GAMS Rev 135 Linux/Intel 01/11/06 10:03:07 Page 1 Min-Cost Network Flow (Williams, p.82) 2 4 5 option limrow=0, limcol=0, solprint=on; 6 7 set node /0*7/; 8 parameter supply(node) /0 10, 1 15, 5 -9, 6 -10, 7 -6/; 9 parameter cost(node,node) / 10 0.2 5 11 1.3 4 12 2.3 2 13 2.4 6 14 2.5 5 15 3.4 1 16 3.7 2 17 4.2 4 18 4.5 6 19 4.6 3 20 7.6 4 21 /; 22 23 alias (node,i,j,k); 24 25 * define a dynamic set that indicates the "legal" arcs 26 set arc(node,node); 27 arc(i,j) = yes$(cost(i,j) > 0); 28 29 positive variable f(node,node); 30 variable totalcost; 31 32 equations balance(node), objective; 33 34 balance(i).. 35 sum(arc(i,k), f(arc)) - sum(arc(j,i), f(arc)) =e= supply(i); 36 objective.. 37 totalcost =e= sum(arc, cost(arc)*f(arc)); 38 39 model mcf/balance, objective/; 40 41 solve mcf using lp minimizing totalcost; 42 43 option f:0:0:2; display f.l; COMPILATION TIME = 0.001 SECONDS 0.8 Mb LNX211-135 GAMS Rev 135 Linux/Intel 01/11/06 10:03:07 Page 2 Min-Cost Network Flow (Williams, p.82) Model Statistics SOLVE mcf Using LP From line 41 MODEL STATISTICS BLOCKS OF EQUATIONS 2 SINGLE EQUATIONS 9 BLOCKS OF VARIABLES 2 SINGLE VARIABLES 12 NON ZERO ELEMENTS 34 GENERATION TIME = 0.014 SECONDS 1.3 Mb LNX211-135 EXECUTION TIME = 0.017 SECONDS 1.3 Mb LNX211-135 GAMS Rev 135 Linux/Intel 01/11/06 10:03:07 Page 3 Min-Cost Network Flow (Williams, p.82) Solution Report SOLVE mcf Using LP From line 41 S O L V E S U M M A R Y MODEL mcf OBJECTIVE totalcost TYPE LP DIRECTION MINIMIZE SOLVER CPLEX FROM LINE 41 **** SOLVER STATUS 1 NORMAL COMPLETION **** MODEL STATUS 1 OPTIMAL **** OBJECTIVE VALUE 209.0000 RESOURCE USAGE, LIMIT 0.010 1000.000 ITERATION COUNT, LIMIT 2 10000 GAMS/Cplex Jun 2, 2003 LNX.CP.CP 21.1 023.025.041.LXI For Cplex 8.1 Cplex 8.1.0, GAMS Link 23 Optimal solution found. Objective : 209.000000 ---- EQU balance LOWER LEVEL UPPER MARGINAL 0 10.0000 10.0000 10.0000 7.0000 1 15.0000 15.0000 15.0000 4.0000 2 . . . 2.0000 3 . . . . 4 . . . -1.0000 5 -9.0000 -9.0000 -9.0000 -3.0000 6 -10.0000 -10.0000 -10.0000 -4.0000 7 -6.0000 -6.0000 -6.0000 -2.0000 LOWER LEVEL UPPER MARGINAL ---- EQU objective . . . 1.0000 ---- VAR f LOWER LEVEL UPPER MARGINAL 0.2 . 10.0000 +INF . 1.3 . 15.0000 +INF . 2.3 . 1.0000 +INF . 2.4 . . +INF 3.0000 2.5 . 9.0000 +INF . 3.4 . 10.0000 +INF . 3.7 . 6.0000 +INF . 4.2 . . +INF 7.0000 4.5 . . +INF 4.0000 4.6 . 10.0000 +INF . 7.6 . . +INF 2.0000 GAMS Rev 135 Linux/Intel 01/11/06 10:03:07 Page 4 Min-Cost Network Flow (Williams, p.82) Solution Report SOLVE mcf Using LP From line 41 LOWER LEVEL UPPER MARGINAL ---- VAR totalcost -INF 209.0000 +INF . **** REPORT SUMMARY : 0 NONOPT 0 INFEASIBLE 0 UNBOUNDED GAMS Rev 135 Linux/Intel 01/11/06 10:03:07 Page 5 Min-Cost Network Flow (Williams, p.82) E x e c u t i o n ---- 43 VARIABLE f.L 0.2 10, 1.3 15 2.3 1, 2.5 9 3.4 10, 3.7 6 4.6 10 EXECUTION TIME = 0.002 SECONDS 1.3 Mb LNX211-135 USER: Computer Sciences Dept. G031114:1111AS-LNX University of Wisconsin-Madison DC2621 **** FILE SUMMARY INPUT /afs/cs.wisc.edu/u/s/w/swright/public/html/635/examples/mincost.gms OUTPUT /afs/cs.wisc.edu/u/s/w/swright/public/html/635/examples/mincost.lst