FindMinimumCostFlow

FindMinimumCostFlow[g,{sd1,sd2,…}] finds the minimum cost flow in the graph g with sd1, sd2, … vertex supplies or demands.

• FindMinimumCostFlow[g,s,t] finds the minimum cost maximum flow between source vertex s and target vertex t in a graph g.
• FindMinimumCostFlow[g,s,t,d] finds the minimum cost flow between source s and target t, with the required flow d.
• FindMinimumCostFlow[m,…] finds the minimum cost flow in a graph with cost matrix m.
• FindMinimumCostFlow[data,…,"property"] returns the value of "property".
• FindMinimumCostFlow[{v->w,…},…] uses rules v->w to specify the graph g.

Examples

(* Find minimum cost flow *)
g = Graph[{1 -> 2, 2 -> 3, 1 -> 3}, 
  EdgeWeight -> {1, 2, 4}, EdgeCapacity -> {5, 3, 2}];
FindMinimumCostFlow[g, 1, 3]

(* Get the cost *)
FindMinimumCostFlow[g, 1, 3, "Cost"]

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