{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exemple de modèle et résolution du problème de Fabrication du perm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32m\u001b[1m    Updating\u001b[22m\u001b[39m registry at `~/.julia/registries/General`\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"
     ]
    },
    {
     "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": [
      "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]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Subject to\n",
      " "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "coeff[1,1,1] + coeff[1,1,2] + coeff[1,1,3] = 1.0\n",
      " coeff[1,2,1] + coeff[1,2,2] + coeff[1,2,3] = 1.0\n",
      " coeff[2,1,1] + coeff[2,1,2] + coeff[2,1,3] = 1.0\n",
      " coeff[2,2,1] + coeff[2,2,2] + coeff[2,2,3] = 1.0\n",
      " coeff[1,1,1] ≤ 1.0\n",
      " coeff[1,1,2] ≤ 1.0\n",
      " coeff[1,1,3] ≤ 1.0\n",
      " coeff[1,2,1] ≤ 1.0\n",
      " coeff[1,2,2] ≤ 1.0\n",
      " coeff[1,2,3] ≤ 1.0\n",
      " coeff[2,1,1] ≤ 1.0\n",
      " coeff[2,1,2] ≤ 1.0\n",
      " coeff[2,1,3] ≤ 1.0\n",
      " coeff[2,2,1] ≤ 1.0\n",
      " coeff[2,2,2] ≤ 1.0\n",
      " coeff[2,2,3] ≤ 1.0\n",
      " 2 coeff[1,1,1] + coeff[2,1,1] ≤ 2.5\n",
      " 2 coeff[1,1,2] + coeff[2,1,2] ≤ 1.0\n",
      " 2 coeff[1,1,3] + coeff[2,1,3] ≤ 2.0\n",
      " 3 coeff[2,2,1] ≤ 1.0\n",
      " 3 coeff[2,2,2] ≤ 2.0\n",
      " 3 coeff[2,2,3] ≤ 1.0\n",
      " coeff[1,1,1] ≥ 0.0\n",
      " coeff[2,1,1] ≥ 0.0\n",
      " coeff[1,2,1] ≥ 0.0\n",
      " coeff[2,2,1] ≥ 0.0\n",
      " coeff[1,1,2] ≥ 0.0\n",
      " coeff[2,1,2] ≥ 0.0\n",
      " coeff[1,2,2] ≥ 0.0\n",
      " coeff[2,2,2] ≥ 0.0\n",
      " coeff[1,1,3] ≥ 0.0\n",
      " coeff[2,1,3] ≥ 0.0\n",
      " coeff[1,2,3] ≥ 0.0\n",
      " coeff[2,2,3] ≥ 0.0\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Presolve 6 (-16) rows, 9 (-3) columns and 15 (-18) elements\n",
      "0  Obj 3.1666666 Primal inf 2.7666637 (3)\n",
      "4  Obj 8\n",
      "Optimal - objective value 8\n",
      "After Postsolve, objective 8, infeasibilities - dual 0 (0), primal 0 (0)\n",
      "Optimal objective 8 - 4 iterations time 0.002, Presolve 0.00\n"
     ]
    }
   ],
   "source": [
    "using Cbc\n",
    "using JuMP\n",
    "\n",
    "# data\n",
    "fluide = [\n",
    "    2 0\n",
    "    1 3\n",
    "]\n",
    "stock = [\n",
    "    2.5 1\n",
    "    1 2\n",
    "    2 1\n",
    "]\n",
    "cout = [\n",
    "    1 1\n",
    "    2 3\n",
    "    3 2\n",
    "]\n",
    "expe = [\n",
    "    1 0 0\n",
    "    0 2 1\n",
    "]\n",
    "\n",
    "X = size(fluide)[1]\n",
    "Y = size(fluide)[2]\n",
    "Z = size(stock)[1]\n",
    "\n",
    "# set optimizer\n",
    "model = Model(Cbc.Optimizer)\n",
    "\n",
    "# define variables\n",
    "@variable(model, coeff[1:X, 1:Y, 1:Z] >= 0)\n",
    "\n",
    "# define objective function\n",
    "@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",
    "\n",
    "# define constraints\n",
    "for i = 1:X\n",
    "    for j = 1:Y \n",
    "        for k = 1:Z\n",
    "            @constraint(model, coeff[i,j,k] <= 1)\n",
    "        end\n",
    "        @constraint(model, sum(coeff[i, j, k] for k = 1:Z) == 1)\n",
    "    end\n",
    "end\n",
    "\n",
    "for j = 1:Y\n",
    "    for k = 1:Z \n",
    "        @constraint(model, sum(coeff[i, j, k] * fluide[i,j] for i = 1:X) <= stock[k,j])\n",
    "    end\n",
    "end\n",
    "\n",
    "println(model)\n",
    "\n",
    "# run optimization\n",
    "optimize!(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution obtenue:\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "coeff[1,1,1] 0.75\n",
      "coeff[1,1,2] 0.25\n",
      "coeff[1,1,3] 0.0\n",
      "coeff[1,2,1] 1.0\n",
      "coeff[1,2,2] 0.0\n",
      "coeff[1,2,3] 0.0\n",
      "coeff[2,1,1] 1.0\n",
      "coeff[2,1,2] 0.0\n",
      "coeff[2,1,3] 0.0\n",
      "coeff[2,2,1] 0.3333333333333333\n",
      "coeff[2,2,2] 0.33333333333333337\n",
      "coeff[2,2,3] 0.3333333333333333\n"
     ]
    }
   ],
   "source": [
    "# print solution\n",
    "println(\"Solution obtenue:\")\n",
    "for i in 1:X\n",
    "    for j in 1:Y\n",
    "        for k in 1:Z \n",
    "            println(\"coeff[$i,$j,$k] $(value(coeff[i,j,k]))\")\n",
    "        end\n",
    "    end\n",
    "end"
   ]
  }
 ],
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