{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exemple de modèle et résolution du problème de Fabrication du produits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "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",
      "Subject to\n",
      " produits[1] + produits[2] + produits[3] + produits[4] + produits[5] + produits[6] = 1.0\n",
      " produits[1] + produits[2] ≥ 0.45\n",
      " produits[3] + produits[4] ≥ 0.3\n",
      " 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",
      " produits[1] ≤ 0.25\n",
      " produits[2] ≤ 0.25\n",
      " produits[3] ≤ 0.25\n",
      " produits[4] ≤ 0.25\n",
      " produits[5] ≤ 0.25\n",
      " produits[6] ≤ 0.25\n",
      " produits[1] ≥ 0.0\n",
      " produits[2] ≥ 0.0\n",
      " produits[3] ≥ 0.0\n",
      " produits[4] ≥ 0.0\n",
      " produits[5] ≥ 0.0\n",
      " produits[6] ≥ 0.0\n",
      "\n",
      "Presolve 4 (-6) rows, 6 (0) columns and 16 (-6) elements\n",
      "0  Obj 0.016999999 Primal inf 1.349997 (3) Dual inf 1.419994 (6)\n",
      "5  Obj 0.28253846\n",
      "Optimal - objective value 0.28253846\n",
      "After Postsolve, objective 0.28253846, infeasibilities - dual 0 (0), primal 0 (0)\n",
      "Optimal objective 0.2825384615 - 5 iterations time 0.002, Presolve 0.00\n"
     ]
    }
   ],
   "source": [
    "using Cbc\n",
    "using JuMP\n",
    "\n",
    "# data\n",
    "N = 6 # nombre de produits disponibles\n",
    "risques = [1.7 1.2 3.7 2.4 2.0 2.9]\n",
    "interets = [ 0.07 0.10 0.19 0.12 0.8 0.14]\n",
    "\n",
    "# set optimizer\n",
    "model = Model(Cbc.Optimizer)\n",
    "\n",
    "# define variables\n",
    "@variable(model, produits[1:N] >= 0)\n",
    "\n",
    "# define objective function\n",
    "@objective(model, Max, sum(interets[i] * produits[i] for i = 1:N))\n",
    "\n",
    "# define constraints\n",
    "@constraint(model, sum(produits[i] for i = 1:N) == 1.0) # somme à 100%\n",
    "@constraint(model, sum(produits[i]*risques[i] for i = 1:N) <= 2.0) # risque total\n",
    "@constraint(model, produits[1] + produits[2] >= 0.45)\n",
    "@constraint(model, produits[3] + produits[4] >= 0.3)\n",
    "for i = 1:N\n",
    "    @constraint(model, produits[i] <= 0.25) # limite de 25%\n",
    "end\n",
    "\n",
    "println(model)\n",
    "\n",
    "# run optimization\n",
    "optimize!(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution obtenue:\n",
      "\t benefice = 0.2825384615384615\n",
      "\t quantite de produits 1 = 0.2\n",
      "\t quantite de produits 2 = 0.25\n",
      "\t quantite de produits 3 = 0.10769230769230764\n",
      "\t quantite de produits 4 = 0.19230769230769232\n",
      "\t quantite de produits 5 = 0.25\n",
      "\t quantite de produits 6 = 0.0\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 produits $i = $(value(produits[i]))\")\n",
    "end"
   ]
  }
 ],
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