diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index 76191cf..7362154 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2024-05-06T18:07:21","documenter_version":"1.4.1"}} \ No newline at end of file +{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2024-05-06T18:12:03","documenter_version":"1.4.1"}} \ No newline at end of file diff --git a/dev/algorithms/index.html b/dev/algorithms/index.html index c9fc81b..3f19651 100644 --- a/dev/algorithms/index.html +++ b/dev/algorithms/index.html @@ -18,7 +18,7 @@ julia> result.cost -3.0source

Transportation Problem

OperationsResearchModels.solve — Method
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(
+3.0
source

Transportation Problem

OperationsResearchModels.solve — Method
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], 
@@ -49,7 +49,7 @@
 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]
source

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 = [
+[-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]
source

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),
@@ -70,7 +70,7 @@
  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 = [
+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),
@@ -97,7 +97,7 @@
  Connection(6, 7, 3.0, "x67")
 
 julia> result.flow
-7.0
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[
+7.0
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),
@@ -120,7 +120,7 @@
  3-element Vector{Connection}:
   Connection(3, 4, 10, "x34")
   Connection(1, 4, 10, "x14")
-  Connection(2, 3, 10, "x23")
source

pmedian

OperationsResearchModels.PMedian.pmedian — Function
pmedian(data, ncenters)

Arguments

  • data::Matrix: Coordinates of locations
  • ncenters::Int: Number of centers

Description

The function calculates Euclidean distances between all possible rows of the matrix data. ncenters locations are then selected that minimizes the total distances to the nearest rows.

Output

  • PMedianResult: PMedianResult object.

Example

julia> data1 = rand(10, 2);
+  Connection(2, 3, 10, "x23")
source

pmedian

OperationsResearchModels.PMedian.pmedian — Function
pmedian(data, ncenters)

Arguments

  • data::Matrix: Coordinates of locations
  • ncenters::Int: Number of centers

Description

The function calculates Euclidean distances between all possible rows of the matrix data. ncenters locations are then selected that minimizes the total distances to the nearest rows.

Output

  • PMedianResult: PMedianResult object.

Example

julia> data1 = rand(10, 2);
 
 julia> data2 = rand(10, 2) .+ 50;
 
@@ -137,7 +137,7 @@
  21
 
  julia> result.objective
- 11.531012240599605
source

pmedian with distances

OperationsResearchModels.PMedian.pmedian_with_distances — Function
pmedian_with_distances(distancematrix, ncenters)

Arguments

  • distancematrix::Matrix: n x n matrix of distances
  • ncenters::Int: Number of centers

Description

  • ncenters locations are selected that minimizes the total distances to the nearest rows.

Output

  • PMedianResult: PMedianResult object.
source

CPM (Critical Path Method)

OperationsResearchModels.solve — Method
solve(problem)

Arguments

  • problem::CpmProblem: The problem in type of CpmProblem.

Output

  • ::CpmResult: The object holds the results

Description

Calculates CPM (Critical Path Method) and reports the critical path for a given set of activities.

Example

julia> A = CpmActivity("A", 2);
+ 11.531012240599605
source

pmedian with distances

OperationsResearchModels.PMedian.pmedian_with_distances — Function
pmedian_with_distances(distancematrix, ncenters)

Arguments

  • distancematrix::Matrix: n x n matrix of distances
  • ncenters::Int: Number of centers

Description

  • ncenters locations are selected that minimizes the total distances to the nearest rows.

Output

  • PMedianResult: PMedianResult object.
source

CPM (Critical Path Method)

OperationsResearchModels.solve — Method
solve(problem)

Arguments

  • problem::CpmProblem: The problem in type of CpmProblem.

Output

  • ::CpmResult: The object holds the results

Description

Calculates CPM (Critical Path Method) and reports the critical path for a given set of activities.

Example

julia> A = CpmActivity("A", 2);
 julia> B = CpmActivity("B", 3);
 julia> C = CpmActivity("C", 2, [A]);
 julia> D = CpmActivity("D", 3, [B]);
@@ -162,7 +162,7 @@
  "I"
 
  julia> result.path == [B, E, G, I]
-true
source

CPM Activity

OperationsResearchModels.CPM.CpmActivity — Type
CpmActivity(name::String, time::Float64, dependencies)

Description

The object that represents an activity in CPM (Critical Path Method).

Arguments

  • name::String: The name of the activity.
  • time::Float64: The time of the activity.
  • dependencies: The dependencies of the activity in type of Vector{CpmActivity}.

Example

julia julia> A = CpmActivity("A", 2, []); julia> B = CpmActivity("B", 3, []); julia> C = CpmActivity("C", 2, [A, B]);`

source

PERT (Project Evalutation and Review Technique)

OperationsResearchModels.solve — Method
solve(problem::PertProblem)::PertResult

Arguments

  • problem::PertProblem: The problem in type of PertProblem.

Example

julia> A = PertActivity("A", 1, 2, 3)
+true
source

CPM Activity

OperationsResearchModels.CPM.CpmActivity — Type
CpmActivity(name::String, time::Float64, dependencies)

Description

The object that represents an activity in CPM (Critical Path Method).

Arguments

  • name::String: The name of the activity.
  • time::Float64: The time of the activity.
  • dependencies: The dependencies of the activity in type of Vector{CpmActivity}.

Example

```julia julia> A = CpmActivity("A", 2, []);

julia> B = CpmActivity("B", 3, []);

julia> C = CpmActivity("C", 2, [A, B]);

````

source

PERT (Project Evalutation and Review Technique)

OperationsResearchModels.solve — Method
solve(problem::PertProblem)::PertResult

Arguments

  • problem::PertProblem: The problem in type of PertProblem.

Example

julia> A = PertActivity("A", 1, 2, 3)
 PertActivity("A", 1.0, 2.0, 3.0, PertActivity[])
 
 julia> B = PertActivity("B", 3, 3, 3)
@@ -186,9 +186,9 @@
 8.0
 
 julia> result.stddev
-0.0
source

PERT Activity

OperationsResearchModels.CPM.PertActivity — Type
PertActivity(name::String, o::Float64, m::Float64, p::Float64)::PertActivity

Description

The object that represents an activity in PERT (Program Evaluation and Review Technique).

Arguments

  • name::String: The name of the activity.
  • o::Float64: The optimistic time of the activity.
  • m::Float64: The most likely time of the activity.
  • p::Float64: The pessimistic time of the activity.
  • dependencies: The dependencies of the activity in type of Vector{PertActivity}.

Example

julia> A = PertActivity("A", 1, 2, 3);
+0.0
source

PERT Activity

OperationsResearchModels.CPM.PertActivity — Type
PertActivity(name::String, o::Float64, m::Float64, p::Float64)::PertActivity

Description

The object that represents an activity in PERT (Program Evaluation and Review Technique).

Arguments

  • name::String: The name of the activity.
  • o::Float64: The optimistic time of the activity.
  • m::Float64: The most likely time of the activity.
  • p::Float64: The pessimistic time of the activity.
  • dependencies: The dependencies of the activity in type of Vector{PertActivity}.

Example

julia> A = PertActivity("A", 1, 2, 3);
 julia> B = PertActivity("B", 3, 3, 4);
-julia> C = PertActivity("C", 5, 6, 7, [A, B]);
source

Knapsack

OperationsResearchModels.solve — Method
knapsack(problem::KnapsackProblem)::KnapsackResult

Description

Solves the knapsack problem.

Arguments

  • problem::KnapsackProblem: The problem in type of KnapsackProblem.

Output

  • KnapsackResult: The custom data type that holds selected items, model, and objective value.

Example

julia> values = [10, 20, 30, 40, 50];
+julia> C = PertActivity("C", 5, 6, 7, [A, B]);
source

Knapsack

OperationsResearchModels.solve — Method
knapsack(problem::KnapsackProblem)::KnapsackResult

Description

Solves the knapsack problem.

Arguments

  • problem::KnapsackProblem: The problem in type of KnapsackProblem.

Output

  • KnapsackResult: The custom data type that holds selected items, model, and objective value.

Example

julia> values = [10, 20, 30, 40, 50];
 julia> weights = [1, 2, 3, 4, 5];
 julia> capacity = 10;
-julia> knapsack(KnapsackProblem(values, weights, capacity));
source
+julia> knapsack(KnapsackProblem(values, weights, capacity));source diff --git a/dev/index.html b/dev/index.html index 298d5c3..df1ef3e 100644 --- a/dev/index.html +++ b/dev/index.html @@ -1,2 +1,2 @@ -- · OperationsResearchModels.jl
GitHub

Operations Research Models

The OperationsResearchModels package includes basic Operations Research subjects such as Transportation Problem, Assignment Problem, Minimum Spanning Tree, Shortest Path, Maximum Flow, and p-medians method for selecting location of facilities.

Package content is incrementaly updated.

Please refer the Algorithms section for the detailed documentation.

+- · OperationsResearchModels.jl
GitHub

Operations Research Models

The OperationsResearchModels package includes basic Operations Research subjects such as Transportation Problem, Assignment Problem, Minimum Spanning Tree, Shortest Path, Maximum Flow, and p-medians method for selecting location of facilities.

Package content is incrementaly updated.

Please refer the Algorithms section for the detailed documentation.

diff --git a/dev/search_index.js b/dev/search_index.js index 23413f4..92879d4 100644 --- a/dev/search_index.js +++ b/dev/search_index.js @@ -1,3 +1,3 @@ var documenterSearchIndex = {"docs": -[{"location":"#Operations-Research-Models","page":"-","title":"Operations Research Models","text":"","category":"section"},{"location":"","page":"-","title":"-","text":"The OperationsResearchModels package includes basic Operations Research subjects such as Transportation Problem, Assignment Problem, Minimum Spanning Tree, Shortest Path, Maximum Flow, and p-medians method for selecting location of facilities. ","category":"page"},{"location":"","page":"-","title":"-","text":"Package content is incrementaly updated.","category":"page"},{"location":"","page":"-","title":"-","text":"Please refer the Algorithms section for the detailed documentation. ","category":"page"},{"location":"algorithms/#Algorithms","page":"Algorithms","title":"Algorithms","text":"","category":"section"},{"location":"algorithms/#Assignment-Problem","page":"Algorithms","title":"Assignment Problem","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.solve(a::AssignmentProblem)","category":"page"},{"location":"algorithms/#OperationsResearchModels.solve-Tuple{AssignmentProblem}","page":"Algorithms","title":"OperationsResearchModels.solve","text":"solve(a)\n\nArguments\n\na::AssignmentProblem: The problem in type of AssignmentProblem\n\nOutput\n\nAssignmentResult: The custom data type that holds problem, solution, and optimum cost. \n\nDescription\n\nSolves an assignment problem given by an object of in type AssignmentProblem.\n\nExample\n\njulia> mat = [\n 4 8 1;\n 3 1 9;\n 1 6 7;\n ];\n\njulia> problem = AssignmentProblem(mat);\n\njulia> result = solve(problem);\n\njulia> result.solution\n\n3×3 Matrix{Float64}:\n 0.0 0.0 1.0\n 0.0 1.0 0.0\n 1.0 0.0 0.0\n\njulia> result.cost\n\n3.0\n\n\n\n\n\n","category":"method"},{"location":"algorithms/#Transportation-Problem","page":"Algorithms","title":"Transportation Problem","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.solve(t::TransportationProblem)","category":"page"},{"location":"algorithms/#OperationsResearchModels.solve-Tuple{TransportationProblem}","page":"Algorithms","title":"OperationsResearchModels.solve","text":"solve(t)\n\nArguments\n\na::TransportationProblem: The problem in type of TransportationProblem\n\nOutput\n\nTransportationResult: The custom data type that holds problem, solution, and optimum cost. \n\nDescription\n\nSolves a transportation problem given by an object of in type TransportationProblem.\n\nExample\n\njulia> t = TransportationProblem(\n [ 1 1 1 1; \n 2 2 2 2; \n 3 3 3 3], \n [100, 100, 100, 100], # Demands \n [100, 100, 100]) # Supplies \nTransportation Problem:\nCosts: [1 1 1 1; 2 2 2 2; 3 3 3 3]\nDemand: [100, 100, 100, 100]\nSupply: [100, 100, 100]\n\njulia> isbalanced(t)\nfalse\n\njulia> result = solve(t)\nTransportation Results:\nMain problem:\nTransportation Problem:\nCosts: [1 1 1 1; 2 2 2 2; 3 3 3 3]\nDemand: [100, 100, 100, 100]\nSupply: [100, 100, 100]\n\nBalanced problem:\nTransportation Problem:\nCosts: [1 1 1 1; 2 2 2 2; 3 3 3 3; 0 0 0 0]\nDemand: [100, 100, 100, 100]\nSupply: [100, 100, 100, 100]\n\nCost:\n600.0\nSolution:\n[-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]\n\n\n\n\n\n","category":"method"},{"location":"algorithms/#Shortest-Path","page":"Algorithms","title":"Shortest Path","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.solve(t::ShortestPathProblem)","category":"page"},{"location":"algorithms/#OperationsResearchModels.solve-Tuple{ShortestPathProblem}","page":"Algorithms","title":"OperationsResearchModels.solve","text":"solve(problem)\n\nDescription\n\nSolves a shortest path problem given by an object of in type ShortestPathProblem.\n\nArguments\n\nproblem::ShortestPathProblem: The problem in type of ShortestPathProblem\n\nOutput\n\nShortestPathResult: The custom data type that holds path and cost.\n\nExample\n\njulia> conns = [\n Connection(1, 2, 3),\n Connection(1, 3, 2),\n Connection(1, 4, 4),\n Connection(2, 5, 3),\n Connection(3, 5, 1),\n Connection(3, 6, 1),\n Connection(4, 6, 2),\n Connection(5, 7, 6),\n Connection(6, 7, 5),\n ];\n\njulia> solve(ShortestPathProblem(conns));\n\njulia> result.path\n3-element Vector{Connection}:\n Connection(1, 3, 2, \"x13\")\n Connection(3, 6, 1, \"x36\")\n Connection(6, 7, 5, \"x67\")\n\njulia> result.cost\n8.0\n\n\n\n\n\n","category":"method"},{"location":"algorithms/#Maximum-Flow","page":"Algorithms","title":"Maximum Flow","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.solve(t::MaximumFlowProblem)","category":"page"},{"location":"algorithms/#OperationsResearchModels.solve-Tuple{MaximumFlowProblem}","page":"Algorithms","title":"OperationsResearchModels.solve","text":"solve(problem)\n\nArguments\n\nproblem::MaximumFlowProblem: The problem in type of MaximumFlowProblem\n\nOutput\n\nMaximumFlowResult: The custom data type that holds path and flow.\n\nExample\n\njulia> conns = [\n Connection(1, 2, 3),\n Connection(1, 3, 2),\n Connection(1, 4, 4),\n Connection(2, 5, 3),\n Connection(3, 5, 1),\n Connection(3, 6, 1),\n Connection(4, 6, 2),\n Connection(5, 7, 6),\n Connection(6, 7, 5),\n ];\njulia> problem = MaximumFlowProblem(conns)\njulia> result = solve(problem);\n\njulia> result.path\n9-element Vector{Connection}:\n Connection(1, 2, 3.0, \"x12\")\n Connection(1, 3, 2.0, \"x13\")\n Connection(1, 4, 2.0, \"x14\")\n Connection(2, 5, 3.0, \"x25\")\n Connection(3, 5, 1.0, \"x35\")\n Connection(3, 6, 1.0, \"x36\")\n Connection(4, 6, 2.0, \"x46\")\n Connection(5, 7, 4.0, \"x57\")\n Connection(6, 7, 3.0, \"x67\")\n\njulia> result.flow\n7.0\n\n\n\n\n\n","category":"method"},{"location":"algorithms/#Minimum-Spanning-Tree","page":"Algorithms","title":"Minimum Spanning Tree","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.solve(p::MstProblem)","category":"page"},{"location":"algorithms/#OperationsResearchModels.solve-Tuple{MstProblem}","page":"Algorithms","title":"OperationsResearchModels.solve","text":"solve(problem::MstProblem)\n\nArguments\n\nproblem::MstProblem: The problem in type of MstProblem\n\nDescription\n\nObtains the minimum spanning tree. \n\nOutput\n\n::MstResult: A MstResult object that holds the results. \n\nExamples\n\njulia> conns = Connection[\n Connection(1, 2, 10),\n Connection(2, 3, 10),\n Connection(3, 4, 10),\n Connection(1, 4, 10)\n ]\n\n4-element Vector{Connection}:\n Connection(1, 2, 10, \"x12\")\n Connection(2, 3, 10, \"x23\")\n Connection(3, 4, 10, \"x34\")\n Connection(1, 4, 10, \"x14\")\n\n julia> result = solve(MstProblem(conns))\n MstResult(Connection[Connection(3, 4, 10, \"x34\"), Connection(1, 4, 10, \"x14\"), Connection(2, 3, 10, \"x23\")], 30.0)\n \n julia> result.distance\n 30.0\n \n julia> result.connections\n 3-element Vector{Connection}:\n Connection(3, 4, 10, \"x34\")\n Connection(1, 4, 10, \"x14\")\n Connection(2, 3, 10, \"x23\")\n\n\n\n\n\n","category":"method"},{"location":"algorithms/#pmedian","page":"Algorithms","title":"pmedian","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.pmedian","category":"page"},{"location":"algorithms/#OperationsResearchModels.PMedian.pmedian","page":"Algorithms","title":"OperationsResearchModels.PMedian.pmedian","text":"pmedian(data, ncenters)\n\nArguments\n\ndata::Matrix: Coordinates of locations \nncenters::Int: Number of centers \n\nDescription\n\nThe function calculates Euclidean distances between all possible rows of the matrix data. ncenters locations are then selected that minimizes the total distances to the nearest rows. \n\nOutput\n\nPMedianResult: PMedianResult object. \n\nExample\n\njulia> data1 = rand(10, 2);\n\njulia> data2 = rand(10, 2) .+ 50;\n\njulia> data3 = rand(10, 2) .+ 100;\n\njulia> data = vcat(data1, data2, data3);\n\njulia> result = pmedian(data, 3);\n\njulia> result.centers\n3-element Vector{Int64}:\n 1\n 16\n 21\n\n julia> result.objective\n 11.531012240599605\n\n\n\n\n\n","category":"function"},{"location":"algorithms/#pmedian-with-distances","page":"Algorithms","title":"pmedian with distances","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.pmedian_with_distances","category":"page"},{"location":"algorithms/#OperationsResearchModels.PMedian.pmedian_with_distances","page":"Algorithms","title":"OperationsResearchModels.PMedian.pmedian_with_distances","text":"pmedian_with_distances(distancematrix, ncenters)\n\nArguments\n\ndistancematrix::Matrix: n x n matrix of distances\nncenters::Int: Number of centers \n\nDescription\n\nncenters locations are selected that minimizes the total distances to the nearest rows. \n\nOutput\n\nPMedianResult: PMedianResult object. \n\n\n\n\n\n","category":"function"},{"location":"algorithms/#CPM-(Critical-Path-Method)","page":"Algorithms","title":"CPM (Critical Path Method)","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.solve(problem::CpmProblem)","category":"page"},{"location":"algorithms/#OperationsResearchModels.solve-Tuple{CpmProblem}","page":"Algorithms","title":"OperationsResearchModels.solve","text":"solve(problem)\n\nArguments\n\nproblem::CpmProblem: The problem in type of CpmProblem.\n\nOutput\n\n::CpmResult: The object holds the results \n\nDescription\n\nCalculates CPM (Critical Path Method) and reports the critical path for a given set of activities. \n\nExample\n\njulia> A = CpmActivity(\"A\", 2);\njulia> B = CpmActivity(\"B\", 3);\njulia> C = CpmActivity(\"C\", 2, [A]);\njulia> D = CpmActivity(\"D\", 3, [B]);\njulia> E = CpmActivity(\"E\", 2, [B]);\njulia> F = CpmActivity(\"F\", 3, [C, D]);\njulia> G = CpmActivity(\"G\", 7, [E]);\njulia> H = CpmActivity(\"H\", 5, [E]);\njulia> I = CpmActivity(\"I\", 6, [G, F]);\njulia> J = CpmActivity(\"J\", 2, [C, D]);\n\njulia> activities = [A, B, C, D, E, F, G, H, I, J];\n\njulia> problem = CpmProblem(activities);\n\njulia> result = solve(problem);\n\njulia> result.pathstr\n4-element Vector{String}:\n \"B\"\n \"E\"\n \"G\"\n \"I\"\n\n julia> result.path == [B, E, G, I]\ntrue\n\n\n\n\n\n","category":"method"},{"location":"algorithms/#CPM-Activity","page":"Algorithms","title":"CPM Activity","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.CpmActivity","category":"page"},{"location":"algorithms/#OperationsResearchModels.CPM.CpmActivity","page":"Algorithms","title":"OperationsResearchModels.CPM.CpmActivity","text":"CpmActivity(name::String, time::Float64, dependencies)\n\nDescription\n\nThe object that represents an activity in CPM (Critical Path Method).\n\nArguments\n\nname::String: The name of the activity.\ntime::Float64: The time of the activity.\ndependencies: The dependencies of the activity in type of Vector{CpmActivity}.\n\nExample\n\njulia julia> A = CpmActivity(\"A\", 2, []); julia> B = CpmActivity(\"B\", 3, []); julia> C = CpmActivity(\"C\", 2, [A, B]);`\n\n\n\n\n\n","category":"type"},{"location":"algorithms/#PERT-(Project-Evalutation-and-Review-Technique)","page":"Algorithms","title":"PERT (Project Evalutation and Review Technique)","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.solve(problem::PertProblem)","category":"page"},{"location":"algorithms/#OperationsResearchModels.solve-Tuple{PertProblem}","page":"Algorithms","title":"OperationsResearchModels.solve","text":"solve(problem::PertProblem)::PertResult\n\nArguments\n\nproblem::PertProblem: The problem in type of PertProblem.\n\nExample\n\njulia> A = PertActivity(\"A\", 1, 2, 3)\nPertActivity(\"A\", 1.0, 2.0, 3.0, PertActivity[])\n\njulia> B = PertActivity(\"B\", 3, 3, 3)\nPertActivity(\"B\", 3.0, 3.0, 3.0, PertActivity[])\n\njulia> C = PertActivity(\"C\", 5, 5, 5, [A, B])\nPertActivity(\"C\", 5.0, 5.0, 5.0, PertActivity[PertActivity(\"A\", 1.0, 2.0, 3.0, PertActivity[]), PertActivity(\"B\", 3.0, 3.0, 3.0, PertActivity[])])\n\njulia> activities = [A, B, C]\n3-element Vector{PertActivity}:\n PertActivity(\"A\", 1.0, 2.0, 3.0, PertActivity[])\n PertActivity(\"B\", 3.0, 3.0, 3.0, PertActivity[])\n PertActivity(\"C\", 5.0, 5.0, 5.0, PertActivity[PertActivity(\"A\", 1.0, 2.0, 3.0, PertActivity[]), PertActivity(\"B\", 3.0, 3.0, 3.0, PertActivity[])])\n\njulia> problem = PertProblem(activities);\n\njulia> result = pert(activities)\nPertResult(PertActivity[PertActivity(\"B\", 3.0, 3.0, 3.0, PertActivity[]), PertActivity(\"C\", 5.0, 5.0, 5.0, PertActivity[PertActivity(\"A\", 1.0, 2.0, 3.0, PertActivity[]), PertActivity(\"B\", 3.0, 3.0, 3.0, PertActivity[])])], 8.0, 0.0)\n\njulia> result.mean\n8.0\n\njulia> result.stddev\n0.0\n\n\n\n\n\n","category":"method"},{"location":"algorithms/#PERT-Activity","page":"Algorithms","title":"PERT Activity","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.PertActivity","category":"page"},{"location":"algorithms/#OperationsResearchModels.CPM.PertActivity","page":"Algorithms","title":"OperationsResearchModels.CPM.PertActivity","text":"PertActivity(name::String, o::Float64, m::Float64, p::Float64)::PertActivity\n\nDescription\n\nThe object that represents an activity in PERT (Program Evaluation and Review Technique).\n\nArguments\n\nname::String: The name of the activity.\no::Float64: The optimistic time of the activity.\nm::Float64: The most likely time of the activity.\np::Float64: The pessimistic time of the activity.\ndependencies: The dependencies of the activity in type of Vector{PertActivity}.\n\nExample\n\njulia> A = PertActivity(\"A\", 1, 2, 3);\njulia> B = PertActivity(\"B\", 3, 3, 4);\njulia> C = PertActivity(\"C\", 5, 6, 7, [A, B]);\n\n\n\n\n\n","category":"type"},{"location":"algorithms/#Knapsack","page":"Algorithms","title":"Knapsack","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.solve(p::KnapsackProblem)","category":"page"},{"location":"algorithms/#OperationsResearchModels.solve-Tuple{KnapsackProblem}","page":"Algorithms","title":"OperationsResearchModels.solve","text":"knapsack(problem::KnapsackProblem)::KnapsackResult\n\nDescription\n\nSolves the knapsack problem.\n\nArguments\n\nproblem::KnapsackProblem: The problem in type of KnapsackProblem.\n\nOutput\n\nKnapsackResult: The custom data type that holds selected items, model, and objective value.\n\nExample\n\njulia> values = [10, 20, 30, 40, 50];\njulia> weights = [1, 2, 3, 4, 5];\njulia> capacity = 10;\njulia> knapsack(KnapsackProblem(values, weights, capacity));\n\n\n\n\n\n","category":"method"}] +[{"location":"#Operations-Research-Models","page":"-","title":"Operations Research Models","text":"","category":"section"},{"location":"","page":"-","title":"-","text":"The OperationsResearchModels package includes basic Operations Research subjects such as Transportation Problem, Assignment Problem, Minimum Spanning Tree, Shortest Path, Maximum Flow, and p-medians method for selecting location of facilities. ","category":"page"},{"location":"","page":"-","title":"-","text":"Package content is incrementaly updated.","category":"page"},{"location":"","page":"-","title":"-","text":"Please refer the Algorithms section for the detailed documentation. ","category":"page"},{"location":"algorithms/#Algorithms","page":"Algorithms","title":"Algorithms","text":"","category":"section"},{"location":"algorithms/#Assignment-Problem","page":"Algorithms","title":"Assignment Problem","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.solve(a::AssignmentProblem)","category":"page"},{"location":"algorithms/#OperationsResearchModels.solve-Tuple{AssignmentProblem}","page":"Algorithms","title":"OperationsResearchModels.solve","text":"solve(a)\n\nArguments\n\na::AssignmentProblem: The problem in type of AssignmentProblem\n\nOutput\n\nAssignmentResult: The custom data type that holds problem, solution, and optimum cost. \n\nDescription\n\nSolves an assignment problem given by an object of in type AssignmentProblem.\n\nExample\n\njulia> mat = [\n 4 8 1;\n 3 1 9;\n 1 6 7;\n ];\n\njulia> problem = AssignmentProblem(mat);\n\njulia> result = solve(problem);\n\njulia> result.solution\n\n3×3 Matrix{Float64}:\n 0.0 0.0 1.0\n 0.0 1.0 0.0\n 1.0 0.0 0.0\n\njulia> result.cost\n\n3.0\n\n\n\n\n\n","category":"method"},{"location":"algorithms/#Transportation-Problem","page":"Algorithms","title":"Transportation Problem","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.solve(t::TransportationProblem)","category":"page"},{"location":"algorithms/#OperationsResearchModels.solve-Tuple{TransportationProblem}","page":"Algorithms","title":"OperationsResearchModels.solve","text":"solve(t)\n\nArguments\n\na::TransportationProblem: The problem in type of TransportationProblem\n\nOutput\n\nTransportationResult: The custom data type that holds problem, solution, and optimum cost. \n\nDescription\n\nSolves a transportation problem given by an object of in type TransportationProblem.\n\nExample\n\njulia> t = TransportationProblem(\n [ 1 1 1 1; \n 2 2 2 2; \n 3 3 3 3], \n [100, 100, 100, 100], # Demands \n [100, 100, 100]) # Supplies \nTransportation Problem:\nCosts: [1 1 1 1; 2 2 2 2; 3 3 3 3]\nDemand: [100, 100, 100, 100]\nSupply: [100, 100, 100]\n\njulia> isbalanced(t)\nfalse\n\njulia> result = solve(t)\nTransportation Results:\nMain problem:\nTransportation Problem:\nCosts: [1 1 1 1; 2 2 2 2; 3 3 3 3]\nDemand: [100, 100, 100, 100]\nSupply: [100, 100, 100]\n\nBalanced problem:\nTransportation Problem:\nCosts: [1 1 1 1; 2 2 2 2; 3 3 3 3; 0 0 0 0]\nDemand: [100, 100, 100, 100]\nSupply: [100, 100, 100, 100]\n\nCost:\n600.0\nSolution:\n[-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]\n\n\n\n\n\n","category":"method"},{"location":"algorithms/#Shortest-Path","page":"Algorithms","title":"Shortest Path","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.solve(t::ShortestPathProblem)","category":"page"},{"location":"algorithms/#OperationsResearchModels.solve-Tuple{ShortestPathProblem}","page":"Algorithms","title":"OperationsResearchModels.solve","text":"solve(problem)\n\nDescription\n\nSolves a shortest path problem given by an object of in type ShortestPathProblem.\n\nArguments\n\nproblem::ShortestPathProblem: The problem in type of ShortestPathProblem\n\nOutput\n\nShortestPathResult: The custom data type that holds path and cost.\n\nExample\n\njulia> conns = [\n Connection(1, 2, 3),\n Connection(1, 3, 2),\n Connection(1, 4, 4),\n Connection(2, 5, 3),\n Connection(3, 5, 1),\n Connection(3, 6, 1),\n Connection(4, 6, 2),\n Connection(5, 7, 6),\n Connection(6, 7, 5),\n ];\n\njulia> solve(ShortestPathProblem(conns));\n\njulia> result.path\n3-element Vector{Connection}:\n Connection(1, 3, 2, \"x13\")\n Connection(3, 6, 1, \"x36\")\n Connection(6, 7, 5, \"x67\")\n\njulia> result.cost\n8.0\n\n\n\n\n\n","category":"method"},{"location":"algorithms/#Maximum-Flow","page":"Algorithms","title":"Maximum Flow","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.solve(t::MaximumFlowProblem)","category":"page"},{"location":"algorithms/#OperationsResearchModels.solve-Tuple{MaximumFlowProblem}","page":"Algorithms","title":"OperationsResearchModels.solve","text":"solve(problem)\n\nArguments\n\nproblem::MaximumFlowProblem: The problem in type of MaximumFlowProblem\n\nOutput\n\nMaximumFlowResult: The custom data type that holds path and flow.\n\nExample\n\njulia> conns = [\n Connection(1, 2, 3),\n Connection(1, 3, 2),\n Connection(1, 4, 4),\n Connection(2, 5, 3),\n Connection(3, 5, 1),\n Connection(3, 6, 1),\n Connection(4, 6, 2),\n Connection(5, 7, 6),\n Connection(6, 7, 5),\n ];\njulia> problem = MaximumFlowProblem(conns)\njulia> result = solve(problem);\n\njulia> result.path\n9-element Vector{Connection}:\n Connection(1, 2, 3.0, \"x12\")\n Connection(1, 3, 2.0, \"x13\")\n Connection(1, 4, 2.0, \"x14\")\n Connection(2, 5, 3.0, \"x25\")\n Connection(3, 5, 1.0, \"x35\")\n Connection(3, 6, 1.0, \"x36\")\n Connection(4, 6, 2.0, \"x46\")\n Connection(5, 7, 4.0, \"x57\")\n Connection(6, 7, 3.0, \"x67\")\n\njulia> result.flow\n7.0\n\n\n\n\n\n","category":"method"},{"location":"algorithms/#Minimum-Spanning-Tree","page":"Algorithms","title":"Minimum Spanning Tree","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.solve(p::MstProblem)","category":"page"},{"location":"algorithms/#OperationsResearchModels.solve-Tuple{MstProblem}","page":"Algorithms","title":"OperationsResearchModels.solve","text":"solve(problem::MstProblem)\n\nArguments\n\nproblem::MstProblem: The problem in type of MstProblem\n\nDescription\n\nObtains the minimum spanning tree. \n\nOutput\n\n::MstResult: A MstResult object that holds the results. \n\nExamples\n\njulia> conns = Connection[\n Connection(1, 2, 10),\n Connection(2, 3, 10),\n Connection(3, 4, 10),\n Connection(1, 4, 10)\n ]\n\n4-element Vector{Connection}:\n Connection(1, 2, 10, \"x12\")\n Connection(2, 3, 10, \"x23\")\n Connection(3, 4, 10, \"x34\")\n Connection(1, 4, 10, \"x14\")\n\n julia> result = solve(MstProblem(conns))\n MstResult(Connection[Connection(3, 4, 10, \"x34\"), Connection(1, 4, 10, \"x14\"), Connection(2, 3, 10, \"x23\")], 30.0)\n \n julia> result.distance\n 30.0\n \n julia> result.connections\n 3-element Vector{Connection}:\n Connection(3, 4, 10, \"x34\")\n Connection(1, 4, 10, \"x14\")\n Connection(2, 3, 10, \"x23\")\n\n\n\n\n\n","category":"method"},{"location":"algorithms/#pmedian","page":"Algorithms","title":"pmedian","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.pmedian","category":"page"},{"location":"algorithms/#OperationsResearchModels.PMedian.pmedian","page":"Algorithms","title":"OperationsResearchModels.PMedian.pmedian","text":"pmedian(data, ncenters)\n\nArguments\n\ndata::Matrix: Coordinates of locations \nncenters::Int: Number of centers \n\nDescription\n\nThe function calculates Euclidean distances between all possible rows of the matrix data. ncenters locations are then selected that minimizes the total distances to the nearest rows. \n\nOutput\n\nPMedianResult: PMedianResult object. \n\nExample\n\njulia> data1 = rand(10, 2);\n\njulia> data2 = rand(10, 2) .+ 50;\n\njulia> data3 = rand(10, 2) .+ 100;\n\njulia> data = vcat(data1, data2, data3);\n\njulia> result = pmedian(data, 3);\n\njulia> result.centers\n3-element Vector{Int64}:\n 1\n 16\n 21\n\n julia> result.objective\n 11.531012240599605\n\n\n\n\n\n","category":"function"},{"location":"algorithms/#pmedian-with-distances","page":"Algorithms","title":"pmedian with distances","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.pmedian_with_distances","category":"page"},{"location":"algorithms/#OperationsResearchModels.PMedian.pmedian_with_distances","page":"Algorithms","title":"OperationsResearchModels.PMedian.pmedian_with_distances","text":"pmedian_with_distances(distancematrix, ncenters)\n\nArguments\n\ndistancematrix::Matrix: n x n matrix of distances\nncenters::Int: Number of centers \n\nDescription\n\nncenters locations are selected that minimizes the total distances to the nearest rows. \n\nOutput\n\nPMedianResult: PMedianResult object. \n\n\n\n\n\n","category":"function"},{"location":"algorithms/#CPM-(Critical-Path-Method)","page":"Algorithms","title":"CPM (Critical Path Method)","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.solve(problem::CpmProblem)","category":"page"},{"location":"algorithms/#OperationsResearchModels.solve-Tuple{CpmProblem}","page":"Algorithms","title":"OperationsResearchModels.solve","text":"solve(problem)\n\nArguments\n\nproblem::CpmProblem: The problem in type of CpmProblem.\n\nOutput\n\n::CpmResult: The object holds the results \n\nDescription\n\nCalculates CPM (Critical Path Method) and reports the critical path for a given set of activities. \n\nExample\n\njulia> A = CpmActivity(\"A\", 2);\njulia> B = CpmActivity(\"B\", 3);\njulia> C = CpmActivity(\"C\", 2, [A]);\njulia> D = CpmActivity(\"D\", 3, [B]);\njulia> E = CpmActivity(\"E\", 2, [B]);\njulia> F = CpmActivity(\"F\", 3, [C, D]);\njulia> G = CpmActivity(\"G\", 7, [E]);\njulia> H = CpmActivity(\"H\", 5, [E]);\njulia> I = CpmActivity(\"I\", 6, [G, F]);\njulia> J = CpmActivity(\"J\", 2, [C, D]);\n\njulia> activities = [A, B, C, D, E, F, G, H, I, J];\n\njulia> problem = CpmProblem(activities);\n\njulia> result = solve(problem);\n\njulia> result.pathstr\n4-element Vector{String}:\n \"B\"\n \"E\"\n \"G\"\n \"I\"\n\n julia> result.path == [B, E, G, I]\ntrue\n\n\n\n\n\n","category":"method"},{"location":"algorithms/#CPM-Activity","page":"Algorithms","title":"CPM Activity","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.CpmActivity","category":"page"},{"location":"algorithms/#OperationsResearchModels.CPM.CpmActivity","page":"Algorithms","title":"OperationsResearchModels.CPM.CpmActivity","text":"CpmActivity(name::String, time::Float64, dependencies)\n\nDescription\n\nThe object that represents an activity in CPM (Critical Path Method).\n\nArguments\n\nname::String: The name of the activity.\ntime::Float64: The time of the activity.\ndependencies: The dependencies of the activity in type of Vector{CpmActivity}.\n\nExample\n\n```julia julia> A = CpmActivity(\"A\", 2, []);\n\njulia> B = CpmActivity(\"B\", 3, []);\n\njulia> C = CpmActivity(\"C\", 2, [A, B]);\n\n````\n\n\n\n\n\n","category":"type"},{"location":"algorithms/#PERT-(Project-Evalutation-and-Review-Technique)","page":"Algorithms","title":"PERT (Project Evalutation and Review Technique)","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.solve(problem::PertProblem)","category":"page"},{"location":"algorithms/#OperationsResearchModels.solve-Tuple{PertProblem}","page":"Algorithms","title":"OperationsResearchModels.solve","text":"solve(problem::PertProblem)::PertResult\n\nArguments\n\nproblem::PertProblem: The problem in type of PertProblem.\n\nExample\n\njulia> A = PertActivity(\"A\", 1, 2, 3)\nPertActivity(\"A\", 1.0, 2.0, 3.0, PertActivity[])\n\njulia> B = PertActivity(\"B\", 3, 3, 3)\nPertActivity(\"B\", 3.0, 3.0, 3.0, PertActivity[])\n\njulia> C = PertActivity(\"C\", 5, 5, 5, [A, B])\nPertActivity(\"C\", 5.0, 5.0, 5.0, PertActivity[PertActivity(\"A\", 1.0, 2.0, 3.0, PertActivity[]), PertActivity(\"B\", 3.0, 3.0, 3.0, PertActivity[])])\n\njulia> activities = [A, B, C]\n3-element Vector{PertActivity}:\n PertActivity(\"A\", 1.0, 2.0, 3.0, PertActivity[])\n PertActivity(\"B\", 3.0, 3.0, 3.0, PertActivity[])\n PertActivity(\"C\", 5.0, 5.0, 5.0, PertActivity[PertActivity(\"A\", 1.0, 2.0, 3.0, PertActivity[]), PertActivity(\"B\", 3.0, 3.0, 3.0, PertActivity[])])\n\njulia> problem = PertProblem(activities);\n\njulia> result = pert(activities)\nPertResult(PertActivity[PertActivity(\"B\", 3.0, 3.0, 3.0, PertActivity[]), PertActivity(\"C\", 5.0, 5.0, 5.0, PertActivity[PertActivity(\"A\", 1.0, 2.0, 3.0, PertActivity[]), PertActivity(\"B\", 3.0, 3.0, 3.0, PertActivity[])])], 8.0, 0.0)\n\njulia> result.mean\n8.0\n\njulia> result.stddev\n0.0\n\n\n\n\n\n","category":"method"},{"location":"algorithms/#PERT-Activity","page":"Algorithms","title":"PERT Activity","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.PertActivity","category":"page"},{"location":"algorithms/#OperationsResearchModels.CPM.PertActivity","page":"Algorithms","title":"OperationsResearchModels.CPM.PertActivity","text":"PertActivity(name::String, o::Float64, m::Float64, p::Float64)::PertActivity\n\nDescription\n\nThe object that represents an activity in PERT (Program Evaluation and Review Technique).\n\nArguments\n\nname::String: The name of the activity.\no::Float64: The optimistic time of the activity.\nm::Float64: The most likely time of the activity.\np::Float64: The pessimistic time of the activity.\ndependencies: The dependencies of the activity in type of Vector{PertActivity}.\n\nExample\n\njulia> A = PertActivity(\"A\", 1, 2, 3);\njulia> B = PertActivity(\"B\", 3, 3, 4);\njulia> C = PertActivity(\"C\", 5, 6, 7, [A, B]);\n\n\n\n\n\n","category":"type"},{"location":"algorithms/#Knapsack","page":"Algorithms","title":"Knapsack","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.solve(p::KnapsackProblem)","category":"page"},{"location":"algorithms/#OperationsResearchModels.solve-Tuple{KnapsackProblem}","page":"Algorithms","title":"OperationsResearchModels.solve","text":"knapsack(problem::KnapsackProblem)::KnapsackResult\n\nDescription\n\nSolves the knapsack problem.\n\nArguments\n\nproblem::KnapsackProblem: The problem in type of KnapsackProblem.\n\nOutput\n\nKnapsackResult: The custom data type that holds selected items, model, and objective value.\n\nExample\n\njulia> values = [10, 20, 30, 40, 50];\njulia> weights = [1, 2, 3, 4, 5];\njulia> capacity = 10;\njulia> knapsack(KnapsackProblem(values, weights, capacity));\n\n\n\n\n\n","category":"method"}] }