149 lines
3.7 KiB
Plaintext
149 lines
3.7 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 ciment"
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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 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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"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 ciments disponibles\n",
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"c = [50,70] # prix de vente par ciment\n",
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"b = [360,480] # temps de disponibilité du four et de l'atelier\n",
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"A = [40 12;20 30] # temps nécessaire de calcination (four) et de broyage (atelier) par ciment\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, ciment[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(c[i]*ciment[i] for i in 1:N))\n",
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"\n",
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"# define constraints\n",
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"for i in 1:length(b)\n",
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" @constraint(model, sum(A[i,j]*ciment[j] for j in 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": 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 = 1137.5\n",
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"\t quantite de ciment 1 = 5.249999999999999\n",
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"\t quantite de ciment 2 = 12.5\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 in 1:N\n",
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" println(\"\\t quantite de ciment $i = $(value(ciment[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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