Min-cost Network Flow Problem Using Network Simplex (optlpe08)
/***************************************************************************/
/* */
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: optlpe08 */
/* TITLE: Min-cost Network Flow Problem Using Network Simplex (optlpe08) */
/* PRODUCT: OR */
/* SYSTEM: ALL */
/* KEYS: OR */
/* PROCS: OPTLP */
/* DATA: */
/* */
/* SUPPORT: UPDATE: */
/* REF: */
/* MISC: Example 8 from the OPTLP chapter of Mathematical */
/* Programming. */
/* */
/***************************************************************************/
data ex8;
input field1 $8. field2 $13. @25 field3 $13. field4 @53 field5 $13. field6;
datalines;
NAME . . . . .
ROWS . . . . .
N obj . . . .
E balance['1'] . . . .
E balance['2'] . . . .
E balance['3'] . . . .
E balance['4'] . . . .
E balance['5'] . . . .
E balance['6'] . . . .
E balance['7'] . . . .
E balance['8'] . . . .
COLUMNS . . . . .
. x['1','4'] obj 2 balance['1'] 1
. x['1','4'] balance['4'] -1 . .
. x['2','1'] obj 1 balance['1'] -1
. x['2','1'] balance['2'] 1 . .
. x['2','3'] balance['2'] 1 balance['3'] -1
. x['2','6'] obj 6 balance['2'] 1
. x['2','6'] balance['6'] -1 . .
. x['3','4'] obj 1 balance['3'] 1
. x['3','4'] balance['4'] -1 . .
. x['3','5'] obj 4 balance['3'] 1
. x['3','5'] balance['5'] -1 . .
. x['4','7'] obj 5 balance['4'] 1
. x['4','7'] balance['7'] -1 . .
. x['5','6'] obj 2 balance['5'] 1
. x['5','6'] balance['6'] -1 . .
. x['5','7'] obj 7 balance['5'] 1
. x['5','7'] balance['7'] -1 . .
. x['6','8'] obj 8 balance['6'] 1
. x['6','8'] balance['8'] -1 . .
. x['7','8'] obj 9 balance['7'] 1
. x['7','8'] balance['8'] -1 . .
RHS . . . . .
. .RHS. balance['1'] 10 . .
. .RHS. balance['2'] 20 . .
. .RHS. balance['4'] -5 . .
. .RHS. balance['7'] -15 . .
. .RHS. balance['8'] -10 . .
BOUNDS . . . . .
UP .BOUNDS. x['1','4'] 15 . .
UP .BOUNDS. x['2','1'] 10 . .
UP .BOUNDS. x['2','3'] 10 . .
UP .BOUNDS. x['2','6'] 10 . .
UP .BOUNDS. x['3','4'] 5 . .
UP .BOUNDS. x['3','5'] 10 . .
UP .BOUNDS. x['4','7'] 10 . .
UP .BOUNDS. x['5','6'] 20 . .
UP .BOUNDS. x['5','7'] 15 . .
UP .BOUNDS. x['6','8'] 10 . .
UP .BOUNDS. x['7','8'] 15 . .
ENDATA . . . . .
;
title1 'The OPTLP Procedure';
proc optlp
presolver = none
printlevel = 2
logfreq = 1
data = ex8
primalout = ex8out
algorithm = ns;
run;
title2 'Primal Solution';
proc print data=ex8out label;
run;
