solve(t)

Arguments

a::TransportationProblem: The problem in type of TransportationProblem

Output

TransportationResult: The custom data type that holds problem, solution, and optimum cost.

Description

Solves a transportation problem given by an object of in type TransportationProblem.

Example

julia> t = TransportationProblem(
                   [   1 1 1 1; 
                       2 2 2 2; 
                       3 3 3 3], 
                   [100, 100, 100, 100], # Demands 
                   [100, 100, 100])      # Supplies 
Transportation Problem:
Costs: [1 1 1 1; 2 2 2 2; 3 3 3 3]
Demand: [100, 100, 100, 100]
Supply: [100, 100, 100]

julia> isbalanced(t)
false

julia> result = solve(t)
Transportation Results:
Main problem:
Transportation Problem:
Costs: [1 1 1 1; 2 2 2 2; 3 3 3 3]
Demand: [100, 100, 100, 100]
Supply: [100, 100, 100]

Balanced problem:
Transportation Problem:
Costs: [1 1 1 1; 2 2 2 2; 3 3 3 3; 0 0 0 0]
Demand: [100, 100, 100, 100]
Supply: [100, 100, 100, 100]

Cost:
600.0
Solution:
[-0.0 -0.0 -0.0 100.0; 100.0 -0.0 -0.0 -0.0; -0.0 -0.0 100.0 -0.0; -0.0 100.0 -0.0 -0.0]

TransportationProblem

Arguments

• costs::Array{T,2}: The cost matrix of the transportation problem.
• demand::Array{T,1}: The demand vector of the transportation problem.
• supply::Array{T,1}: The supply vector of the transportation problem.

Description

The TransportationProblem struct represents a transportation problem with a cost matrix, demand vector, and supply vector.

TransportationResult(problem, balancedProblem, solution, cost)

Arguments

• problem::TransportationProblem: The original transportation problem.
• balancedProblem::TransportationProblem: The balanced transportation problem.
• solution::Matrix: The solution matrix of the transportation problem.
• cost::Real: The optimal cost of the transportation problem.

Description

The TransportationResult struct represents the result of solving a transportation problem. It contains the original problem, the balanced problem, the solution matrix, and the optimal cost.

northwestcorner(a::TransportationProblem)::TransportationResult

Description

The northwest corner method is a heuristic for finding an initial basic feasible solution to a transportation problem. It starts at the northwest corner of the cost matrix and allocates as much as possible to the cell, then moves either down or right depending on whether the supply or demand has been met. The method continues until all supply and demand constraints are satisfied.

Arguments

• a::TransportationProblem: The problem in type of TransportationProblem

Output

• TransportationResult: The custom data type that holds problem, solution, and optimum cost.

leastcost(a::TransportationProblem)::TransportationResult

Description

The least cost method is a heuristic for finding an initial basic feasible solution to a transportation problem. It starts by selecting the cell with the lowest cost and allocating as much as possible to that cell, then it moves to the next lowest cost cell and repeats the process until all supply and demand constraints are satisfied.

Arguments

• a::TransportationProblem: The problem in type of TransportationProblem

Output

• TransportationResult: The custom data type that holds problem, solution, and optimum cost.