169 lines
4.8 KiB
Plaintext
169 lines
4.8 KiB
Plaintext
{
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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"
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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": 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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"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",
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"Subject to\n",
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" produits[1] + produits[2] + produits[3] + produits[4] + produits[5] + produits[6] = 1.0\n",
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" produits[1] + produits[2] ≥ 0.45\n",
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" produits[3] + produits[4] ≥ 0.3\n",
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" 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",
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" produits[1] ≤ 0.25\n",
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" produits[2] ≤ 0.25\n",
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" produits[3] ≤ 0.25\n",
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" produits[4] ≤ 0.25\n",
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" produits[5] ≤ 0.25\n",
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" produits[6] ≤ 0.25\n",
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" produits[1] ≥ 0.0\n",
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" produits[2] ≥ 0.0\n",
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" produits[3] ≥ 0.0\n",
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" produits[4] ≥ 0.0\n",
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" produits[5] ≥ 0.0\n",
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" produits[6] ≥ 0.0\n",
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"\n",
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"Presolve 4 (-6) rows, 6 (0) columns and 16 (-6) elements\n",
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"0 Obj 0.016999999 Primal inf 1.349997 (3) Dual inf 1.419994 (6)\n",
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"5 Obj 0.28253846\n",
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"Optimal - objective value 0.28253846\n",
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"After Postsolve, objective 0.28253846, infeasibilities - dual 0 (0), primal 0 (0)\n",
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"Optimal objective 0.2825384615 - 5 iterations time 0.002, Presolve 0.00\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 = 6 # nombre de produits disponibles\n",
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"risques = [1.7 1.2 3.7 2.4 2.0 2.9]\n",
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"interets = [ 0.07 0.10 0.19 0.12 0.8 0.14]\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, produits[1:N] >= 0)\n",
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"\n",
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"# define objective function\n",
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"@objective(model, Max, sum(interets[i] * produits[i] for i = 1:N))\n",
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"\n",
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"# define constraints\n",
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"@constraint(model, sum(produits[i] for i = 1:N) == 1.0) # somme à 100%\n",
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"@constraint(model, sum(produits[i]*risques[i] for i = 1:N) <= 2.0) # risque total\n",
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"@constraint(model, produits[1] + produits[2] >= 0.45)\n",
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"@constraint(model, produits[3] + produits[4] >= 0.3)\n",
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"for i = 1:N\n",
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" @constraint(model, produits[i] <= 0.25) # limite de 25%\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": 9,
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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 = 0.2825384615384615\n",
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"\t quantite de produits 1 = 0.2\n",
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"\t quantite de produits 2 = 0.25\n",
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"\t quantite de produits 3 = 0.10769230769230764\n",
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"\t quantite de produits 4 = 0.19230769230769232\n",
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"\t quantite de produits 5 = 0.25\n",
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"\t quantite de produits 6 = 0.0\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 produits $i = $(value(produits[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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