2021-12-08-blog-post_mixed_integer_programming.ipynb

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   "source": [
    "# Import Solver\n",
    "import gurobipy as gp\n",
    "from gurobipy import GRB"
   ]
  },
  {
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   "execution_count": 2,
   "id": "6a5dde57-516c-4396-98c2-85b4c3d77e49",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Restricted license - for non-production use only - expires 2023-10-25\n"
     ]
    }
   ],
   "source": [
    "# Instantiate the model\n",
    "mip = gp.Model('example')"
   ]
  },
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   "execution_count": 3,
   "id": "198757c2-57d7-4386-b909-c10ae1edc2b8",
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   "source": [
    "# Define the decision variables\n",
    "x1 = mip.addVar(vtype=GRB.CONTINUOUS, name=\"x1\")\n",
    "x2 = mip.addVar(vtype=GRB.CONTINUOUS, name=\"x2\")\n",
    "x3 = mip.addVar(vtype=GRB.INTEGER, name=\"x3\")\n",
    "x4 = mip.addVar(vtype=GRB.INTEGER, name=\"x4\")"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "The constraints are\n",
    "\n",
    "$$\\begin{array}{r}\n",
    "x_1 + 2x_3 \\leq 700 \\\\\n",
    "2x_2−8x_3 \\leq 0 \\\\\n",
    "x_2−2x_3+x_4 \\geq 1 \\\\ \n",
    "x_1 + x_2 + x_3 + x_4 = 10 \\\\\n",
    "0 \\leq x_1 \\leq 10 \\\\\n",
    "0 \\leq x_2 \\leq 10 \\\\\n",
    "0 \\leq x_3 \\leq 10 \\\\\n",
    "0 \\leq x_4 \\leq 10 \\\\\n",
    "x_1, x_2\\in\\mathbb{R}, x_3,x_4\\in\\mathbb{Z}\n",
    "\\end{array}$$"
   ]
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  {
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   "execution_count": 4,
   "id": "cfb68c1c-9978-4dc2-9a34-824c4cdad20e",
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   "source": [
    "# Define the constraints\n",
    "c1 = mip.addConstr(x1+2*x3 <= 700, name='c1')\n",
    "c2 = mip.addConstr(2*x2-8*x3 <= 0, name='c2')\n",
    "c3 = mip.addConstr(x2-2*x3+x4 >= 1, name='c3')\n",
    "c4 = mip.addConstr(x1+x2+x3+x4 == 10, name='c4')\n",
    "c5 = mip.addConstr(0 <= x1, name='c5')\n",
    "c6 = mip.addConstr(0 <= x2, name='c6')\n",
    "c7 = mip.addConstr(0 <= x3, name='c7')\n",
    "c8 = mip.addConstr(0 <= x4, name='c8')\n",
    "c9 = mip.addConstr(x1 <= 10, name='c9')\n",
    "c10 = mip.addConstr(x2 <= 10, name='c10')\n",
    "c11 = mip.addConstr(x3 <= 10, name='c11')\n",
    "c12 = mip.addConstr(x4 <= 10, name='c12')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fb0edf7-0640-46bc-9bbf-013ddbf2f9b8",
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   "source": [
    "The objective function is\n",
    "\n",
    "$$\\max x_1+x_2+2x_3-2x_4$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2bb0271c-075d-49ae-9f25-e0f7fc730ff4",
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   "outputs": [],
   "source": [
    "# Define objective function\n",
    "mip.setObjective(x1+x2+2*x3-2*x4, GRB.MAXIMIZE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e69d527f-f48d-4c16-a72f-d80fd51f27b2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "Optimize a model with 12 rows, 4 columns and 19 nonzeros\n",
      "Model fingerprint: 0x46c3d51d\n",
      "Variable types: 2 continuous, 2 integer (0 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 8e+00]\n",
      "  Objective range  [1e+00, 2e+00]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [1e+00, 7e+02]\n",
      "Presolve removed 9 rows and 1 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 3 rows, 3 columns, 8 nonzeros\n",
      "Variable types: 0 continuous, 3 integer (0 binary)\n",
      "Found heuristic solution: objective 11.0000000\n",
      "Found heuristic solution: objective 13.0000000\n",
      "\n",
      "Explored 0 nodes (0 simplex iterations) in 0.25 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 2: 13 11 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 1.300000000000e+01, best bound 1.300000000000e+01, gap 0.0000%\n"
     ]
    }
   ],
   "source": [
    "# Solve the optimization problem\n",
    "mip.optimize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
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    {
     "name": "stdout",
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     "text": [
      "x1=0.0\n",
      "x2=7.0\n",
      "x3=3.0\n",
      "x4=-0.0\n"
     ]
    }
   ],
   "source": [
    "# Optimal values\n",
    "print(f\"x1={x1.x}\")\n",
    "print(f\"x2={x2.x}\")\n",
    "print(f\"x3={x3.x}\")\n",
    "print(f\"x4={x4.x}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6fde6bd0-516f-4df9-89e0-a652d512eca1",
   "metadata": {},
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   "source": [
    "# Save the optimization model\n",
    "mip.write('example.lp')"
   ]
  },
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   "cell_type": "code",
   "execution_count": 11,
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     "text": [
      "Last updated: Thu Dec 09 2021\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.9.9\n",
      "IPython version      : 7.27.0\n",
      "\n",
      "watermark: 2.2.0\n",
      "gurobipy : 9.5.0\n",
      "\n",
      "Watermark: 2.2.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w"
   ]
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