{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exemple de modèle et résolution du problème de Fabrication du ciment"
   ]
  },
  {
   "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 50 ciment[1] + 70 ciment[2]\n",
      "Subject to\n",
      " 40 ciment[1] + 12 ciment[2] ≤ 360.0\n",
      " 20 ciment[1] + 30 ciment[2] ≤ 480.0\n",
      " ciment[1] ≥ 0.0\n",
      " ciment[2] ≥ 0.0\n",
      "\n",
      "Presolve 2 (0) rows, 2 (0) columns and 4 (0) elements\n",
      "0  Obj -0 Dual inf 120 (2)\n",
      "2  Obj 1137.5\n",
      "Optimal - objective value 1137.5\n",
      "Optimal objective 1137.5 - 2 iterations time 0.002\n"
     ]
    }
   ],
   "source": [
    "using Cbc\n",
    "using JuMP\n",
    "\n",
    "# data\n",
    "N = 2 # nombre de ciments disponibles\n",
    "c = [50,70] # prix de vente par ciment\n",
    "b = [360,480] # temps de disponibilité du four et de l'atelier\n",
    "A = [40 12;20 30] # temps nécessaire de calcination (four) et de broyage (atelier) par ciment\n",
    "\n",
    "# set optimizer\n",
    "model = Model(Cbc.Optimizer)\n",
    "\n",
    "# define variables\n",
    "@variable(model, ciment[1:N] >= 0)\n",
    "\n",
    "# define objective function\n",
    "@objective(model, Max, sum(c[i]*ciment[i] for i in 1:N))\n",
    "\n",
    "# define constraints\n",
    "for i in 1:length(b)\n",
    "    @constraint(model, sum(A[i,j]*ciment[j] for j in 1:N) <= b[i])\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 = 1137.5\n",
      "\t quantite de ciment 1 = 5.249999999999999\n",
      "\t quantite de ciment 2 = 12.5\n"
     ]
    }
   ],
   "source": [
    "# print solution\n",
    "println(\"Solution obtenue:\")\n",
    "println(\"\\t benefice = $(objective_value(model))\")\n",
    "for i in 1:N\n",
    "    println(\"\\t quantite de ciment $i = $(value(ciment[i]))\")\n",
    "end"
   ]
  }
 ],
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