Network Models

Shortest Path

OperationsResearchModels.solve — Method

solve(problem)

Description

Solves a shortest path problem given by an object of in type ShortestPathProblem.

Arguments

problem::ShortestPathProblem: The problem in type of ShortestPathProblem

Output

ShortestPathResult: The custom data type that holds path and cost.

Example

julia> conns = [
                   Connection(1, 2, 3),
                   Connection(1, 3, 2),
                   Connection(1, 4, 4),
                   Connection(2, 5, 3),
                   Connection(3, 5, 1),
                   Connection(3, 6, 1),
                   Connection(4, 6, 2),
                   Connection(5, 7, 6),
                   Connection(6, 7, 5),
               ];

julia> solve(ShortestPathProblem(conns));

julia> result.path
3-element Vector{Connection}:
 Connection(1, 3, 2, "x13")
 Connection(3, 6, 1, "x36")
 Connection(6, 7, 5, "x67")

julia> result.cost
8.0

source

Maximum Flow

OperationsResearchModels.solve — Method

solve(problem)

Arguments

problem::MaximumFlowProblem: The problem in type of MaximumFlowProblem

Output

MaximumFlowResult: The custom data type that holds path and flow.

Example

julia> conns = [
                   Connection(1, 2, 3),
                   Connection(1, 3, 2),
                   Connection(1, 4, 4),
                   Connection(2, 5, 3),
                   Connection(3, 5, 1),
                   Connection(3, 6, 1),
                   Connection(4, 6, 2),
                   Connection(5, 7, 6),
                   Connection(6, 7, 5),
               ];
julia> problem = MaximumFlowProblem(conns)
julia> result = solve(problem);

julia> result.path
9-element Vector{Connection}:
 Connection(1, 2, 3.0, "x12")
 Connection(1, 3, 2.0, "x13")
 Connection(1, 4, 2.0, "x14")
 Connection(2, 5, 3.0, "x25")
 Connection(3, 5, 1.0, "x35")
 Connection(3, 6, 1.0, "x36")
 Connection(4, 6, 2.0, "x46")
 Connection(5, 7, 4.0, "x57")
 Connection(6, 7, 3.0, "x67")

julia> result.flow
7.0

source

Minimum Cost Flow

OperationsResearchModels.solve — Method

solve(problem)

Description

This function solves the Minimum Cost Flow problem by first solving the Maximum Flow problem and then using the flow value to solve the Minimum Cost Flow problem.

Arguments

problem::MinimumCostFlowProblem: The problem in type of MinimumCostFlowProblem

source

OperationsResearchModels.solve — Method

solve(problem, flow)

Description

This function solves the Minimum Cost Flow problem given a flow value.

Arguments

problem::MinimumCostFlowProblem: The problem in type of MinimumCostFlowProblem
flow::Float64: The flow value to be used in the problem.

source

Minimum Spanning Tree

OperationsResearchModels.solve — Method

solve(problem::MstProblem)

Arguments

problem::MstProblem: The problem in type of MstProblem

Description

Obtains the minimum spanning tree.

Output

::MstResult: A MstResult object that holds the results.

Examples

julia> conns = Connection[
                       Connection(1, 2, 10),
                       Connection(2, 3, 10),
                       Connection(3, 4, 10),
                       Connection(1, 4, 10)
                   ]

4-element Vector{Connection}:
 Connection(1, 2, 10, "x12")
 Connection(2, 3, 10, "x23")
 Connection(3, 4, 10, "x34")
 Connection(1, 4, 10, "x14")

 julia> result = solve(MstProblem(conns))
 MstResult(Connection[Connection(3, 4, 10, "x34"), Connection(1, 4, 10, "x14"), Connection(2, 3, 10, "x23")], 30.0)
 
 julia> result.distance
 30.0
 
 julia> result.connections
 3-element Vector{Connection}:
  Connection(3, 4, 10, "x34")
  Connection(1, 4, 10, "x14")
  Connection(2, 3, 10, "x23")

source