187 lines
6.8 KiB
Plaintext
187 lines
6.8 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 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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