ ""*(%$%(+* +)'("'+* +,+)+*J ( (()"&7 &+)"'+ =( (& ,)+(+ *(" &&(>"'+ " "+ + $%$+ '( )+,%(/+*. E &" ,):%" (& ())+) =( *( +$(( $:* " $('+ (* =( &" <%" *( %&%/" B%"$(( "& ,)%%,%+ '(& ,)+(+7 (* '(%)7 "& '(*"))+&&") ,&" * ,)+)"$"% '(*,<* *( (&" ( &" ,")(' (& '%")"$" )(*&"(7 +&>%':'+*( ')"( (& )(*+ '( &" >%'" '(& ,)+(+. E& >()'"'()+ >"&+) '( &" <%" )(*&" $:* "'+ *( ",&%" ( #+)$" '%:$%". A $('%'" =( *( ,)(*(" @(@+* + %)*"%"* %$,)(>%*"*7 (& $<+'+ '( &" )" )%" ,)+,+)%+" (& $('%+ %'("& ,")" %'(%#%") ""&%/") &" ((*%'"' '( )(,&"(") + )(,)+)"$") (& ,)+(+7 )('%('+ "& $%$+ (& )(*&"'+ "'>()*+ '( '%@"* +%(%"*. D(& $%*$+ $+'+7 "'+ *( ,)(*(" " +,+)%'"' ,")" $(9+)") &" ,)+)"$"% '(& ,)+(+7 &" <%" ,()$%( '(()$%") #:%&$(( =( "%>%'"'(* '(( *() "(&()"'"* ,")" =( *( &+)( '%@" $(9+)".
METODOLOGIA E& $<+'+ '( &" )" )%" +*" :*%"$(( '( '+* %&+* 1. P&"("% ,)+)"$"% 2. E9(% C+)+& E& ,)%$() %&+ ()$%" @"*" =( +'"* &"* ,()*+"* '%)(+)"* + )(*,+*"&(* '( &+* '%>()*+* ,)+(*+* =( %()>%(( ( (& ,)+(+ (*: ,&("$(( '( "()'+ + (& '(*"))+&&+7 %($,+*7 +*+*7 (&($(+* %&%/"'+*7 ++)'%"%7 (.7 +$"'+
+$+
"*(
&"
)('
'(
"$%+
)%+
'%*("'"
"&
(#(+.
A& ()$%") &" ,)%$()" )('7 (()"&$(( @" "$%+* ( &"* "%>%'"'(* +$,+((*7 ( &"* *((%"*7 ( &+* %($,+* "&"* >((* ( &+* +*+*7 ,+) &+ =( @" ((*%'"' '( '%*(") (>"* )('(* @"*" =( (;%*" +$,&(+ "()'+ '( &"* ,()*+"* =( %()" (& ),+ '( (9(%. E& *('+ %&+ ()$%" "& %($,+ '( @"() &" B&%$" "%>%'"' '(& ,)+(+ ()( "+ (;%*( "9*(* +*"(* '(%'+ " &"* '%#()(%"* =( *( ,)(*(" ()( (& )""9+ ,)+)"$"'+ (& )("&%/"'+. S(): ((*")%+ )"#%") ( &+* (*=($"* '( +)+& +'"* &"* '(%*%+(* +$"'"* ,")" "9*") " &" )("&%'"' (& ,&" +)%%"&. C+ +9(+ '( (('() (*( ,)+(*+. C+*%'()"'+ =( (& ,)%%,"& +9(%>+ '( (*( )""9+ +*%*( ( (*"&(() &" $(+'+&+" '( &" +*)% '( &" )(' '(& "$%+ )%+ *( "")"): B%"$(( (& ,)%$() %&+7 + +9(+ '( ,)(*(") &" (&"+)"% '( &" )(' '(& "$%+ )%+ (%('" ** >("9"* &%$%"%+(*. E& ,)%$() %&+ *( +$,+( '( &"* *%%((* (","* '(#%%% '(& ,)+(+7 &%*" '( "%>%'"'(*7 $")%/ '( *((%"*7 $")%/ '( %($,+*7 )(' '( "%>%'"'(*7 +*+* ,('%((*7 +$,)(*% '( &" )('7 &%$%"%+(* '( %($,+7 '( )()*+* (+$%+*7 $")%/ '( (&"*%%'"'.
6.".4 COMPRENSIÓN DE REDES E& $<+'+ '(& "$%+ )%+ (* ,)+(*+ "'$%%*)"%>+ '( ,&"("%7 ,)+)"$"%7 (9(% +)+& '( +'"* "'" " '( &"* "%>%'"'(* +$,+((* '( ,)+(+ =( '(( '(*"))+&&")*( '()+ '( %($,+ )%+ "& +*+ ,%$+. E& "$,+ '( "% '( (*( $<+'+ (* $ "$,&%+7 '"'" * )" #&(;%%&%'"' "'","%&%'"' " "&=%() ,)+(+ )"'( + ,(=(+. P")" +(() &+* $(9+)(* )(*&"'+* '(( ",&%")*( " &+* ,)+(+* =( ,+*(" &"* *%%((*
")"()*%"* ". ( (& ,)+(+ *(" B%+7 + )(,(%%>+7 ( "&"* ,")(* + ( * +"&%'"'. . ( *( '(" (9(") +'+ (& ,)+(+ + ,")( '( (&7 ( %($,+ $%$+7 *% >")%"%+(*7 (* '(%)7 ( %($,+ )%+. . ( *( '(*(( (& +*+ '( +,()"% $:* "9+ ,+*%&( '()+ '( %($,+ '%*,+%&(. D()+ '(& :$%+ ",&%"%7 (& $<+'+ *( @" (*"'+ *"'+ ,")" &" ,&"("% +)+& '( '%>()*"* "%>%'"'(*7 "&(* +$+ +*)% '( ,)(*"*7 ",())" '( "$%+*7 ,">%$("%7 +*)% '( "*"* ('%#%%+*7 )(,")"% '( ")+*7 %>(*%"% '( $()"'+*7 $+>%$%(+* '( +&+%/"%7 (*'%+* (+$%+* )(%+"&(*7 "'%+)"*7 ,&"("% '( "))()"* %>()*%")%"*7 '%*)%% '( %($,+* '( *"&"* '( +,()"%+(*7 "$,&%"%+(* '( #:)%"7 ,&"("% '( %%()")%+* ,")" +)"/"*7 ,&"(* '( >("7 (*+* '( ,+&"%7 (.. DIERENCIAS ENTRE PERT Y CPM C+$+ *( %'% "(*7 &" ,)%%,"& '%#()(%" ()( PERT CPM (* &" $"()" ( =( *( )("&%/" &+* (*%$"'+* '( %($,+. E1 PERT *,+( =( (& %($,+ ,")" )("&%/") "'" " '( &"* "%>%'"'(* (* " >")%"&( "&("+)%" '(*)%" ,+) " '%*)%% '( ,)+"%&%'"'. E1 CPM ,+) +)" ,")(7 %#%()( =( &+* %($,+* '( &"* "%>%'"'(* *( ++( ( #+)$" '(()$%*%"* *( ,('( >")%") "$%"'+ (& %>(& '( )()*+* %&%/"'+*. L" '%*)%% '( %($,+ =( *,+( (& PERT ,")" " "%>%'"' (* " '%*)%% (". L" '%*)%% ,")" "&=%() "%>%'"' *( '(#%( ,+) )(* (*%$"'+* 1 (& (*%$"'+ '( %($,+ $:* ,)+"&(7 $J 2 (& (*%$"'+ '( %($,+ $:* +,%$%*"7 "J
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
6.".! AN(LISIS DE UNA RED PERT. E*%$"% '( &+* %($,+* '( &"* "%>%'"'(*
A& ",&%") PERTCPM " ,)+(+* '( +*)% $"(%$%(+7 (* ,+*%&( +") + (*%$"%+(* "*"( ,)(%*"* '( &+* %($,+* '( &"*
"%>%'"'(* " =( (* ,)+"&( =( *( '%*,+" '( '"+* @%*)%+* '"'+ =( &" (+&+" =( *( %&%/" (* $:* + $(+*
(*"&(. E &+* ,)+(+* '(& %,+ %>(*%"% '(*"))+&&+7 ( &+* =( &" (+&+" "$%" + )",%'(/ &+* ,)+'+* + *+ +$(*7 (* ,+*%&( =( *(" '%#%& +") + (*%$"%+(* ,)(%*"* '( &+* %($,+* '( &"* "%>%'"'(*.
C+ (& #% '( (() ( (" &" %()%'$)(7 &"* ,()*+"* =( '(*"))+&&")+ PERT ,()$%%()+ " &+* *")%+* %&%/") )(* (*%$"'+)(* ,")" &+* %($,+* '( "'" " '( &"* "%>%'"'(* 1.- E& %($,+ $:* ,)+"&( $ E& %($,+ =( *( )(=%()( ,")" ()$%") &" "%>%'"' "9+ +'%%+(* +)$"&(*. 2.-
E& %($,+ ,(*%$%*" , E& %($,+ $:;%$+ =( *( ((*%")" ,")" ()$%")
&" "%>%'"' *% *( (+)")" '($+)"* +*%'()"&(* ( (& ,)+(+. 3.-
E& %($,+ +,%$%*" + E& %($,+ $%$+ =( *( )(=%()( ,")" ()$%") &"
"%>%'"' *% +'+ +))( ( #+)$" %'("&.
6.' PROGRAMACIÓN Y CONTROL DE PROYECTOS BASADOS EN COSTOS.
L"
" "'$%%*)"% '(
,)+(+*
"
,&"("%7 ,)+)"$"% ++)'%"% %'"'+*" %())(&"%+"'"*.
A&
,)%%,%")
'(*"))+&&")+ ,)+('%$%(+* #+)$"&(*
&" "*"'+*
'(
'<"'" (
)" (*"&" )(=%()( $@"* '( *+
"%>%'"'(* 150
'( )('(*
*( '(
&"* <%"* '( )('(* ,")" "'") ( (*"* ")("*. E)( &+* ,)+('%$%(+* $:* *+)(*"&%((* *( (()" (& PERT <%" '( (>"&"% )(>%*% '( ,)+)"$"* (& CPM $<+'+ '( &" )" )%".A=( +)%%"&$(( &+* *%*($"* %,+ PERT *( ",&%")+ ,")" (>"&") &" ,)+)"$"% '( ,)+(+
'( %>(*%"% '(*"))+&&+7 "$%< *( *" ,")" +)+&") (& ">"( '( +)+* %,+* '( ,)+(+ (*,(%"&(*. C+$+ (9($,&+* *( ,('( %") ,)+)"$"* '( +*)%7 &" ,)+)"$"% '( +$,"'+)"*7 &" ,)(,")"% '( ,)+,(*"* ,)(*,(*+*7 &" ,&"("% '(& $"(%$%(+ &" %*"&"% '( *%*($"* '( $,+7 (*( %,+ '( <%" *( @" >(%'+ ",&%"'+ " " &" ,)+'% '( ,(&&"*7 " &"* +$,""* ,+&%"* " +,()"%+(* =%)B)%"* +$,&(9"*. E& +9(%>+ '( &+* *%*($"* %,+ PERT +*%*( ( "'") ( &" ,&"("% (& +)+&7 ,+) &+ =( + %$,&%" $@" +,%$%/"% '%)(". A&"* >((* (& +9(%>+ ,)%$")%+ (* '(()$%") &" ,)+"%&%'"' '( $,&%) + #(@"* '( ()(" (*,(#%"*. T"$%< %'(%#%" "=(&&"* "%>%'"'(* =( *+ $:* ,)+"&(* =( *( +>%()" ( (&&+* '( +(&&" *("&"7 ,+) (4'(7 ( =( ,+* '(( @"()*( (& $"+) (*#()/+ ,")" + (() )()"*+*. U ()() +9(%>+ (* (>"&") (& (#(+ '( &+* "$%+* '(& ,)+)"$". P+) (9($,&+7 *( ,('( >"&+)") (& (#(+ '( ,+*%&( "$%+ ( &" "*%"% '( )()*+* '( &"* "%>%'"'(* $(+* )%"* " "=(&&"* =( *( %'(%#%")+ + (&&+* '( +(&&". O)" ",&%"% %$,+)"( (* &" (>"&"% '(& (#(+ '( '(*>%")*( '( &+ ,)+)"$"'+. T+'+* &+* *%*($"* %,+ PERT ($,&(" " )(' '( ,)+(+ ,")" >%*"&%/") ):#%"$(( &" %())(&"% ()( ** (&($(+*. E*" )(,)(*("% '(& ,&" '( ,)+(+ $(*)" +'"* &"* )(&"%+(* '( ,)+('(%"7 )(*,(+ "& +)'( ( =( *( '(( )("&%/") &"* "%>%'"'(*. E &" %. 1 *< $(*)" (*"* ")"()*%"* ,")" &" )(' '( ,)+(+ %%%"& ,")" &" +*)% '( " "*". E*" )(' %'%" =( &" (;">"% '(( @"()*( "(* '( ,+() &+* %$%(+* '(*,<* &+* %$%(+* '(( +$,&(")*( "(* '( +&+") &"* ,")('(*. U" >(/ =( *( &(>"" &"* ,")('(* *( ,('( )("&%/") )(* "%>%'"'(* ( ,")"&(&+. A& *(%)&" )(' @"%" '(&"( *( >( (& +)'( '( &"* ")("* **(((*. E &" ()$%+&+" '( PERT7 "'" ")+ '( &" )(' )(,)(*(" " "%>%'"'7 (* '(%)7 " '( &"* ")("* =( )(=%()( (& ,)+(+7 "'" +'+ )(,)(*(" (>(+ =( ,+) &+ (()"& *( '(#%( + (& $+$(+ (=( *( ()$%" +'"* &"* "%>%'"'(* =( &&(" " (*( +'+7 L"* ,"* '( #&(@" %'%" &" *((%" ( &"
=(3 '(( +))%) "'" + '( (*+* (>(+*. L+ =( (* $:*7 (>(+ '(( ,)(('() " &" %%%"% '( &"* "%>%'"'(* =( &&(" " (*( +'+. L"* ,"* '( #&(@" %'%" &" *((%" ( &" =( '(( +))%) "'" + '( (*+* (>(+*. L+ =( (* $:*7 (>(+ '(( ,)(('() " &" %%%"% '( &"* "%>%'"'(* =( *"&( '( (*( +'+. E &" )("&%'"'7 + #)((%" *( ,('( )"*&",") (","* *(*%>"* '( ,)+(+7 ,+) &+ =( &" )(' ,('( )(,)(*(") " ",)+;%$"% %'("&%/"'" '(& ,&" '( ,)+(+. E& +'+ @"%" (& =( +'"* &"* "%>%'"'(* *( '%)%( (* (& (>(+ =( +))(*,+'( " &" ()$%"% '(*'( * +(,%7 + %(7 *% (& ,)+(+ " +$(/7 (& ,&" ,")" * ()$%"%. E <& B&%$+ "*+7 "'" +'+ '( &" )(' *% ")+* =( &&(" )(,)(*(" (& (>(+ '( +%") " "%>%'"' ( $")@" + (& (>(+ '( %%%") "
(>"
"%>%'"'
=(
,('(
+$(/")
(
"&=%()
$+$(+.
C"'" ")+ 9(" '+&( ,",(&7 (& '( )(,)(*(") " "%>%'"' (& '( "'") " )(,)(*(") &"* )(&"%+(* '( ,)+('(%" ()( &"* '%*%"* "%>%'"'(*. E +"*%+(*7 *( ((*%" ")+ ,")" '(#%%) &"* )(&"%+(* '( ,)+('(%" " "'+ + @"" " "%>%'"' )("& =( )(,)(*("). E (*( "*+7 *( %)+'( " "%>%'"' #%%%" =( )(=%()( %($,+ ()+7 ( '+'( (& ")+ =( )(,)(*(" (*" "%>%'"' #%%%" *( $(*)" +$+ " #&(@" ,("'" =( %'%" (*" )(&"% '( ,)+('(%". P+) (9($,&+7 +*%'<)(*( (& ")+ 5 Q 8 =( )(,)(*(" " "%>%'"' #%%%" ( &" %. 1J (& B%+ +9(+ '( (*( ")+ (* %'%") =( &" +&+"% '( &" ()" '(( (*") ()$%"'" "(* '( ,+'() +$(/") &+* (;()%+)(*. U" )(&" +$B ,")" +*)%) (*( %,+ '( )('(* (* =( '+* +'+* + ,('( (*") +("'+* '%)("$(( ,+) $:* '( ")+. L"* "%>%'"'(* #%%%"* "$%< *( ,('( *") ,")" (>%") >%+&") (*" )(&" "'+ *( %(( '+* + $:* "%>%'"'(* +))((*J ( &" %. 1 *( %&*)" (*+ + (& ")+ 11Q 12. E& B%+ ,)+,*%+ '( (*( ")+ (* %'%") =( '(( ()$%")*( &" +&+"% '( ,%*+* "(* '( %*"&") &+* """'+* %()%+)(* *% (() '+* ")+* '(& +'+ "& +'+ 12. U" >(/ '(*"))+&&"'" &" )(' &" )(' '( ,)+(+7 (& *%%(( ,"*+ (* (*%$") (& %($,+ =( *( )(=%()( ,")" "'" "%>%'"'. E*"* (*%$"%+(* ,")" (& (9($,&+
'( &" +*)% '( " "*" '( &" #%)" 1. *( $(*)" ( &" #%)" 2 + &+* B$()+* $:* +*)+* ( %'"'(* '( '"* '( )""9+ =( ",")(( 9+ " &+* ")+*. E*+* %($,+* *( *" ,")" "&&") '+* "%'"'(* :*%"* ,")" "'" (>(+7 " *"()7 * %($,+ $:* ,);%$+ * %($,+ $:* &(9"+. E& %($,+ $:* ,);%$+ ,")" (>(+ (* (& %($,+ (*%$"'+ ( (& =( +))%): (& (>(+ *% &"* "%>%'"'(* =( &+ ,)+('( +$%(/" &+ $:* ,)++ ,+*%&(. L+* %($,+* $:* ,);%$+* *( +%(( "& (#(") " ,"*"'" @"%" '(&"( " )"><* '( &" )('7 +$(/"'+ + &+* (>(+* %%%"&(* )""9"'+ @"%" '(&"( ( (& %($,+7 @"*" &+* (>(+* #%"&(*7 ,")" "'" (>(+ *( @"( :&&+ '(& %($,+ ( (& =( +))%): "'" +7 *% "'" (>(+ ,)+('(( %$('%"+ +))( ( * %($,+ $:* ,);%$+ "'" "%>%'"' =( %()>%(( +*$( (;""$(( * %($,+ (*%$"'+. L" %%%"% '(& ,)+(+ *( '(( (%=(") + (& %($,+ 0. (*( ,)+(*+ *( $(*)" ( &" "&" 1. ,")" (& (9($,&+ +*%'()"'+ ( &"* #%)"* 1 2. &+* %($,+* $:* ,);%$+* =( *( +>%()+ (*: )(%*)"'+* ( &" #%)" 27 + (& ,)%$()+ '( &+* '+* B$()+* =( *( '" ,")" "'" +'+. E& %($,+ $:* &(9"+ ,")" (>(+ (* (& B&%$+ $+$(+ (*%$"'+ ( (& =( ,('( +))%) *% )()"*") &" ()$%"% '(& ,)+(+ $:* "&&: '( * %($,+ $:* ,);%$+.
CONCLUSIÓN L+* $+'(&+* '( )('(* *+ ",&%"&(* " " (;(*" >")%('"' '( ,)+&($"* '( '(%*%7 &+* "&(* ,('( *() $+'(&"'+* +$+ ,)+&($"* '( +,%$%/"% '( )('(* =( ,('( *() (#%%(( (#(%>"$(( )(*(&+*. A&+* '( (*+*,)+&($"* '( '(%*% *+ )("&$(( ,)+&($"* #*%+*7 "&(* +$+ (&)"*, +)( + #&9+ '( %((* $"()%"&(*. S% ($")+7 $@+* ,)+&($"* '( )('(* *+
$:* =( " )(,)(*("% "*)"" '( ,)+(*+* + "%>%'"'(*7 "&(* +$+ (& "$%+ )%+ ( &"* "%>%'"'(* ()( &"* )('(* '( ,)+(+ ()(%"&.