```! Min Cut (dual of Max Flow) problem; ! Given a network, e.g., a railroad network, where each arc (i,j) has a cost to remove, C(i,j), and a source node and a sink, Find a minimum cost set of arcs to delete so that there is no flow (or path) from the source node to the sink node; ! References: Ford and Fulkerson, Harris and Ross; ! Keywords: Min cut, Max flow, Network, Interdiction; SETS: NODE: Y; ARC( NODE, NODE): C, Z; ENDSETSDATA: NODE = S 1 2 3 4 5 6 7 8 9 T; ! The arcs and their costs to delete; ARC, C = S 1 23 S 2 29 1 3 6 1 4 9 2 3 19 3 4 9 3 5 17 4 6 11 4 7 13 5 6 8 5 8 7 6 7 12 6 9 14 6 T 6 7 T 21 8 9 15 9 T 16; ENDDATA SUBMODEL MINCUT: ! Variables: Z(i,j) = 1 if we delete arc i,j Y(i) = 1 if node i is on the Source side of cut, 0 otherwise; ! Get number of nodes in network; NODET = @SIZE( NODE); ! Minimize the cost of deleted arcs; MIN = @SUM( ARC(i,j) : C(i,j)*Z(i,j)); ! Node 1, the Source, is definitely on S side, Node T is not; [FLO1] Y(1) - Y(NODET) >= 1; ! If arc (i,j) is on the cut (deleted), then node i must be on the S side of cut, and j is not. If node i is on the S side of the cut, then so is node j, except if arc (i,j) has been deleted; @FOR( ARC(i,j): [FLO] Z(i,j) - Y(i) + Y(j) >= 0; ); ENDSUBMODEL CALC: @SOLVE( MINCUT); @WRITE( 'The Minimum Cost Set of Arcs to Delete to', @NEWLINE(1),' Split a Network.',@NEWLINE(1)); @WRITE(' Arc deleted Cost',@NEWLINE(1)); SUMDEL = 0; @FOR( ARC(i,j) | Z(i,j) #GT# 0.5: @WRITE( ' (', NODE(i),', ',NODE(j),') ', C(i,j),@NEWLINE(1)); SUMDEL = SUMDEL + C(i,j); ); @WRITE(' Total removal cost= ',SUMDEL,@NEWLINE(1)); ENDCALC ```