Finds the minimum cost flow of a directed graph.
Usage
MinCostFlow(
arcSources,
arcTargets,
arcCapacities,
arcCosts,
nodeSupplies,
numNodes,
algorithm = "NetworkSimplex"
)Arguments
- arcSources
Vector corresponding to the source nodes of a graph's edges
- arcTargets
Vector corresponding to the destination nodes of a graph's edges
- arcCapacities
Vector corresponding to the capacities of nodes of a graph's edges
- arcCosts
Vector corresponding to the capacities of nodes of a graph's edges
- nodeSupplies
Vector corresponding to the supplies of each node
- numNodes
The number of nodes in the graph
- algorithm
Choices of algorithm include "NetworkSimplex", "CostScaling", "CapacityScaling", and "CycleCancelling". NetworkSimplex is the default.
Value
A named list containing four entries: 1) "flows": A vector corresponding to the flows of arcs in the graph, 2) "potentials": A vector of potentials of the graph's nodes, 3) "cost": the total cost of the flows in the graph, i.e. the mincostflow value, and 4) "feasibility": LEMON's feasibility type, demonstrating how feasible the graph problem is, one of "INFEASIBLE", "OPTIMAL", and "UNBOUNDED"
Details
For details on LEMON's implementation, including differences between the algorithms, see https://lemon.cs.elte.hu/pub/doc/1.3.1/a00612.html.