two_stage_stochastic_scheduling.ipynb

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      "source": [
        "references:\n",
        "\n",
        "*   https://coin-or.github.io/pulp/CaseStudies/a_two_stage_production_planning_problem.html\n",
        "*   to read for fun: https://www.quora.com/Why-do-so-many-statisticians-not-want-to-become-data-scientists-Why-are-they-not-interested-in-Big-Data/answer/Adrian-Olszewski-1?ch=10&oid=39581408&share=8169356a&srid=MByz&target_type=answer\n",
        "\n"
      ],
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        "id": "m92rBjKZ9i3W"
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    {
      "cell_type": "code",
      "source": [
        "!pip install pulp"
      ],
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          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Requirement already satisfied: pulp in /usr/local/lib/python3.7/dist-packages (2.6.0)\n"
          ]
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        "id": "ZbjB219rnn4K"
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      "source": [
        "from pulp import *\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "import time"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data=pd.read_excel('/content/stochastic_data.xlsx',sheet_name='d10')"
      ],
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              "   production_capacity_P1  production_capacity_P2  storage_capacity  \\\n",
              "0                     400                     400             800.0   \n",
              "1                     400                     400               NaN   \n",
              "2                     400                     400               NaN   \n",
              "3                     400                     400               NaN   \n",
              "4                     400                     400               NaN   \n",
              "5                     400                     400               NaN   \n",
              "6                     400                     400               NaN   \n",
              "7                     400                     400               NaN   \n",
              "8                     400                     400               NaN   \n",
              "9                     400                     400               NaN   \n",
              "\n",
              "   initial_inventory_P1  initial_inventory_P2  holding_cost  final_value_P1  \\\n",
              "0                   0.0                   0.0         100.0            41.0   \n",
              "1                   NaN                   NaN           NaN             NaN   \n",
              "2                   NaN                   NaN           NaN             NaN   \n",
              "3                   NaN                   NaN           NaN             NaN   \n",
              "4                   NaN                   NaN           NaN             NaN   \n",
              "5                   NaN                   NaN           NaN             NaN   \n",
              "6                   NaN                   NaN           NaN             NaN   \n",
              "7                   NaN                   NaN           NaN             NaN   \n",
              "8                   NaN                   NaN           NaN             NaN   \n",
              "9                   NaN                   NaN           NaN             NaN   \n",
              "\n",
              "   final_value_P2  demand_P1  demand_P2  loading_pace_V1  loading_pace_V2  \\\n",
              "0            41.0      300.0      300.0            300.0            300.0   \n",
              "1             NaN        NaN        NaN              NaN              NaN   \n",
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              "8             NaN        NaN        NaN              NaN              NaN   \n",
              "9             NaN        NaN        NaN              NaN              NaN   \n",
              "\n",
              "   total_products  penalty_cost_V1  penalty_cost_V2  \n",
              "0             2.0             20.0             20.0  \n",
              "1             NaN              NaN              NaN  \n",
              "2             NaN              NaN              NaN  \n",
              "3             NaN              NaN              NaN  \n",
              "4             NaN              NaN              NaN  \n",
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              "6             NaN              NaN              NaN  \n",
              "7             NaN              NaN              NaN  \n",
              "8             NaN              NaN              NaN  \n",
              "9             NaN              NaN              NaN  "
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      "source": [
        "#parameters\n",
        "nbr_of_periods=int(len(data.production_capacity_P1)) #T\n",
        "nbr_of_products=int(data.total_products[0])\n",
        "nbr_of_vessels=int(data.total_products[0])#1 vessel = 1 product\n",
        "#nbr_of_PLs=1\n",
        "\n",
        "#planning horizon\n",
        "periods=range(nbr_of_periods)\n",
        "\n",
        "#nbr of inventory periods=nbr of production periods+1\n",
        "inventory_periods=range(nbr_of_periods+1)\n",
        "\n",
        "\n",
        "#production capacity\n",
        "products=range(nbr_of_products)\n",
        "production_capacity_P1=list(data.production_capacity_P1)\n",
        "production_capacity_P2=list(data.production_capacity_P2)\n",
        "production_capacity=[production_capacity_P1,production_capacity_P2]\n",
        "\n",
        "#storage\n",
        "storage_capacity_PL=data.storage_capacity[0]\n",
        "initial_inventory=[data.initial_inventory_P1[0], data.initial_inventory_P2[0]]\n",
        "holding_cost=data.holding_cost[0]\n",
        "final_unit_value_remaining_inventory=[data.final_value_P1[0],data.final_value_P2[0]]\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "ChYpTfXgnqGG"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#generate time arrival uniform distribution sample\n",
        "#minimum vessel arrival time???????????????? is 0 possible????????\n",
        "def generate_uniform_ETA(number_of_scenarios,number_of_periods,number_of_vessels,min_ETA):\n",
        "  return np.random.uniform(low=min_ETA,high=number_of_periods,size=(number_of_scenarios,number_of_vessels))\n",
        "\n"
      ],
      "metadata": {
        "id": "sz6sqp2gEfWz"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#example: 10 scenarios, 50 time periods, 5 vessels, min_ETA=1\n",
        "generate_uniform_ETA(10,50,5,1)"
      ],
      "metadata": {
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          "base_uri": "https://localhost:8080/"
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        "id": "-shPvSEqtNOw",
        "outputId": "567d45cb-3fd3-4578-f675-38d9c38b3a43"
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              "array([[28.58005784, 23.7831613 , 26.35744349, 25.37888217, 23.67964877],\n",
              "       [28.37815612, 18.78077033, 44.39607403, 42.77305848,  7.5915763 ],\n",
              "       [30.58504008, 48.88621981, 18.30809919, 21.69790924, 18.29588719],\n",
              "       [ 7.55317138, 44.35176349, 40.67727921, 39.25128104,  4.11903731],\n",
              "       [42.7857418 , 31.6293181 , 39.14285508, 47.59171765, 49.36982377],\n",
              "       [ 3.88339007,  1.55744928, 30.25219254, 24.62273797, 28.61958145],\n",
              "       [19.19528814, 40.42612601, 48.43828305, 30.50810663,  7.66956565],\n",
              "       [29.12175344, 34.58335702, 29.38055597,  2.53422681, 34.22087681],\n",
              "       [ 3.92425888,  8.92709812,  8.81404977, 10.03309858, 30.87347471],\n",
              "       [42.4741834 , 15.09214605, 34.20492442, 12.58040681, 19.30018381]])"
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      "source": [
        "plt.figure()\n",
        "sns.distplot(generate_uniform_ETA(100,50,100,0))#100 scenarios, 50 time periods, 1000 vessels (just an example)\n",
        "plt.show()\n",
        "#the density function of uniform probability distribution U([a,b]) is 1/(b-a)=1/(50-0)\n",
        "#when number of vessels tends to infinity the data distribution converges to the theoretic U([0,50])\n"
      ],
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        "outputId": "2a54908f-f14d-4e42-c705-8c854b885359"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
            "  warnings.warn(msg, FutureWarning)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "we suppose that scenarios are equiprobable, so p_s=1/number_of_scenerios"
      ],
      "metadata": {
        "id": "AnbcLeoMxK8y"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "number_of_scenarios=5\n",
        "scenarios=list(range(number_of_scenarios))\n",
        "number_of_periods=10\n",
        "number_of_vessels=2\n",
        "vessels=range(number_of_vessels)\n",
        "minimum_ETA=1"
      ],
      "metadata": {
        "id": "vulYzVTk5LhY"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "ETA=generate_uniform_ETA(number_of_scenarios,number_of_periods,number_of_vessels,minimum_ETA)#replace nbr_of_periods by max_eta!!!!!!\n",
        "ETA.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "07ZP1aeH4veW",
        "outputId": "45f43bab-1aaf-46d5-9441-073c3d058949"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(5, 2)"
            ]
          },
          "metadata": {},
          "execution_count": 370
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "ETA"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9RxKeTMN5zQM",
        "outputId": "7a373d2c-6042-46bf-9d92-d451a199cf7a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[5.77823476, 9.21107099],\n",
              "       [9.95766835, 8.1990265 ],\n",
              "       [3.35068863, 2.47397795],\n",
              "       [8.04620469, 1.68131117],\n",
              "       [5.09995543, 3.35010185]])"
            ]
          },
          "metadata": {},
          "execution_count": 371
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(int(ETA[0][0]),int(ETA[0][1]) )"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DdEGHVzV53Ye",
        "outputId": "0eb99b71-ac6d-46fa-9fd7-64c53435adee"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "5 9\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "so the vessel can start loading at int(ETA)+1"
      ],
      "metadata": {
        "id": "qK5tVsnK6YNm"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "penalty_cost=[data.penalty_cost_V1[0],data.penalty_cost_V2[0]]\n",
        "nominal_loading_pace=[data.loading_pace_V1[0], data.loading_pace_V2[0]]\n",
        "demand=[[data.demand_P1[0], 0],[0, data.demand_P2[0]]]"
      ],
      "metadata": {
        "id": "gIyGUSLUu1er"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# get the start time\n",
        "st = time.time()\n",
        "#define our optimisation problem\n",
        "\n",
        "prob = LpProblem(\"Fertilizers_production_planning\", LpMinimize)"
      ],
      "metadata": {
        "id": "ilHMx8Pmzjn1"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Decision Variables\n",
        "#production_vars = pulp.LpVariable.dicts(\n",
        "    #\"production\", (scenarios, products), lowBound=0, cat=\"Continuous\"\n",
        "#)\n",
        "U = LpVariable.dicts(\"U\", (scenarios,vessels,periods), cat=\"Binary\")\n",
        "Z = LpVariable.dicts(\"Z\", (scenarios,vessels,periods), cat=\"Binary\")\n",
        "Q = LpVariable.dicts(\"Q\", (scenarios,products,vessels,periods),lowBound=0, cat=\"Continuous\")#\n",
        "#X = LpVariable.dicts(\"X\", (vessels), cat=\"Binary\")\n",
        "\n",
        "I = LpVariable.dicts(\"I\", (scenarios,products,inventory_periods),lowBound=0, cat=\"Continuous\")\n",
        "\n",
        "#do not depend on scenario\n",
        "P = LpVariable.dicts(\"P\", (products,periods),lowBound=0, cat=\"Continuous\")\n",
        "#J = LpVariable.dicts(\"J\", (raw_materials,inventory_periods),lowBound=0, cat=\"Continuous\")\n",
        "Y = LpVariable.dicts(\"Y\", (products,periods), cat=\"Binary\")\n",
        "#W = LpVariable.dicts(\"W\", (products,products,periods), cat=\"Binary\")"
      ],
      "metadata": {
        "id": "chahACaWYOed"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#make clear the formulas!!!!!\n",
        "\n",
        "# Objective Function\n",
        "prob += ( lpSum([lpSum( [1/number_of_scenarios*(penalty_cost[k]*max(t-ETA[s][k],0)+lpSum([holding_cost*demand[i][k]*max(ETA[s][k]-t,0)\n",
        "                              for i in products])) for s in scenarios] )*U[s][k][t]\n",
        "                  for k in vessels for t in periods for s in scenarios] )#finished with penalty loss\n",
        "        +lpSum( [(lpSum([holding_cost*I[s][i][t] for t in range(1,nbr_of_periods+1)])-\n",
        "                  (final_unit_value_remaining_inventory[i]*I[s][i][nbr_of_periods])) for i in products for s in scenarios] )\n",
        "        , \"Total penalty cost\" )\n",
        "\n",
        "#prob += (lpSum([penalty_cost[i][j]*Z[i][j] for i in vessels for j in periods])\n",
        " #       +lpSum( [(holding_cost*I[i][t]) for t in periods for i in products] ), \"Total penalty cost\")\n",
        "\n",
        "\n",
        "\n",
        "#constraints\n",
        "\n",
        "#1\n",
        "for i in products:\n",
        "  for t in range(1,number_of_periods+1):\n",
        "    for s in scenarios:\n",
        "      prob+=(I[s][i][t]==I[s][i][t-1]+P[i][t-1]-lpSum([Q[s][i][k][t-1] for k in vessels]))\n",
        "\n",
        "\n",
        "#3\n",
        "for t in inventory_periods:\n",
        "  for s in scenarios:\n",
        "    prob+=(lpSum([I[s][i][t] for i in products])<=storage_capacity_PL)\n",
        "\n",
        "\n",
        "#4\n",
        "#for t in range(1,nbr_of_periods+1):\n",
        " # for r in raw_materials:\n",
        "  #  prob+=J[r][t]==J[r][t-1]+replinishment_RM[r][t]-lpSum([consumption_RM[r][i]*P[i][t-1] for i in products])\n",
        "\n",
        "#5\n",
        "#for t in inventory_periods:\n",
        " # for r in raw_materials:\n",
        "  #  prob+=J[r][t]<=storage_capacity_RM[r]\n",
        "\n",
        "#6: only one single product can be produced at time t on one production line\n",
        "for t in periods:\n",
        "  prob+=lpSum([Y[i][t] for i in products])<=1\n",
        "\n",
        "#7\n",
        "for i in products:\n",
        "  for t in periods:\n",
        "    prob+=P[i][t]<=production_capacity[i][t]*Y[i][t]\n",
        "\n",
        "#8\n",
        "#for i in products:\n",
        " # for t in periods:\n",
        "  #  prob+=P[i][t]<=production_capacity[i][t]-lpSum([changeover_amount_of_capacity[i][j]*W[i][j][t] for j in products])\n",
        "\n",
        "#9\n",
        "#for i in products:\n",
        " # for j in products:\n",
        "  #  for t in range(1,nbr_of_periods):\n",
        "   #   prob+=W[i][j][t]>=Y[i][t-1]+Y[j][t]-1\n",
        "\n",
        "#10\n",
        "#for i in products:\n",
        " # for j in products:\n",
        "  #  for t in range(1,nbr_of_periods):\n",
        "   #   prob+=W[i][j][t]<=Y[i][t-1]\n",
        "\n",
        "#11\n",
        "#for i in products:\n",
        " # for j in products:\n",
        "  #  for t in periods:\n",
        "   #   prob+=W[i][j][t]<=Y[j][t]\n",
        "\n",
        "\n",
        "#12: the loaded quantity is constrained by the loading pace\n",
        "for i in products:\n",
        "  for k in vessels:\n",
        "    for t in periods:\n",
        "      for s in scenarios:\n",
        "        prob+=Q[s][i][k][t]<=nominal_loading_pace[k]*Z[s][k][t]\n",
        "\n",
        "\n",
        "\n",
        "#13: ensures that loaded quantity of product i=demand of i\n",
        "for k in vessels:\n",
        "  for i in products:\n",
        "    for s in scenarios:\n",
        "      prob+=lpSum([Q[s][i][k][t] for t in periods])==demand[i][k]\n",
        "\n",
        "\n",
        "#14: after i removed this constraint the problem of loading interruption was resolved\n",
        "#for i in products:\n",
        " # for k in vessels:\n",
        "  #  for t in periods:\n",
        "   #   prob+=Q[i][k][t]<=nominal_loading_pace[k]*X[k]#because vessel 0 load P0, V1 loads P1,...(one product = one vessel)\n",
        "\n",
        "#15\n",
        "#for k in vessels:\n",
        " # prob+=(X[k]==1)\n",
        "\n",
        "#16: no vessel can load before arrival time\n",
        "#depends on s??????????????????????????????????????????\n",
        "#for k in vessels:\n",
        " # for t in range(ETA[k]):\n",
        "  #  prob+=Z[k][t]==0\n",
        "   # prob+=lpSum([Q[i][k][t] for i in products])==0\n",
        "\n",
        "#17: every vessel starts loading at ETA+1\n",
        "#for k in vessels:\n",
        " # prob+=Z[k][ETA[k]]==1\n",
        "\n",
        "#18: initial product inventory\n",
        "for i in products:\n",
        "  for s in scenarios:\n",
        "    prob+=I[s][i][0]==initial_inventory[i]\n",
        "\n",
        "\n",
        "\n",
        "#19: initial raw material inventory\n",
        "#for r in raw_materials:\n",
        " # prob+=J[r][0]==replinishment_RM[r][0]\n",
        "\n",
        "#20: constraint added to prevent W_iit=1\n",
        "#for i in products:\n",
        " # for t in periods:\n",
        "  #  prob+=W[i][i][t]==0\n",
        "\n",
        "\n",
        "#23\n",
        "for k in vessels:\n",
        "  for t in periods:\n",
        "    for s in scenarios:\n",
        "      prob+=U[s][k][t]<=Z[s][k][t]\n",
        "\n",
        "\n",
        "\n",
        "#24\n",
        "for k in vessels:\n",
        "  for s in scenarios:\n",
        "    prob+=lpSum([U[s][k][t] for t in periods])==1\n",
        "\n",
        "\n",
        "#25\n",
        "for k in vessels:\n",
        "  for t in range(1,number_of_periods):\n",
        "    for s in scenarios:\n",
        "      prob+=(Z[s][k][t]-Z[s][k][t-1]<=U[s][k][t])\n",
        "\n",
        "\n",
        "\n",
        "#26 in overleaf\n",
        "for k in vessels:\n",
        "  for t in range(1,nbr_of_periods):\n",
        "    for s in scenarios:\n",
        "      prob+=(Z[s][k][t]<=lpSum([U[s][k][n] for n in range(t+1)]))\n",
        "\n",
        "\n",
        "\n",
        "#27 commented in overleaf\n",
        "for k in vessels:\n",
        "  for t in range(1,nbr_of_periods):\n",
        "    for s in scenarios:\n",
        "      prob+=(lpSum([Z[s][k][n] for n in range(t)])+U[s][k][t]<=1)\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "Q7rD7yN1z02O"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "status = prob.solve()\n",
        "print(LpStatus[status])\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dQhYj379CeXC",
        "outputId": "355d0877-e3da-4af0-dcc4-c88a38076fe3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Optimal\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# get the end time\n",
        "et = time.time()\n",
        "\n",
        "# get the execution time\n",
        "elapsed_time = et - st\n",
        "print('Execution time:', elapsed_time, 'seconds')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bmkrBlYcUU-U",
        "outputId": "f32912d8-52c2-4916-f5b2-b1cb2ca7a957"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Execution time: 0.5083715915679932 seconds\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for v in prob.variables():\n",
        "  print(v.name, \"=\", v.varValue)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aH2QmfXJCkZO",
        "outputId": "d14ee88a-f450-4f07-a3fe-b892d5f5a037"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "I_0_0_0 = 0.0\n",
            "I_0_0_1 = 0.0\n",
            "I_0_0_10 = 0.0\n",
            "I_0_0_2 = 0.0\n",
            "I_0_0_3 = 0.0\n",
            "I_0_0_4 = 0.0\n",
            "I_0_0_5 = 0.0\n",
            "I_0_0_6 = 0.0\n",
            "I_0_0_7 = 0.0\n",
            "I_0_0_8 = 0.0\n",
            "I_0_0_9 = 0.0\n",
            "I_0_1_0 = 0.0\n",
            "I_0_1_1 = 0.0\n",
            "I_0_1_10 = 0.0\n",
            "I_0_1_2 = 0.0\n",
            "I_0_1_3 = 0.0\n",
            "I_0_1_4 = 0.0\n",
            "I_0_1_5 = 0.0\n",
            "I_0_1_6 = 0.0\n",
            "I_0_1_7 = 0.0\n",
            "I_0_1_8 = 0.0\n",
            "I_0_1_9 = 0.0\n",
            "I_1_0_0 = 0.0\n",
            "I_1_0_1 = 0.0\n",
            "I_1_0_10 = 0.0\n",
            "I_1_0_2 = 0.0\n",
            "I_1_0_3 = 0.0\n",
            "I_1_0_4 = 0.0\n",
            "I_1_0_5 = 0.0\n",
            "I_1_0_6 = 0.0\n",
            "I_1_0_7 = 0.0\n",
            "I_1_0_8 = 0.0\n",
            "I_1_0_9 = 0.0\n",
            "I_1_1_0 = 0.0\n",
            "I_1_1_1 = 0.0\n",
            "I_1_1_10 = 0.0\n",
            "I_1_1_2 = 0.0\n",
            "I_1_1_3 = 0.0\n",
            "I_1_1_4 = 0.0\n",
            "I_1_1_5 = 0.0\n",
            "I_1_1_6 = 0.0\n",
            "I_1_1_7 = 0.0\n",
            "I_1_1_8 = 0.0\n",
            "I_1_1_9 = 0.0\n",
            "I_2_0_0 = 0.0\n",
            "I_2_0_1 = 0.0\n",
            "I_2_0_10 = 0.0\n",
            "I_2_0_2 = 0.0\n",
            "I_2_0_3 = 0.0\n",
            "I_2_0_4 = 0.0\n",
            "I_2_0_5 = 0.0\n",
            "I_2_0_6 = 0.0\n",
            "I_2_0_7 = 0.0\n",
            "I_2_0_8 = 0.0\n",
            "I_2_0_9 = 0.0\n",
            "I_2_1_0 = 0.0\n",
            "I_2_1_1 = 0.0\n",
            "I_2_1_10 = 0.0\n",
            "I_2_1_2 = 0.0\n",
            "I_2_1_3 = 0.0\n",
            "I_2_1_4 = 0.0\n",
            "I_2_1_5 = 0.0\n",
            "I_2_1_6 = 0.0\n",
            "I_2_1_7 = 0.0\n",
            "I_2_1_8 = 0.0\n",
            "I_2_1_9 = 0.0\n",
            "I_3_0_0 = 0.0\n",
            "I_3_0_1 = 0.0\n",
            "I_3_0_10 = 0.0\n",
            "I_3_0_2 = 0.0\n",
            "I_3_0_3 = 0.0\n",
            "I_3_0_4 = 0.0\n",
            "I_3_0_5 = 0.0\n",
            "I_3_0_6 = 0.0\n",
            "I_3_0_7 = 0.0\n",
            "I_3_0_8 = 0.0\n",
            "I_3_0_9 = 0.0\n",
            "I_3_1_0 = 0.0\n",
            "I_3_1_1 = 0.0\n",
            "I_3_1_10 = 0.0\n",
            "I_3_1_2 = 0.0\n",
            "I_3_1_3 = 0.0\n",
            "I_3_1_4 = 0.0\n",
            "I_3_1_5 = 0.0\n",
            "I_3_1_6 = 0.0\n",
            "I_3_1_7 = 0.0\n",
            "I_3_1_8 = 0.0\n",
            "I_3_1_9 = 0.0\n",
            "I_4_0_0 = 0.0\n",
            "I_4_0_1 = 0.0\n",
            "I_4_0_10 = 0.0\n",
            "I_4_0_2 = 0.0\n",
            "I_4_0_3 = 0.0\n",
            "I_4_0_4 = 0.0\n",
            "I_4_0_5 = 0.0\n",
            "I_4_0_6 = 0.0\n",
            "I_4_0_7 = 0.0\n",
            "I_4_0_8 = 0.0\n",
            "I_4_0_9 = 0.0\n",
            "I_4_1_0 = 0.0\n",
            "I_4_1_1 = 0.0\n",
            "I_4_1_10 = 0.0\n",
            "I_4_1_2 = 0.0\n",
            "I_4_1_3 = 0.0\n",
            "I_4_1_4 = 0.0\n",
            "I_4_1_5 = 0.0\n",
            "I_4_1_6 = 0.0\n",
            "I_4_1_7 = 0.0\n",
            "I_4_1_8 = 0.0\n",
            "I_4_1_9 = 0.0\n",
            "P_0_0 = 0.0\n",
            "P_0_1 = 0.0\n",
            "P_0_2 = 0.0\n",
            "P_0_3 = 0.0\n",
            "P_0_4 = 0.0\n",
            "P_0_5 = 0.0\n",
            "P_0_6 = 0.0\n",
            "P_0_7 = 0.0\n",
            "P_0_8 = 300.0\n",
            "P_0_9 = 0.0\n",
            "P_1_0 = 0.0\n",
            "P_1_1 = 0.0\n",
            "P_1_2 = 0.0\n",
            "P_1_3 = 0.0\n",
            "P_1_4 = 0.0\n",
            "P_1_5 = 0.0\n",
            "P_1_6 = 0.0\n",
            "P_1_7 = 0.0\n",
            "P_1_8 = 0.0\n",
            "P_1_9 = 300.0\n",
            "Q_0_0_0_0 = 0.0\n",
            "Q_0_0_0_1 = 0.0\n",
            "Q_0_0_0_2 = 0.0\n",
            "Q_0_0_0_3 = 0.0\n",
            "Q_0_0_0_4 = 0.0\n",
            "Q_0_0_0_5 = 0.0\n",
            "Q_0_0_0_6 = 0.0\n",
            "Q_0_0_0_7 = 0.0\n",
            "Q_0_0_0_8 = 300.0\n",
            "Q_0_0_0_9 = 0.0\n",
            "Q_0_0_1_0 = 0.0\n",
            "Q_0_0_1_1 = 0.0\n",
            "Q_0_0_1_2 = 0.0\n",
            "Q_0_0_1_3 = 0.0\n",
            "Q_0_0_1_4 = 0.0\n",
            "Q_0_0_1_5 = 0.0\n",
            "Q_0_0_1_6 = 0.0\n",
            "Q_0_0_1_7 = 0.0\n",
            "Q_0_0_1_8 = 0.0\n",
            "Q_0_0_1_9 = 0.0\n",
            "Q_0_1_0_0 = 0.0\n",
            "Q_0_1_0_1 = 0.0\n",
            "Q_0_1_0_2 = 0.0\n",
            "Q_0_1_0_3 = 0.0\n",
            "Q_0_1_0_4 = 0.0\n",
            "Q_0_1_0_5 = 0.0\n",
            "Q_0_1_0_6 = 0.0\n",
            "Q_0_1_0_7 = 0.0\n",
            "Q_0_1_0_8 = 0.0\n",
            "Q_0_1_0_9 = 0.0\n",
            "Q_0_1_1_0 = 0.0\n",
            "Q_0_1_1_1 = 0.0\n",
            "Q_0_1_1_2 = 0.0\n",
            "Q_0_1_1_3 = 0.0\n",
            "Q_0_1_1_4 = 0.0\n",
            "Q_0_1_1_5 = 0.0\n",
            "Q_0_1_1_6 = 0.0\n",
            "Q_0_1_1_7 = 0.0\n",
            "Q_0_1_1_8 = 0.0\n",
            "Q_0_1_1_9 = 300.0\n",
            "Q_1_0_0_0 = 0.0\n",
            "Q_1_0_0_1 = 0.0\n",
            "Q_1_0_0_2 = 0.0\n",
            "Q_1_0_0_3 = 0.0\n",
            "Q_1_0_0_4 = 0.0\n",
            "Q_1_0_0_5 = 0.0\n",
            "Q_1_0_0_6 = 0.0\n",
            "Q_1_0_0_7 = 0.0\n",
            "Q_1_0_0_8 = 300.0\n",
            "Q_1_0_0_9 = 0.0\n",
            "Q_1_0_1_0 = 0.0\n",
            "Q_1_0_1_1 = 0.0\n",
            "Q_1_0_1_2 = 0.0\n",
            "Q_1_0_1_3 = 0.0\n",
            "Q_1_0_1_4 = 0.0\n",
            "Q_1_0_1_5 = 0.0\n",
            "Q_1_0_1_6 = 0.0\n",
            "Q_1_0_1_7 = 0.0\n",
            "Q_1_0_1_8 = 0.0\n",
            "Q_1_0_1_9 = 0.0\n",
            "Q_1_1_0_0 = 0.0\n",
            "Q_1_1_0_1 = 0.0\n",
            "Q_1_1_0_2 = 0.0\n",
            "Q_1_1_0_3 = 0.0\n",
            "Q_1_1_0_4 = 0.0\n",
            "Q_1_1_0_5 = 0.0\n",
            "Q_1_1_0_6 = 0.0\n",
            "Q_1_1_0_7 = 0.0\n",
            "Q_1_1_0_8 = 0.0\n",
            "Q_1_1_0_9 = 0.0\n",
            "Q_1_1_1_0 = 0.0\n",
            "Q_1_1_1_1 = 0.0\n",
            "Q_1_1_1_2 = 0.0\n",
            "Q_1_1_1_3 = 0.0\n",
            "Q_1_1_1_4 = 0.0\n",
            "Q_1_1_1_5 = 0.0\n",
            "Q_1_1_1_6 = 0.0\n",
            "Q_1_1_1_7 = 0.0\n",
            "Q_1_1_1_8 = 0.0\n",
            "Q_1_1_1_9 = 300.0\n",
            "Q_2_0_0_0 = 0.0\n",
            "Q_2_0_0_1 = 0.0\n",
            "Q_2_0_0_2 = 0.0\n",
            "Q_2_0_0_3 = 0.0\n",
            "Q_2_0_0_4 = 0.0\n",
            "Q_2_0_0_5 = 0.0\n",
            "Q_2_0_0_6 = 0.0\n",
            "Q_2_0_0_7 = 0.0\n",
            "Q_2_0_0_8 = 300.0\n",
            "Q_2_0_0_9 = 0.0\n",
            "Q_2_0_1_0 = 0.0\n",
            "Q_2_0_1_1 = 0.0\n",
            "Q_2_0_1_2 = 0.0\n",
            "Q_2_0_1_3 = 0.0\n",
            "Q_2_0_1_4 = 0.0\n",
            "Q_2_0_1_5 = 0.0\n",
            "Q_2_0_1_6 = 0.0\n",
            "Q_2_0_1_7 = 0.0\n",
            "Q_2_0_1_8 = 0.0\n",
            "Q_2_0_1_9 = 0.0\n",
            "Q_2_1_0_0 = 0.0\n",
            "Q_2_1_0_1 = 0.0\n",
            "Q_2_1_0_2 = 0.0\n",
            "Q_2_1_0_3 = 0.0\n",
            "Q_2_1_0_4 = 0.0\n",
            "Q_2_1_0_5 = 0.0\n",
            "Q_2_1_0_6 = 0.0\n",
            "Q_2_1_0_7 = 0.0\n",
            "Q_2_1_0_8 = 0.0\n",
            "Q_2_1_0_9 = 0.0\n",
            "Q_2_1_1_0 = 0.0\n",
            "Q_2_1_1_1 = 0.0\n",
            "Q_2_1_1_2 = 0.0\n",
            "Q_2_1_1_3 = 0.0\n",
            "Q_2_1_1_4 = 0.0\n",
            "Q_2_1_1_5 = 0.0\n",
            "Q_2_1_1_6 = 0.0\n",
            "Q_2_1_1_7 = 0.0\n",
            "Q_2_1_1_8 = 0.0\n",
            "Q_2_1_1_9 = 300.0\n",
            "Q_3_0_0_0 = 0.0\n",
            "Q_3_0_0_1 = 0.0\n",
            "Q_3_0_0_2 = 0.0\n",
            "Q_3_0_0_3 = 0.0\n",
            "Q_3_0_0_4 = 0.0\n",
            "Q_3_0_0_5 = 0.0\n",
            "Q_3_0_0_6 = 0.0\n",
            "Q_3_0_0_7 = 0.0\n",
            "Q_3_0_0_8 = 300.0\n",
            "Q_3_0_0_9 = 0.0\n",
            "Q_3_0_1_0 = 0.0\n",
            "Q_3_0_1_1 = 0.0\n",
            "Q_3_0_1_2 = 0.0\n",
            "Q_3_0_1_3 = 0.0\n",
            "Q_3_0_1_4 = 0.0\n",
            "Q_3_0_1_5 = 0.0\n",
            "Q_3_0_1_6 = 0.0\n",
            "Q_3_0_1_7 = 0.0\n",
            "Q_3_0_1_8 = 0.0\n",
            "Q_3_0_1_9 = 0.0\n",
            "Q_3_1_0_0 = 0.0\n",
            "Q_3_1_0_1 = 0.0\n",
            "Q_3_1_0_2 = 0.0\n",
            "Q_3_1_0_3 = 0.0\n",
            "Q_3_1_0_4 = 0.0\n",
            "Q_3_1_0_5 = 0.0\n",
            "Q_3_1_0_6 = 0.0\n",
            "Q_3_1_0_7 = 0.0\n",
            "Q_3_1_0_8 = 0.0\n",
            "Q_3_1_0_9 = 0.0\n",
            "Q_3_1_1_0 = 0.0\n",
            "Q_3_1_1_1 = 0.0\n",
            "Q_3_1_1_2 = 0.0\n",
            "Q_3_1_1_3 = 0.0\n",
            "Q_3_1_1_4 = 0.0\n",
            "Q_3_1_1_5 = 0.0\n",
            "Q_3_1_1_6 = 0.0\n",
            "Q_3_1_1_7 = 0.0\n",
            "Q_3_1_1_8 = 0.0\n",
            "Q_3_1_1_9 = 300.0\n",
            "Q_4_0_0_0 = 0.0\n",
            "Q_4_0_0_1 = 0.0\n",
            "Q_4_0_0_2 = 0.0\n",
            "Q_4_0_0_3 = 0.0\n",
            "Q_4_0_0_4 = 0.0\n",
            "Q_4_0_0_5 = 0.0\n",
            "Q_4_0_0_6 = 0.0\n",
            "Q_4_0_0_7 = 0.0\n",
            "Q_4_0_0_8 = 300.0\n",
            "Q_4_0_0_9 = 0.0\n",
            "Q_4_0_1_0 = 0.0\n",
            "Q_4_0_1_1 = 0.0\n",
            "Q_4_0_1_2 = 0.0\n",
            "Q_4_0_1_3 = 0.0\n",
            "Q_4_0_1_4 = 0.0\n",
            "Q_4_0_1_5 = 0.0\n",
            "Q_4_0_1_6 = 0.0\n",
            "Q_4_0_1_7 = 0.0\n",
            "Q_4_0_1_8 = 0.0\n",
            "Q_4_0_1_9 = 0.0\n",
            "Q_4_1_0_0 = 0.0\n",
            "Q_4_1_0_1 = 0.0\n",
            "Q_4_1_0_2 = 0.0\n",
            "Q_4_1_0_3 = 0.0\n",
            "Q_4_1_0_4 = 0.0\n",
            "Q_4_1_0_5 = 0.0\n",
            "Q_4_1_0_6 = 0.0\n",
            "Q_4_1_0_7 = 0.0\n",
            "Q_4_1_0_8 = 0.0\n",
            "Q_4_1_0_9 = 0.0\n",
            "Q_4_1_1_0 = 0.0\n",
            "Q_4_1_1_1 = 0.0\n",
            "Q_4_1_1_2 = 0.0\n",
            "Q_4_1_1_3 = 0.0\n",
            "Q_4_1_1_4 = 0.0\n",
            "Q_4_1_1_5 = 0.0\n",
            "Q_4_1_1_6 = 0.0\n",
            "Q_4_1_1_7 = 0.0\n",
            "Q_4_1_1_8 = 0.0\n",
            "Q_4_1_1_9 = 300.0\n",
            "U_0_0_0 = 0.0\n",
            "U_0_0_1 = 0.0\n",
            "U_0_0_2 = 0.0\n",
            "U_0_0_3 = 0.0\n",
            "U_0_0_4 = 0.0\n",
            "U_0_0_5 = 0.0\n",
            "U_0_0_6 = 0.0\n",
            "U_0_0_7 = 0.0\n",
            "U_0_0_8 = 1.0\n",
            "U_0_0_9 = 0.0\n",
            "U_0_1_0 = 0.0\n",
            "U_0_1_1 = 0.0\n",
            "U_0_1_2 = 0.0\n",
            "U_0_1_3 = 0.0\n",
            "U_0_1_4 = 0.0\n",
            "U_0_1_5 = 0.0\n",
            "U_0_1_6 = 0.0\n",
            "U_0_1_7 = 0.0\n",
            "U_0_1_8 = 0.0\n",
            "U_0_1_9 = 1.0\n",
            "U_1_0_0 = 0.0\n",
            "U_1_0_1 = 0.0\n",
            "U_1_0_2 = 0.0\n",
            "U_1_0_3 = 0.0\n",
            "U_1_0_4 = 0.0\n",
            "U_1_0_5 = 0.0\n",
            "U_1_0_6 = 0.0\n",
            "U_1_0_7 = 0.0\n",
            "U_1_0_8 = 1.0\n",
            "U_1_0_9 = 0.0\n",
            "U_1_1_0 = 0.0\n",
            "U_1_1_1 = 0.0\n",
            "U_1_1_2 = 0.0\n",
            "U_1_1_3 = 0.0\n",
            "U_1_1_4 = 0.0\n",
            "U_1_1_5 = 0.0\n",
            "U_1_1_6 = 0.0\n",
            "U_1_1_7 = 0.0\n",
            "U_1_1_8 = 0.0\n",
            "U_1_1_9 = 1.0\n",
            "U_2_0_0 = 0.0\n",
            "U_2_0_1 = 0.0\n",
            "U_2_0_2 = 0.0\n",
            "U_2_0_3 = 0.0\n",
            "U_2_0_4 = 0.0\n",
            "U_2_0_5 = 0.0\n",
            "U_2_0_6 = 0.0\n",
            "U_2_0_7 = 0.0\n",
            "U_2_0_8 = 1.0\n",
            "U_2_0_9 = 0.0\n",
            "U_2_1_0 = 0.0\n",
            "U_2_1_1 = 0.0\n",
            "U_2_1_2 = 0.0\n",
            "U_2_1_3 = 0.0\n",
            "U_2_1_4 = 0.0\n",
            "U_2_1_5 = 0.0\n",
            "U_2_1_6 = 0.0\n",
            "U_2_1_7 = 0.0\n",
            "U_2_1_8 = 0.0\n",
            "U_2_1_9 = 1.0\n",
            "U_3_0_0 = 0.0\n",
            "U_3_0_1 = 0.0\n",
            "U_3_0_2 = 0.0\n",
            "U_3_0_3 = 0.0\n",
            "U_3_0_4 = 0.0\n",
            "U_3_0_5 = 0.0\n",
            "U_3_0_6 = 0.0\n",
            "U_3_0_7 = 0.0\n",
            "U_3_0_8 = 1.0\n",
            "U_3_0_9 = 0.0\n",
            "U_3_1_0 = 0.0\n",
            "U_3_1_1 = 0.0\n",
            "U_3_1_2 = 0.0\n",
            "U_3_1_3 = 0.0\n",
            "U_3_1_4 = 0.0\n",
            "U_3_1_5 = 0.0\n",
            "U_3_1_6 = 0.0\n",
            "U_3_1_7 = 0.0\n",
            "U_3_1_8 = 0.0\n",
            "U_3_1_9 = 1.0\n",
            "U_4_0_0 = 0.0\n",
            "U_4_0_1 = 0.0\n",
            "U_4_0_2 = 0.0\n",
            "U_4_0_3 = 0.0\n",
            "U_4_0_4 = 0.0\n",
            "U_4_0_5 = 0.0\n",
            "U_4_0_6 = 0.0\n",
            "U_4_0_7 = 0.0\n",
            "U_4_0_8 = 1.0\n",
            "U_4_0_9 = 0.0\n",
            "U_4_1_0 = 0.0\n",
            "U_4_1_1 = 0.0\n",
            "U_4_1_2 = 0.0\n",
            "U_4_1_3 = 0.0\n",
            "U_4_1_4 = 0.0\n",
            "U_4_1_5 = 0.0\n",
            "U_4_1_6 = 0.0\n",
            "U_4_1_7 = 0.0\n",
            "U_4_1_8 = 0.0\n",
            "U_4_1_9 = 1.0\n",
            "Y_0_0 = 0.0\n",
            "Y_0_1 = 0.0\n",
            "Y_0_2 = 0.0\n",
            "Y_0_3 = 1.0\n",
            "Y_0_4 = 0.0\n",
            "Y_0_5 = 0.0\n",
            "Y_0_6 = 0.0\n",
            "Y_0_7 = 0.0\n",
            "Y_0_8 = 1.0\n",
            "Y_0_9 = 0.0\n",
            "Y_1_0 = 0.0\n",
            "Y_1_1 = 0.0\n",
            "Y_1_2 = 0.0\n",
            "Y_1_3 = 0.0\n",
            "Y_1_4 = 0.0\n",
            "Y_1_5 = 0.0\n",
            "Y_1_6 = 0.0\n",
            "Y_1_7 = 0.0\n",
            "Y_1_8 = 0.0\n",
            "Y_1_9 = 1.0\n",
            "Z_0_0_0 = 0.0\n",
            "Z_0_0_1 = 0.0\n",
            "Z_0_0_2 = 0.0\n",
            "Z_0_0_3 = 0.0\n",
            "Z_0_0_4 = 0.0\n",
            "Z_0_0_5 = 0.0\n",
            "Z_0_0_6 = 0.0\n",
            "Z_0_0_7 = 0.0\n",
            "Z_0_0_8 = 1.0\n",
            "Z_0_0_9 = 1.0\n",
            "Z_0_1_0 = 0.0\n",
            "Z_0_1_1 = 0.0\n",
            "Z_0_1_2 = 0.0\n",
            "Z_0_1_3 = 0.0\n",
            "Z_0_1_4 = 0.0\n",
            "Z_0_1_5 = 0.0\n",
            "Z_0_1_6 = 0.0\n",
            "Z_0_1_7 = 0.0\n",
            "Z_0_1_8 = 0.0\n",
            "Z_0_1_9 = 1.0\n",
            "Z_1_0_0 = 0.0\n",
            "Z_1_0_1 = 0.0\n",
            "Z_1_0_2 = 0.0\n",
            "Z_1_0_3 = 0.0\n",
            "Z_1_0_4 = 0.0\n",
            "Z_1_0_5 = 0.0\n",
            "Z_1_0_6 = 0.0\n",
            "Z_1_0_7 = 0.0\n",
            "Z_1_0_8 = 1.0\n",
            "Z_1_0_9 = 1.0\n",
            "Z_1_1_0 = 0.0\n",
            "Z_1_1_1 = 0.0\n",
            "Z_1_1_2 = 0.0\n",
            "Z_1_1_3 = 0.0\n",
            "Z_1_1_4 = 0.0\n",
            "Z_1_1_5 = 0.0\n",
            "Z_1_1_6 = 0.0\n",
            "Z_1_1_7 = 0.0\n",
            "Z_1_1_8 = 0.0\n",
            "Z_1_1_9 = 1.0\n",
            "Z_2_0_0 = 0.0\n",
            "Z_2_0_1 = 0.0\n",
            "Z_2_0_2 = 0.0\n",
            "Z_2_0_3 = 0.0\n",
            "Z_2_0_4 = 0.0\n",
            "Z_2_0_5 = 0.0\n",
            "Z_2_0_6 = 0.0\n",
            "Z_2_0_7 = 0.0\n",
            "Z_2_0_8 = 1.0\n",
            "Z_2_0_9 = 1.0\n",
            "Z_2_1_0 = 0.0\n",
            "Z_2_1_1 = 0.0\n",
            "Z_2_1_2 = 0.0\n",
            "Z_2_1_3 = 0.0\n",
            "Z_2_1_4 = 0.0\n",
            "Z_2_1_5 = 0.0\n",
            "Z_2_1_6 = 0.0\n",
            "Z_2_1_7 = 0.0\n",
            "Z_2_1_8 = 0.0\n",
            "Z_2_1_9 = 1.0\n",
            "Z_3_0_0 = 0.0\n",
            "Z_3_0_1 = 0.0\n",
            "Z_3_0_2 = 0.0\n",
            "Z_3_0_3 = 0.0\n",
            "Z_3_0_4 = 0.0\n",
            "Z_3_0_5 = 0.0\n",
            "Z_3_0_6 = 0.0\n",
            "Z_3_0_7 = 0.0\n",
            "Z_3_0_8 = 1.0\n",
            "Z_3_0_9 = 1.0\n",
            "Z_3_1_0 = 0.0\n",
            "Z_3_1_1 = 0.0\n",
            "Z_3_1_2 = 0.0\n",
            "Z_3_1_3 = 0.0\n",
            "Z_3_1_4 = 0.0\n",
            "Z_3_1_5 = 0.0\n",
            "Z_3_1_6 = 0.0\n",
            "Z_3_1_7 = 0.0\n",
            "Z_3_1_8 = 0.0\n",
            "Z_3_1_9 = 1.0\n",
            "Z_4_0_0 = 0.0\n",
            "Z_4_0_1 = 0.0\n",
            "Z_4_0_2 = 0.0\n",
            "Z_4_0_3 = 0.0\n",
            "Z_4_0_4 = 0.0\n",
            "Z_4_0_5 = 0.0\n",
            "Z_4_0_6 = 0.0\n",
            "Z_4_0_7 = 0.0\n",
            "Z_4_0_8 = 1.0\n",
            "Z_4_0_9 = 1.0\n",
            "Z_4_1_0 = 0.0\n",
            "Z_4_1_1 = 0.0\n",
            "Z_4_1_2 = 0.0\n",
            "Z_4_1_3 = 0.0\n",
            "Z_4_1_4 = 0.0\n",
            "Z_4_1_5 = 0.0\n",
            "Z_4_1_6 = 0.0\n",
            "Z_4_1_7 = 0.0\n",
            "Z_4_1_8 = 0.0\n",
            "Z_4_1_9 = 1.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Total Cost  = \", value(prob.objective))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XTrFzpfv7b9z",
        "outputId": "f286bed0-3817-490f-bf25-a3e4a0ff561a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Total Cost  =  67049.65485373682\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "prob.writeLP(\"fertilizers_prod_planning.lp\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TipnC1BQoNHD",
        "outputId": "7a41e1b4-3d56-4ff1-b6f6-05d4ce137bf8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[I_0_0_0,\n",
              " I_0_0_1,\n",
              " I_0_0_10,\n",
              " I_0_0_2,\n",
              " I_0_0_3,\n",
              " I_0_0_4,\n",
              " I_0_0_5,\n",
              " I_0_0_6,\n",
              " I_0_0_7,\n",
              " I_0_0_8,\n",
              " I_0_0_9,\n",
              " I_0_1_0,\n",
              " I_0_1_1,\n",
              " I_0_1_10,\n",
              " I_0_1_2,\n",
              " I_0_1_3,\n",
              " I_0_1_4,\n",
              " I_0_1_5,\n",
              " I_0_1_6,\n",
              " I_0_1_7,\n",
              " I_0_1_8,\n",
              " I_0_1_9,\n",
              " I_1_0_0,\n",
              " I_1_0_1,\n",
              " I_1_0_10,\n",
              " I_1_0_2,\n",
              " I_1_0_3,\n",
              " I_1_0_4,\n",
              " I_1_0_5,\n",
              " I_1_0_6,\n",
              " I_1_0_7,\n",
              " I_1_0_8,\n",
              " I_1_0_9,\n",
              " I_1_1_0,\n",
              " I_1_1_1,\n",
              " I_1_1_10,\n",
              " I_1_1_2,\n",
              " I_1_1_3,\n",
              " I_1_1_4,\n",
              " I_1_1_5,\n",
              " I_1_1_6,\n",
              " I_1_1_7,\n",
              " I_1_1_8,\n",
              " I_1_1_9,\n",
              " I_2_0_0,\n",
              " I_2_0_1,\n",
              " I_2_0_10,\n",
              " I_2_0_2,\n",
              " I_2_0_3,\n",
              " I_2_0_4,\n",
              " I_2_0_5,\n",
              " I_2_0_6,\n",
              " I_2_0_7,\n",
              " I_2_0_8,\n",
              " I_2_0_9,\n",
              " I_2_1_0,\n",
              " I_2_1_1,\n",
              " I_2_1_10,\n",
              " I_2_1_2,\n",
              " I_2_1_3,\n",
              " I_2_1_4,\n",
              " I_2_1_5,\n",
              " I_2_1_6,\n",
              " I_2_1_7,\n",
              " I_2_1_8,\n",
              " I_2_1_9,\n",
              " I_3_0_0,\n",
              " I_3_0_1,\n",
              " I_3_0_10,\n",
              " I_3_0_2,\n",
              " I_3_0_3,\n",
              " I_3_0_4,\n",
              " I_3_0_5,\n",
              " I_3_0_6,\n",
              " I_3_0_7,\n",
              " I_3_0_8,\n",
              " I_3_0_9,\n",
              " I_3_1_0,\n",
              " I_3_1_1,\n",
              " I_3_1_10,\n",
              " I_3_1_2,\n",
              " I_3_1_3,\n",
              " I_3_1_4,\n",
              " I_3_1_5,\n",
              " I_3_1_6,\n",
              " I_3_1_7,\n",
              " I_3_1_8,\n",
              " I_3_1_9,\n",
              " I_4_0_0,\n",
              " I_4_0_1,\n",
              " I_4_0_10,\n",
              " I_4_0_2,\n",
              " I_4_0_3,\n",
              " I_4_0_4,\n",
              " I_4_0_5,\n",
              " I_4_0_6,\n",
              " I_4_0_7,\n",
              " I_4_0_8,\n",
              " I_4_0_9,\n",
              " I_4_1_0,\n",
              " I_4_1_1,\n",
              " I_4_1_10,\n",
              " I_4_1_2,\n",
              " I_4_1_3,\n",
              " I_4_1_4,\n",
              " I_4_1_5,\n",
              " I_4_1_6,\n",
              " I_4_1_7,\n",
              " I_4_1_8,\n",
              " I_4_1_9,\n",
              " P_0_0,\n",
              " P_0_1,\n",
              " P_0_2,\n",
              " P_0_3,\n",
              " P_0_4,\n",
              " P_0_5,\n",
              " P_0_6,\n",
              " P_0_7,\n",
              " P_0_8,\n",
              " P_0_9,\n",
              " P_1_0,\n",
              " P_1_1,\n",
              " P_1_2,\n",
              " P_1_3,\n",
              " P_1_4,\n",
              " P_1_5,\n",
              " P_1_6,\n",
              " P_1_7,\n",
              " P_1_8,\n",
              " P_1_9,\n",
              " Q_0_0_0_0,\n",
              " Q_0_0_0_1,\n",
              " Q_0_0_0_2,\n",
              " Q_0_0_0_3,\n",
              " Q_0_0_0_4,\n",
              " Q_0_0_0_5,\n",
              " Q_0_0_0_6,\n",
              " Q_0_0_0_7,\n",
              " Q_0_0_0_8,\n",
              " Q_0_0_0_9,\n",
              " Q_0_0_1_0,\n",
              " Q_0_0_1_1,\n",
              " Q_0_0_1_2,\n",
              " Q_0_0_1_3,\n",
              " Q_0_0_1_4,\n",
              " Q_0_0_1_5,\n",
              " Q_0_0_1_6,\n",
              " Q_0_0_1_7,\n",
              " Q_0_0_1_8,\n",
              " Q_0_0_1_9,\n",
              " Q_0_1_0_0,\n",
              " Q_0_1_0_1,\n",
              " Q_0_1_0_2,\n",
              " Q_0_1_0_3,\n",
              " Q_0_1_0_4,\n",
              " Q_0_1_0_5,\n",
              " Q_0_1_0_6,\n",
              " Q_0_1_0_7,\n",
              " Q_0_1_0_8,\n",
              " Q_0_1_0_9,\n",
              " Q_0_1_1_0,\n",
              " Q_0_1_1_1,\n",
              " Q_0_1_1_2,\n",
              " Q_0_1_1_3,\n",
              " Q_0_1_1_4,\n",
              " Q_0_1_1_5,\n",
              " Q_0_1_1_6,\n",
              " Q_0_1_1_7,\n",
              " Q_0_1_1_8,\n",
              " Q_0_1_1_9,\n",
              " Q_1_0_0_0,\n",
              " Q_1_0_0_1,\n",
              " Q_1_0_0_2,\n",
              " Q_1_0_0_3,\n",
              " Q_1_0_0_4,\n",
              " Q_1_0_0_5,\n",
              " Q_1_0_0_6,\n",
              " Q_1_0_0_7,\n",
              " Q_1_0_0_8,\n",
              " Q_1_0_0_9,\n",
              " Q_1_0_1_0,\n",
              " Q_1_0_1_1,\n",
              " Q_1_0_1_2,\n",
              " Q_1_0_1_3,\n",
              " Q_1_0_1_4,\n",
              " Q_1_0_1_5,\n",
              " Q_1_0_1_6,\n",
              " Q_1_0_1_7,\n",
              " Q_1_0_1_8,\n",
              " Q_1_0_1_9,\n",
              " Q_1_1_0_0,\n",
              " Q_1_1_0_1,\n",
              " Q_1_1_0_2,\n",
              " Q_1_1_0_3,\n",
              " Q_1_1_0_4,\n",
              " Q_1_1_0_5,\n",
              " Q_1_1_0_6,\n",
              " Q_1_1_0_7,\n",
              " Q_1_1_0_8,\n",
              " Q_1_1_0_9,\n",
              " Q_1_1_1_0,\n",
              " Q_1_1_1_1,\n",
              " Q_1_1_1_2,\n",
              " Q_1_1_1_3,\n",
              " Q_1_1_1_4,\n",
              " Q_1_1_1_5,\n",
              " Q_1_1_1_6,\n",
              " Q_1_1_1_7,\n",
              " Q_1_1_1_8,\n",
              " Q_1_1_1_9,\n",
              " Q_2_0_0_0,\n",
              " Q_2_0_0_1,\n",
              " Q_2_0_0_2,\n",
              " Q_2_0_0_3,\n",
              " Q_2_0_0_4,\n",
              " Q_2_0_0_5,\n",
              " Q_2_0_0_6,\n",
              " Q_2_0_0_7,\n",
              " Q_2_0_0_8,\n",
              " Q_2_0_0_9,\n",
              " Q_2_0_1_0,\n",
              " Q_2_0_1_1,\n",
              " Q_2_0_1_2,\n",
              " Q_2_0_1_3,\n",
              " Q_2_0_1_4,\n",
              " Q_2_0_1_5,\n",
              " Q_2_0_1_6,\n",
              " Q_2_0_1_7,\n",
              " Q_2_0_1_8,\n",
              " Q_2_0_1_9,\n",
              " Q_2_1_0_0,\n",
              " Q_2_1_0_1,\n",
              " Q_2_1_0_2,\n",
              " Q_2_1_0_3,\n",
              " Q_2_1_0_4,\n",
              " Q_2_1_0_5,\n",
              " Q_2_1_0_6,\n",
              " Q_2_1_0_7,\n",
              " Q_2_1_0_8,\n",
              " Q_2_1_0_9,\n",
              " Q_2_1_1_0,\n",
              " Q_2_1_1_1,\n",
              " Q_2_1_1_2,\n",
              " Q_2_1_1_3,\n",
              " Q_2_1_1_4,\n",
              " Q_2_1_1_5,\n",
              " Q_2_1_1_6,\n",
              " Q_2_1_1_7,\n",
              " Q_2_1_1_8,\n",
              " Q_2_1_1_9,\n",
              " Q_3_0_0_0,\n",
              " Q_3_0_0_1,\n",
              " Q_3_0_0_2,\n",
              " Q_3_0_0_3,\n",
              " Q_3_0_0_4,\n",
              " Q_3_0_0_5,\n",
              " Q_3_0_0_6,\n",
              " Q_3_0_0_7,\n",
              " Q_3_0_0_8,\n",
              " Q_3_0_0_9,\n",
              " Q_3_0_1_0,\n",
              " Q_3_0_1_1,\n",
              " Q_3_0_1_2,\n",
              " Q_3_0_1_3,\n",
              " Q_3_0_1_4,\n",
              " Q_3_0_1_5,\n",
              " Q_3_0_1_6,\n",
              " Q_3_0_1_7,\n",
              " Q_3_0_1_8,\n",
              " Q_3_0_1_9,\n",
              " Q_3_1_0_0,\n",
              " Q_3_1_0_1,\n",
              " Q_3_1_0_2,\n",
              " Q_3_1_0_3,\n",
              " Q_3_1_0_4,\n",
              " Q_3_1_0_5,\n",
              " Q_3_1_0_6,\n",
              " Q_3_1_0_7,\n",
              " Q_3_1_0_8,\n",
              " Q_3_1_0_9,\n",
              " Q_3_1_1_0,\n",
              " Q_3_1_1_1,\n",
              " Q_3_1_1_2,\n",
              " Q_3_1_1_3,\n",
              " Q_3_1_1_4,\n",
              " Q_3_1_1_5,\n",
              " Q_3_1_1_6,\n",
              " Q_3_1_1_7,\n",
              " Q_3_1_1_8,\n",
              " Q_3_1_1_9,\n",
              " Q_4_0_0_0,\n",
              " Q_4_0_0_1,\n",
              " Q_4_0_0_2,\n",
              " Q_4_0_0_3,\n",
              " Q_4_0_0_4,\n",
              " Q_4_0_0_5,\n",
              " Q_4_0_0_6,\n",
              " Q_4_0_0_7,\n",
              " Q_4_0_0_8,\n",
              " Q_4_0_0_9,\n",
              " Q_4_0_1_0,\n",
              " Q_4_0_1_1,\n",
              " Q_4_0_1_2,\n",
              " Q_4_0_1_3,\n",
              " Q_4_0_1_4,\n",
              " Q_4_0_1_5,\n",
              " Q_4_0_1_6,\n",
              " Q_4_0_1_7,\n",
              " Q_4_0_1_8,\n",
              " Q_4_0_1_9,\n",
              " Q_4_1_0_0,\n",
              " Q_4_1_0_1,\n",
              " Q_4_1_0_2,\n",
              " Q_4_1_0_3,\n",
              " Q_4_1_0_4,\n",
              " Q_4_1_0_5,\n",
              " Q_4_1_0_6,\n",
              " Q_4_1_0_7,\n",
              " Q_4_1_0_8,\n",
              " Q_4_1_0_9,\n",
              " Q_4_1_1_0,\n",
              " Q_4_1_1_1,\n",
              " Q_4_1_1_2,\n",
              " Q_4_1_1_3,\n",
              " Q_4_1_1_4,\n",
              " Q_4_1_1_5,\n",
              " Q_4_1_1_6,\n",
              " Q_4_1_1_7,\n",
              " Q_4_1_1_8,\n",
              " Q_4_1_1_9,\n",
              " U_0_0_0,\n",
              " U_0_0_1,\n",
              " U_0_0_2,\n",
              " U_0_0_3,\n",
              " U_0_0_4,\n",
              " U_0_0_5,\n",
              " U_0_0_6,\n",
              " U_0_0_7,\n",
              " U_0_0_8,\n",
              " U_0_0_9,\n",
              " U_0_1_0,\n",
              " U_0_1_1,\n",
              " U_0_1_2,\n",
              " U_0_1_3,\n",
              " U_0_1_4,\n",
              " U_0_1_5,\n",
              " U_0_1_6,\n",
              " U_0_1_7,\n",
              " U_0_1_8,\n",
              " U_0_1_9,\n",
              " U_1_0_0,\n",
              " U_1_0_1,\n",
              " U_1_0_2,\n",
              " U_1_0_3,\n",
              " U_1_0_4,\n",
              " U_1_0_5,\n",
              " U_1_0_6,\n",
              " U_1_0_7,\n",
              " U_1_0_8,\n",
              " U_1_0_9,\n",
              " U_1_1_0,\n",
              " U_1_1_1,\n",
              " U_1_1_2,\n",
              " U_1_1_3,\n",
              " U_1_1_4,\n",
              " U_1_1_5,\n",
              " U_1_1_6,\n",
              " U_1_1_7,\n",
              " U_1_1_8,\n",
              " U_1_1_9,\n",
              " U_2_0_0,\n",
              " U_2_0_1,\n",
              " U_2_0_2,\n",
              " U_2_0_3,\n",
              " U_2_0_4,\n",
              " U_2_0_5,\n",
              " U_2_0_6,\n",
              " U_2_0_7,\n",
              " U_2_0_8,\n",
              " U_2_0_9,\n",
              " U_2_1_0,\n",
              " U_2_1_1,\n",
              " U_2_1_2,\n",
              " U_2_1_3,\n",
              " U_2_1_4,\n",
              " U_2_1_5,\n",
              " U_2_1_6,\n",
              " U_2_1_7,\n",
              " U_2_1_8,\n",
              " U_2_1_9,\n",
              " U_3_0_0,\n",
              " U_3_0_1,\n",
              " U_3_0_2,\n",
              " U_3_0_3,\n",
              " U_3_0_4,\n",
              " U_3_0_5,\n",
              " U_3_0_6,\n",
              " U_3_0_7,\n",
              " U_3_0_8,\n",
              " U_3_0_9,\n",
              " U_3_1_0,\n",
              " U_3_1_1,\n",
              " U_3_1_2,\n",
              " U_3_1_3,\n",
              " U_3_1_4,\n",
              " U_3_1_5,\n",
              " U_3_1_6,\n",
              " U_3_1_7,\n",
              " U_3_1_8,\n",
              " U_3_1_9,\n",
              " U_4_0_0,\n",
              " U_4_0_1,\n",
              " U_4_0_2,\n",
              " U_4_0_3,\n",
              " U_4_0_4,\n",
              " U_4_0_5,\n",
              " U_4_0_6,\n",
              " U_4_0_7,\n",
              " U_4_0_8,\n",
              " U_4_0_9,\n",
              " U_4_1_0,\n",
              " U_4_1_1,\n",
              " U_4_1_2,\n",
              " U_4_1_3,\n",
              " U_4_1_4,\n",
              " U_4_1_5,\n",
              " U_4_1_6,\n",
              " U_4_1_7,\n",
              " U_4_1_8,\n",
              " U_4_1_9,\n",
              " Y_0_0,\n",
              " Y_0_1,\n",
              " Y_0_2,\n",
              " Y_0_3,\n",
              " Y_0_4,\n",
              " Y_0_5,\n",
              " Y_0_6,\n",
              " Y_0_7,\n",
              " Y_0_8,\n",
              " Y_0_9,\n",
              " Y_1_0,\n",
              " Y_1_1,\n",
              " Y_1_2,\n",
              " Y_1_3,\n",
              " Y_1_4,\n",
              " Y_1_5,\n",
              " Y_1_6,\n",
              " Y_1_7,\n",
              " Y_1_8,\n",
              " Y_1_9,\n",
              " Z_0_0_0,\n",
              " Z_0_0_1,\n",
              " Z_0_0_2,\n",
              " Z_0_0_3,\n",
              " Z_0_0_4,\n",
              " Z_0_0_5,\n",
              " Z_0_0_6,\n",
              " Z_0_0_7,\n",
              " Z_0_0_8,\n",
              " Z_0_0_9,\n",
              " Z_0_1_0,\n",
              " Z_0_1_1,\n",
              " Z_0_1_2,\n",
              " Z_0_1_3,\n",
              " Z_0_1_4,\n",
              " Z_0_1_5,\n",
              " Z_0_1_6,\n",
              " Z_0_1_7,\n",
              " Z_0_1_8,\n",
              " Z_0_1_9,\n",
              " Z_1_0_0,\n",
              " Z_1_0_1,\n",
              " Z_1_0_2,\n",
              " Z_1_0_3,\n",
              " Z_1_0_4,\n",
              " Z_1_0_5,\n",
              " Z_1_0_6,\n",
              " Z_1_0_7,\n",
              " Z_1_0_8,\n",
              " Z_1_0_9,\n",
              " Z_1_1_0,\n",
              " Z_1_1_1,\n",
              " Z_1_1_2,\n",
              " Z_1_1_3,\n",
              " Z_1_1_4,\n",
              " Z_1_1_5,\n",
              " Z_1_1_6,\n",
              " Z_1_1_7,\n",
              " Z_1_1_8,\n",
              " Z_1_1_9,\n",
              " Z_2_0_0,\n",
              " Z_2_0_1,\n",
              " Z_2_0_2,\n",
              " Z_2_0_3,\n",
              " Z_2_0_4,\n",
              " Z_2_0_5,\n",
              " Z_2_0_6,\n",
              " Z_2_0_7,\n",
              " Z_2_0_8,\n",
              " Z_2_0_9,\n",
              " Z_2_1_0,\n",
              " Z_2_1_1,\n",
              " Z_2_1_2,\n",
              " Z_2_1_3,\n",
              " Z_2_1_4,\n",
              " Z_2_1_5,\n",
              " Z_2_1_6,\n",
              " Z_2_1_7,\n",
              " Z_2_1_8,\n",
              " Z_2_1_9,\n",
              " Z_3_0_0,\n",
              " Z_3_0_1,\n",
              " Z_3_0_2,\n",
              " Z_3_0_3,\n",
              " Z_3_0_4,\n",
              " Z_3_0_5,\n",
              " Z_3_0_6,\n",
              " Z_3_0_7,\n",
              " Z_3_0_8,\n",
              " Z_3_0_9,\n",
              " Z_3_1_0,\n",
              " Z_3_1_1,\n",
              " Z_3_1_2,\n",
              " Z_3_1_3,\n",
              " Z_3_1_4,\n",
              " Z_3_1_5,\n",
              " Z_3_1_6,\n",
              " Z_3_1_7,\n",
              " Z_3_1_8,\n",
              " Z_3_1_9,\n",
              " Z_4_0_0,\n",
              " Z_4_0_1,\n",
              " Z_4_0_2,\n",
              " Z_4_0_3,\n",
              " Z_4_0_4,\n",
              " Z_4_0_5,\n",
              " Z_4_0_6,\n",
              " Z_4_0_7,\n",
              " Z_4_0_8,\n",
              " Z_4_0_9,\n",
              " Z_4_1_0,\n",
              " Z_4_1_1,\n",
              " Z_4_1_2,\n",
              " Z_4_1_3,\n",
              " Z_4_1_4,\n",
              " Z_4_1_5,\n",
              " Z_4_1_6,\n",
              " Z_4_1_7,\n",
              " Z_4_1_8,\n",
              " Z_4_1_9]"
            ]
          },
          "metadata": {},
          "execution_count": 381
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#ask about the way to compare different versions and how to show the benefit of stochastic optimisation\n",
        "#correct Z,U"
      ],
      "metadata": {
        "id": "NUM4dtMOZ7be"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}