UnitCommitmentLP.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimisation Assignment 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution for Assignment 1: Unit Commitment Problem Using Linear Programming\n",
    "\n",
    "By writing my/our name/s below and submitting this file, I/we declare that this file is my/our own work, and that I/we have not seen any work on this assignment by another student/group.\n",
    "\n",
    "#### Student name(s): Kalyani Prashant Kawale, Harshitha Bengaluru Raghuram\n",
    "#### Student ID(s): 21237189, 21235396"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Formulation:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Unit Commitment (Electricity Generation Scheduling) Formulation:\n",
    "\n",
    "Given the data in generators_info.csv, demand.csv and solar_curve.csv, the formulation is,\n",
    "\n",
    "#### Objective Function:\n",
    "Minimise the total cost of electricity produced by all the generators for each hour. \n",
    "\n",
    "**To minimise Σ a<sub>i</sub> * x<sub>i,j</sub> ∀ i and j** where,\n",
    " \n",
    "i = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} where indexes 0 to 9 corresponds to generators [A, B, C, D, E, F, G, H, I, J]\n",
    "\n",
    "j = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23} \n",
    "\n",
    "#### Decision Variables:\n",
    "Let x<sub>ij</sub> be the supply in MW by generator i at hour j,\n",
    "\n",
    "i = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}\n",
    "\n",
    "j = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23} \n",
    "\n",
    "#### Constraints:\n",
    "**1. Capacity Constraint:**\n",
    "\n",
    "Supply of each generator i should be between lower and upper bound.\n",
    "\n",
    "**lb<sub>i</sub> ≤ x<sub>ij</sub> ≤ ub<sub>i</sub> ∀ i**, \n",
    "\n",
    "lb<sub>i</sub> = minimum electricity (in MW) that can be produced by generator i\n",
    "\n",
    "ub<sub>i</sub> = maximum electricity (in MW) that can be produced by generator i\n",
    "\n",
    "**2. Solar Constraint:**\n",
    "\n",
    "Capacity of the electricity produced from the solar generators depends on the time of the day.\n",
    "\n",
    "**x<sub>ij</sub> ≤ δ<sub>j</sub> * ub<sub>i</sub> ∀ i and j**,\n",
    "\n",
    "i ∈ {8,  9} corresponding to solar generators [I, J]\n",
    "\n",
    "δ<sub>j</sub> = percentage of electricity that can be achieved at hour j\n",
    "\n",
    "ub<sub>i</sub> = maximum MW that can be generated by generator i\n",
    "\n",
    "**3. Solid Constraint:**\n",
    "\n",
    "The output from the solid generator remains constant for each hour.\n",
    "\n",
    "**x<sub>i0</sub> == x<sub>ij</sub> ∀ i and j**,\n",
    "\n",
    "i ∈ {4, 5, 6} corresponding to solid generators [E, F, G]\n",
    "\n",
    "**4. Demand Constraint:**\n",
    "\n",
    "Supply from all generators at a given hour should be equal to the demand for the electricity at that hour.\n",
    "\n",
    "**Σ x<sub>ij</sub> = d<sub>j</sub> ∀ i and j** where,\n",
    " \n",
    "d<sub>i</sub> = electricity demand at j<sup>th</sup> hour.\n",
    "\n",
    "##### Note: Ignoring CO<sub>2</sub> emissions, since it is not affecting the cost/demand\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generators: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n",
      "Hours: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]\n",
      "Number of decision variables: 240\n",
      "Number of constraints: 144\n",
      "\n",
      "SOLUTION FOR LP:\n",
      "Values of 240 decision variables:\n",
      "x[0,0] = 68.99999999999997 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[1,0] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[2,0] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[3,0] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[4,0] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 6.128431095930864e-14 EUR\n",
      "x[5,0] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 6.128431095930864e-14 EUR\n",
      "x[6,0] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 6.128431095930864e-14 EUR\n",
      "x[7,0] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 7.7 EUR\n",
      "x[8,0] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[9,0] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[0,1] = 54.00000000000003 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[1,1] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[2,1] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[3,1] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[4,1] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,1] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,1] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,1] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 7.7 EUR\n",
      "x[8,1] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[9,1] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[0,2] = 54.00000000000003 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[1,2] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[2,2] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[3,2] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[4,2] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,2] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,2] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,2] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 7.7 EUR\n",
      "x[8,2] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[9,2] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[0,3] = 45.999999999999886 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[1,3] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[2,3] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[3,3] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[4,3] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,3] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,3] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,3] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 7.7 EUR\n",
      "x[8,3] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[9,3] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[0,4] = 32.99999999999994 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[1,4] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[2,4] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[3,4] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[4,4] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,4] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,4] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,4] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 7.7 EUR\n",
      "x[8,4] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[9,4] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[0,5] = 27.999999999999943 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[1,5] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[2,5] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[3,5] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[4,5] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,5] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,5] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,5] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 7.7 EUR\n",
      "x[8,5] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[9,5] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[0,6] = 74.99999999999994 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[1,6] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[2,6] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[3,6] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[4,6] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,6] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,6] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,6] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 7.7 EUR\n",
      "x[8,6] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[9,6] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[0,7] = 100.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[1,7] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[2,7] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[3,7] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[4,7] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,7] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,7] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,7] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 2.6999999999999993 EUR\n",
      "x[8,7] = 10.999999999999961 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[9,7] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[0,8] = 100.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[1,8] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[2,8] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[3,8] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[4,8] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,8] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,8] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,8] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 2.6999999999999993 EUR\n",
      "x[8,8] = 14.999999999999947 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[9,8] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[0,9] = 100.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[1,9] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[2,9] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[3,9] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[4,9] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,9] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,9] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,9] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 2.6999999999999993 EUR\n",
      "x[8,9] = 11.999999999999957 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[9,9] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[0,10] = 100.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[1,10] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[2,10] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[3,10] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[4,10] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,10] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,10] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,10] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 2.6999999999999993 EUR\n",
      "x[8,10] = 11.999999999999957 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[9,10] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[0,11] = 100.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[1,11] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[2,11] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[3,11] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[4,11] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,11] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,11] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,11] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 2.6999999999999993 EUR\n",
      "x[8,11] = 9.999999999999964 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[9,11] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[0,12] = 100.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[1,12] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[2,12] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[3,12] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[4,12] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,12] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,12] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,12] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 2.6999999999999993 EUR\n",
      "x[8,12] = 5.999999999999979 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[9,12] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[0,13] = 100.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[1,13] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[2,13] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[3,13] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[4,13] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,13] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,13] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,13] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 2.6999999999999993 EUR\n",
      "x[8,13] = 3.999999999999986 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[9,13] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[0,14] = 100.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[1,14] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[2,14] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[3,14] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[4,14] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,14] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,14] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,14] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 7.7 EUR\n",
      "x[8,14] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[9,14] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[0,15] = 100.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -3.8999999999999493 EUR\n",
      "x[1,15] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -3.8999999999999493 EUR\n",
      "x[2,15] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -3.8999999999999493 EUR\n",
      "x[3,15] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -3.8999999999999493 EUR\n",
      "x[4,15] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,15] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,15] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,15] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 3.8000000000000504 EUR\n",
      "x[8,15] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 1.1000000000000512 EUR\n",
      "x[9,15] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 1.1000000000000512 EUR\n",
      "x[0,16] = 100.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[1,16] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[2,16] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[3,16] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[4,16] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,16] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,16] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,16] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 7.7 EUR\n",
      "x[8,16] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[9,16] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[0,17] = 100.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[1,17] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[2,17] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[3,17] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[4,17] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,17] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,17] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,17] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 2.6999999999999993 EUR\n",
      "x[8,17] = 16.99999999999994 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[9,17] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[0,18] = 100.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[1,18] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[2,18] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[3,18] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -5.0 EUR\n",
      "x[4,18] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,18] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,18] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,18] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 2.6999999999999993 EUR\n",
      "x[8,18] = 15.999999999999908 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[9,18] = 10.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[0,19] = 100.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -7.699999999999999 EUR\n",
      "x[1,19] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -7.699999999999999 EUR\n",
      "x[2,19] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -7.699999999999999 EUR\n",
      "x[3,19] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -7.699999999999999 EUR\n",
      "x[4,19] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,19] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,19] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,19] = 125.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[8,19] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[9,19] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[0,20] = 100.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -7.699999999999999 EUR\n",
      "x[1,20] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -7.699999999999999 EUR\n",
      "x[2,20] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -7.699999999999999 EUR\n",
      "x[3,20] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -7.699999999999999 EUR\n",
      "x[4,20] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,20] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,20] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,20] = 123.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[8,20] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[9,20] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[0,21] = 100.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -7.699999999999999 EUR\n",
      "x[1,21] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -7.699999999999999 EUR\n",
      "x[2,21] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -7.699999999999999 EUR\n",
      "x[3,21] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost -7.699999999999999 EUR\n",
      "x[4,21] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,21] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,21] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,21] = 105.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[8,21] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[9,21] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[0,22] = 86.99999999999991 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[1,22] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[2,22] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[3,22] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[4,22] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,22] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,22] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,22] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 7.7 EUR\n",
      "x[8,22] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[9,22] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[0,23] = 70.99999999999997 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[1,23] = 80.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[2,23] = 60.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[3,23] = 10.0 MW;\t Coefficient 1.4 EUR/MW;\t Reduced cost 4.440892098500626e-16 EUR\n",
      "x[4,23] = 442.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[5,23] = 600.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[6,23] = 100.0 MW;\t Coefficient 4.4 EUR/MW;\t Reduced cost 0.0 EUR\n",
      "x[7,23] = 100.0 MW;\t Coefficient 9.1 EUR/MW;\t Reduced cost 7.7 EUR\n",
      "x[8,23] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "x[9,23] = 0.0 MW;\t Coefficient 6.4 EUR/MW;\t Reduced cost 5.000000000000001 EUR\n",
      "\n",
      "Optimal objective value: 151504.5 EUR\n"
     ]
    }
   ],
   "source": [
    "# Importing pywraplp module of or-tools to create a solver to perform linear programming\n",
    "from ortools.linear_solver import pywraplp\n",
    "# Importing pandas to read given csv files\n",
    "import pandas as pd\n",
    "\n",
    "def create_decision_variables(solver, generators_info, generators, hours):\n",
    "    \"\"\"\n",
    "        Method to create decision variables for Unit Commitment Problem\n",
    "    \"\"\"    \n",
    "    # Initializing Lower Bound\n",
    "    lb = 0.0\n",
    "    # Initializing Upper Bound\n",
    "    ub = 0.0\n",
    "    \n",
    "    # Initializing decision variables for each generator at every hour of the day\n",
    "    # Constraint Number 1. Setting the lower and upper limit on production of electricity per hour for each generator\n",
    "    x = {} # x: dictionary of decision variables\n",
    "    for i in generators:\n",
    "        lb = float(generators_info.iloc[i]['lower_bound (MW)'])\n",
    "        ub = float(generators_info.iloc[i]['upper_bound (MW)'])\n",
    "        for j in hours:\n",
    "            x[i,j] = solver.NumVar(lb, ub, \"x[%i,%i]\" % (i, j))\n",
    "    return x\n",
    "\n",
    "\n",
    "def add_constraints(solver, x, hours, generators, generators_info):\n",
    "    \"\"\"\n",
    "        Method to add all constraints on the electricity generation to the solver\n",
    "    \"\"\"    \n",
    "    ## Constraint 1. lower and upper limit on production of electricity per hour for each generator \n",
    "    # was set while creation of decision variables \n",
    "    \n",
    "    ## Constraint 2. Solar generator supply constraint for each hour j\n",
    "    # x[solar_generator(i), j] <= solar_generator_supply(j) * generator's max supply (upper bound)\n",
    "    # Reading solar generator supply percent relative to maximum for each hour j\n",
    "    solar_generator_supply = pd.read_csv('solar_curve.csv', header=None)\n",
    "    # Initializing solar_generators using generator indexes corresponding to solar generator I and J\n",
    "    solar_generators = [8, 9]\n",
    "    for i in solar_generators:\n",
    "            for j in hours:\n",
    "                max_supply_per_hour = solar_generator_supply.iloc[j][0] * generators_info.iloc[i]['upper_bound (MW)']\n",
    "                solver.Add(x[i, j] <= max_supply_per_hour, \n",
    "                           name=\"limit on supply of solar generator \"\n",
    "                           + generators_info.iloc[i]['name'] + \" at hour \" + str(j))\n",
    "    \n",
    "    \n",
    "    ## Constraint 3: Solid fuel generators have same production every hour\n",
    "    # x[solid_generator(i), 0] = x[solid_generator(i), j] for all j\n",
    "    # Initializing solid_generators using generator indexes corresponding to solar generator E, F and G\n",
    "    solid_generators = [4, 5, 6]\n",
    "    for i in solid_generators:\n",
    "        for j in hours:\n",
    "            solver.Add(x[i, 0] == x[i, j], \n",
    "                       name=\"equal amount of supply for solid generator \" \n",
    "                       + generators_info.iloc[i]['name'])\n",
    "\n",
    "    \n",
    "    ## Constraint 4. Electricity demand at each hour\n",
    "    # reading demand.csv file using pandas to get the demand at each hour j\n",
    "    demand = pd.read_csv('demand.csv', header=None)\n",
    "    # Sum of MW generated by each generator i == demand at hour j,\n",
    "    for j in hours:\n",
    "        solver.Add(x[0, j] + x[1, j] + x[2, j] + x[3, j] + x[4, j] + x[5, j] + x[6, j] + x[7, j] + x[8, j] + x[9,j] \n",
    "                   == demand.iloc[j][0], name=\"limit on electricity generation for hour \" + str(j))\n",
    "\n",
    "def set_objective_and_solve(solver, x, generators, hours, generators_info):\n",
    "    \"\"\" \n",
    "        Method to set the objective function to minimize the cost of electricity generation at each hour\n",
    "        and print the solution\n",
    "    \"\"\" \n",
    "    objective = solver.Objective()\n",
    "    # Setting the coefficient a(i) (Cost per MW produced) for each generator    \n",
    "    for i in generators:\n",
    "        cost_per_mw = generators_info.iloc[i]['cost (EUR/MW)']\n",
    "        for j in hours:            \n",
    "            objective.SetCoefficient(x[i, j], cost_per_mw)\n",
    "    # Minimize the objective function\n",
    "    objective.SetMinimization()\n",
    "    \n",
    "    ## Solve the Unit Commitment LP\n",
    "    return solver.Solve(), objective\n",
    "    \n",
    "        \n",
    "def sensitivity_analysis(solver):\n",
    "    \"\"\"\n",
    "        Method to get sensitivity information from the solved LP\n",
    "    \"\"\"    \n",
    "    binding = []\n",
    "    # looping through all constraints and identifying the binding constraints    \n",
    "    for constraint, activity in zip(solver.constraints(), solver.ComputeConstraintActivities()):      \n",
    "        eps = 0.0000001\n",
    "        # Checking if the shadow price is greater than eps (shadow price != 0 for binding constraints)        \n",
    "        # Saving the name, activity and shadow price for each constraint\n",
    "        if abs(constraint.DualValue()) > eps:            \n",
    "            binding.append({\"name\":constraint.name(), \"activity\": activity, \"shadow_price\": constraint.DualValue()})            \n",
    "        \n",
    "    # Saving the binding constraints in a csv file using pandas\n",
    "    binding_df = pd.DataFrame.from_dict(binding)\n",
    "    binding_df.to_csv('binding_constraints.csv', index=False)\n",
    "\n",
    "    \n",
    "def UnitCommitmentLP():\n",
    "    # Instantiating LP solver using the Google's Linear Programming solver for Unit Commitment Problem\n",
    "    solver = pywraplp.Solver('UnitCommitment', pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)\n",
    "    \n",
    "    # Reading all the generator information from the given generator_info.csv file using pandas\n",
    "    generators_info = pd.read_csv('generator_info.csv')\n",
    "    \n",
    "    # Creating a list of 10 generators where the generators A through J are represented by numbers 0 to 9\n",
    "    generators = list(range(10))\n",
    "    print(\"Generators:\", generators)\n",
    "    \n",
    "    # Creating a list of all hours in a day, using range, starting from hour 0 and ending on hour 23  \n",
    "    hours = list(range(24))\n",
    "    print(\"Hours:\", hours)\n",
    "    \n",
    "    # Getting the decision variables for optimising electricity generation by all generators in a day\n",
    "    x = create_decision_variables(solver, generators_info, generators, hours)\n",
    "    print(\"Number of decision variables:\", solver.NumVariables())\n",
    "\n",
    "    # Adding the constraints on electricity generation\n",
    "    add_constraints(solver, x, hours, generators, generators_info)\n",
    "    print(\"Number of constraints:\", solver.NumConstraints())\n",
    "    \n",
    "    # Setting objective function and solving the LP\n",
    "    result, objective = set_objective_and_solve(solver, x, generators, hours, generators_info)\n",
    "    \n",
    "    solution = []\n",
    "    # Checking if the solution is optimal and printing the values for decision variables and the objective function\n",
    "    if result == solver.OPTIMAL:\n",
    "        print(\"\\nSOLUTION FOR LP:\")\n",
    "        # Printing and saving values of decision variables into solution list\n",
    "        print(\"Values of 240 decision variables:\")\n",
    "        for j in hours:\n",
    "            row = {}\n",
    "            for i in generators:\n",
    "                row[generators_info.iloc[i]['name']] = x[i, j].solution_value()\n",
    "                print(f\"{x[i, j]} = {x[i, j].solution_value()} MW;\\t Coefficient {objective.GetCoefficient(x[i, j])} EUR/MW;\\t Reduced cost {x[i, j].reduced_cost()} EUR\")\n",
    "            solution.append(row)\n",
    "        print(f\"\\nOptimal objective value:\", objective.Value(), \"EUR\")\n",
    "    else:\n",
    "        print(\"Problem is not feasible\")\n",
    "        \n",
    "    # Saving decision variables to a csv file\n",
    "    decision_variable_df = pd.DataFrame(solution)    \n",
    "    decision_variable_df.to_csv('decision_variables.csv', index=False)\n",
    "            \n",
    "    # Performing Sensitivity Analysis\n",
    "    sensitivity_analysis(solver)\n",
    "    \n",
    "if __name__ == \"__main__\":\n",
    "    UnitCommitmentLP()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution:\n",
    "\n",
    "From the output of above code we get the following results:\n",
    "\n",
    "1. Objective function value i.e. **minimum cost required to meet the electricity supply demand for a day** is **151504.5 EUROS**\n",
    "\n",
    "#### Values of decision variables are as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Visualizing the decision variables as a heatmap\n",
    "\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# Reading decision variables from the saved csv file\n",
    "decision_variables = pd.read_csv(\"decision_variables.csv\")\n",
    "print(\"Decision Variable Values:\\n\", decision_variables)\n",
    "\n",
    "# Setting the heatmap figure\n",
    "plt.figure(figsize=(12, 12))\n",
    "plt.title(\"Decision Variables calcuated by LP for Unit Commitment Problem; Minimised cost = 151504.5 Euros\")\n",
    "p=sns.heatmap(decision_variables, annot=True, cmap ='YlGnBu', linewidths=0.1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. From the sensitivity analysis data provided by or-tools we get the following information,\n",
    "    - Out of 144 constraints, 99 are binding.\n",
    "    - All the constraints for demand at any given hour are binding and changing any of the demand by 1 unit or 1 MW        would reduce the total cost by the subsequent shadow price.\n",
    "    - Similarly, all constraints for solid fuel generators, and the constraints on solar generator I and solar generator J for hours 19, 20 and 21 i.e. x[I, 19] <= 0.5 * 70, x[I, 20] <= 0.5 * 70, x[I, 21] <= 0.5 * 70, x[I, 19] <= 0.5 * 20, x[I, 20] <= 0.5 * 20 and x[I, 21] <= 0.5 * 20 are also preventing the cost from minimising.\n",
    "    \n",
    "#### Binding Constraints for Unit Commitment Problem with their shadow prices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                               name  activity  shadow_price\n",
      "0   limit on supply of solar generator I at hour 19       0.0          -2.7\n",
      "1   limit on supply of solar generator I at hour 20       0.0          -2.7\n",
      "2   limit on supply of solar generator I at hour 21       0.0          -2.7\n",
      "3   limit on supply of solar generator J at hour 19       0.0          -2.7\n",
      "4   limit on supply of solar generator J at hour 20       0.0          -2.7\n",
      "5   limit on supply of solar generator J at hour 21       0.0          -2.7\n",
      "6      equal amount of supply for solid generator E       0.0          -3.0\n",
      "7      equal amount of supply for solid generator E       0.0          -3.0\n",
      "8      equal amount of supply for solid generator E       0.0          -3.0\n",
      "9      equal amount of supply for solid generator E       0.0          -3.0\n",
      "10     equal amount of supply for solid generator E       0.0          -3.0\n",
      "11     equal amount of supply for solid generator E       0.0          -3.0\n",
      "12     equal amount of supply for solid generator E       0.0           2.0\n",
      "13     equal amount of supply for solid generator E       0.0           2.0\n",
      "14     equal amount of supply for solid generator E       0.0           2.0\n",
      "15     equal amount of supply for solid generator E       0.0           2.0\n",
      "16     equal amount of supply for solid generator E       0.0           2.0\n",
      "17     equal amount of supply for solid generator E       0.0           2.0\n",
      "18     equal amount of supply for solid generator E       0.0           2.0\n",
      "19     equal amount of supply for solid generator E       0.0          -3.0\n",
      "20     equal amount of supply for solid generator E       0.0           0.9\n",
      "21     equal amount of supply for solid generator E       0.0          -3.0\n",
      "22     equal amount of supply for solid generator E       0.0           2.0\n",
      "23     equal amount of supply for solid generator E       0.0           2.0\n",
      "24     equal amount of supply for solid generator E       0.0           4.7\n",
      "25     equal amount of supply for solid generator E       0.0           4.7\n",
      "26     equal amount of supply for solid generator E       0.0           4.7\n",
      "27     equal amount of supply for solid generator E       0.0          -3.0\n",
      "28     equal amount of supply for solid generator E       0.0          -3.0\n",
      "29     equal amount of supply for solid generator F       0.0          -3.0\n",
      "30     equal amount of supply for solid generator F       0.0          -3.0\n",
      "31     equal amount of supply for solid generator F       0.0          -3.0\n",
      "32     equal amount of supply for solid generator F       0.0          -3.0\n",
      "33     equal amount of supply for solid generator F       0.0          -3.0\n",
      "34     equal amount of supply for solid generator F       0.0          -3.0\n",
      "35     equal amount of supply for solid generator F       0.0           2.0\n",
      "36     equal amount of supply for solid generator F       0.0           2.0\n",
      "37     equal amount of supply for solid generator F       0.0           2.0\n",
      "38     equal amount of supply for solid generator F       0.0           2.0\n",
      "39     equal amount of supply for solid generator F       0.0           2.0\n",
      "40     equal amount of supply for solid generator F       0.0           2.0\n",
      "41     equal amount of supply for solid generator F       0.0           2.0\n",
      "42     equal amount of supply for solid generator F       0.0          -3.0\n",
      "43     equal amount of supply for solid generator F       0.0           0.9\n",
      "44     equal amount of supply for solid generator F       0.0          -3.0\n",
      "45     equal amount of supply for solid generator F       0.0           2.0\n",
      "46     equal amount of supply for solid generator F       0.0           2.0\n",
      "47     equal amount of supply for solid generator F       0.0           4.7\n",
      "48     equal amount of supply for solid generator F       0.0           4.7\n",
      "49     equal amount of supply for solid generator F       0.0           4.7\n",
      "50     equal amount of supply for solid generator F       0.0          -3.0\n",
      "51     equal amount of supply for solid generator F       0.0          -3.0\n",
      "52     equal amount of supply for solid generator G       0.0          -3.0\n",
      "53     equal amount of supply for solid generator G       0.0          -3.0\n",
      "54     equal amount of supply for solid generator G       0.0          -3.0\n",
      "55     equal amount of supply for solid generator G       0.0          -3.0\n",
      "56     equal amount of supply for solid generator G       0.0          -3.0\n",
      "57     equal amount of supply for solid generator G       0.0          -3.0\n",
      "58     equal amount of supply for solid generator G       0.0           2.0\n",
      "59     equal amount of supply for solid generator G       0.0           2.0\n",
      "60     equal amount of supply for solid generator G       0.0           2.0\n",
      "61     equal amount of supply for solid generator G       0.0           2.0\n",
      "62     equal amount of supply for solid generator G       0.0           2.0\n",
      "63     equal amount of supply for solid generator G       0.0           2.0\n",
      "64     equal amount of supply for solid generator G       0.0           2.0\n",
      "65     equal amount of supply for solid generator G       0.0          -3.0\n",
      "66     equal amount of supply for solid generator G       0.0           0.9\n",
      "67     equal amount of supply for solid generator G       0.0          -3.0\n",
      "68     equal amount of supply for solid generator G       0.0           2.0\n",
      "69     equal amount of supply for solid generator G       0.0           2.0\n",
      "70     equal amount of supply for solid generator G       0.0           4.7\n",
      "71     equal amount of supply for solid generator G       0.0           4.7\n",
      "72     equal amount of supply for solid generator G       0.0           4.7\n",
      "73     equal amount of supply for solid generator G       0.0          -3.0\n",
      "74     equal amount of supply for solid generator G       0.0          -3.0\n",
      "75       limit on electricity generation for hour 0    1461.0           1.4\n",
      "76       limit on electricity generation for hour 1    1446.0           1.4\n",
      "77       limit on electricity generation for hour 2    1446.0           1.4\n",
      "78       limit on electricity generation for hour 3    1438.0           1.4\n",
      "79       limit on electricity generation for hour 4    1425.0           1.4\n",
      "80       limit on electricity generation for hour 5    1420.0           1.4\n",
      "81       limit on electricity generation for hour 6    1467.0           1.4\n",
      "82       limit on electricity generation for hour 7    1503.0           6.4\n",
      "83       limit on electricity generation for hour 8    1507.0           6.4\n",
      "84       limit on electricity generation for hour 9    1504.0           6.4\n",
      "85      limit on electricity generation for hour 10    1504.0           6.4\n",
      "86      limit on electricity generation for hour 11    1502.0           6.4\n",
      "87      limit on electricity generation for hour 12    1498.0           6.4\n",
      "88      limit on electricity generation for hour 13    1496.0           6.4\n",
      "89      limit on electricity generation for hour 14    1492.0           1.4\n",
      "90      limit on electricity generation for hour 15    1492.0           5.3\n",
      "91      limit on electricity generation for hour 16    1492.0           1.4\n",
      "92      limit on electricity generation for hour 17    1509.0           6.4\n",
      "93      limit on electricity generation for hour 18    1518.0           6.4\n",
      "94      limit on electricity generation for hour 19    1517.0           9.1\n",
      "95      limit on electricity generation for hour 20    1515.0           9.1\n",
      "96      limit on electricity generation for hour 21    1497.0           9.1\n",
      "97      limit on electricity generation for hour 22    1479.0           1.4\n",
      "98      limit on electricity generation for hour 23    1463.0           1.4\n"
     ]
    }
   ],
   "source": [
    "# Reading constraints from binding constraints csv file and printing the dataframe\n",
    "binding = pd.read_csv(\"binding_constraints.csv\")\n",
    "pd.set_option(\"display.max_rows\", len(binding))\n",
    "print(binding)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Acknowledgements\n",
    "1. https://developers.google.com/optimization/lp/stigler_diet on 18 October 2021\n",
    "2. https://developers.google.com/optimization/lp/lp_example on 18 October 2021\n",
    "3. https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.from_dict.html on 19 October 2021\n",
    "4. https://pandas.pydata.org/docs/user_guide/options.html on 19 October 2021\n",
    "5. https://seaborn.pydata.org/generated/seaborn.heatmap.html on 20 October 2021"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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