exercicios_1_2.ipynb

{
 "cells": [
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 1: Diet Problem\n",
    "\n",
    "**Problem Statement:**\n",
    "A nutritionist wants to design a diet that meets the daily nutritional requirements at the lowest possible cost. The diet consists of different food items, each with a specific cost and nutritional content (e.g., calories, protein, fat). The goal is to minimize the cost while ensuring that the diet meets minimum daily nutritional requirements.\n",
    "\n",
    "**Mathematical Model:**\n",
    "\n",
    "Let:\n",
    "- $x_i $ be the quantity of food item $i $ in the diet.\n",
    "- $c_i $ be the cost per unit of food item $i $.\n",
    "- $a_{ij} $ be the amount of nutrient $j $ in one unit of food item $i $.\n",
    "- $b_j $ be the minimum requirement of nutrient $j $.\n",
    "\n",
    "**Objective:**\n",
    "Minimize the total cost:\n",
    "\n",
    "$\n",
    "\\text{Minimize } \\sum_i c_i x_i\n",
    "$\n",
    "\n",
    "**Constraints:**\n",
    "For each nutrient $j $:\n",
    "\n",
    "$\n",
    "\\sum_i a_{ij} x_i \\geq b_j\n",
    "$\n",
    "$x_i \\geq 0 $ for all $i $.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2025-01-17\n",
      "Gurobi Optimizer version 11.0.3 build v11.0.3rc0 (linux64 - \"Gentoo Linux\")\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i9-14900K, instruction set [SSE2|AVX|AVX2]\n",
      "Thread count: 32 physical cores, 32 logical processors, using up to 32 threads\n",
      "\n",
      "Optimize a model with 12 rows, 3 columns and 18 nonzeros\n",
      "Model fingerprint: 0x254323d8\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 2e+02]\n",
      "  Objective range  [2e-01, 1e+00]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [2e+01, 3e+03]\n",
      "Presolve removed 9 rows and 0 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 3 rows, 3 columns, 9 nonzeros\n",
      "\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    0.0000000e+00   2.137500e+02   0.000000e+00      0s\n",
      "       1    1.2000000e+01   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 1 iterations and 0.00 seconds (0.00 work units)\n",
      "Optimal objective  1.200000000e+01\n",
      "x[Bread]: 16.0\n",
      "x[Milk]: 0.0\n",
      "x[Eggs]: 20.0\n",
      "Optimal cost: 12.0\n"
     ]
    }
   ],
   "source": [
    "import gurobipy as gp\n",
    "from gurobipy import GRB\n",
    "\n",
    "# Parameters\n",
    "foods = [\"Bread\", \"Milk\", \"Eggs\"]\n",
    "costs = {\"Bread\": 0.5, \"Milk\": 1.0, \"Eggs\": 0.2}\n",
    "nutrition = {\n",
    "    \"Calories\": {\"Bread\": 100, \"Milk\": 150, \"Eggs\": 70},\n",
    "    \"Protein\": {\"Bread\": 4, \"Milk\": 8, \"Eggs\": 6},\n",
    "    \"Fat\": {\"Bread\": 1, \"Milk\": 5, \"Eggs\": 5}\n",
    "}\n",
    "requirements = {\"Calories\": 3000, \"Protein\": 50, \"Fat\": 70}\n",
    "\n",
    "# Model\n",
    "model = gp.Model(\"Diet Problem\")\n",
    "\n",
    "# Decision variables\n",
    "food_vars = model.addVars(foods, name=\"x\", vtype=GRB.CONTINUOUS, lb=0)\n",
    "\n",
    "# Objective function\n",
    "model.setObjective(gp.quicksum(costs[i] * food_vars[i] for i in foods), GRB.MINIMIZE)\n",
    "\n",
    "# Constraints\n",
    "for nutrient, req in requirements.items():\n",
    "    model.addConstr(\n",
    "        gp.quicksum(nutrition[nutrient][i] * food_vars[i] for i in foods) >= req,\n",
    "        name=nutrient\n",
    "    )\n",
    "\n",
    "    # add maximum constraint for each food\n",
    "    for food in foods:\n",
    "        model.addConstr(food_vars[food] <= 20)\n",
    "\n",
    "# Optimize\n",
    "model.optimize()\n",
    "\n",
    "# Display solution\n",
    "for v in model.getVars():\n",
    "    print(f\"{v.varName}: {v.x}\")\n",
    "\n",
    "print(f\"Optimal cost: {model.objVal}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "quantities = [v.x for v in model.getVars()]\n",
    "plt.bar(foods, quantities)\n",
    "plt.xlabel('Food Item')\n",
    "plt.ylabel('Quantity')\n",
    "plt.title('Optimal Diet Composition')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Example 2: Transportation Problem\n",
    "\n",
    "**Problem Statement:**\n",
    "A company needs to transport goods from multiple warehouses to several stores. Each warehouse has a limited supply, and each store has a demand. The goal is to minimize the transportation cost.\n",
    "\n",
    "**Mathematical Model:**\n",
    "\n",
    "Let:\n",
    "- $x_{ij} $ be the number of units transported from warehouse $i $ to store $j $.\n",
    "- $c_{ij} $ be the cost per unit of transporting from warehouse $i $ to store $j $.\n",
    "- $s_i $ be the supply at warehouse $i $.\n",
    "- $d_j $ be the demand at store $j $.\n",
    "\n",
    "**Objective:**\n",
    "Minimize the total transportation cost:\n",
    "$\n",
    "\\text{Minimize } \\sum_{i,j} c_{ij} x_{ij}\n",
    "$\n",
    "\n",
    "**Constraints:**\n",
    "Supply constraints for each warehouse $i $:\n",
    "$\n",
    "\\sum_j x_{ij} \\leq s_i\n",
    "$\n",
    "Demand constraints for each store $j $:\n",
    "$\n",
    "\\sum_i x_{ij} \\geq d_j\n",
    "$\n",
    "$x_{ij} \\geq 0 $ for all $i, j $.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gurobi Optimizer version 11.0.3 build v11.0.3rc0 (linux64 - \"Gentoo Linux\")\n",
      "\n",
      "CPU model: Intel(R) Core(TM) i9-14900K, instruction set [SSE2|AVX|AVX2]\n",
      "Thread count: 32 physical cores, 32 logical processors, using up to 32 threads\n",
      "\n",
      "Optimize a model with 5 rows, 6 columns and 12 nonzeros\n",
      "Model fingerprint: 0x73745d63\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [1e+00, 7e+00]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [7e+01, 2e+02]\n",
      "Presolve time: 0.00s\n",
      "Presolved: 5 rows, 6 columns, 12 nonzeros\n",
      "\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    0.0000000e+00   2.500000e+02   0.000000e+00      0s\n",
      "       5    7.8000000e+02   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 5 iterations and 0.00 seconds (0.00 work units)\n",
      "Optimal objective  7.800000000e+02\n",
      "x[W1,S1]: 30.0\n",
      "x[W1,S2]: 0.0\n",
      "x[W1,S3]: 70.0\n",
      "x[W2,S1]: 50.0\n",
      "x[W2,S2]: 100.0\n",
      "x[W2,S3]: 0.0\n",
      "Optimal cost: 780.0\n"
     ]
    }
   ],
   "source": [
    "# Parameters\n",
    "warehouses = [\"W1\", \"W2\"]\n",
    "stores = [\"S1\", \"S2\", \"S3\"]\n",
    "costs = {\n",
    "    (\"W1\", \"S1\"): 2, (\"W1\", \"S2\"): 3, (\"W1\", \"S3\"): 1,\n",
    "    (\"W2\", \"S1\"): 5, (\"W2\", \"S2\"): 4, (\"W2\", \"S3\"): 7\n",
    "}\n",
    "supply = {\"W1\": 100, \"W2\": 150}\n",
    "demand = {\"S1\": 80, \"S2\": 100, \"S3\": 70}\n",
    "\n",
    "# Model\n",
    "model = gp.Model(\"Transportation Problem\")\n",
    "\n",
    "# Decision variables\n",
    "transport_vars = model.addVars(warehouses, stores, name=\"x\", vtype=GRB.CONTINUOUS, lb=0)\n",
    "\n",
    "# Objective function\n",
    "model.setObjective(gp.quicksum(costs[i, j] * transport_vars[i, j] for i in warehouses for j in stores), GRB.MINIMIZE)\n",
    "\n",
    "# Constraints\n",
    "for i in warehouses:\n",
    "    model.addConstr(gp.quicksum(transport_vars[i, j] for j in stores) <= supply[i], name=f\"Supply_{i}\")\n",
    "for j in stores:\n",
    "    model.addConstr(gp.quicksum(transport_vars[i, j] for i in warehouses) >= demand[j], name=f\"Demand_{j}\")\n",
    "\n",
    "# Optimize\n",
    "model.optimize()\n",
    "\n",
    "# Display solution\n",
    "for v in model.getVars():\n",
    "    print(f\"{v.varName}: {v.x}\")\n",
    "\n",
    "print(f\"Optimal cost: {model.objVal}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "import numpy as np\n",
    "\n",
    "transport_matrix = np.array([[transport_vars[i, j].x for j in stores] for i in warehouses])\n",
    "sns.heatmap(transport_matrix, annot=True, cmap=\"YlGnBu\", xticklabels=stores, yticklabels=warehouses)\n",
    "plt.xlabel('Stores')\n",
    "plt.ylabel('Warehouses')\n",
    "plt.title('Transportation Plan')\n",
    "plt.show()\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}