Adaptive-robust-optimization-GEP-nb.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Packages\n",
    "using JuMP\n",
    "using HiGHS\n",
    "using CSV\n",
    "using DataFrames\n",
    "using Plots\n",
    "using StatsPlots\n",
    "using Printf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# include the helper functions\n",
    "include(\"functions-to-import-data.jl\");\n",
    "include(\"functions-to-export-data.jl\");\n",
    "include(\"functions-to-plot-results.jl\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# include the file with the functions for the stochastic GEP model\n",
    "include(\"Adaptive-robust-optimization-GEP.jl\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Folders names\n",
    "input_folder = joinpath(@__DIR__, \"inputs/aro\");\n",
    "output_folder = joinpath(@__DIR__, \"outputs/aro\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# read the data\n",
    "sets, params = read_aro_data(input_folder);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A JuMP Model\n",
       "Minimization problem with:\n",
       "Variables: 5\n",
       "Objective function type: AffExpr\n",
       "`VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 5 constraints\n",
       "`VariableRef`-in-`MathOptInterface.Integer`: 4 constraints\n",
       "Model mode: AUTOMATIC\n",
       "CachingOptimizer state: EMPTY_OPTIMIZER\n",
       "Solver name: HiGHS\n",
       "Names registered in the model: v_investment, v_theta"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "first_stage_model = create_first_stage_model(sets, params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration  Lower Bound  Upper Bound          Gap\n",
      "        1  -1.0000e+03   1.5030e+06   1.0007e+00\n",
      "        2   1.1368e+05   1.3296e+06   9.1450e-01\n",
      "        3   3.8342e+05   3.8342e+05   1.8218e-15\n",
      "Terminating with the optimal solution\n"
     ]
    }
   ],
   "source": [
    "# Benders decomposition algorithm\n",
    "\n",
    "# Define constants\n",
    "MAXIMUM_ITERATIONS = 100       # maximum number of iterations\n",
    "ABSOLUTE_OPTIMALITY_GAP = 1e-6 # gap between lower and upper bounds to stop the algorithm\n",
    "\n",
    "# Define outputs\n",
    "df_Benders_interations = DataFrame(;\n",
    "    iteration=Int[],\n",
    "    lower_bound=Float64[],\n",
    "    upper_bound=Float64[],\n",
    "    gap=Float64[],\n",
    ")\n",
    "\n",
    "df_investment_per_iteration =\n",
    "    DataFrame(; iteration=Int[], generator=String[], investment=Float64[])\n",
    "\n",
    "# Start Benders' Decomposition\n",
    "upper_bound = Inf\n",
    "println(\"Iteration  Lower Bound  Upper Bound          Gap\")\n",
    "for iteration in 1:MAXIMUM_ITERATIONS\n",
    "    optimize!(first_stage_model)\n",
    "    @assert is_solved_and_feasible(first_stage_model)\n",
    "    lower_bound = objective_value(first_stage_model)\n",
    "    p_investment = value.(first_stage_model[:v_investment])\n",
    "    subproblem = create_and_solve_subproblem(sets, params, p_investment)\n",
    "    upper_bound = minimum([upper_bound,\n",
    "        objective_value(first_stage_model) - value.(first_stage_model[:v_theta]) + objective_value(subproblem)\n",
    "    ])\n",
    "    gap = (upper_bound - lower_bound) / upper_bound\n",
    "    push!(df_Benders_interations, (iteration, lower_bound, upper_bound, gap))\n",
    "    print_iteration(iteration, lower_bound, upper_bound, gap)\n",
    "\n",
    "    if gap < ABSOLUTE_OPTIMALITY_GAP\n",
    "        println(\"Terminating with the optimal solution\")\n",
    "        break\n",
    "    end\n",
    "    add_cut(first_stage_model, subproblem, sets, params, iteration)\n",
    "\n",
    "    for g in sets[:G]\n",
    "        push!(df_investment_per_iteration, (iteration, g, p_investment[g]))\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plotly()\n",
    "plot_gap(df_Benders_interations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_bounds(df_Benders_interations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1-dimensional DenseAxisArray{Float64,1,...} with index sets:\n",
       "    Dimension 1, String7[\"ocgt\", \"ccgt\", \"wind\", \"solar\"]\n",
       "And data, a 4-element Vector{Float64}:\n",
       "  -0.0\n",
       "   3.0\n",
       "   6.0\n",
       " 138.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "optimize!(first_stage_model)\n",
    "@assert is_solved_and_feasible(first_stage_model)\n",
    "v_investment_optimal = value.(first_stage_model[:v_investment])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KyitXrmzbtm3ChAlLly69y3MGBQV17do1Pz//5Zdfnj17Nnmd4tKlS6Ojo5sMte3Tp89vv/32yiuvTJ48OSAgwMfHx+Xw1+jo6Llz565Zs2bw4MErVqzo3Lnz1atXFy5cqNfr58yZ02RgFOpAvHXdBmpP7jKzTJM1V61aBQDffPNNk+XkBYUA4Hz5oLOLFy8+9thjTT69QqFw9erV5Arvvvuu8yQgZD3PPfdcY2Oj40muXbvWv39/x6wiTWaWabJHMo8dl2aTyOsNZs2a5bzwzz//JCf0ciaRSBzX5Dlmlmmyi//9738A8NFHHzmW6HS6Z5991jFHWnNmltm8eTObzXbst1u3boWFhU1W/vHHHx2zYzt06dLFcfmjY2aZO+2uiduvI6yqqho1apRj9I3zzDIHDx68fQRmZGRkeno6uYJjZpnbd3T+/Pnw8HDnf9MFCxYsX74cAL777jvHao2NjVOnTnW8D3eZWcZqtTb5qNDp9HfeecdqtTrWccws06QYsod/l1kOUBuFvz6BWoDdbienkSQn+AAAm81WWlrKYrGafP+q1WqVSiUUCm8fmED+je/r60s2xFy6cuVKXl6eTqcTCoURERGJiYnOw/0bGxtzc3PLy8v1er1EIunVq1eTmc9IFoulurrabDbzeDxy1GVxcTGVSo2MjHReTalU6nQ6iUTiHDN6vb6qqsrPz6/JEEeCIC5cuPD333/r9frg4OCoqKhevXo5j/4oKipiMBjO3+kAoNVqa2pqyBlnmhRZVVWl1+vpdHpERITLt6KwsDA2NnbYsGGHDh2qra3NyspSq9WxsbEDBw5sMhbU8apPnTp1/fp1q9UqFovj4+Odp6wzmUyVlZWON+SeioqKbDZbdHR0k8st7HZ7VVWV0Whks9lku5Jks9nOnTuXn59vNBpDQkKio6Od5wu906eFZDQac3JyiouLeTzewIEDQ0NDyU9RUFDQ7b/RQb5vNBqN/Nesrq7WaDTh4eHO/4jk8uzsbPLXKgYNGtTkIkuDwaBQKG7/KNbU1Gi12iYfCdQOYBAi1CY5B6G3a0GobcPBMgghhDo0DEKEEEIdGo4aRahNCgwMXLlyZVRUlLcLQajNw3OECCGEOjRsjSKEEOrQMAgRQgh1aBiECCGEOjQMQoQQQh0aBiFCCKEODYMQIYRQh9ZKg/Do0aN//PGHt6tACCHUupDTZLfsc7bSIDx27JjLHzBDCCHUkZnNZovF0rLP2UqDECGEEPIMDEKEEEIdGgYhQgihDs0tk27b7faLFy9eunTJarX27t3b+ce7Gxoa9u3bBwCjR4/29/d3x94RQgih5nPLEWFRUdHzzz9/8ODBY8eODRs2bMGCBeRyhULRrVu3nTt3pqWldevWTS6Xu2PvCCGEUPO5/dcnzpw58/jjj2s0GjabvXDhwuLi4p9//hkApk6dGhERsXLlSpdbLVu2jEajLV261K21IYQQaltMJhOFQmEymS34nG4/R6jRaPh8PoPBAIC9e/empKSQy1NSUvbs2ePuvSOEEEJ358Yf5p08ebJcLi8rK/v9999pNBoAVFZWhoaGko+GhobepTVaW1t77dq1Tz75hLzLZDJnzJjB5XLdVy1CCKFWTldmLNldxeDR46eFNXMTGo1Gpd7jkM+NQTh79myNRvP9998vXrz40KFDNBrNbrdTKBRHcVar9U7bGo1Gg8GgUqnIuxQKxWg0stls91WLEEKo1bLp7RWZtTW5GiCAIyZsNlszN7xnCoJbg3DgwIEAMHLkyMDAwNOnTz/22GNisVipVJKPVldXSySSO20bFhYWGRl5v+cI//vf//7vf/97mJrbqG+//TYxMdHbVSCEkBsQoMxTF++usuisFBpF1M8/bISwZY+L3BiEpIaGBqPRSF4p8cQTTxw8ePCpp54CgMzMzMGDB7fsvi5cuDBy5MiJEye27NO2cu+//35xcTEGIUKo/WmsNMrS5JoSPQD4x3ClqRIaHxydxZbiliDcunXrvn37unXrZjKZfvnllwkTJnTp0gUA5s2b169fP19fXwqF8uOPP/71118tvuuIiIiOFgkBAQHeLgEhhFqY1WArO6BUnFARdoLpR48aGyJK4gOAyWRq8X25JQjHjh1LoVAKCws5HM7atWuffPJJMsDj4uLy8vJ++uknAMjLy4uOjnbH3hFCCLVptX83yNIVFq2VQqVIkgMjRwXT2G68xsEtQSgQCF544QWXD0VHRy9evNgdO0UIIdTWGZQmWbpCXaADAL9orjRVzBW7fZik288RIoQQQvdkM9srj9aWH64hbATTlx41LkSUyIcWPhvoGgYhQgghL1Pla2XpclO9BSggSuJHTxDTuTSP7R2DECGEkNcYasxFu+T1V3UAwAvjSCdJfCM4Hq4BgxAhhJAX2M32iqO1FVk1ditB96FFPCmSJAd6phfaBAZh61VWVlZaWpqcnOztQhBCqIWp8rVFuxRGlZnshXYaH8LgeS2PMAhbr5ycnB9++GH//v3eLgQhhFqMsc4sS1fUX9ECAC+ULZ0k8Y308W5JGITuRRDETz/9dPz4cQAYM2bM2LFjAaCsrGzTpk2lpaVRUVEzZ84MDg42Go1ffvnl1atXhwwZwuPxAgICevTo8fPPP1+7dm3BggU8Hm/JkiXefikIIfRQ7BZ7xZF/eqEcWsQIkXiAgEL1RjP0Vu08CE/XEKU69/7gogMFYKiEGsC6ZeFrr72Wn5//zjvvUCiUq1evjh07tqCg4PHHH3/zzTefffbZa9euVVRUBAcHP/PMM0wmc/r06VlZWdu2bZs3b16fPn06depUXl6emJjIYrHusE+EEGob1Nd1sjSFQWlqDb3QJlpLHe6gMkH/3Vabh3IQAODVzsSGATeH/BYWFv7000+lpaWBgYGOhStWrHjxxRfJ+cRHjhwJAAUFBdnZ2QqFwsfHZ/To0dnZ2QDA5XL79etXUFDw9NNPe+4FIIRQSzM3WEr2Vitz1QDAlbClqRK/Tl7uhTbRnoMwgAXv96Reb/DQ7qgUeCn2lkmALl++HBsb65yC5ML33nvPeUlRUVF0dLSPz41PRvfu3d1dKkIIeQBhIxQnVKX7q20mO41JDX8yKPQJYWvohTbRnoOQArA8yXOXZN5OIBDU19c3WRgQEOD4nUVSYGBgTU0NQRDkjKxKpTIuLg6g5WdYRwghj2kobJSlyfXVJgAQJPhKJ0lYfIa3i3LNjdOYosTERIIgfvjhB/JubW0tAEycOHHdunVkQJrNZo1G06tXLxaL9d133wFATk7OkSNHyPUDAwMrKyub//uTCCHUGpg11oLtFRfXFeurTZwgVrfXoxJmRLbaFAQMQrficDg7d+5csWJFQkJC165dZ8+eDQCvvvrqsGHD4uLi+vTpExMTc+nSJQaDkZ6evmnTpuDg4C+++GLs2LFcLhcAnnjiicjIyPDwcPIAESGEWjnCTsj/qMtbWaDMVVOZ1IgRot7vxfDjed6u6x7ac2u0NejTp8/ly5dramooFIpQKAQAKpX6+eefr1ixQqFQBAcHkyNCe/bsSf46o91u7969+6uvvgoATCYzIyPDu/UjhFAzNcgaZWkKfZURyF5oqoQV0HqPAp1hEHpCUFBQkyUMBiMiIsJx94svvigrKxMKhYcOHRKLxcOGDfNsgQgh9ODMWmtJRpUyTw0EsIVM6URxQBdfbxd1HzAIW4UpU6YcPXq0vr5+4cKFw4cPp1KxZY0QagsIqPpLVZJRbTXaqAxq2BBh2NAgKr2NDfTDIGwVQkJCpkyZ4u0qEELoPujKDYVpcl2ZAQAECb7RKWK2gOntoh4EBmGrlp2dTU635u1CEELoJqveVpaplOfUAQEsPqPTBLGwp5+3i3pwGISt2tatW7t06YJBiBBqLQhQ5qmLf1dYGm0UGkXcXxA5JpjGbNtnczAI3ctoNK5du/b8+fPh4eFvvfWWWCwml2dlZe3cubOhoaFnz57vvfcelUq9fv36l19+2dDQ8Morr+Tm5j777LNyuTw3N7e4uLi2trZXr17PPvusd18LQqiD01UaZTvl2lI9APBjudEpEp/g9jATcjsPQtP1v601lZ7ZF4XBZHfpQ+X5Oy9MSUnhcDizZ8/OyspKSkq6cuWKn5/fpk2b/v3vf69YsUIikfzxxx82m62hoWHAgAHvvvtu3759165de/DgwUGDBoWGhkokkoiIiGHDhoWEhHjmVSCE0O2sBlvZAaXihIqwE0w/etTYEFES39tFtZj2HIR2vbZm3QIgPDfrNvfREQHPznfcvXTp0okTJyorK3k83pAhQ3JycrZt2zZr1qx//etfW7ZsGT58OAAMGjQIAH788cc+ffqQc5B2796djD0yCGNjY/FqCoSQ15C90N1VFp2VQqNIkgMjRwfTWG27F9pEew5CKofnP2aaVVXtsT1yHx3pfLewsDAmJobHuzGrQu/evQsLCxsaGhQKRZ8+fZzXLC4u7tKlC3lbIBDg8R9CqDVolBtlaXJNsR4A/KVcaarEJ6Q99EKbaM9BCBSK77DJXty/QCBwnl+7rq4uPj6ex+Ox2eza2lo+/2ZjISgoKD8/n7xtNpvr6uo8XStCCDmxme3lB2sqj9Xe7IUm8qGNXR/YXO3q8La1SUxMNBqN6enpAFBYWJiRkTFmzBgajZaSkvLRRx9ZrVYAqKqqstvtKSkpGRkZJ0+etFgsH3/8sdlsJp9BJBIVFRV58zUghDoeVb727MrrFUdqAECSHJi4IE6U1G5TEDAI3YrL5e7YsWPhwoVxcXHJycmffvpp7969AeCrr75qbGwMDw/v2rXrwIEDbTZbXFzc999//8Ybb8TFxXG5XLFYTDZUZ8yYceHChaioqPnz599rbwgh9LAMNaZL60subyo1qS1+0dxeb0ujJ4pp7HaeFO26NdoKJCcnX7t2TaPR+PndvNo0MDAwLS3NbDYbDAZ//xujTFNSUlJSUgBAJpN9/PHHUVFRACCVSnNycrxROEKoY7Gb7RVHa8sP1xA2gu5Di3hSJEkObMdHgc4wCD3BOQUdmEwmk3lzOqKpU6eKxWIqlfrLL798+OGHHA7HgwUihDo0Vb5Wli431VuAAqIkfvQEMZ3rzV819zAMwtbi448/PnPmjNVqfeWVVzp37uztchBCHYKx1ixLl9df1QEAL4wjTZX4Rna4v8IxCFsFnU4nEAgmT/bmGFeEUIdit9grjtRWZNXYrQSdQ4sYIRIPEFCoHaMZeisMwlZh/fr1V65c2bRpk7cLQQh1CKp8bdEuhVFlJnuhncaHMHgdNw467itHCKEOyFhnLtqlUF3WAgA3lB2TKvGN8vF2UV6GQehe+/fv37Jli0ajiYqKWrRoUVhYmN1u/+abb44cORIQEPDaa6/17dvXeX2TyfTll1+eOXPGZrM98cQTs2bNotPpADB//vwpU6Zs3LjRZrN9//33Xno1CKE2jLARihOq0n3VNrO9g/dCm2jnQXhacba6scYz+6IAPBraR8gROJYUFBRMnz79f//7n0QiuXjxosFgAID33nvv5MmTK1euLCoqGjFixNGjR3v16uXYxGg0AsD8+fNtNtsHH3ygUqk++OADANi8efOff/65aNGigIAAz7wchFB7or7eKEuTG5SmG73QcSEM33b+/d987fmN0Ji0/3fkQwI8N+n2aOmw9x+d67hbVVXF5XK7dOkSGRlJ/qagxWL5+uuvz507l5CQMHDgwAsXLnz99dffffedYxN/f///+7//k8vl1dXVL7300n/+8x8yCAFgyZIl48aN89hrQQi1D+YGS8neamWuGgA4IpY0RcyP43m7qNalPQehH8t3duIrpQ3lntkdg8YYIx3uvGTAgAGjR4/u2bOnVCp9+umn3377bblcbrfbHfNr9+jRY+vWrc6b1NXVjR071m63R0ZGarXa6uqbM4bHx8d74FUghNqNG73Q/dU2k53GpIYOFoYPC6LQsBfaVHsOQgB4uvN4L+6dSqV+9dVXq1evPnLkyPvvv89gMF577VtvclIAACAASURBVDWr1VpfXy8QCABAqVQKhULnTb777ru4uLgtW7YAwLFjx5x/jJc8WYgQQs3RIGuUpcn1VSYAECT4SidJWHyGt4tqpdr5DHLeVVxcXFFRwWAwRowY0aNHj4aGBl9f3yFDhqxcuRIAampqvvvuuwkTJjhvYrfbNRqN3W43Go2fffaZlwpHCLVhZo21YHvFxXXF+ioTJ4jZ9bWohBmRmIJ3gQcZblRWVjZ9+nTyVya6deu2Zs0aAPj+++9ffvnl0NBQu90+Y8aMKVOmAACPxyN/lenVV1/dvXt3eHg4h8N5/fXXa2tryaeKiopiMPBzjBC6G8JOKHJUpQeqbUY7lUkNGywMGxpEpWMv9B4wCN1o0KBBMpnMZDLR6XQa7cbEfZGRkUeOHDGbzc4Tjb7xxhvkDaFQePLkSYPBQM41Sv5mPQCcO3fOs7UjhNoYTVGjLE3RqDAC2QtNlbAC8K/nZsEgdDsWy8UPOjun4O1wxm2EUPNZG20l+6qr/lIBAexApjRFHNDF19tFtSUYhAgh1GYRoMxTF/2usDbaqAxq2BDshT4IDEKvIQiisLAwJiaGQmnWp7a4uDgiIsLRYkUIdXC6CoNsp1xbZgAAQYJvdIqYLbhbqwndCQah1xgMhri4OKPR6LJ3eruEhITi4uKQkBB3F4YQauWsBlvZAaU8pw4IYPEZkaODRUl8bxfVhmEQeg2bzT5z5szdTxYihNAtCFDmqYt3V1l0VgqNIu4viBwdTGPhhXAPBd8+N7py5conn3xC3l67du3atWvJ28uXL7969arVav3vf/9rs9kAYOXKlceOHXv99deHDx++cuVKciEAHD9+PDU1dfz48ceOHfPGK0AItSK6SuPfa4sKtldYdFb/GG7vd2OiJ4oxBR9eOz8irL2gMdaaPLQzCiWol7/zeOWQkJDly5fPmzePw+GsWrUKAObMmWMwGD755JNZs2ZZrdbNmzevX7+eTqf/9ttv27ZtW7lypUAgeOmllyIiIqZOnVpQUDB+/Phvv/02Pj5+8eLFFovFQy8EIdTKkL1QxQkVYSeYfvSosSHYC21B7TkIrY22q5vLPLlHQ7Up9tlQx92AgIAuXbqcOHEiKCgoJiaGIIiLFy9WVVV17do1ICBAr9c7bztnzpyxY8cCwLRp006cODF16tTvvvtu6tSpzzzzDAB8/vnne/fu9eRrQQi1CmQvNKPKorVSqBRJciD2Qltcew5COpcW87TEWOepAykK3P432tChQ7OysoKCgoYOHUoQxOHDh6urq4cOHXr71pGRkeQNf3//q1evAkBJScmAAQPIhXFxcVQqfvQR6lga5UZZmlxTrAcAfylXmiL2EbO9XVQ71J6DEABCHhPceyV3Gjp06OLFi4OCgpYuXWq325cvX15dXU3ONXpPQUFBSqWSvF1TU2O3291ZKUKoFbGZ7ZVHa8sP1xA2gulLjxoXIkrkA14f6B7tPAi9bsCAAfn5+f7+/klJSQBw9uxZjUbz+OOPN2fblJSUadOmzZw5UyKRfPLJJ8283BAh1Nap8rWyNLlJbQEKhDwmiBoXTGfjBcRuhEHoXj4+PmPHjuXxeOSPKI0cOVKv15MzqFGpVKlUSsabRCLx8fEhN/H39w8KCgKAoUOHzpkzJzExkcVizZ49u3Pnzng1PULtm6HGLEuXq6/pAIAXzolJlfAicMJFt6MQhOd+wL35li1bRqPRli5del9bvf7664mJia+99pqbqmqdnn766cmTJ0+aNMnbhSCEHpzdbK84WluRVWO3EnQfWsSTIklyIPZCb2cymSgUSstegY1HhAgh5GWqfK0sXW6qt5Bj7jpNEDO42P7xHAxChBDyGmOdWZauqL+iBQBeGEeaKvaN9PF2UR0OBiFCCHmB3WKvOPJPL5RDixghEg8QUKjYDPUCDEKEEPI0Vb62aJfCqDLf6IWOD2Hw8NvYa/CtRwghzzGpLaX7qpW5agDgStjSSRK/KOyFehkGIUIIeQJhIxQnVKX7q20mO51NixiJvdDWAoMQIYTcrqGwUZYm11ebAECQ4CudJGHxGffcCnlGuwpCf3//119//fXXX/d2IZ7WAV8yQm2FWWMt2VNF9kI5QSxpqpgfx/N2UegW7SoIV61aRf7aEUIIeZ1zL5TKpIYNFoYPC6LQsBfa6rSrIEQIoVaiQdYoS1Poq4xA9kJTJc4/VopaFQxChBBqSWattSSjSpmnBgLYQqY0RRLQGXuhrRoGIUIItQzCTihyVKUHqm1GO5VBDRsiDBsaRKVjL7S1wyBECKEWoCs3FKbJdWUGABAk+EaniNmClpwYGrkPBiFCCD0Uq95WlqmU59QBAexAZvREsSDB19tFofuAQYgQQg+KAGWeuvh3haXRRqFRQgcJI0aKsBfa5mAQIoTQg9BVGGRpcm2pAQD4sTxpqpgjYnm7KPQgMAgRQuj+WA22sgNKxQkVYSeY/oyoMcGiJL63i0IPDoMQIYSajeyF7q6y6KwUGkWSHBg5OpjGonq7LPRQMAgRQqhZGiuNsjS5pkQPAP4xXGmKxCcEe6HtAQYhQgjdg9VoK9v/Ty/Ujx41NgR7oe3JzSAsLy8/f/58MzcbMmQIl8t1T0kIIdSK1P7dIEtXWLRWCpUiSQ6MHBVMY2MvtF25GYSHDx+ePn16Mze7du1aXFyce0pCCKFWwaA0ydIV6gIdAPhFc6WpYq6Y7e2iUMu7pTWamJi4efPme27Ts2dPd5WDEEKtgM1srzxaW364hrARTF961LgQUSIf8PrAduqWIPTx8enWrZu3SkEIodZAla+VpctN9RaggCiJHz1BTOfSvF0UcqObQTh16tTU1NTmbFNTU8Pn44lihFB7Y6gxF+2S11/VAQAvjCOdJPGN4Hi7KOR2N4OQxWKxWM0aCiwQCNxWD0IIeYHdbK84WluRVWO3EnQOLWKESJIciL3QDsL15RONjY0EQfB4N35Da//+/adPn05MTBw7dqwHa0MIIU9Q5WuLdimMKjPZC+00PoTBw0vLOhDX/9gDBw4cOXLk8uXLAWDTpk0zZsygUql2u33FihULFizwbIUIIeQuxjqzLF1Rf0ULALxQtjRV4hvl4+2ikKe5uBrGZDKdP39+9OjR5N1Vq1aNGTPGYDCsXr165cqVRqPRsxUihFDLs1uJskzl2U+v11/R0jm06KfEPedLMQU7JhdBqFKp7HZ7aGgoABQVFRUUFMyaNYvJZM6YMaOhoaG0tNTjRSKEUEtSX9ed+7ywLFNptxGiJH7iwljJwEAKFU8JdlAuWqN+fn4AUFtbGxUV9dtvvzEYjOTkZACgUqkA0NjY6OESEUKopZgbLCV7q5W5agDgStjSVIlfJzwK7OhcBCGXy+3Ro8eHH344Z86c9evXP/HEE76+vgBw/fp1ACCPFBFCqG0hbITihKp0f7XNZKcxqaGDheHDgig0PApEdxgs8/XXXz/11FN79uwRCoU//fQTufCXX37p1KlTcHCwB8tDCKEW0FDYKEuT66tNACBI8JVOkrD4DG8XhVoL10GYnJysUCiKiooiIyM5nBvXk6ampj777LMerA0hhB6WWWMt2VNF9kI5QSxpipgfz/N2Uah1cT2H+tdff11TU9O5c2dHCgJAaGhoZmampwpDCKGHQtgJ+R91eSsLlLlqKpMaMULU+70YTEF0O9dB+PHHH98+OrS0tBQvIkQItQkNssZzn8uKflPYjHZBgm/i+7ERI0RUOp4RRC7cx+wJGo2GHDWDEEKtlllrLcmoUuapgQC2kCmdKA7ogl9c6G5uCcIzZ84cOXIEABobG7dt23b8+HHHQxaLZefOnV27dvV0gQgh1EwEKPPURb8rrI02KoMaNkQYNjQIjwLRPd0ShDk5OY7m5zfffOP8EIvF6tat25o1a5r5vFartaCgwG63x8bGOs/lTRDE5cuXASAhIYFCwQ8oQqhl6MoNsjS5tswAAIIE3+gUMVvA9HZRqG24JQjnz58/f/58AAgJCUlPT+/fv/+DPenBgweff/75gIAAFotVW1u7ffv2J554AgB0Ot3IkSPr6uooFIpAIDhw4IBjXm+EEHowVr2tLFMpz6kDAlh8RqcJYmFPP28XhdoS14NlTp069cgjjzzwk4aFhZ08efLatWsXLlyYO3fuG2+8QS7/5ptvGAzGpUuXLl68yGQy161b98C7QAghIECZq85bUSA/XkehUiTJgY+8H4spiO6X6yCMjIxks9kP/KQJCQlSqZS83b9//+rqavL2jh07pk2bRqPRaDTatGnTduzY8cC7QAh1cLpK499fFRVsr7A02vix3N7vxkRPFNNYrr/TELqLm63R7du3z549e9myZfPmzYuPj1cqlS43qK+vv68dbNiw4amnniJvl5WVderUibwdHR1dVlZ2p630en1NTc3hw4fJuzQabeDAgTQa7b52jRBql6wGW9kBpeKEirATTD961NgQURLf20WhNuxmEMbHx7/xxhu9e/cGgJdeekmr1T78s69Zs+bUqVN//fUXeddgMDgGzrDZ7LvM311eXn769GlHUlKp1PDw8JCQkIcvCSHUhhGg+lsnz6y3NtooNErQo37iYQFUJkWn03m7MuQhJpOJQqEwmc0dCcVms+n0e1woePPhxMTExMRE8vaiRYserERn33777Zo1a7KzswMDA8klwcHBKpWKvF1XV3eXYIuPj09ISFi6dOnDl4EQah8a5UZZmlxTrAcAfylXmirxCWHdcyvUzjAYjPsKwua4jwvq78vmzZs/+eSTI0eOREZGOhYmJSWdOHFi1KhRAHDixIk+ffq4ae8IofbEZraXH6ypPFZ7sxeayAe8/Aq1kDsGYUlJyd69e+Vyuc1mc16+cuXKez5pZmbmjBkz5s2bl5WVlZWVBQAvv/wyg8F48803R48e3aVLFwqFsnbt2r179z78C0AItW+qfK0sTW5SW8hxoZGjgmlsHBGDWpLrINywYcObb75pNpv9/PyaDFFpThDyeLx3330XAIqKisgldrsdAPr3779jx45NmzYBwC+//PLA1ykihDoCQ41JlqZQF+gAwK+TjzRVwpU8+Gh2hO6EQhBEk0UEQQiFwj59+mzevNlb41OWLVtGo9HwHCFCHZPdbK84Wlt+uIawEXQfWsSTIklyIPZCEdz/YJnmcHFEWFNTo1KpPvzwQxyliRDyPFW+VpYuN9VbgAKiJH6nCWIGFy+dQm7kIgj5fD6Px7vLtQ0IIeQOxlqzbJei/ooWAHhhHGmqxDeSc8+tEHpILoKQyWS+9957q1at6t+//8PML4MQQs1kt9grjtRWZNXYrQSdQ4sYIRIPEFCo2AxFnuB6sAyVSr148WJ8fPyQIUOCg4OdH2rOYBmEEGo+Vb62aJfCqDLf6IWOD2Hw3HVlF0K3c/1p++GHHwwGAwD8/vvvTR7CIEQItRRjnblol0J1WQsA3FC2NFXiF+Xj7aJQh+M6CK9du+bhOhBCHQphIxQnVKX7qm1mO/ZCkXdh/wEh5Gnq641F6XJ9tQkAhD39pSlihi9+FyGvcf3hKy0tbTKhjEN0dLQ760EItWfmBkvJ3mplrhoAOCKWNEXMj8Nf50Ze5joI+/Xr5/gRwSZuvwAfIYTu6UYvdH+1zWSnMamhg4Xhw4IoNOyFIu9zHYQbN240Go2OuxqNJjs7OyMj45NPPvFUYQih9qNB1ihLk+urTAAgSPCVpkpYAQxvF4XQDa6DcNy4cU2WvPLKKytWrPjll19mzpzp/qoQQu2EWWMt2VOlzFMDAZwgZvRESUBn7IWi1uU+TlA/99xzixYtKioqwtOECKF7IuyEIkdVeqDaZrRTmdSwwcKwoUFUOvZCUatzH0Go0WgAQK/Xu60YhFA7oSlqlKUpGhVGABAk+EaniNmClpwlGaEW1KxRo1arVSaTLV261N/fPy4uzlO1IYTaHqveVpaplOfUAQHsQKY0RRzQxdfbRSF0N/cxalQsFv/www8t++MXCKH2gwBlnrrod4W10UZlUMOGYC8UtQ3NGjVKp9NDQ0N79OiBc3AjhFzSVRhkO+XaMgMA8GN50lQxR8TydlEINUtzR40ihJBLVoOt7IBScUJF2AmmPyNqTLAoie/tohC6DzitEULoQRGgzFMX766y6KwUGkWSHBg5OpjGonq7LITuz82PbFZW1qJFi5qzzcSJE+VyudtKQgi1AY2Vxr/XFhVsr7DorP4x3N7vxkRPFGMKorbo5qe2rKwsJyenOdvs3r1bp9O5rSSEUKtmNdiKdinOfyHTluiZfvS4qWHdZ3XyCcYzgqituqU1ev78+X79+t1zG7vd7rZ6EEKtGNkLzaiyaK0UKvZCUTtxMwijoqKGDRvWnG0mTpzo64sXBiHUsRiUJlm6Ql2gAwB/KVeaIvYR4zBy1B7cDMLBgwcPHjzYi6UghFonm9leebS2/HANYSOYvvSocSGiRD7g9YGovcBRowihu1Hla2VpcpPaAhQIeUwQNS6YzqZ5uyiEWhIGIULINUONuWiXvP6qDgB44ZyYVAkvguPtohBqeRiECKGm7GZ7xdHaiqwau5Wg+9AinhRJkgOxF4raKwxChNAtVPlaWbrcVG8BCoiS+J0miBlc7IWi9gyDECF0g7HOLEtX1F/RAgAvjCNNFftG+ni7KITczvUFQBkZGXV1dU0W1tXV/frrr+4vCSHkaXaLvSxTefbT6/VXtHQOLfopcc950ZiCqINwfUT46quvpqen9+/f33lhQUHBM888QxCERwpDCHmI6rK2KF1hVJlv9ELHhzB42CtCHch9fNz1er2PD/6FiFD7YVJbSvdVK3PVAMCVsKWpEr9O+H8cdTi3BGFBQcHff/8NAEaj8ciRI5WVlY6H9Hr95s2b8efpEWofCBuhOKEq3V9tM9npbFrESJF4gIBCxYGhqCO6JQj37t379ttvk7f/9a9/NVk1ODh48+bNnikLIeQ+DYWNsjS5vtoEAIIEX+kkCYvP8HZRCHnNLUE4ffr0CRMmAEC/fv2++eabRx55xPEQl8sNDg72dHUIoRZl1lhL9lSRvVBOEEuaKubH8bxdFEJedksQ+vv7+/v7A0BWVlZ0dDSPh/9DEGonCDuhyLnRC6UyqWGDheHDgig07IUidIfBMj169PBwHQgh92mQNcrSFPoqI5C90FQJKwB7oQjd4DoINRrNqlWrfvvtN4VC0eR6CZVK5ZHCEEItwKy1lmRUKfPUQABbyJSmSAI6Y6cHoVu4DsKpU6ceOHBg3LhxKSkpXC7XwzUhhB4e2QstO6C0Gm1UBjVsiDBsaBCVjr1QhJpyEYQmkykzM/M///nP3LlzPV8QQujh6coNhWlyXZkBAAQJvtEpYraA6e2iEGqlXAShRqOxWq3JycmerwYh9JCseltZplKeUwcEsAOZ0RPFggRfbxeFUKvmIgiDgoK6du169uzZ3r17e74ghNADIkCZpy7+XWFptFFoFHF/QeSYYBrT9XzCCCEH1+cIt2zZ8vzzz/P5/BEjRuBFFAi1froKgyxNoS3VAwA/litNlXBELG8XhVDb4DoIx4wZU11dPWnSpNsfwkm3EWpVrAZb2QGl4oSKsBNMf0bUmGBREt/bRSHUlrgOwiVLljQ2Nnq4FITQ/SF7oburLDorhUaRJAdGjg6msbAXitD9cR2Ec+bM8XAdCKH70ig3ynbKNSV6APCP4UpTJD4h2AtF6EHc42eYGhoaGhoaIiIiPFMNQuierEZb2f5/eqF+9KixIaJEPuD1gQg9KNdBSBDEV199tXr16vLy8tDQ0IqKCgB4//33CYJYtWqVZytECN2kytfK0uQmtYVCpUiSAyNHBdPY2AtF6KG4/i/02WefvfPOOyNGjFi4cKFjYd++fTds2GCxWDxVG0LoJoPSdGl9yeVNpSa1xS+a2+sdafREMaYgQg/Pxf8im8326aeffvDBBxs3bhwxYoRjeVJSUkNDA3l0iBDyGLvZXpapPPtZobpAR+fSYp6W9JjdiStme7suhNoJF61RpVKpUqkmTpzYZHlgYCAA1NbWdurUyROlIYTIXmi63FRvAQqIkvjRE8R0Ls3bRSHUrrgIQh8fHwqFUldX12T5tWvXACAoKMgTdSHU4RlrzbJ0ef1VHQDwwjjSSRLfCI63i0KoHXIRhP7+/n369Fm5cuWjjz5KodwYi2Y0GpcsWdK5c+eoqCiPFohQx2O32CuO1FZk1ditBJ1DixghkiQH4rhQhNzE9ajRL774YujQoT179uzWrZtOp3vnnXd2795dXFy8Z88eD9eHUEejytcW7VIYVWayF9ppfAiDd4/LnBBCD8P1kLP+/fufOHEiKioqIyOjoaHhyy+/FIlEhw8fHjlypIfrQ6jjMNaZL39XenlTqVFl5oWye74ZHTc1DFMQIXe74/+xRx55ZP/+/WazWavV+vj4cDh4cgIhdyFsRGV2bdkBpaMXKh4goFCxGYqQJ9zjj00mk0kOFkUIuYn6uk6WpjAoTTd6oeNCGL54FIiQ59zx/9vFixd3794tl8utVqvz8m+//db9VSHUIZgbLCV7q5W5agDgStjSVIlfJx9vF4VQh+M6CNeuXfvWW28xmczg4GA6Hf84RaiFETZCcUJVur/aZrLTmNTQwcLwYUEUGvZCEfICFyFns9kWLFjw3HPPrVu3ztfX1/M1IdS+NRQ2ytLk+moTAAgSfKWTJCw+w9tFIdRxuQjCuro6vV7/1ltvYQoi1LLMGmvJniqyF8oJYkpTJPx4nreLQqijcxGEQqEwLCysvLw8KSnJ8wUh1C4RdkKRoyo9UG0z2qlMathgYdjQICode6EIeZ+LIKRSqWvXrl24cGF0dHTPnj09XxNC7YymqFGWpmhUGIHshaZKWAHYC0WotXA9EGb06NHp6em9evUSiUQ83i2tG5lM5pHCEGoPzFprSUaVMk8NBLADmdIUcUAXPOOAUOviOghfffXVH374ISkpKT4+nsvlergmhNoDApR56qLfFdZGG5VBDRuCvVCEWikXQaj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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_investment_per_iteration(df_investment_per_iteration)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A JuMP Model\n",
       "Maximization problem with:\n",
       "Variables: 748\n",
       "Objective function type: AffExpr\n",
       "`AffExpr`-in-`MathOptInterface.EqualTo{Float64}`: 168 constraints\n",
       "`AffExpr`-in-`MathOptInterface.LessThan{Float64}`: 865 constraints\n",
       "`VariableRef`-in-`MathOptInterface.EqualTo{Float64}`: 2 constraints\n",
       "`VariableRef`-in-`MathOptInterface.GreaterThan{Float64}`: 434 constraints\n",
       "`VariableRef`-in-`MathOptInterface.LessThan{Float64}`: 50 constraints\n",
       "`VariableRef`-in-`MathOptInterface.ZeroOne`: 288 constraints\n",
       "Model mode: AUTOMATIC\n",
       "CachingOptimizer state: ATTACHED_OPTIMIZER\n",
       "Solver name: HiGHS\n",
       "Names registered in the model: c_balance, c_csc_max_ens_a, c_csc_max_ens_b, c_csc_max_exc_a, c_csc_max_exc_b, c_csc_max_prod_a, c_csc_max_prod_b, c_csc_min_ens_a, c_csc_min_ens_b, c_csc_min_exc_a, c_csc_min_exc_b, c_csc_min_prod_a, c_csc_min_prod_b, c_dual_ens, c_dual_exc, c_dual_prod, c_max_ens, c_max_exc, c_max_prod, c_min_ens, c_min_exc, c_min_prod, c_uncertainty_budget, v_avai, v_csc_max_ens, v_csc_max_exc, v_csc_max_prod, v_csc_min_ens, v_csc_min_exc, v_csc_min_prod, v_dual_balance, v_dual_max_ens, v_dual_max_exc, v_dual_max_prod, v_dual_min_ens, v_dual_min_exc, v_dual_min_prod, v_ens, v_exc, v_production"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "subproblem = create_and_solve_subproblem(sets, params, v_investment_optimal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_two_stage_investment(first_stage_model, sets, params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_aro_production(subproblem, params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "save_results_benders_first_stage_to_csv(output_folder, first_stage_model)"
   ]
  }
 ],
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   "mimetype": "application/julia",
   "name": "julia",
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