187 lines
6.8 KiB
Plaintext
187 lines
6.8 KiB
Plaintext
|
{
|
||
|
|
"cells": [
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"Exemple de modèle et résolution du problème de Fabrication du voitures"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 6,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"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"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"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": 7,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"Max 10000 voitures[1] + 9000 voitures[2]\n",
|
||
|
|
"Subject to\n",
|
||
|
|
" 10 voitures[1] + 20 voitures[2] ≤ 15000.0\n",
|
||
|
|
" 6 voitures[1] + 5 voitures[2] ≤ 6000.0\n",
|
||
|
|
" voitures[1] ≤ 800.0\n",
|
||
|
|
" voitures[1] ≥ 0.0\n",
|
||
|
|
" voitures[2] ≥ 0.0\n",
|
||
|
|
" voitures[1] integer\n",
|
||
|
|
" voitures[2] integer\n",
|
||
|
|
"\n",
|
||
|
|
"Welcome to the CBC MILP Solver \n",
|
||
|
|
"Version: 2.10.5 \n",
|
||
|
|
"Build Date: Jan 1 1970 \n",
|
||
|
|
"\n",
|
||
|
|
"command line - Cbc_C_Interface -solve -quit (default strategy 1)\n",
|
||
|
|
"Continuous objective value is 1.02857e+07 - 0.00 seconds\n",
|
||
|
|
"Cgl0004I processed model has 2 rows, 2 columns (2 integer (0 of which binary)) and 4 elements\n",
|
||
|
|
"Cutoff increment increased from 1e-05 to 1000\n",
|
||
|
|
"Cbc0012I Integer solution of -10272000 found by DiveCoefficient after 0 iterations and 0 nodes (0.00 seconds)\n",
|
||
|
|
"Cbc0012I Integer solution of -10284000 found by DiveCoefficient after 3 iterations and 0 nodes (0.01 seconds)\n",
|
||
|
|
"Cbc0031I 1 added rows had average density of 2\n",
|
||
|
|
"Cbc0013I At root node, 1 cuts changed objective from -10285714 to -10284000 in 21 passes\n",
|
||
|
|
"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",
|
||
|
|
"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",
|
||
|
|
"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",
|
||
|
|
"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",
|
||
|
|
"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",
|
||
|
|
"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",
|
||
|
|
"Cbc0001I Search completed - best objective -10284000, took 3 iterations and 0 nodes (0.01 seconds)\n",
|
||
|
|
"Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost\n",
|
||
|
|
"Cuts at root node changed objective from -1.02857e+07 to -1.0284e+07\n",
|
||
|
|
"Probing was tried 21 times and created 47 cuts of which 0 were active after adding rounds of cuts (0.001 seconds)\n",
|
||
|
|
"Gomory was tried 21 times and created 4 cuts of which 0 were active after adding rounds of cuts (0.001 seconds)\n",
|
||
|
|
"Knapsack was tried 21 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
|
||
|
|
"Clique was tried 21 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
|
||
|
|
"MixedIntegerRounding2 was tried 21 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
|
||
|
|
"FlowCover was tried 21 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
|
||
|
|
"TwoMirCuts was tried 1 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
|
||
|
|
"ZeroHalf was tried 1 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
|
||
|
|
"\n",
|
||
|
|
"Result - Optimal solution found\n",
|
||
|
|
"\n",
|
||
|
|
"Objective value: 10284000.00000000\n",
|
||
|
|
"Enumerated nodes: 0\n",
|
||
|
|
"Total iterations: 3\n",
|
||
|
|
"Time (CPU seconds): 0.01\n",
|
||
|
|
"Time (Wallclock seconds): 0.01\n",
|
||
|
|
"\n",
|
||
|
|
"Total time (CPU seconds): 0.01 (Wallclock seconds): 0.01\n",
|
||
|
|
"\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"using Cbc\n",
|
||
|
|
"using JuMP\n",
|
||
|
|
"\n",
|
||
|
|
"# data\n",
|
||
|
|
"N = 2 # nombre de voitures disponibles\n",
|
||
|
|
"c = [10000, 9000] # prix de vente par voitures\n",
|
||
|
|
"b = [15000, 6000, 800] \n",
|
||
|
|
"A = [10 20 ; 6 5 ; 1 0]\n",
|
||
|
|
"\n",
|
||
|
|
"# set optimizer\n",
|
||
|
|
"model = Model(Cbc.Optimizer)\n",
|
||
|
|
"\n",
|
||
|
|
"# define variables\n",
|
||
|
|
"@variable(model, voitures[1:N] >= 0, integer=true)\n",
|
||
|
|
"\n",
|
||
|
|
"# define objective function\n",
|
||
|
|
"@objective(model, Max, sum(c[i] * voitures[i] for i = 1:N))\n",
|
||
|
|
"\n",
|
||
|
|
"# define constraints\n",
|
||
|
|
"for i = 1:length(b)\n",
|
||
|
|
" @constraint(model, sum(A[i, j] * voitures[j] for j = 1:N) <= b[i])\n",
|
||
|
|
"end\n",
|
||
|
|
"\n",
|
||
|
|
"println(model)\n",
|
||
|
|
"\n",
|
||
|
|
"# run optimization\n",
|
||
|
|
"optimize!(model)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 8,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"Solution obtenue:\n",
|
||
|
|
"\t benefice = 1.0284e7\n",
|
||
|
|
"\t quantite de voitures 1 = 645.0\n",
|
||
|
|
"\t quantite de voitures 2 = 426.0\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 voitures $i = $(value(voitures[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
|
||
|
|
}
|