From 966afce93a3ed9fc7390f731dd2b4f018d6c7945 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Thu, 18 Apr 2024 18:39:51 +0000 Subject: [PATCH] build based on a934a49 --- dev/.documenter-siteinfo.json | 2 +- dev/algorithms/index.html | 14 +++++++------- dev/index.html | 2 +- dev/search_index.js | 2 +- 4 files changed, 10 insertions(+), 10 deletions(-) diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index 32a188b..3de9b2b 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2024-04-18T18:25:09","documenter_version":"1.4.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2024-04-18T18:39:48","documenter_version":"1.4.0"}} \ No newline at end of file diff --git a/dev/algorithms/index.html b/dev/algorithms/index.html index 08f4839..354deb5 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 and Maximum Flow

solve(c::Vector{Connection}; problem::Union{::ShortestPathProblem, ::MaximumFlowProblem} = ShortestPathProblem)

Arguments

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 and Maximum Flow

solve(c::Vector{Connection}; problem::Union{::ShortestPathProblem, ::MaximumFlowProblem} = ShortestPathProblem)

Arguments

Example

julia> conns = [
                    Connection(1, 2, 3),
                    Connection(1, 3, 2),
                    Connection(1, 4, 4),
@@ -87,7 +87,7 @@
  Connection(6, 7, 3.0, "x67")
 
 julia> result.flow
-7.0

pmedian

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

Arguments

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

# Descriptions

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);
+7.0

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;
 
@@ -104,7 +104,7 @@
  21
 
  julia> result.objective
- 11.531012240599605
source
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

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

Output

  • PMedianResult: PMedianResult object.
source

Minimum Spanning Tree

OperationsResearchModels.MinimumSpanningTree.mst — Function
mst(connections)

Arguments

  • connections::Vector{Connection}: Vector of Connections

Description

Obtains the minimum spanning tree.

Output

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

Examples

julia> conns = Connection[
+ 11.531012240599605
source
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

Minimum Spanning Tree

OperationsResearchModels.MinimumSpanningTree.mst — Function
mst(connections)

Arguments

  • connections::Vector{Connection}: Vector of Connections

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),
@@ -127,7 +127,7 @@
  3-element Vector{Connection}:
   Connection(3, 4, 10, "x34")
   Connection(1, 4, 10, "x14")
-  Connection(2, 3, 10, "x23")
source

CPM (Critical Path Method)

OperationsResearchModels.CPM.cpm — Function
cpm(activities)

Arguments

  • activities::Vector{CpmActivity}

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);
+  Connection(2, 3, 10, "x23")
source

CPM (Critical Path Method)

OperationsResearchModels.CPM.cpm — Function
cpm(activities)

Arguments

  • activities::Vector{CpmActivity}

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]);
@@ -150,7 +150,7 @@
  "I"
 
  julia> result.path == [B, E, G, I]
-true
source

PERT (Project Evalutation and Review Technique)

PERT (Project Evalutation and Review Technique)

OperationsResearchModels.CPM.pert — Function
pert(activities)

Arguments

  • activities::Vector{PertActivity}: Vector of Pert Activities.

Example

julia> A = PertActivity("A", 1, 2, 3)
 PertActivity("A", 1.0, 2.0, 3.0, PertActivity[])
 
 julia> B = PertActivity("B", 3, 3, 3)
@@ -172,4 +172,4 @@
 8.0
 
 julia> result.stddev
-0.0
source
+0.0source diff --git a/dev/index.html b/dev/index.html index 187384c..68370ef 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 5f6944b..bd96c74 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-and-Maximum-Flow","page":"Algorithms","title":"Shortest Path and Maximum Flow","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"solve(c::Vector{Connection}; problem::Union{::ShortestPathProblem, ::MaximumFlowProblem} = ShortestPathProblem)","category":"page"},{"location":"algorithms/#Arguments","page":"Algorithms","title":"Arguments","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"c::Vector{Connection}: Vector of connections \nproblem: Type of problem. Either ShortestPathProblem or MaximumFlowProblem","category":"page"},{"location":"algorithms/#Example","page":"Algorithms","title":"Example","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"julia> 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(conns, problem = ShortestPathProblem);\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\njulia> result = solve(conns, problem = MaximumFlowProblem);\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","category":"page"},{"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\n# Descriptions \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/","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\n# Descriptions ncenters 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/#Minimum-Spanning-Tree","page":"Algorithms","title":"Minimum Spanning Tree","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.mst","category":"page"},{"location":"algorithms/#OperationsResearchModels.MinimumSpanningTree.mst","page":"Algorithms","title":"OperationsResearchModels.MinimumSpanningTree.mst","text":"mst(connections)\n\nArguments\n\nconnections::Vector{Connection}: Vector of Connections \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 = mst(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":"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.cpm","category":"page"},{"location":"algorithms/#OperationsResearchModels.CPM.cpm","page":"Algorithms","title":"OperationsResearchModels.CPM.cpm","text":"cpm(activities)\n\nArguments\n\nactivities::Vector{CpmActivity}\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> result = cpm(activities);\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":"function"},{"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.pert","category":"page"},{"location":"algorithms/#OperationsResearchModels.CPM.pert","page":"Algorithms","title":"OperationsResearchModels.CPM.pert","text":"pert(activities)\n\nArguments\n\nactivities::Vector{PertActivity}: Vector of Pert Activities. \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> 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":"function"}] +[{"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-and-Maximum-Flow","page":"Algorithms","title":"Shortest Path and Maximum Flow","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"solve(c::Vector{Connection}; problem::Union{::ShortestPathProblem, ::MaximumFlowProblem} = ShortestPathProblem)","category":"page"},{"location":"algorithms/#Arguments","page":"Algorithms","title":"Arguments","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"c::Vector{Connection}: Vector of connections \nproblem: Type of problem. Either ShortestPathProblem or MaximumFlowProblem","category":"page"},{"location":"algorithms/#Example","page":"Algorithms","title":"Example","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"julia> 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(conns, problem = ShortestPathProblem);\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\njulia> result = solve(conns, problem = MaximumFlowProblem);\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","category":"page"},{"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/","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/#Minimum-Spanning-Tree","page":"Algorithms","title":"Minimum Spanning Tree","text":"","category":"section"},{"location":"algorithms/","page":"Algorithms","title":"Algorithms","text":"OperationsResearchModels.mst","category":"page"},{"location":"algorithms/#OperationsResearchModels.MinimumSpanningTree.mst","page":"Algorithms","title":"OperationsResearchModels.MinimumSpanningTree.mst","text":"mst(connections)\n\nArguments\n\nconnections::Vector{Connection}: Vector of Connections \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 = mst(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":"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.cpm","category":"page"},{"location":"algorithms/#OperationsResearchModels.CPM.cpm","page":"Algorithms","title":"OperationsResearchModels.CPM.cpm","text":"cpm(activities)\n\nArguments\n\nactivities::Vector{CpmActivity}\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> result = cpm(activities);\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":"function"},{"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.pert","category":"page"},{"location":"algorithms/#OperationsResearchModels.CPM.pert","page":"Algorithms","title":"OperationsResearchModels.CPM.pert","text":"pert(activities)\n\nArguments\n\nactivities::Vector{PertActivity}: Vector of Pert Activities. \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> 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":"function"}] }