c06 network model ppt
TRANSCRIPT
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Instructions
Page 1
Chapter 6
Operations Research Models and Methods
Paul A. Jensen and Jonathan F. Bard
Network Flow Programming Methods
nstructions•
•
•
Sect. Network Flow Programming Methods1 !ransportation Pro"lem Add#ins use
Example Problem for the Transportation Algorithm Teach Transp
2 $hortest Path Pro"lemExample for the section Math Program
Example for the section with length of arc #2$ %& change' to -1( Math Program
) Ma%imum Flow Pro"lemExample for the section Math Program
* Pure Minimum Cost FlowExample with basis n+ , 2$ *$ %$ /$ n1 , 0/ Teach Networ
Example with basis n+ , 2$ )$ 0$ /$ n1 , *$%/ Teach Networ
Example with iterations to optimal Teach Networ
!ransportation &%ample with the !each !ransportation add#inExample for the section Teach Transp
http://www.me.utexas.edu/~jensen/ORMM/computation/unit/mp_add/index.html
http!!www.me.3texas.e'3!45ensen!67MM!metho's!3nit!networ!s3b3nits!teachnet!in'ex.html
http!!www.me.3texas.e'3!45ensen!67MM!comp3tation!3nit!mp8a''!s3b3nits!sol"er!nfsol"er.html
To 3se this worboo$ 9o3 m3st first loa' the Teach Transportation an' Teach Networ a''-ins. See
the Excel help file topic :Abo3t a''-ins: before contin3ing.
;or cases 3sing the Networ Sol"er 9o3 m3st first loa' the Math Programming an'
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Instructions
Page
rtation
ming - Networ!Networ Sol"er
ming - Networ!Networ Sol"er
ming - Networ!Networ Sol"er
rtation
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!each !ransportationName Example &nter transportation data and press the "utton.
T9pe TeachTrans
S3pplies )
No8S3p 0 $elect the Relink Buttons command 'rom the OR(MM menu
6ption =emo !rans. Cost 1 2 ) * 0=ela9 1 Name = 1 = 2 = ) = * = 0 S3ppl9
1 S 1 10 10 1 11 11 10
2 S 2 1) 11 10 > 10
) S ) 12 11 % 10
=eman 0 1( 10 0 1(
ter) Press the "utton to restart the $imple% process.
Cost) *%0
$tatus) 6ptim3m *emanders
&nter) 1 2 ) * 0
+ea,e) 1 10 2 10 ( 1 ( 11 ( 11 1
( N 0 B 0 B 0 B ( N
2 1) * 11 ( 10 ) > 2 (
$uppliers ( N 0 B ( N ( N 1( B
) ( 12 2 11 ( % 1 )
?e9 0 B ( N 1( B ( N ( N
@ost 7e'. @ostmand 0 1( 10 0 1(
;low N-B al,/ 1) 10 1 11 1(
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"e'ore clicking a "utton.
$uppl*ual
( s3p. 'em. t9pe Se =elta
10 ) 1 = 1 (
-* ) * = 2 -1
10 2 0 = ) (
-0 2 2 S * (
10 ) ) S 0 1
1 2 = (
1 ) = % -1
;low @hange 0
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;low
0
0
1(
0
0
0
1(
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Network Model Name SPT Sol"er
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Ph. 1 Dter. 12
Total Dter. 10
@omp. Time (((1
Stat3s 6ptimal
=3al a +asis
ce Con ( 21
+alance 12 %
( 2
( 1( )
( 1* 1%
( 1(
( 1 11
( 1* 1)
( 1) 1*
( 1> 10
(
(
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Algorithmic *etails 'or pro"lem $P!. a''e' to basis tree. Arc goes from 1) to *.
Artifical Arc )( a''e' to basis tree. Arc goes from 1) to 0.
Artifical Arc )1 a''e' to basis tree. Arc goes from 1) to .
Artifical Arc )2 a''e' to basis tree. Arc goes from 1) to %.
Artifical Arc )) a''e' to basis tree. Arc goes from 1) to .
Artifical Arc )* a''e' to basis tree. Arc goes from 1) to >.
Artifical Arc )0 a''e' to basis tree. Arc goes from 1) to 1(.
Artifical Arc ) a''e' to basis tree. Arc goes from 1) to 11.
Artifical Arc )% a''e' to basis tree. Arc goes from 1) to 12.
$tart P2A$&(3
Dterations Dter. Enters Bea"es 7e'. @ost ;low @hg Select1 1 2% -2 1 ;irst
2 2 2 -2 1 ;irst
) ) 2> -2 1 ;irst
* * )2 -2 1 ;irst
0 0 )( -2 1 ;irst
)1 -2 1 ;irst
% 1) )) -2 1 ;irst
1* )* -2 1 ;irst
> 10 -2 -2 1 ;irst
1( 22 ) -1 ( ;irst
11 20 )% -1 ( ;irst12 21 )0 -1 ( ;irst
$tart P2A$&(4
Dterations Dter. Enters Bea"es 7e'. @ost ;low @hg Select
1) % 1 -2 * ;irst
1* 1% 0 -* 1 ;irst
10 11 * -* 2 ;irst
Finish 6ptimal F , 11
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Network Model Name SPT2 Sol"er
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Ph. 1 Dter. 12
Total Dter. 1*
@omp. Time (((1
Stat3s 6ptimal
=3al a +asis
ce Con ( 21
+alance 12 %
( 2
( 1( )
( 1* 1%
( 1(
( 2 *
( 1* 1)
( 1) 1*
( ) 10
(
(
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Algorithmic *etails 'or pro"lem $P!4. a''e' to basis tree. Arc goes from 1) to *.
Artifical Arc )( a''e' to basis tree. Arc goes from 1) to 0.
Artifical Arc )1 a''e' to basis tree. Arc goes from 1) to .
Artifical Arc )2 a''e' to basis tree. Arc goes from 1) to %.
Artifical Arc )) a''e' to basis tree. Arc goes from 1) to .
Artifical Arc )* a''e' to basis tree. Arc goes from 1) to >.
Artifical Arc )0 a''e' to basis tree. Arc goes from 1) to 1(.
Artifical Arc ) a''e' to basis tree. Arc goes from 1) to 11.
Artifical Arc )% a''e' to basis tree. Arc goes from 1) to 12.
$tart P2A$&(3
Dterations Dter. Enters Bea"es 7e'. @ost ;low @hg Select1 1 2% -2 1 ;irst
2 2 2 -2 1 ;irst
) ) 2> -2 1 ;irst
* * )2 -2 1 ;irst
0 0 )( -2 1 ;irst
)1 -2 1 ;irst
% 1) )) -2 1 ;irst
1* )* -2 1 ;irst
> 10 -2 -2 1 ;irst
1( 22 ) -1 ( ;irst
11 20 )% -1 ( ;irst12 21 )0 -1 ( ;irst
$tart P2A$&(4
Dterations Dter. Enters Bea"es 7e'. @ost ;low @hg Select
1) % 1 -2 * ;irst
1* 1% 0 -* 1 ;irst
Finish 6ptimal F ,
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Network Model Name ax;low Sol"er
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Ph. 1 Dter.
Total Dter. 1)
@omp. Time (((1
Stat3s 6ptimal
=3al al +asis
d Balance Con ( >
;ixe' +alance 1 -*
( ( ( 2
( ( 1 -%
( ( 1 -
( ( 1 -1(
( (
( (
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Algorithmic *etails 'or pro"lem Ma%Flow. to 1.
Artifical Arc 1 a''e' to basis tree. Arc goes from > to 2.Artifical Arc 1% a''e' to basis tree. Arc goes from > to ).
Artifical Arc 1 a''e' to basis tree. Arc goes from > to *.
Artifical Arc 1> a''e' to basis tree. Arc goes from > to 0.
Artifical Arc 2( a''e' to basis tree. Arc goes from > to .
Artifical Arc 21 a''e' to basis tree. Arc goes from > to %.
Artifical Arc 22 a''e' to basis tree. Arc goes from > to .
$tart P2A$&(3
Dterations Dter. Enters Bea"es 7e'. @ost ;low @hg Select
1 11 21 -1 ( ;irst
2 1* 22 -1 ( ;irst
) > 10 -1 ( ;irst
* 1 1 -1 ( ;irst0 2 1% -1 ( ;irst
) 1 -1 ( ;irst
% * 1> -1 ( ;irst
% 2( -1 ( ;irst
$tart P2A$&(4
Dterations Dter. Enters Bea"es 7e'. @ost ;low @hg Select
> 1( 1* -1 ( ;irst
1( 1) ) -1 0 ;irst
11 0 0 -1 0 ;irst
12 1 -1 ( ;irst
1) -1 0 ;irstFinish 6ptimal F , -10
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!each Network $imple%NameP3reNet 6b5ecti"e Min Press the "utton to
T9pe eachNet al3e 1** $elect the Relink Bu
Arcs 12
No'es 0 Phase) 2 ter.) 1
Cains P3re $tatus)Not Optimumtificals *
6ption =emo
=ela9 1 Arc n'ormation Optimalit1 n'ormation
N3m. Name ;low 6rigin Term. Gpper @ost @ost 1 7e'. @os Stat3s + ;low
1 Arc 1 ( 1 2 0 11 ( 12 B (
2 Arc 2 ) 1 ) * 1 ( ( ! (
) Arc ) ( 2 ) ) 12 ( -0 B (
* Arc * 2 2 * * 1 ( ( ! (
0 Arc 0 ) ) * ) 1) ( 12 " )
Arc ( ) 0 0 -20 ( 2 B (
% Arc % 1 0 2 ) 1( ( ( ! (
Arc 1 0 1 0 11 ( ( ! (
> Art 1 ( 1 0 ( >>>> 1 1((1( B (
1( Art 2 ( 2 0 ( >>>> 1 1(((> B (
11 Art ) ( 0 ) ( >>>> 1 >>%2 B (
12 Art * ( 0 * ( >>>> 1 >>%1 B (
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estart the $imple% process.
tons command 'rom the OR(MM menu "e'ore clicking a "utton.
&nter) 34 +ea,e) 34
Name Art * Name Art *
Node n'ormation Basis n'ormation
N3m. Name ;ixe' +alance '5. Ext. +asis 6rigin Term. Bower Gpper @ost
1 No'e 1 2 ( 2 5 0 1 ( 0 11
2 No'e 2 1 ( 1 0 2 ( ) 1(
) No'e ) ( ( -) 4 1 ) ( * 1
* No'e * -0 ( -2 7 2 * ( * 1
0 Slac 2 ( 2 8 ( ( ( >>>> (
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Enter Arc )
6rigin 2
Terminal )
7atio )
Cain 1
=3al ;low =elta 7atio
11 1 -1 1
1( 1 1 2
2% ) -1 )
2 2 ( >>>>
( ( ( >>>>
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!each Network $imple%Name 3reNet1 6b5ecti"e Min Press the "utton to
T9pe eachNet al3e 122 $elect the Relink Bu
Arcs 12
No'es 0 Phase) 2 ter.)
Cains P3re $tatus)Optimal $olutiontificals *
6ption =emo
=ela9 1 Arc n'ormation Optimalit1 n'ormation
N3m. Name ;low 6rigin Term. Gpper @ost @ost 1 7e'. @os Stat3s + ;low
1 Arc 1 ( 1 2 0 11 ( % B (
2 Arc 2 2 1 ) * 1 ( ( ! (
) Arc ) ( 2 ) ) 12 ( ( ! (
* Arc * * 2 * * 1 ( -% " *
0 Arc 0 1 ) * ) 1) ( ( ! (
Arc 1 ) 0 0 -20 ( ( ! (
% Arc % ) 0 2 ) 1( ( -) " )
Arc ( 0 1 0 11 ( 2 B (
> Art 1 ( 1 0 ( >>>> 1 1((( B (
1( Art 2 ( 2 0 ( >>>> 1 1((12 B (
11 Art ) ( 0 ) ( >>>> 1 >>%* B (
12 Art * ( 0 * ( >>>> 1 >>1 B (
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estart the $imple% process.
tons command 'rom the OR(MM menu "e'ore clicking a "utton.
&nter) 9 +ea,e)
Name Arc ) Name Arc %
Node n'ormation Basis n'ormation
N3m. Name ;ixe' +alance '5. Ext. +asis 6rigin Term. Bower Gpper @ost
1 No'e 1 2 ( 2 #4 ) 1 -* ( -1
2 No'e 2 1 ( ( #9 ) 2 -) ( -12
) No'e ) ( ( ( #6 0 ) -0 ( 20
* No'e * -0 ( -1 : ) * ( ) 1)
0 Slac 2 ( -1 8 ( ( ( >>>> (
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Enter Arc )
6rigin 2
Terminal )
7atio )
Cain 1
=3al ;low =elta 7atio
> -2 ( >>>>
1) ( 1 (
20 -1 ( >>>>
) 1 ( >>>>
( ( ( >>>>
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!each NetworkName 3reNet2 6b5ecti"e Min Press the "utton to restart the $imple% process.
T9pe eachNet al3e 122 $elect the Relink Buttons command 'rom the OR(MM menu
Arcs 12
No'es 0 Phase) 2 ter.)
Cains P3re $tatus) Optimal $olution
tificals *
6ption =emo
=ela9 1 Arc n'ormation Optimalit1 n'ormation Node n'ormationN3m. Name ;low 6rigin Term. Gpper @ost @ost 1 7e'. @os Stat3s + ;lows N3m. Name ;ixe' +alance '5.
1 Arc 1 ( 1 2 0 11 ( % B ( 1 No'e 1 2 (
2 Arc 2 2 1 ) * 1 ( ( ! ( 2 No'e 2 1 (
) Arc ) ( 2 ) ) 12 ( ( ! ( ) No'e ) ( (
* Arc * * 2 * * 1 ( -% " * * No'e * -0 (
0 Arc 0 1 ) * ) 1) ( ( ! ( 0 Slac 2 (
Arc 1 ) 0 0 -20 ( ( ! (
% Arc % ) 0 2 ) 1( ( -) " )
Arc ( 0 1 0 11 ( 2 B (
> Art 1 ( 1 0 ( >>>> 1 1((( B (
1( Art 2 ( 2 0 ( >>>> 1 1((12 B (
11 Art ) ( 0 ) ( >>>> 1 >>%* B (
12 Art * ( 0 * ( >>>> 1 >>1 B (
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Enter Arc )
6rigin 2
e clicking a "utton. Terminal )
&nter) 9 +ea,e) 7atio )
Name Arc ) Name Arc % Cain 1
sis n'ormation+asis 6rigin Term. Bower Gpper @ost =3al ;low =elta 7atio
#4 ) 1 -* ( -1 > -2 ( >>>>
#9 ) 2 -) ( -12 1) ( 1 (
#6 0 ) -0 ( 20 20 -1 ( >>>>
: ) * ( ) 1) ) 1 ( >>>>
8 ( ( ( >>>> ( ( ( ( >>>>
Starting Sol3tion - Dteration 1
+asis 6rigin Term. Bower Gpper @ost =3al ;low =elta 7atio
#; 0 1 ->>>> ( -1 -1 -2 ( >>>>
#38 0 2 ->>>> ( -1 -1 -1 1 1
33 0 ) ( >>>> 1 1 ( -1 (
34 0 * ( >>>> 1 1 0 ( >>>>
8 ( ( ( >>>> ( ( ( ( >>>>
Dteration 2
+asis 6rigin Term. Bower Gpper @ost =3al ;low =elta 7atio
#; 0 1 ->>>> ( -1 -1 -2 ( >>>>
#38 0 2 ->>>> ( -1 -1 -1 ( >>>>
4 1 ) ( * ( -1 ( -1 (
34 0 * ( >>>> 1 1 0 ( >>>>
8 ( ( ( >>>> ( ( ( ( >>>>
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Dteration )
+asis 6rigin Term. Bower Gpper @ost =3al ;low =elta 7atio
#; 0 1 ->>>> ( -1 -1 -2 ( >>>>
#7 * 2 -* ( ( 1 -1 1 1
4 1 ) ( * ( -1 ( ( >>>>
34 0 * ( >>>> 1 1 * ( >>>>
8 ( ( ( >>>> ( ( ( ( >>>>
Dteration *
+asis 6rigin Term. Bower Gpper @ost =3al ;low =elta 7atio
#3 2 1 -0 ( ( 1 -2 1 2
#7 * 2 -* ( ( 1 -) ( >>>>
4 1 ) ( * ( 1 ( ( >>>>
34 0 * ( >>>> 1 1 2 ( >>>>
8 ( ( ( >>>> ( ( ( ( >>>>
Dteration 0
+asis 6rigin Term. Bower Gpper @ost =3al ;low =elta 7atio#3 2 1 -0 ( ( ( -2 ( >>>>
0 2 ( ) ( ( 1 -1 1
4 1 ) ( * ( ( ( ( >>>>
34 0 * ( >>>> 1 1 1 ( >>>>
8 ( ( ( >>>> ( ( ( ( >>>>
Dteration
+asis 6rigin Term. Bower Gpper @ost =3al ;low =elta 7atio
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#3 2 1 -0 ( -11 -1 -1 ( >>>>
0 2 ( ) 1( 1( 2 ( >>>>
4 1 ) ( * 1 10 1 ( >>>>
: ) * ( ) 1) 2 1 -1 1
8 ( ( ( >>>> ( ( ( ( >>>>
Dteration %
+asis 6rigin Term. Bower Gpper @ost =3al ;low =elta 7atio
#4 ) 1 -* ( -1 > -2 ( >>>>
0 2 ( ) 1( 1( ) ( >>>>
#6 0 ) -0 ( 20 20 -1 1 1
: ) * ( ) 1) ) 1 ( >>>>
8 ( ( ( >>>> ( ( ( ( >>>>
Dteration - 6ptimal
+asis 6rigin Term. Bower Gpper @ost =3al ;low =elta 7atio
#4 ) 1 -* ( -1 > -2 ( >>>>
#9 ) 2 -) ( -12 1) ( 1 (
#6 0 ) -0 ( 20 20 -1 ( >>>>
: ) * ( ) 1) ) 1 ( >>>>8 ( ( ( >>>> ( ( ( ( >>>>
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!each !ransportationName eachTrans &nter transportation data and press the "utton.
T9pe TeachTrans $elect the Relink Buttons command 'rom the OR(MM
S3pplies 0
No8S3p
6ption 73n !rans. Cost 1 2 ) * 0=ela9 1 Name = 1 = 2 = ) = * = 0 == S3ppl9
1 S 1 10 1( 1% 1) ( 1*
2 S 2 11 > % * ( 22
) S ) 1* 10 0 ( 22
* S * 0 1% > 11 ( 22
0 S 0 12 1( 1( 1 10 ( 2
=eman 1> 21 2( 10 1% 1*
ter) 11 Press the "utton to restart the $imple% process.
Cost) 0>)
$tatus) 6ptim3m *emanders
&nter) 1 2 ) * 0
+ea,e) 1 10 11 ( 1( 2 1% 12 1) >
( N 1* B ( N ( N ( N
2 11 % > 1 ( % 2 * (
$uppliers ( N ( N 0 B ( N 1% B
) 1* 1( 10 % ( 0 ( 2
?e9 ( N ( N % B 10 B ( N
@ost 7e'. @ost * 0 ( 1% > ( 2 11
;low N-B 1> B ( N ) B ( N ( N
0 12 1( ( 1( ( 1 > 10 >
( N % B 0 B ( N ( N
*emand 1> 21 2( 10 1%
*ual,/ -* ( ( -) -*
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menu "e'ore clicking a "utton.
$uppl*ual
( 2 s3p. 'em. t9pe
( N 1* * 1 =
( 2 ) * =
( N 22 2 0 =
( 2 0 =
( N 22 2 ) S
( 1 > ) ) S
( N 22 * ) S
( ( 1( 0 2 S
1* B 2 1 2 =
1* 1 ) =
-1(
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Se =elta ;low
1 ( 1>
2 ( 10
) ( 1%
* ( 1*
0 ( 0
( %
% ( )
-1 12
> 1 >
1( -1 0