feat: ajout de deux notebooks
This commit is contained in:
Laureηt
parent
be1cfaa57e
commit
9f1515c8b8
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@ -9,43 +9,68 @@
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
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"\u001b[32m\u001b[1mNo Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.5/Project.toml`\n",
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"\u001b[32m\u001b[1mNo Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.5/Manifest.toml`\n",
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"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n",
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"\u001b[32m\u001b[1mNo Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.5/Project.toml`\n",
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"\u001b[32m\u001b[1mNo Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.5/Manifest.toml`\n"
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"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.6/Project.toml`\n",
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"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.6/Manifest.toml`\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.6/Project.toml`\n",
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"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.6/Manifest.toml`\n"
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]
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}
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],
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"source": [
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"#importer les packages utiles\n",
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"import Pkg; Pkg.add(\"Cbc\")\n",
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"import Pkg;\n",
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"Pkg.add(\"Cbc\")\n",
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"Pkg.add(\"JuMP\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"execution_count": 8,
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"metadata": {},
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"outputs": [
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{
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"ename": "LoadError",
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"evalue": "\u001b[91mMethodError: no method matching Model(::Type{Cbc.Optimizer})\u001b[39m\n\u001b[91m\u001b[0mClosest candidates are:\u001b[39m\n\u001b[91m\u001b[0m Model(::Any, \u001b[91m::Any\u001b[39m, \u001b[91m::Any\u001b[39m, \u001b[91m::Any\u001b[39m, \u001b[91m::Any\u001b[39m, \u001b[91m::Any\u001b[39m, \u001b[91m::Any\u001b[39m, \u001b[91m::Any\u001b[39m) at /Users/sungueve/.julia/packages/JuMP/MsUSY/src/JuMP.jl:126\u001b[39m\n\u001b[91m\u001b[0m Model(; caching_mode, solver) at /Users/sungueve/.julia/packages/JuMP/MsUSY/src/JuMP.jl:161\u001b[39m\n\u001b[91m\u001b[0m Model(\u001b[91m::MathOptInterface.AbstractOptimizer\u001b[39m, \u001b[91m::Dict{MathOptInterface.ConstraintIndex,AbstractShape}\u001b[39m, \u001b[91m::Set{Any}\u001b[39m, \u001b[91m::Any\u001b[39m, \u001b[91m::Any\u001b[39m, \u001b[91m::Dict{Symbol,Any}\u001b[39m, \u001b[91m::Int64\u001b[39m, \u001b[91m::Dict{Symbol,Any}\u001b[39m) at /Users/sungueve/.julia/packages/JuMP/MsUSY/src/JuMP.jl:126\u001b[39m\n\u001b[91m\u001b[0m ...\u001b[39m",
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"output_type": "error",
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"traceback": [
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"\u001b[91mMethodError: no method matching Model(::Type{Cbc.Optimizer})\u001b[39m\n\u001b[91m\u001b[0mClosest candidates are:\u001b[39m\n\u001b[91m\u001b[0m Model(::Any, \u001b[91m::Any\u001b[39m, \u001b[91m::Any\u001b[39m, \u001b[91m::Any\u001b[39m, \u001b[91m::Any\u001b[39m, \u001b[91m::Any\u001b[39m, \u001b[91m::Any\u001b[39m, \u001b[91m::Any\u001b[39m) at /Users/sungueve/.julia/packages/JuMP/MsUSY/src/JuMP.jl:126\u001b[39m\n\u001b[91m\u001b[0m Model(; caching_mode, solver) at /Users/sungueve/.julia/packages/JuMP/MsUSY/src/JuMP.jl:161\u001b[39m\n\u001b[91m\u001b[0m Model(\u001b[91m::MathOptInterface.AbstractOptimizer\u001b[39m, \u001b[91m::Dict{MathOptInterface.ConstraintIndex,AbstractShape}\u001b[39m, \u001b[91m::Set{Any}\u001b[39m, \u001b[91m::Any\u001b[39m, \u001b[91m::Any\u001b[39m, \u001b[91m::Dict{Symbol,Any}\u001b[39m, \u001b[91m::Int64\u001b[39m, \u001b[91m::Dict{Symbol,Any}\u001b[39m) at /Users/sungueve/.julia/packages/JuMP/MsUSY/src/JuMP.jl:126\u001b[39m\n\u001b[91m\u001b[0m ...\u001b[39m",
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"",
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"Stacktrace:",
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" [1] top-level scope at In[3]:11",
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" [2] include_string(::Function, ::Module, ::String, ::String) at ./loading.jl:1091"
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Max 50 ciment[1] + 70 ciment[2]\n",
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"Subject to\n",
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" 40 ciment[1] + 12 ciment[2] ≤ 360.0\n",
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" 20 ciment[1] + 30 ciment[2] ≤ 480.0\n",
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" ciment[1] ≥ 0.0\n",
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" ciment[2] ≥ 0.0\n",
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"\n",
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"Presolve 2 (0) rows, 2 (0) columns and 4 (0) elements\n",
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"0 Obj -0 Dual inf 120 (2)\n",
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"2 Obj 1137.5\n",
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"Optimal - objective value 1137.5\n",
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"Optimal objective 1137.5 - 2 iterations time 0.002\n"
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]
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}
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],
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@ -76,12 +101,12 @@
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"println(model)\n",
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"\n",
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"# run optimization\n",
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"optimize!(model)\n"
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"optimize!(model)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"execution_count": 9,
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"metadata": {},
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"outputs": [
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{
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@ -101,28 +126,21 @@
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"println(\"\\t benefice = $(objective_value(model))\")\n",
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"for i in 1:N\n",
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" println(\"\\t quantite de ciment $i = $(value(ciment[i]))\")\n",
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"end\n"
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"end"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Julia 1.5.3",
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"display_name": "Julia 1.6.3",
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"language": "julia",
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"name": "julia-1.5"
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"name": "julia-1.6"
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},
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"language_info": {
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"file_extension": ".jl",
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"mimetype": "application/julia",
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"name": "julia",
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"version": "1.5.3"
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"version": "1.6.3"
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}
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},
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"nbformat": 4,
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186
exo1/voitures.ipynb
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186
exo1/voitures.ipynb
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@ -0,0 +1,186 @@
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Exemple de modèle et résolution du problème de Fabrication du voitures"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.6/Project.toml`\n",
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"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.6/Manifest.toml`\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.6/Project.toml`\n",
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"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.6/Manifest.toml`\n"
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]
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}
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],
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"source": [
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"#importer les packages utiles\n",
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"import Pkg;\n",
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"Pkg.add(\"Cbc\")\n",
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"Pkg.add(\"JuMP\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Max 10000 voitures[1] + 9000 voitures[2]\n",
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"Subject to\n",
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" 10 voitures[1] + 20 voitures[2] ≤ 15000.0\n",
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" 6 voitures[1] + 5 voitures[2] ≤ 6000.0\n",
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" voitures[1] ≤ 800.0\n",
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" voitures[1] ≥ 0.0\n",
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" voitures[2] ≥ 0.0\n",
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" voitures[1] integer\n",
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" voitures[2] integer\n",
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"\n",
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"Welcome to the CBC MILP Solver \n",
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"Version: 2.10.5 \n",
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"Build Date: Jan 1 1970 \n",
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"\n",
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"command line - Cbc_C_Interface -solve -quit (default strategy 1)\n",
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"Continuous objective value is 1.02857e+07 - 0.00 seconds\n",
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"Cgl0004I processed model has 2 rows, 2 columns (2 integer (0 of which binary)) and 4 elements\n",
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"Cutoff increment increased from 1e-05 to 1000\n",
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"Cbc0012I Integer solution of -10272000 found by DiveCoefficient after 0 iterations and 0 nodes (0.00 seconds)\n",
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"Cbc0012I Integer solution of -10284000 found by DiveCoefficient after 3 iterations and 0 nodes (0.01 seconds)\n",
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"Cbc0031I 1 added rows had average density of 2\n",
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"Cbc0013I At root node, 1 cuts changed objective from -10285714 to -10284000 in 21 passes\n",
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"Cbc0014I Cut generator 0 (Probing) - 0 row cuts average 0.0 elements, 47 column cuts (47 active) in 0.001 seconds - new frequency is 1\n",
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"Cbc0014I Cut generator 1 (Gomory) - 4 row cuts average 2.0 elements, 0 column cuts (0 active) in 0.001 seconds - new frequency is 1\n",
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"Cbc0014I Cut generator 2 (Knapsack) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n",
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"Cbc0014I Cut generator 3 (Clique) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n",
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"Cbc0014I Cut generator 4 (MixedIntegerRounding2) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n",
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"Cbc0014I Cut generator 5 (FlowCover) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n",
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"Cbc0001I Search completed - best objective -10284000, took 3 iterations and 0 nodes (0.01 seconds)\n",
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"Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost\n",
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"Cuts at root node changed objective from -1.02857e+07 to -1.0284e+07\n",
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"Probing was tried 21 times and created 47 cuts of which 0 were active after adding rounds of cuts (0.001 seconds)\n",
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"Gomory was tried 21 times and created 4 cuts of which 0 were active after adding rounds of cuts (0.001 seconds)\n",
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"Knapsack was tried 21 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
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"Clique was tried 21 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
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"MixedIntegerRounding2 was tried 21 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
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"FlowCover was tried 21 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
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"TwoMirCuts was tried 1 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
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"ZeroHalf was tried 1 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
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"\n",
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"Result - Optimal solution found\n",
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"\n",
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"Objective value: 10284000.00000000\n",
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"Enumerated nodes: 0\n",
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"Total iterations: 3\n",
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"Time (CPU seconds): 0.01\n",
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"Time (Wallclock seconds): 0.01\n",
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"\n",
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"Total time (CPU seconds): 0.01 (Wallclock seconds): 0.01\n",
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"\n"
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]
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}
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],
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"source": [
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"using Cbc\n",
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"using JuMP\n",
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"\n",
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"# data\n",
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"N = 2 # nombre de voitures disponibles\n",
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"c = [10000, 9000] # prix de vente par voitures\n",
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"b = [15000, 6000, 800] \n",
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"A = [10 20 ; 6 5 ; 1 0]\n",
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"\n",
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"# set optimizer\n",
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"model = Model(Cbc.Optimizer)\n",
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"\n",
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"# define variables\n",
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"@variable(model, voitures[1:N] >= 0, integer=true)\n",
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"\n",
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"# define objective function\n",
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"@objective(model, Max, sum(c[i] * voitures[i] for i = 1:N))\n",
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"\n",
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"# define constraints\n",
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"for i = 1:length(b)\n",
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" @constraint(model, sum(A[i, j] * voitures[j] for j = 1:N) <= b[i])\n",
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"end\n",
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"\n",
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"println(model)\n",
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"\n",
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"# run optimization\n",
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"optimize!(model)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Solution obtenue:\n",
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"\t benefice = 1.0284e7\n",
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"\t quantite de voitures 1 = 645.0\n",
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"\t quantite de voitures 2 = 426.0\n"
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]
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}
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],
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"source": [
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"# print solution\n",
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"println(\"Solution obtenue:\")\n",
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"println(\"\\t benefice = $(objective_value(model))\")\n",
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"for i = 1:N\n",
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" println(\"\\t quantite de voitures $i = $(value(voitures[i]))\")\n",
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"end"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Julia 1.6.3",
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"language": "julia",
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"name": "julia-1.6"
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},
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"language_info": {
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"file_extension": ".jl",
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"mimetype": "application/julia",
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"name": "julia",
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"version": "1.6.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}
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168
exo3/bourse.ipynb
Normal file
168
exo3/bourse.ipynb
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@ -0,0 +1,168 @@
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Exemple de modèle et résolution du problème de Fabrication du produits"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n"
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]
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.6/Project.toml`\n",
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"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.6/Manifest.toml`\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.6/Project.toml`\n",
|
||||
"\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.6/Manifest.toml`\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"#importer les packages utiles\n",
|
||||
"import Pkg;\n",
|
||||
"Pkg.add(\"Cbc\")\n",
|
||||
"Pkg.add(\"JuMP\")"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Max 0.07 produits[1] + 0.1 produits[2] + 0.19 produits[3] + 0.12 produits[4] + 0.8 produits[5] + 0.14 produits[6]\n",
|
||||
"Subject to\n",
|
||||
" produits[1] + produits[2] + produits[3] + produits[4] + produits[5] + produits[6] = 1.0\n",
|
||||
" produits[1] + produits[2] ≥ 0.45\n",
|
||||
" produits[3] + produits[4] ≥ 0.3\n",
|
||||
" 1.7 produits[1] + 1.2 produits[2] + 3.7 produits[3] + 2.4 produits[4] + 2 produits[5] + 2.9 produits[6] ≤ 2.0\n",
|
||||
" produits[1] ≤ 0.25\n",
|
||||
" produits[2] ≤ 0.25\n",
|
||||
" produits[3] ≤ 0.25\n",
|
||||
" produits[4] ≤ 0.25\n",
|
||||
" produits[5] ≤ 0.25\n",
|
||||
" produits[6] ≤ 0.25\n",
|
||||
" produits[1] ≥ 0.0\n",
|
||||
" produits[2] ≥ 0.0\n",
|
||||
" produits[3] ≥ 0.0\n",
|
||||
" produits[4] ≥ 0.0\n",
|
||||
" produits[5] ≥ 0.0\n",
|
||||
" produits[6] ≥ 0.0\n",
|
||||
"\n",
|
||||
"Presolve 4 (-6) rows, 6 (0) columns and 16 (-6) elements\n",
|
||||
"0 Obj 0.016999999 Primal inf 1.349997 (3) Dual inf 1.419994 (6)\n",
|
||||
"5 Obj 0.28253846\n",
|
||||
"Optimal - objective value 0.28253846\n",
|
||||
"After Postsolve, objective 0.28253846, infeasibilities - dual 0 (0), primal 0 (0)\n",
|
||||
"Optimal objective 0.2825384615 - 5 iterations time 0.002, Presolve 0.00\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"using Cbc\n",
|
||||
"using JuMP\n",
|
||||
"\n",
|
||||
"# data\n",
|
||||
"N = 6 # nombre de produits disponibles\n",
|
||||
"risques = [1.7 1.2 3.7 2.4 2.0 2.9]\n",
|
||||
"interets = [ 0.07 0.10 0.19 0.12 0.8 0.14]\n",
|
||||
"\n",
|
||||
"# set optimizer\n",
|
||||
"model = Model(Cbc.Optimizer)\n",
|
||||
"\n",
|
||||
"# define variables\n",
|
||||
"@variable(model, produits[1:N] >= 0)\n",
|
||||
"\n",
|
||||
"# define objective function\n",
|
||||
"@objective(model, Max, sum(interets[i] * produits[i] for i = 1:N))\n",
|
||||
"\n",
|
||||
"# define constraints\n",
|
||||
"@constraint(model, sum(produits[i] for i = 1:N) == 1.0) # somme à 100%\n",
|
||||
"@constraint(model, sum(produits[i]*risques[i] for i = 1:N) <= 2.0) # risque total\n",
|
||||
"@constraint(model, produits[1] + produits[2] >= 0.45)\n",
|
||||
"@constraint(model, produits[3] + produits[4] >= 0.3)\n",
|
||||
"for i = 1:N\n",
|
||||
" @constraint(model, produits[i] <= 0.25) # limite de 25%\n",
|
||||
"end\n",
|
||||
"\n",
|
||||
"println(model)\n",
|
||||
"\n",
|
||||
"# run optimization\n",
|
||||
"optimize!(model)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 9,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Solution obtenue:\n",
|
||||
"\t benefice = 0.2825384615384615\n",
|
||||
"\t quantite de produits 1 = 0.2\n",
|
||||
"\t quantite de produits 2 = 0.25\n",
|
||||
"\t quantite de produits 3 = 0.10769230769230764\n",
|
||||
"\t quantite de produits 4 = 0.19230769230769232\n",
|
||||
"\t quantite de produits 5 = 0.25\n",
|
||||
"\t quantite de produits 6 = 0.0\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"# print solution\n",
|
||||
"println(\"Solution obtenue:\")\n",
|
||||
"println(\"\\t benefice = $(objective_value(model))\")\n",
|
||||
"for i = 1:N\n",
|
||||
" println(\"\\t quantite de produits $i = $(value(produits[i]))\")\n",
|
||||
"end"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Julia 1.6.3",
|
||||
"language": "julia",
|
||||
"name": "julia-1.6"
|
||||
},
|
||||
"language_info": {
|
||||
"file_extension": ".jl",
|
||||
"mimetype": "application/julia",
|
||||
"name": "julia",
|
||||
"version": "1.6.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 4
|
||||
}
|
||||
Loading…
Reference in a new issue