Jefferson-Optimization-Toy-Data.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "Populations: [27744, 25178, 19951, 14610, 9225, 3292]\n",
      "Quotas: [9.98784, 9.06408, 7.18236, 5.2596, 3.321, 1.18512]\n"
     ]
    }
   ],
   "source": [
    "# (hypothetical) state populations\n",
    "p = [27744, 25178, 19951, 14610, 9225, 3292]\n",
    "\n",
    "# number of states\n",
    "n = len(p)\n",
    "\n",
    "# total country population\n",
    "p_total = sum( p[i] for i in range(n) )\n",
    "\n",
    "# total number of seats to distribute\n",
    "k = 36\n",
    "\n",
    "# state quotas\n",
    "q = [ k * p[i] / p_total for i in range(n) ]\n",
    "\n",
    "print(\"Populations:\",p)\n",
    "print(\"Quotas:\",q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import gurobipy as gp\n",
    "from gurobipy import GRB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "--------------------------------------------\n",
      "Warning: your license will expire in 7 days\n",
      "--------------------------------------------\n",
      "\n",
      "Academic license - for non-commercial use only - expires 2021-06-27\n",
      "Using license file C:\\Users\\buchanan\\gurobi.lic\n"
     ]
    }
   ],
   "source": [
    "# create model object\n",
    "m = gp.Model()\n",
    "\n",
    "# create integer vars x, with x[i] being the number of seats for state i\n",
    "x = m.addVars( n, vtype=GRB.INTEGER )\n",
    "\n",
    "# distribute k seats\n",
    "m.addConstr( gp.quicksum( x[i] for i in range(n) ) == k )\n",
    "\n",
    "# each state gets at least one seat\n",
    "for i in range(n):\n",
    "    x[i].LB = 1\n",
    "\n",
    "m.update()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gurobi Optimizer version 9.1.1 build v9.1.1rc0 (win64)\n",
      "Thread count: 4 physical cores, 8 logical processors, using up to 8 threads\n",
      "Optimize a model with 7 rows, 7 columns and 18 nonzeros\n",
      "Model fingerprint: 0x1bffcd12\n",
      "Variable types: 1 continuous, 6 integer (0 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 3e+04]\n",
      "  Objective range  [1e+00, 1e+00]\n",
      "  Bounds range     [1e+00, 1e+00]\n",
      "  RHS range        [4e+01, 4e+01]\n",
      "Presolve time: 0.00s\n",
      "Presolved: 7 rows, 7 columns, 18 nonzeros\n",
      "Variable types: 1 continuous, 6 integer (0 binary)\n",
      "Found heuristic solution: objective 0.0094168\n",
      "\n",
      "Root relaxation: objective 3.600000e-04, 6 iterations, 0.00 seconds\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0    0.00036    0    6    0.00942    0.00036  96.2%     -    0s\n",
      "H    0     0                       0.0003972    0.00036  9.36%     -    0s\n",
      "*    0     0               0       0.0003965    0.00040  0.00%     -    0s\n",
      "\n",
      "Explored 1 nodes (11 simplex iterations) in 0.02 seconds\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 3: 0.000396482 0.000397172 0.00941677 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 3.964821222607e-04, best bound 3.964821222607e-04, gap 0.0000%\n"
     ]
    }
   ],
   "source": [
    "# Variable y introduced to linearize the max term y = (max_i x_i/p_i)\n",
    "y = m.addVar()\n",
    "m.addConstrs( x[i] <= p[i] * y for i in range(n) )\n",
    "\n",
    "# Add objective function for Jefferson's method: min_x max_i { x_i / p_i }\n",
    "m.setObjective( y, GRB.MINIMIZE )\n",
    "\n",
    "m.optimize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal solution : [11.0, 9.0, 7.0, 5.0, 3.0, 1.0]\n",
      "Compare to quotas: [9.98784, 9.06408, 7.18236, 5.2596, 3.321, 1.18512]\n"
     ]
    }
   ],
   "source": [
    "sol = [ x[i].x for i in range(n) ]\n",
    "print(\"Optimal solution :\", sol)\n",
    "print(\"Compare to quotas:\", q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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