Detailed Description

A simple and efficient min-cost flow interface.

This is as fast as GenericMinCostFlow<ReverseArcStaticGraph>, which is the fastest, but is uses more memory in order to hide the somewhat involved construction of the static graph.

Todo:: (user): If the need arises, extend this interface to support warm start and incrementality between solves. Note that this is already supported by the GenericMinCostFlow<> interface.

Definition at line 213 of file min_cost_flow.h.

Public Types
enum	Status { NOT_SOLVED, OPTIMAL, FEASIBLE, INFEASIBLE, UNBALANCED, BAD_RESULT, BAD_COST_RANGE }

Public Member Functions
	SimpleMinCostFlow ()
	The constructor takes no size. More...

ArcIndex	AddArcWithCapacityAndUnitCost (NodeIndex tail, NodeIndex head, FlowQuantity capacity, CostValue unit_cost)
	Adds a directed arc from tail to head to the underlying graph with a given capacity and cost per unit of flow. More...

void	SetNodeSupply (NodeIndex node, FlowQuantity supply)
	Sets the supply of the given node. More...

Status	Solve ()
	Solves the problem, and returns the problem status. More...

Status	SolveMaxFlowWithMinCost ()
	Same as Solve(), but does not have the restriction that the supply must match the demand or that the graph has enough capacity to serve all the demand or use all the supply. More...

CostValue	OptimalCost () const
	Returns the cost of the minimum-cost flow found by the algorithm when the returned Status is OPTIMAL. More...

FlowQuantity	MaximumFlow () const
	Returns the total flow of the minimum-cost flow found by the algorithm when the returned Status is OPTIMAL. More...

FlowQuantity	Flow (ArcIndex arc) const
	Returns the flow on arc, this only make sense for a successful Solve(). More...

NodeIndex	NumNodes () const
	Accessors for the user given data. More...

ArcIndex	NumArcs () const

NodeIndex	Tail (ArcIndex arc) const

NodeIndex	Head (ArcIndex arc) const

FlowQuantity	Capacity (ArcIndex arc) const

FlowQuantity	Supply (NodeIndex node) const

CostValue	UnitCost (ArcIndex arc) const

Member Enumeration Documentation

◆ Status

enum operations_research::MinCostFlowBase::Status

inherited

Enumerator
NOT_SOLVED
OPTIMAL
FEASIBLE
INFEASIBLE
UNBALANCED
BAD_RESULT
BAD_COST_RANGE

Definition at line 194 of file min_cost_flow.h.

Constructor & Destructor Documentation

◆ SimpleMinCostFlow()

operations_research::SimpleMinCostFlow::SimpleMinCostFlow ( )

The constructor takes no size.

New node indices will be created lazily by AddArcWithCapacityAndUnitCost() or SetNodeSupply() such that the set of valid nodes will always be [0, NumNodes()).

Member Function Documentation

◆ AddArcWithCapacityAndUnitCost()

ArcIndex operations_research::SimpleMinCostFlow::AddArcWithCapacityAndUnitCost	(	NodeIndex	tail,
		NodeIndex	head,
		FlowQuantity	capacity,
		CostValue	unit_cost
	)

Adds a directed arc from tail to head to the underlying graph with a given capacity and cost per unit of flow.

Node indices and the capacity must be non-negative (>= 0).
The unit cost can take any integer value (even negative).
Self-looping and duplicate arcs are supported.
After the method finishes, NumArcs() == the returned ArcIndex + 1.

◆ Capacity()

FlowQuantity operations_research::SimpleMinCostFlow::Capacity ( ArcIndex arc ) const

◆ Flow()

FlowQuantity operations_research::SimpleMinCostFlow::Flow ( ArcIndex arc ) const

Returns the flow on arc, this only make sense for a successful Solve().

Note: It is possible that there is more than one optimal solution. The algorithm is deterministic so it will always return the same solution for a given problem. However, there is no guarantee of this from one code version to the next (but the code does not change often).

◆ Head()

NodeIndex operations_research::SimpleMinCostFlow::Head ( ArcIndex arc ) const

◆ MaximumFlow()

FlowQuantity operations_research::SimpleMinCostFlow::MaximumFlow ( ) const

Returns the total flow of the minimum-cost flow found by the algorithm when the returned Status is OPTIMAL.

◆ NumArcs()

ArcIndex operations_research::SimpleMinCostFlow::NumArcs ( ) const

◆ NumNodes()

NodeIndex operations_research::SimpleMinCostFlow::NumNodes ( ) const

Accessors for the user given data.

The implementation will crash if "arc" is not in [0, NumArcs()) or "node" is not in [0, NumNodes()).

◆ OptimalCost()

CostValue operations_research::SimpleMinCostFlow::OptimalCost ( ) const

Returns the cost of the minimum-cost flow found by the algorithm when the returned Status is OPTIMAL.

◆ SetNodeSupply()

void operations_research::SimpleMinCostFlow::SetNodeSupply	(	NodeIndex	node,
		FlowQuantity	supply
	)

Sets the supply of the given node.

The node index must be non-negative (>= 0). Nodes implicitly created will have a default supply set to 0. A demand is modeled as a negative supply.

◆ Solve()

Status operations_research::SimpleMinCostFlow::Solve ( )

inline

Solves the problem, and returns the problem status.

This function requires that the sum of all node supply minus node demand is zero and that the graph has enough capacity to send all supplies and serve all demands. Otherwise, it will return INFEASIBLE.

Definition at line 239 of file min_cost_flow.h.

◆ SolveMaxFlowWithMinCost()

Status operations_research::SimpleMinCostFlow::SolveMaxFlowWithMinCost ( )

inline

Same as Solve(), but does not have the restriction that the supply must match the demand or that the graph has enough capacity to serve all the demand or use all the supply.

This will compute a maximum-flow with minimum cost. The value of the maximum-flow will be given by MaximumFlow().

Definition at line 248 of file min_cost_flow.h.

◆ Supply()

FlowQuantity operations_research::SimpleMinCostFlow::Supply ( NodeIndex node ) const

◆ Tail()

NodeIndex operations_research::SimpleMinCostFlow::Tail ( ArcIndex arc ) const

◆ UnitCost()

CostValue operations_research::SimpleMinCostFlow::UnitCost ( ArcIndex arc ) const

The documentation for this class was generated from the following file:

min_cost_flow.h