c06 network model ppt

8/19/2019 c06 NEtwork model ppt

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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



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

(

(


8/29

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


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


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


> 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 (


19/29

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 ( ( ( >>>> (


20/29

Enter Arc )

6rigin 2

Terminal )

7atio )

Cain 1

=3al ;low =elta 7atio

> -2 ( >>>>

1) ( 1 (

20 -1 ( >>>>

) 1 ( >>>>

( ( ( >>>>


21/29

!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 (


22/29


23/29


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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


#; 0 1 ->>>> ( -1 -1 -2 ( >>>>

#38 0 2 ->>>> ( -1 -1 -1 ( >>>>

4 1 ) ( * ( -1 ( -1 (

34 0 * ( >>>> 1 1 0 ( >>>>

8 ( ( ( >>>> ( ( ( ( >>>>


25/29

Dteration )


#; 0 1 ->>>> ( -1 -1 -2 ( >>>>

#7 * 2 -* ( ( 1 -1 1 1

4 1 ) ( * ( -1 ( ( >>>>

34 0 * ( >>>> 1 1 * ( >>>>

8 ( ( ( >>>> ( ( ( ( >>>>

Dteration *


#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



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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 %


#4 ) 1 -* ( -1 > -2 ( >>>>

0 2 ( ) 1( 1( ) ( >>>>

#6 0 ) -0 ( 20 20 -1 1 1

: ) * ( ) 1) ) 1 ( >>>>

8 ( ( ( >>>> ( ( ( ( >>>>

Dteration - 6ptimal


#4 ) 1 -* ( -1 > -2 ( >>>>

#9 ) 2 -) ( -12 1) ( 1 (

#6 0 ) -0 ( 20 20 -1 ( >>>>

: ) * ( ) 1) ) 1 ( >>>>8 ( ( ( >>>> ( ( ( ( >>>>


27/29

!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,/ -* ( ( -) -*


28/29

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(


29/29

Se =elta ;low

1 ( 1>

2 ( 10

) ( 1%

* ( 1*

0 ( 0

( %

% ( )

-1 12

> 1 >

1( -1 0

c06 network model ppt

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