254 lines
6.4 KiB
Plaintext
254 lines
6.4 KiB
Plaintext
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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 perm"
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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": 1,
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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 Updating\u001b[22m\u001b[39m registry at `~/.julia/registries/General`\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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"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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"Min 2 coeff[1,1,1] + 2 coeff[1,1,2] + 3 coeff[1,1,3] + 2 coeff[1,2,1] + 3 coeff[1,2,2] + 2 coeff[1,2,3] + coeff[2,1,1] + 4 coeff[2,1,2] + 4 coeff[2,1,3] + coeff[2,2,1] + 5 coeff[2,2,2] + 3 coeff[2,2,3]"
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]
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},
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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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"\n",
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"Subject to\n",
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" "
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]
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},
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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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"coeff[1,1,1] + coeff[1,1,2] + coeff[1,1,3] = 1.0\n",
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" coeff[1,2,1] + coeff[1,2,2] + coeff[1,2,3] = 1.0\n",
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" coeff[2,1,1] + coeff[2,1,2] + coeff[2,1,3] = 1.0\n",
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" coeff[2,2,1] + coeff[2,2,2] + coeff[2,2,3] = 1.0\n",
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" coeff[1,1,1] ≤ 1.0\n",
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" coeff[1,1,2] ≤ 1.0\n",
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" coeff[1,1,3] ≤ 1.0\n",
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" coeff[1,2,1] ≤ 1.0\n",
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" coeff[1,2,2] ≤ 1.0\n",
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" coeff[1,2,3] ≤ 1.0\n",
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" coeff[2,1,1] ≤ 1.0\n",
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" coeff[2,1,2] ≤ 1.0\n",
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" coeff[2,1,3] ≤ 1.0\n",
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" coeff[2,2,1] ≤ 1.0\n",
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" coeff[2,2,2] ≤ 1.0\n",
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" coeff[2,2,3] ≤ 1.0\n",
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" 2 coeff[1,1,1] + coeff[2,1,1] ≤ 2.5\n",
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" 2 coeff[1,1,2] + coeff[2,1,2] ≤ 1.0\n",
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" 2 coeff[1,1,3] + coeff[2,1,3] ≤ 2.0\n",
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" 3 coeff[2,2,1] ≤ 1.0\n",
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" 3 coeff[2,2,2] ≤ 2.0\n",
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" 3 coeff[2,2,3] ≤ 1.0\n",
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" coeff[1,1,1] ≥ 0.0\n",
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" coeff[2,1,1] ≥ 0.0\n",
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" coeff[1,2,1] ≥ 0.0\n",
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" coeff[2,2,1] ≥ 0.0\n",
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" coeff[1,1,2] ≥ 0.0\n",
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" coeff[2,1,2] ≥ 0.0\n",
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" coeff[1,2,2] ≥ 0.0\n",
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" coeff[2,2,2] ≥ 0.0\n",
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" coeff[1,1,3] ≥ 0.0\n",
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" coeff[2,1,3] ≥ 0.0\n",
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" coeff[1,2,3] ≥ 0.0\n",
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" coeff[2,2,3] ≥ 0.0\n",
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"\n"
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]
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},
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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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"Presolve 6 (-16) rows, 9 (-3) columns and 15 (-18) elements\n",
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"0 Obj 3.1666666 Primal inf 2.7666637 (3)\n",
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"4 Obj 8\n",
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"Optimal - objective value 8\n",
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"After Postsolve, objective 8, infeasibilities - dual 0 (0), primal 0 (0)\n",
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"Optimal objective 8 - 4 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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"fluide = [\n",
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" 2 0\n",
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" 1 3\n",
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"]\n",
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"stock = [\n",
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" 2.5 1\n",
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" 1 2\n",
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" 2 1\n",
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"]\n",
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"cout = [\n",
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" 1 1\n",
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" 2 3\n",
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" 3 2\n",
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"]\n",
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"expe = [\n",
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" 1 0 0\n",
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" 0 2 1\n",
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"]\n",
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"\n",
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"X = size(fluide)[1]\n",
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"Y = size(fluide)[2]\n",
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"Z = size(stock)[1]\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, coeff[1:X, 1:Y, 1:Z] >= 0)\n",
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"\n",
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"# define objective function\n",
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"@objective(model, Min, sum(cout[k, j] * coeff[i, j, k] + coeff[i, j, k] * expe[i, k] for i = 1:X for j = 1:Y for k in 1:Z))\n",
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"\n",
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"# define constraints\n",
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"for i = 1:X\n",
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" for j = 1:Y \n",
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" for k = 1:Z\n",
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" @constraint(model, coeff[i,j,k] <= 1)\n",
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" end\n",
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" @constraint(model, sum(coeff[i, j, k] for k = 1:Z) == 1)\n",
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" end\n",
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"end\n",
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"\n",
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"for j = 1:Y\n",
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" for k = 1:Z \n",
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" @constraint(model, sum(coeff[i, j, k] * fluide[i,j] for i = 1:X) <= stock[k,j])\n",
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" end\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": 10,
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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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]
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},
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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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"coeff[1,1,1] 0.75\n",
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"coeff[1,1,2] 0.25\n",
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"coeff[1,1,3] 0.0\n",
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"coeff[1,2,1] 1.0\n",
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"coeff[1,2,2] 0.0\n",
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"coeff[1,2,3] 0.0\n",
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"coeff[2,1,1] 1.0\n",
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"coeff[2,1,2] 0.0\n",
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"coeff[2,1,3] 0.0\n",
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"coeff[2,2,1] 0.3333333333333333\n",
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"coeff[2,2,2] 0.33333333333333337\n",
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"coeff[2,2,3] 0.3333333333333333\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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"for i in 1:X\n",
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" for j in 1:Y\n",
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" for k in 1:Z \n",
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" println(\"coeff[$i,$j,$k] $(value(coeff[i,j,k]))\")\n",
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" end\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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"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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