<< min_lcost_flow1 Flows min_qcost_flow >>

metanet >> metanet > Flows > min_lcost_flow2

min_lcost_flow2

minimum linear cost flow

Calling Sequence

[c,phi,flag] = min_lcost_flow2(g)

Parameters

g

a graph_data_structure.

c

value of cost

phi

row vector of the value of flow on the arcs

flag

feasible problem flag (0 or 1)

Description

min_lcost_flow2 computes the minimum linear cost flow in the network g. It returns the total cost of the flows on the arcs c and the row vector of the flows on the arcs phi. If the problem is not feasible (impossible to find a compatible flow for instance), flag is equal to 0, otherwise it is equal to 1.

The bounds of the flow are given by the g.edges.data.min_cap and g.edges.data.max_cap fields of the graph.

The value of the minimum capacity and of the maximum capacity must be non negative and must be integer numbers. The value of the maximum capacity must be greater than or equal to the value of the minimum capacity.

If the value of min_cap or max_cap is not given it is assumed to be equal to 0 on each edge.

The costs on the edges are given by the element g.edges.data.cost of the fields of the graph. The costs must be non negative. If the value of cost is not given, it is assumed to be equal to 0 on each edge.

The demand on the nodes are given by the g.edges.data.demand field of the graph. The demands must be integer numbers. Note that the sum of the demands must be equal to zero for the problem to be feasible. If the value of demand is not given, it is assumed to be equal to 0 on each node.

If the min_cap or max_cap or cost data fields are not present in the graph structure they can be added and set using the add_edge_data function. If the demand data field is not present in the graph structure it can be added and set using the add_node_data function.

This functions uses a relaxation algorithm due to D. Bertsekas.

Examples

ta=[1 1 2 2 2 3 4 4 5 6 6 6 7 7 7 8 9 10 12 12 13 13 13 14 15 14 9 11 10 1 8];
he=[2 6 3 4 5 1 3 5 1 7 10 11 5 8 9 5 8 11 10 11 9 11 15 13 14 4 6 9 1 12 14];
g=make_graph('foo',1,15,ta,he);
g.nodes.graphics.x=[194 191 106 194 296 305 305 418 422 432 552 550 549 416 548];
g.nodes.graphics.y=[56 221 316 318 316 143 214 321 217 126 215 80 330 437 439];
show_graph(g);

g=add_edge_data(g,'max_cap',[37,24,23,30,25,27,27,24,34,40,21,38,35,23,38,28,26,..
                       22,40,22,28,24,31,25,26,24,23,30,22,24,35]);
g=add_edge_data(g,'cost',[10,6,3,8,10,8,11,1,2,6,5,6,5,3,4,2,4,4,8,2,4,5,4,8,8,3,4,3,7,10,10]);
g=add_node_data(g,'demand',[22,-29,18,-3,-16,20,-9,7,-6,17,21,-6,-8,-37,9]);

[c,phi,flag]=min_lcost_flow2(g);flag

g.edges.graphics.foreground(find(phi<>0))=color('red');
g=add_edge_data(g,'flow',phi)
g.edges.graphics.display='flow';
g.nodes.graphics.display='demand';

show_graph(g);

See Also


<< min_lcost_flow1 Flows min_qcost_flow >>