{
 "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": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Min perm[1,1] + 2 perm[1,2] + 3 perm[1,3] + 4 perm[1,4] + 2 perm[2,1] + 3 perm[2,2] + perm[2,3] + 4 perm[2,4] + 2 perm[3,1] + perm[3,2] + 3 perm[3,3] + 4 perm[3,4] + 4 perm[4,1] + 2 perm[4,2] + 3 perm[4,3] + perm[4,4]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Subject to\n",
      " "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "perm[1,1] + perm[1,2] + perm[1,3] + perm[1,4] = 1.0\n",
      " perm[1,1] + perm[2,1] + perm[3,1] + perm[4,1] = 1.0\n",
      " perm[2,1] + perm[2,2] + perm[2,3] + perm[2,4] = 1.0\n",
      " perm[1,2] + perm[2,2] + perm[3,2] + perm[4,2] = 1.0\n",
      " perm[3,1] + perm[3,2] + perm[3,3] + perm[3,4] = 1.0\n",
      " perm[1,3] + perm[2,3] + perm[3,3] + perm[4,3] = 1.0\n",
      " perm[4,1] + perm[4,2] + perm[4,3] + perm[4,4] = 1.0\n",
      " perm[1,4] + perm[2,4] + perm[3,4] + perm[4,4] = 1.0\n",
      " perm[1,1] binary\n",
      " perm[2,1] binary\n",
      " perm[3,1] binary\n",
      " perm[4,1] binary\n",
      " perm[1,2] binary\n",
      " perm[2,2] binary\n",
      " perm[3,2] binary\n",
      " perm[4,2] binary\n",
      " perm[1,3] binary\n",
      " perm[2,3] binary\n",
      " perm[3,3] binary\n",
      " perm[4,3] binary\n",
      " perm[1,4] binary\n",
      " perm[2,4] binary\n",
      " perm[3,4] binary\n",
      " perm[4,4] binary\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "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 4 - 0.00 seconds\n",
      "Cgl0004I processed model has 8 rows, 16 columns (16 integer (16 of which binary)) and 32 elements\n",
      "Cutoff increment increased from 1e-05 to 0.9999\n",
      "Cbc0038I Initial state - 0 integers unsatisfied sum - 0\n",
      "Cbc0038I Solution found of 4\n",
      "Cbc0038I Before mini branch and bound, 16 integers at bound fixed and 0 continuous\n",
      "Cbc0038I Mini branch and bound did not improve solution (0.01 seconds)\n",
      "Cbc0038I After 0.01 seconds - Feasibility pump exiting with objective of 4 - took 0.00 seconds\n",
      "Cbc0012I Integer solution of 4 found by feasibility pump after 0 iterations and 0 nodes (0.01 seconds)\n",
      "Cbc0001I Search completed - best objective 4, took 0 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 4 to 4\n",
      "Probing was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
      "Gomory was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
      "Knapsack was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
      "Clique was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
      "MixedIntegerRounding2 was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
      "FlowCover was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
      "TwoMirCuts was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n",
      "ZeroHalf was tried 0 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:                4.00000000\n",
      "Enumerated nodes:               0\n",
      "Total iterations:               0\n",
      "Time (CPU seconds):             0.01\n",
      "Time (Wallclock seconds):       0.01\n",
      "\n",
      "Total time (CPU seconds):       0.01   (Wallclock seconds):       0.02\n",
      "\n"
     ]
    }
   ],
   "source": [
    "using Cbc\n",
    "using JuMP\n",
    "\n",
    "# data\n",
    "N = 4\n",
    "M = [\n",
    "    1 2 3 4\n",
    "    2 3 1 4\n",
    "    2 1 3 4\n",
    "    4 2 3 1\n",
    "]\n",
    "\n",
    "# set optimizer\n",
    "model = Model(Cbc.Optimizer)\n",
    "\n",
    "# define variables\n",
    "@variable(model, perm[1:N, 1:N], binary=true)\n",
    "\n",
    "# define objective function\n",
    "@objective(model, Min, sum(M[i, j] * perm[i, j] for i = 1:N for j = 1:N))\n",
    "\n",
    "# define constraints\n",
    "for i = 1:N\n",
    "    @constraint(model, sum(perm[i, j] for j = 1:N) == 1)\n",
    "    @constraint(model, sum(perm[j, i] for j = 1:N) == 1)\n",
    "end\n",
    "\n",
    "println(model)\n",
    "\n",
    "# run optimization\n",
    "optimize!(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution obtenue:\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0 0.0 0.0 0.0 \n",
      "0.0 0.0 1.0 0.0 \n",
      "0.0 1.0 0.0 0.0 \n",
      "0.0 0.0 0.0 1.0 \n"
     ]
    }
   ],
   "source": [
    "# print solution\n",
    "println(\"Solution obtenue:\")\n",
    "for i in 1:N\n",
    "    for j in 1:N \n",
    "        print(\"$(value(perm[i,j])) \")\n",
    "    end\n",
    "    println()\n",
    "end"
   ]
  }
 ],
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