Migration: Maximum Flow (lpsole07)
/**********************************************************************/
/* */
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: lpsole07 */
/* TITLE: Migration: Maximum Flow (lpsole07) */
/* PRODUCT: OR */
/* SYSTEM: ALL */
/* KEYS: OR */
/* PROCS: OPTMODEL */
/* DATA: */
/* */
/* SUPPORT: UPDATE: */
/* REF: */
/* MISC: Example 7 from the Linear Programming Solver */
/* chapter of Mathematical Programming. */
/* */
/**********************************************************************/
title 'Maximum Flow Problem';
data arcs;
input _from_ $ _to_ $ _cost_ _capac_;
datalines;
S a . .
S b . .
a c 1 7
b c 2 9
a d 3 5
b d 4 8
c e 5 15
d f 6 20
e g 7 11
f g 8 6
e h 9 12
f h 10 4
g T . .
h T . .
;
proc optmodel;
str source = 'S';
str sink = 'T';
set <str> NODES;
num _supdem_ {i in NODES} = (if i in {source, sink} then . else 0);
set <str,str> ARCS;
num _lo_ {ARCS} init 0;
num _capac_ {ARCS} init .;
num _cost_ {ARCS} init 0;
read data arcs nomiss into ARCS=[_from_ _to_] _cost_ _capac_;
NODES = (union {<i,j> in ARCS} {i,j});
var Flow {<i,j> in ARCS} >= _lo_[i,j];
for {<i,j> in ARCS: _capac_[i,j] ne .} Flow[i,j].ub = _capac_[i,j];
max obj = sum {<i,j> in ARCS: j = sink} Flow[i,j];
con balance {i in NODES diff {source, sink}}:
sum {<(i),j> in ARCS} Flow[i,j]
- sum {<j,(i)> in ARCS} Flow[j,i] = _supdem_[i];
solve;
num _supply_ {<i,j> in ARCS} =
(if _supdem_[i] ne 0 then _supdem_[i] else .);
num _demand_ {<i,j> in ARCS} =
(if _supdem_[j] ne 0 then -_supdem_[j] else .);
num _fcost_ {<i,j> in ARCS} = _cost_[i,j] * Flow[i,j].sol;
create data gout3 from [_from_ _to_]
_cost_ _capac_ _lo_ _supply_ _demand_ _flow_=Flow _fcost_;
quit;
proc print data=gout3;
run;