diet.ipynb

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      "\n",
      "Diet for a maximum of unlimited calories\n",
      "Optimal value: 9.0\n",
      "QPounder                      : 1.0 dishes --> 1.00 added to objective\n",
      "McLean                        : 3.0 dishes --> 1.00 added to objective\n",
      "Big Mac                       : 1.0 dishes --> 1.00 added to objective\n",
      "FFilet                        : 1.0 dishes --> 1.00 added to objective\n",
      "Chicken                       : 1.0 dishes --> 1.00 added to objective\n",
      "Fries                         : 1.0 dishes --> 1.00 added to objective\n",
      "McMuffin                      : 1.0 dishes --> 1.00 added to objective\n",
      "1% LFMilk                     : 2.0 dishes --> 1.00 added to objective\n",
      "OrgJuice                      : 1.0 dishes --> 1.00 added to objective\n",
      "amount spent: 9.0\n",
      "amount of nutrients:\n",
      "Cal                           : 3755.00\n",
      "Carbo                         : 358.00\n",
      "Protein                       : 207.00\n",
      "VitA                          : 102.00\n",
      "VitC                          : 196.00\n",
      "Calc                          : 227.00\n",
      "Iron                          : 137.00\n",
      "\n",
      "Diet for a maximum of 3500 calories\n",
      "Optimal value: 8.0\n",
      "QPounder                      : 1.0 dishes --> 1.00 added to objective\n",
      "McLean                        : 1.0 dishes --> 1.00 added to objective\n",
      "Big Mac                       : 1.0 dishes --> 1.00 added to objective\n",
      "FFilet                        : 1.0 dishes --> 1.00 added to objective\n",
      "Chicken                       : 1.0 dishes --> 1.00 added to objective\n",
      "McMuffin                      : 1.0 dishes --> 1.00 added to objective\n",
      "1% LFMilk                     : 5.0 dishes --> 1.00 added to objective\n",
      "OrgJuice                      : 4.0 dishes --> 1.00 added to objective\n",
      "amount spent: 8.0\n",
      "amount of nutrients:\n",
      "Cal                           : 3365.00\n",
      "Carbo                         : 358.00\n",
      "Protein                       : 186.00\n",
      "VitA                          : 108.00\n",
      "VitC                          : 533.00\n",
      "Calc                          : 283.00\n",
      "Iron                          : 101.00\n",
      "\n",
      "Diet for a maximum of 3000 calories\n",
      "Optimal value: 6.0\n",
      "QPounder                      : 1.0 dishes --> 1.00 added to objective\n",
      "McLean                        : 3.0 dishes --> 1.00 added to objective\n",
      "Chicken                       : 1.0 dishes --> 1.00 added to objective\n",
      "Fries                         : 1.0 dishes --> 1.00 added to objective\n",
      "1% LFMilk                     : 2.0 dishes --> 1.00 added to objective\n",
      "OrgJuice                      : 6.0 dishes --> 1.00 added to objective\n",
      "amount spent: 6.0\n",
      "amount of nutrients:\n",
      "Cal                           : 2940.00\n",
      "Carbo                         : 351.00\n",
      "Protein                       : 158.00\n",
      "VitA                          : 100.00\n",
      "VitC                          : 794.00\n",
      "Calc                          : 177.00\n",
      "Iron                          : 102.00\n",
      "\n",
      "Diet for a maximum of 2500 calories\n",
      "Optimal value: 3.0\n",
      "McLean                        : 4.0 dishes --> 1.00 added to objective\n",
      "1% LFMilk                     : 2.0 dishes --> 1.00 added to objective\n",
      "OrgJuice                      : 10.0 dishes --> 1.00 added to objective\n",
      "amount spent: 3.0\n",
      "amount of nutrients:\n",
      "Cal                           : 2500.00\n",
      "Carbo                         : 364.00\n",
      "Protein                       : 124.00\n",
      "VitA                          : 100.00\n",
      "VitC                          : 1248.00\n",
      "Calc                          : 160.00\n",
      "Iron                          : 100.00\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "diet.py: model for the modern diet problem\n",
    "Copyright (c) by Joao Pedro PEDROSO and Mikio KUBO, 2012\n",
    "\"\"\"\n",
    "# todo: can we make it work as \"from pyscipopt import *\"?\n",
    "from pyscipopt import Model, quicksum, multidict\n",
    "\n",
    "def diet(F,N,a,b,c,d):\n",
    "    \"\"\"diet -- model for the modern diet problem\n",
    "    Parameters:\n",
    "        - F: set of foods\n",
    "        - N: set of nutrients\n",
    "        - a[i]: minimum intake of nutrient i\n",
    "        - b[i]: maximum intake of nutrient i\n",
    "        - c[j]: cost of food j\n",
    "        - d[j][i]: amount of nutrient i in food j\n",
    "    Returns a model, ready to be solved.\n",
    "    \"\"\"\n",
    "\n",
    "    model = Model(\"modern diet\")\n",
    "\n",
    "    # Create variables\n",
    "    x,y,z = {},{},{}\n",
    "    for j in F:\n",
    "        x[j] = model.addVar(vtype=\"I\", name=\"x(%s)\"%j)\n",
    "        y[j] = model.addVar(vtype=\"B\", name=\"y(%s)\"%j)\n",
    "    for i in N:\n",
    "        z[i] = model.addVar(lb=a[i], ub=b[i], name=\"z(%s)\"%j)\n",
    "    v = model.addVar(vtype=\"C\", name=\"v\")\n",
    "\n",
    "    # Constraints:\n",
    "    for i in N:\n",
    "        model.addCons(quicksum(d[j][i]*x[j] for j in F) == z[i], name=\"Nutr(%s)\"%i)\n",
    "\n",
    "    model.addCons(quicksum(c[j]*x[j] for j in F) == v, name=\"Cost\")\n",
    "\n",
    "    for j in F:\n",
    "        model.addCons(y[j] <= x[j], name=\"Eat(%s)\"%j)\n",
    "\n",
    "    # Objective:\n",
    "    model.setObjective(quicksum(y[j] for j in F), \"maximize\")\n",
    "    model.data = x,y,z,v\n",
    "\n",
    "    return model\n",
    "\n",
    "\n",
    "def make_inst():\n",
    "    \"\"\"make_inst: prepare data for the diet model\"\"\"\n",
    "    F,c,d = multidict({       # cost # composition\n",
    "        \"QPounder\" :  [ 1.84, {\"Cal\":510, \"Carbo\":34, \"Protein\":28,\n",
    "                               \"VitA\":15, \"VitC\":  6, \"Calc\":30, \"Iron\":20}],\n",
    "        \"McLean\"   :  [ 2.19, {\"Cal\":370, \"Carbo\":35, \"Protein\":24, \"VitA\":15,\n",
    "                               \"VitC\": 10, \"Calc\":20, \"Iron\":20}],\n",
    "        \"Big Mac\"  :  [ 1.84, {\"Cal\":500, \"Carbo\":42, \"Protein\":25,\n",
    "                               \"VitA\": 6, \"VitC\":  2, \"Calc\":25, \"Iron\":20}],\n",
    "        \"FFilet\"   :  [ 1.44, {\"Cal\":370, \"Carbo\":38, \"Protein\":14,\n",
    "                               \"VitA\": 2, \"VitC\":  0, \"Calc\":15, \"Iron\":10}],\n",
    "        \"Chicken\"  :  [ 2.29, {\"Cal\":400, \"Carbo\":42, \"Protein\":31,\n",
    "                               \"VitA\": 8, \"VitC\": 15, \"Calc\":15, \"Iron\": 8}],\n",
    "        \"Fries\"    :  [  .77, {\"Cal\":220, \"Carbo\":26, \"Protein\": 3,\n",
    "                               \"VitA\": 0, \"VitC\": 15, \"Calc\": 0, \"Iron\": 2}],\n",
    "        \"McMuffin\" :  [ 1.29, {\"Cal\":345, \"Carbo\":27, \"Protein\":15,\n",
    "                               \"VitA\": 4, \"VitC\":  0, \"Calc\":20, \"Iron\":15}],\n",
    "        \"1% LFMilk\":  [  .60, {\"Cal\":110, \"Carbo\":12, \"Protein\": 9,\n",
    "                               \"VitA\":10, \"VitC\":  4, \"Calc\":30, \"Iron\": 0}],\n",
    "        \"OrgJuice\" :  [  .72, {\"Cal\": 80, \"Carbo\":20, \"Protein\": 1,\n",
    "                               \"VitA\": 2, \"VitC\":120, \"Calc\": 2, \"Iron\": 2}],\n",
    "        })\n",
    "\n",
    "    N,a,b = multidict({       # min,max intake\n",
    "        \"Cal\"     : [ 2000,  None ],\n",
    "        \"Carbo\"   : [  350,  375 ],\n",
    "        \"Protein\" : [   55,  None ],\n",
    "        \"VitA\"    : [  100,  None ],\n",
    "        \"VitC\"    : [  100,  None ],\n",
    "        \"Calc\"    : [  100,  None ],\n",
    "        \"Iron\"    : [  100,  None ],\n",
    "     })\n",
    "\n",
    "    return F,N,a,b,c,d\n",
    "\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "\n",
    "    F,N,a,b,c,d = make_inst()\n",
    "\n",
    "    for b[\"Cal\"] in [None,3500,3000,2500]:\n",
    "\n",
    "        print(\"\\nDiet for a maximum of {0} calories\".format(b[\"Cal\"] if b[\"Cal\"] != None else \"unlimited\"))\n",
    "        model = diet(F,N,a,b,c,d)\n",
    "        model.hideOutput() # silent mode\n",
    "        model.optimize()\n",
    "\n",
    "        print(\"Optimal value:\",model.getObjVal())\n",
    "        x,y,z,v = model.data\n",
    "        for j in x:\n",
    "            if model.getVal(x[j]) > 0:\n",
    "                print(\"{0:30s}: {1:3.1f} dishes --> {2:4.2f} added to objective\".format(j,model.getVal(x[j]),model.getVal(y[j])))\n",
    "        print(\"amount spent:\",model.getObjVal())\n",
    "\n",
    "        print(\"amount of nutrients:\")\n",
    "        for i in z:\n",
    "            print(\"{0:30s}: {1:4.2f}\".format(i,model.getVal(z[i])))"
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