aula-05-sensibilidade.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Análise de Sensibilidade"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Primal\n",
    "\n",
    "Max: $z = 4.0x_{mad} + 6.0x_{al}$\n",
    "\n",
    "S.a: \n",
    "\n",
    "$\n",
    "\\begin{align}\n",
    "\\text{corte } 1.5x_{mad} + 4.0x_{al} \\le 24 \\\\\n",
    "\\text{montagem } 3.0x_{mad} + 1.5x_{al} \\le 21  \\\\\n",
    "\\text{acabamento } 1.0x_{mad} + 1.0x_{al} \\le 8  \\\\\n",
    "x_{mad}, x_{al} \\ge 0\n",
    "\\end{align}\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#include<iostream>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "#include \"setup.h\"\n",
    "#include \"ortools/linear_solver/linear_solver.h\"\n",
    "#include \"ortools/linear_solver/linear_solver.pb.h\"\n",
    "\n",
    "using namespace operations_research;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Número de variáveis = 2\n",
      "Número de restrições = 3\n",
      "Solução:\n",
      "Valor da função objetivo = 41.6\n",
      "x_mad = 3.2\n",
      "x_al = 4.8\n"
     ]
    }
   ],
   "source": [
    "{\n",
    "  // 1. Escolha o solver.\n",
    "  MPSolver solver(\"programa_simples\", MPSolver::GLOP_LINEAR_PROGRAMMING);\n",
    "\n",
    "  // 2. Crie as variáveis: \n",
    "  auto const x_mad = solver.MakeNumVar(0.0, solver.infinity(), \"x_mad\");\n",
    "  auto const x_al = solver.MakeNumVar(0.0, solver.infinity(), \"x_al\");\n",
    "  \n",
    "  std::cout << \"Número de variáveis = \" << solver.NumVariables() << std::endl;\n",
    "\n",
    "  // 3. Defina as restrições: \n",
    "  auto const ct1 = solver.MakeRowConstraint(-solver.infinity(), 24.0, \"corte\"); \n",
    "  ct1->SetCoefficient(x_mad, 1.5);\n",
    "  ct1->SetCoefficient(x_al,  4.0);\n",
    "\n",
    "  auto const ct2 = solver.MakeRowConstraint(-solver.infinity(), 21.0, \"montagem\"); \n",
    "  ct2->SetCoefficient(x_mad, 3.0);\n",
    "  ct2->SetCoefficient(x_al,  1.5);\n",
    "    \n",
    "  auto const ct3 = solver.MakeRowConstraint(-solver.infinity(), 8.0, \"acabamento\"); \n",
    "  ct3->SetCoefficient(x_mad, 1.0);\n",
    "  ct3->SetCoefficient(x_al,  1.0);\n",
    "\n",
    "  std::cout << \"Número de restrições = \" << solver.NumConstraints() << std::endl;\n",
    "\n",
    "  // 4. Defina a função objetivo: \n",
    "  auto const objective = solver.MutableObjective();\n",
    "  objective->SetCoefficient(x_mad, 4.0);\n",
    "  objective->SetCoefficient(x_al, 6.0);\n",
    "  objective->SetMaximization();\n",
    "\n",
    "  // 5. Execute o solver e exiba os resultados.\n",
    "  auto status = solver.Solve();\n",
    "  if (status == MPSolver::OPTIMAL)\n",
    "  {\n",
    "      std::cout << \"Solução:\" << std::endl;\n",
    "      std::cout << \"Valor da função objetivo = \" << objective->Value() << std::endl;\n",
    "      std::cout << \"x_mad = \" << x_mad->solution_value() << std::endl;\n",
    "      std::cout << \"x_al = \" << x_al->solution_value() << std::endl;\n",
    "  }\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dual\n",
    "\n",
    "Min: $w = 24y_1 + 21y_2 + 8y_3$\n",
    "\n",
    "S.a: \n",
    "\n",
    "\\begin{align}\n",
    "1.5y_1 + 3.0y_2 + y_3 \\ge 4 \\\\\n",
    "4.0y_1 + 1.5y_2 + y_3 \\ge 6 \\\\\n",
    "y_1, y_2, y_3 \\ge 0\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Número de variáveis = 3\n",
      "Número de restrições = 2\n",
      "Solução:\n",
      "Valor da função objetivo = 41.6\n",
      "corte = 0.8\n",
      "montagem = 0\n",
      "acabamento = 2.8\n"
     ]
    }
   ],
   "source": [
    "{\n",
    "  // 1. Escolha o solver.\n",
    "  MPSolver solver(\"programa_simples\", MPSolver::GLOP_LINEAR_PROGRAMMING);\n",
    "\n",
    "  // 2. Crie as variáveis: \n",
    "  auto const y1 = solver.MakeNumVar(0.0, solver.infinity(), \"corte\"); \n",
    "  auto const y2 = solver.MakeNumVar(0.0, solver.infinity(), \"montagem\"); \n",
    "  auto const y3 = solver.MakeNumVar(0.0, solver.infinity(), \"acabamento\"); \n",
    "  \n",
    "  std::cout << \"Número de variáveis = \" << solver.NumVariables() << std::endl;\n",
    "\n",
    "  // 3. Defina as restrições: \n",
    "  auto const ct1 = solver.MakeRowConstraint(4.0, solver.infinity(), \"ct1\");\n",
    "  ct1->SetCoefficient(y1, 1.5);\n",
    "  ct1->SetCoefficient(y2, 3.0);\n",
    "  ct1->SetCoefficient(y3, 1.0);\n",
    "\n",
    "  auto const ct2 = solver.MakeRowConstraint(6.0, solver.infinity(), \"ct2\");\n",
    "  ct2->SetCoefficient(y1, 4.0);\n",
    "  ct2->SetCoefficient(y2, 1.5);\n",
    "  ct2->SetCoefficient(y3, 1.0);\n",
    "    \n",
    "  std::cout << \"Número de restrições = \" << solver.NumConstraints() << std::endl;\n",
    "\n",
    "  // 4. Defina a função objetivo: \n",
    "  auto const objective = solver.MutableObjective();\n",
    "  objective->SetCoefficient(y1, 24.0);\n",
    "  objective->SetCoefficient(y2, 21.0);\n",
    "  objective->SetCoefficient(y3, 8.0);\n",
    "  objective->SetMinimization();\n",
    "\n",
    "  // 5. Execute o solver e exiba os resultados.\n",
    "  auto status = solver.Solve();\n",
    "  if (status == MPSolver::OPTIMAL)\n",
    "  {\n",
    "      std::cout << \"Solução:\" << std::endl;\n",
    "      std::cout << \"Valor da função objetivo = \" << objective->Value() << std::endl;\n",
    "      std::cout << \"corte = \" << y1->solution_value() << std::endl;\n",
    "      std::cout << \"montagem = \" << y2->solution_value() << std::endl;\n",
    "      std::cout << \"acabamento = \" << y3->solution_value() << std::endl;\n",
    "  }\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exemplo da Fábrica de Esquadrias (slide 52)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Número de variáveis = 5\n",
      "Número de restrições = 3\n",
      "Solução:\n",
      "Valor da função objetivo = 41.6\n",
      "x_mad : solução = 3.2\n",
      "x_al  : solução = 4.8\n",
      "x3 : custo reduzido = -0.8\n",
      "x4 : custo reduzido = 0\n",
      "x5 : custo reduzido = -2.8\n",
      "corte : dual = 0.8 atividade = 24\n",
      "montagem : dual = -0 atividade = 16.8\n",
      "acabamento : dual = 2.8 atividade = 8\n"
     ]
    }
   ],
   "source": [
    "#include<vector>\n",
    "\n",
    "{\n",
    "  // 1. Escolha o solver.\n",
    "  MPSolver solver(\"programa_simples\", MPSolver::GLOP_LINEAR_PROGRAMMING);\n",
    "\n",
    "  // 2. Crie as variáveis: \n",
    "  auto const x1 = solver.MakeNumVar(0.0, solver.infinity(), \"x1\");\n",
    "  auto const x2 = solver.MakeNumVar(0.0, solver.infinity(), \"x2\");\n",
    "  auto const x3 = solver.MakeNumVar(0.0, solver.infinity(), \"x3\");\n",
    "  auto const x4 = solver.MakeNumVar(0.0, solver.infinity(), \"x4\");\n",
    "  auto const x5 = solver.MakeNumVar(0.0, solver.infinity(), \"x5\");\n",
    "  \n",
    "  std::cout << \"Número de variáveis = \" << solver.NumVariables() << std::endl;\n",
    "\n",
    "  // 3. Defina as restrições: \n",
    "  auto const ct1 = solver.MakeRowConstraint(-solver.infinity(), 24.0, \"corte\"); \n",
    "  ct1->SetCoefficient(x1, 1.5);\n",
    "  ct1->SetCoefficient(x2, 4.0);\n",
    "  ct1->SetCoefficient(x3, 1.0);\n",
    "\n",
    "  auto const ct2 = solver.MakeRowConstraint(-solver.infinity(), 21.0, \"montagem\"); \n",
    "  ct2->SetCoefficient(x1, 3.0);\n",
    "  ct2->SetCoefficient(x2, 1.5);\n",
    "  ct2->SetCoefficient(x4, 1.0);\n",
    "    \n",
    "  auto const ct3 = solver.MakeRowConstraint(-solver.infinity(), 8.0, \"acabamento\");\n",
    "  ct3->SetCoefficient(x1, 1.0);\n",
    "  ct3->SetCoefficient(x2, 1.0);\n",
    "  ct3->SetCoefficient(x5, 1.0);\n",
    "\n",
    "  std::cout << \"Número de restrições = \" << solver.NumConstraints() << std::endl;\n",
    "\n",
    "  // 4. Defina a função objetivo: \n",
    "  auto const objective = solver.MutableObjective();\n",
    "  objective->SetCoefficient(x1, 4.0);\n",
    "  objective->SetCoefficient(x2, 6.0);\n",
    "    \n",
    "  //LEIAME: descomente a linha abaixo para reproduzir os resultados do slide 57\n",
    "  //objective->SetCoefficient(x5, 2.0);\n",
    "\n",
    "  objective->SetMaximization();\n",
    "\n",
    "  // 5. Execute o solver e exiba os resultados.\n",
    "  auto status = solver.Solve();\n",
    "  if (status == MPSolver::OPTIMAL)\n",
    "  {\n",
    "      std::cout << \"Solução:\" << std::endl;\n",
    "      std::cout << \"Valor da função objetivo = \" << objective->Value() << std::endl;\n",
    "      std::cout << \"x_mad : solução = \" << x1->solution_value() << std::endl;\n",
    "      std::cout << \"x_al  : solução = \" << x2->solution_value() << std::endl;\n",
    "\n",
    "      std::cout << \"x3 : custo reduzido = \" << x3->reduced_cost() << std::endl;\n",
    "      std::cout << \"x4 : custo reduzido = \" << x4->reduced_cost() << std::endl;\n",
    "      std::cout << \"x5 : custo reduzido = \" << x5->reduced_cost() << std::endl;\n",
    "      \n",
    "      std::vector<double> activities = solver.ComputeConstraintActivities();\n",
    "\n",
    "      auto constraints = solver.constraints();\n",
    "      \n",
    "      for(auto c_value : constraints)\n",
    "          std::cout << c_value->name() << \" : \" \n",
    "          << \"dual = \" << c_value->dual_value() \n",
    "          << \" atividade = \" << activities[c_value->index()] << std::endl;\n",
    "  }\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exemplo da Fábrica de Cadeiras (slide 63)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "#include<vector>\n",
    "\n",
    "#define MIX 1\n",
    "\n",
    "{\n",
    "\n",
    "  // 1. Escolha o solver.\n",
    "  MPSolver solver(\"programa_simples\", MPSolver::GLOP_LINEAR_PROGRAMMING);\n",
    "\n",
    "  // 2. Crie as variáveis: \n",
    "  auto const x1 = solver.MakeNumVar(0.0, solver.infinity(), \"x1\");\n",
    "  auto const x2 = solver.MakeNumVar(0.0, solver.infinity(), \"x2\");\n",
    "  auto const x3 = solver.MakeNumVar(0.0, solver.infinity(), \"x3\");\n",
    "  auto const x4 = solver.MakeNumVar(0.0, solver.infinity(), \"x4\");\n",
    "  \n",
    "  std::cout << \"Número de variáveis = \" << solver.NumVariables() << std::endl;\n",
    "\n",
    "  // 3. Defina as restrições: \n",
    "  auto const ct1 = solver.MakeRowConstraint(-solver.infinity(), 50.0, \"madeira\"); \n",
    "  ct1->SetCoefficient(x1, 1.0);\n",
    "  #if MIX > 1\n",
    "  ct1->SetCoefficient(x2, 4.0);\n",
    "  #if MIX > 2\n",
    "  ct1->SetCoefficient(x3, 3.0);\n",
    "  #if MIX > 3\n",
    "  ct1->SetCoefficient(x4, 1.0);\n",
    "  #endif\n",
    "  #endif\n",
    "  #endif\n",
    "\n",
    "  auto const ct2 = solver.MakeRowConstraint(-solver.infinity(), 75.0, \"tecido\"); \n",
    "  ct2->SetCoefficient(x1, 1.0);\n",
    "  #if MIX > 1\n",
    "  ct2->SetCoefficient(x2, 1.0);\n",
    "  #if MIX > 2\n",
    "  ct2->SetCoefficient(x3, 1.0);\n",
    "  #if MIX > 3\n",
    "  ct2->SetCoefficient(x4, 2.0);\n",
    "  #endif\n",
    "  #endif\n",
    "  #endif\n",
    "    \n",
    "  std::cout << \"Número de restrições = \" << solver.NumConstraints() << std::endl;\n",
    "\n",
    "  // 4. Defina a função objetivo: \n",
    "  auto const objective = solver.MutableObjective();\n",
    "  objective->SetCoefficient(x1, 150.0);\n",
    "  #if MIX > 1\n",
    "  objective->SetCoefficient(x2, 400.0);\n",
    "  #if MIX > 2\n",
    "  objective->SetCoefficient(x3, 300.0);\n",
    "  #if MIX > 3\n",
    "  objective->SetCoefficient(x4, 200.0);\n",
    "  #endif\n",
    "  #endif\n",
    "  #endif\n",
    "\n",
    "  objective->SetMaximization();\n",
    "\n",
    "  // 5. Execute o solver e exiba os resultados.\n",
    "  auto status = solver.Solve();\n",
    "  if (status == MPSolver::OPTIMAL)\n",
    "  {\n",
    "      std::cout << \"Solução:\" << std::endl;\n",
    "      std::cout << \"Valor da função objetivo = \" << objective->Value() << std::endl;\n",
    "      std::cout << \"x1 : solução = \" << x1->solution_value() << std::endl;\n",
    "      std::cout << \"x2 : solução = \" << x2->solution_value() << std::endl;\n",
    "      std::cout << \"x3 : solução = \" << x3->solution_value() << std::endl;\n",
    "      std::cout << \"x4 : solução = \" << x4->solution_value() << std::endl;\n",
    "\n",
    "      std::cout << \"x1 : custo reduzido = \" << x1->reduced_cost() << std::endl;\n",
    "      std::cout << \"x2 : custo reduzido = \" << x2->reduced_cost() << std::endl;\n",
    "      std::cout << \"x3 : custo reduzido = \" << x3->reduced_cost() << std::endl;\n",
    "      std::cout << \"x4 : custo reduzido = \" << x4->reduced_cost() << std::endl;\n",
    "      \n",
    "      std::vector<double> activities = solver.ComputeConstraintActivities();\n",
    "\n",
    "      auto constraints = solver.constraints();\n",
    "      \n",
    "      for(auto c_value : constraints)\n",
    "          std::cout << c_value->name() << \" : \" \n",
    "          << \"dual = \" << c_value->dual_value() \n",
    "          << \" atividade = \" << activities[c_value->index()] << std::endl;\n",
    "  }\n",
    "}"
   ]
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