notebooks/04.05-Scheduling-Multipurpose-Batch-Processes-using-State-Task_Networks.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "# Scheduling Multipurpose Batch Processes using State-Task Networks\n",
    "\n",
    "Keywords: cbc usage, state-task networks, gdp, disjunctive programming, batch processes\n",
    "\n",
    "The State-Task Network (STN) is an approach to modeling multipurpose batch process for the purpose of short term scheduling. It was first developed by Kondili, et al., in 1993, and subsequently developed and extended by others. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from IPython.display import display, HTML\n",
    "    \n",
    "import shutil\n",
    "import sys\n",
    "import os.path\n",
    "\n",
    "if not shutil.which(\"pyomo\"):\n",
    "    !pip install -q pyomo\n",
    "    assert(shutil.which(\"pyomo\"))\n",
    "\n",
    "if not (shutil.which(\"cbc\") or os.path.isfile(\"cbc\")):\n",
    "    if \"google.colab\" in sys.modules:\n",
    "        !apt-get install -y -qq coinor-cbc\n",
    "    else:\n",
    "        try:\n",
    "            !conda install -c conda-forge coincbc \n",
    "        except:\n",
    "            pass\n",
    "\n",
    "assert(shutil.which(\"cbc\") or os.path.isfile(\"cbc\"))\n",
    "from pyomo.environ import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "## References\n",
    "\n",
    "Floudas, C. A., & Lin, X. (2005). Mixed integer linear programming in process scheduling: Modeling, algorithms, and applications. Annals of Operations Research, 139(1), 131-162.\n",
    "\n",
    "Harjunkoski, I., Maravelias, C. T., Bongers, P., Castro, P. M., Engell, S., Grossmann, I. E., ... & Wassick, J. (2014). Scope for industrial applications of production scheduling models and solution methods. Computers & Chemical Engineering, 62, 161-193.\n",
    "\n",
    "Kondili, E., Pantelides, C. C., & Sargent, R. W. H. (1993). A general algorithm for short-term scheduling of batch operations—I. MILP formulation. Computers & Chemical Engineering, 17(2), 211-227.\n",
    "\n",
    "Méndez, C. A., Cerdá, J., Grossmann, I. E., Harjunkoski, I., & Fahl, M. (2006). State-of-the-art review of optimization methods for short-term scheduling of batch processes. Computers & Chemical Engineering, 30(6), 913-946.\n",
    "\n",
    "Shah, N., Pantelides, C. C., & Sargent, R. W. H. (1993). A general algorithm for short-term scheduling of batch operations—II. Computational issues. Computers & Chemical Engineering, 17(2), 229-244.\n",
    "\n",
    "Wassick, J. M., & Ferrio, J. (2011). Extending the resource task network for industrial applications. Computers & chemical engineering, 35(10), 2124-2140."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "## Example (Kondili, et al., 1993)\n",
    "\n",
    "A state-task network is a graphical representation of the activities in a multi-product batch process. The representation includes the minimum details needed for short term scheduling of batch operations.\n",
    "\n",
    "A well-studied example due to Kondili (1993) is shown below. Other examples are available in the references cited above.\n",
    "\n",
    "![Kondili_1993.png](https://github.com/jckantor/ND-Pyomo-Cookbook/blob/master/notebooks/figures/Kondili_1993.png?raw=1)\n",
    "\n",
    "Each circular node in the diagram designates material in a particular state.  The materials are generally held in suitable vessels with a known capacity. The relevant information for each state is the initial inventory, storage capacity, and the unit price of the material in each state. The price of materials in intermediate states may be assigned penalties in order to minimize the amount of work in progress.\n",
    "\n",
    "The rectangular nodes denote process tasks. When scheduled for execution, each task is assigned an appropriate piece of equipment, and assigned a batch of material according to the incoming arcs. Each incoming arc begins at a state where the associated label indicates the mass fraction of the batch coming from that particular state. Outgoing arcs indicate the disposition of the batch to product states. The outgoing are labels indicate the fraction of the batch assigned to each product state, and the time necessary to produce that product. \n",
    "\n",
    "Not shown in the diagram is the process equipment used to execute the tasks. A separate list of process units is available, each characterized by a capacity and list of tasks which can be performed in that unit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "### Exercise\n",
    "\n",
    "Read this recipe for Hollandaise Sauce: http://www.foodnetwork.com/recipes/tyler-florence/hollandaise-sauce-recipe-1910043. Assume the available equipment consists of one sauce pan and a double-boiler on a stove. Draw a state-task network outlining the basic steps in the recipe."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "## Encoding the STN data\n",
    "\n",
    "The basic data structure specifies the states, tasks, and units comprising a state-task network. The intention is for all relevant problem data to be contained in a single JSON-like structure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [],
   "source": [
    "# planning horizon\n",
    "H = 10\n",
    "\n",
    "Kondili = {\n",
    "    # time grid\n",
    "    'TIME':  range(0, H+1),\n",
    "    \n",
    "    # states\n",
    "    'STATES': {\n",
    "        'Feed_A'   : {'capacity': 500, 'initial': 500, 'price':  0},\n",
    "        'Feed_B'   : {'capacity': 500, 'initial': 500, 'price':  0},\n",
    "        'Feed_C'   : {'capacity': 500, 'initial': 500, 'price':  0},\n",
    "        'Hot_A'    : {'capacity': 100, 'initial':   0, 'price': -100},\n",
    "        'Int_AB'   : {'capacity': 200, 'initial':   0, 'price': -100},\n",
    "        'Int_BC'   : {'capacity': 150, 'initial':   0, 'price': -100},\n",
    "        'Impure_E' : {'capacity': 100, 'initial':   0, 'price': -100},\n",
    "        'Product_1': {'capacity': 500, 'initial':   0, 'price': 10},\n",
    "        'Product_2': {'capacity': 500, 'initial':   0, 'price': 10},\n",
    "    },\n",
    "    \n",
    "    # state-to-task arcs indexed by (state, task)\n",
    "    'ST_ARCS': {\n",
    "        ('Feed_A',   'Heating')   : {'rho': 1.0},\n",
    "        ('Feed_B',   'Reaction_1'): {'rho': 0.5},\n",
    "        ('Feed_C',   'Reaction_1'): {'rho': 0.5},\n",
    "        ('Feed_C',   'Reaction_3'): {'rho': 0.2},\n",
    "        ('Hot_A',    'Reaction_2'): {'rho': 0.4},\n",
    "        ('Int_AB',   'Reaction_3'): {'rho': 0.8},\n",
    "        ('Int_BC',   'Reaction_2'): {'rho': 0.6},\n",
    "        ('Impure_E', 'Separation'): {'rho': 1.0},\n",
    "    },\n",
    "    \n",
    "    # task-to-state arcs indexed by (task, state)\n",
    "    'TS_ARCS': {\n",
    "        ('Heating',    'Hot_A')    : {'dur': 1, 'rho': 1.0},\n",
    "        ('Reaction_2', 'Product_1'): {'dur': 2, 'rho': 0.4},\n",
    "        ('Reaction_2', 'Int_AB')   : {'dur': 2, 'rho': 0.6},\n",
    "        ('Reaction_1', 'Int_BC')   : {'dur': 2, 'rho': 1.0},\n",
    "        ('Reaction_3', 'Impure_E') : {'dur': 1, 'rho': 1.0},\n",
    "        ('Separation', 'Int_AB')   : {'dur': 2, 'rho': 0.1},\n",
    "        ('Separation', 'Product_2'): {'dur': 1, 'rho': 0.9},\n",
    "    },\n",
    "    \n",
    "    # unit data indexed by (unit, task)\n",
    "    'UNIT_TASKS': {\n",
    "        ('Heater',    'Heating')   : {'Bmin': 0, 'Bmax': 100, 'Cost': 1, 'vCost': 0, 'Tclean': 0},\n",
    "        ('Reactor_1', 'Reaction_1'): {'Bmin': 0, 'Bmax':  80, 'Cost': 1, 'vCost': 0, 'Tclean': 0},\n",
    "        ('Reactor_1', 'Reaction_2'): {'Bmin': 0, 'Bmax':  80, 'Cost': 1, 'vCost': 0, 'Tclean': 0},\n",
    "        ('Reactor_1', 'Reaction_3'): {'Bmin': 0, 'Bmax':  80, 'Cost': 1, 'vCost': 0, 'Tclean': 0},\n",
    "        ('Reactor_2', 'Reaction_1'): {'Bmin': 0, 'Bmax':  80, 'Cost': 1, 'vCost': 0, 'Tclean': 0},\n",
    "        ('Reactor_2', 'Reaction_2'): {'Bmin': 0, 'Bmax':  80, 'Cost': 1, 'vCost': 0, 'Tclean': 0},\n",
    "        ('Reactor_2', 'Reaction_3'): {'Bmin': 0, 'Bmax':  80, 'Cost': 1, 'vCost': 0, 'Tclean': 0},\n",
    "        ('Still',     'Separation'): {'Bmin': 0, 'Bmax': 200, 'Cost': 1, 'vCost': 0, 'Tclean': 0},\n",
    "    },\n",
    "}\n",
    "\n",
    "STN = Kondili"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "H = 16\n",
    "\n",
    "Hydrolubes = {\n",
    "    # time grid\n",
    "    'TIME':  range(0, H+1),\n",
    "    \n",
    "    # states\n",
    "    'STATES': {\n",
    "        'Feed_A'   : {'capacity': 500, 'initial': 500, 'price':  0},\n",
    "        'Feed_B'   : {'capacity': 500, 'initial': 500, 'price':  0},\n",
    "        'Feed_C'   : {'capacity': 500, 'initial': 500, 'price':  0},\n",
    "        'Hot_A'    : {'capacity': 100, 'initial':   0, 'price': -100},\n",
    "        'Int_AB'   : {'capacity': 200, 'initial':   0, 'price': -100},\n",
    "        'Int_BC'   : {'capacity': 150, 'initial':   0, 'price': -100},\n",
    "        'Impure_E' : {'capacity': 100, 'initial':   0, 'price': -100},\n",
    "        'Product_1': {'capacity': 500, 'initial':   0, 'price': 10},\n",
    "        'Product_2': {'capacity': 500, 'initial':   0, 'price': 10},\n",
    "    },\n",
    "    \n",
    "    # state-to-task arcs indexed by (state, task)\n",
    "    'ST_ARCS': {\n",
    "        ('Feed_A',   'Heating')   : {'rho': 1.0},\n",
    "        ('Feed_B',   'Reaction_1'): {'rho': 0.5},\n",
    "        ('Feed_C',   'Reaction_1'): {'rho': 0.5},\n",
    "        ('Feed_C',   'Reaction_3'): {'rho': 0.2},\n",
    "        ('Hot_A',    'Reaction_2'): {'rho': 0.4},\n",
    "        ('Int_AB',   'Reaction_3'): {'rho': 0.8},\n",
    "        ('Int_BC',   'Reaction_2'): {'rho': 0.6},\n",
    "        ('Impure_E', 'Separation'): {'rho': 1.0},\n",
    "    },\n",
    "    \n",
    "    # task-to-state arcs indexed by (task, state)\n",
    "    'TS_ARCS': {\n",
    "        ('Heating',    'Hot_A')    : {'dur': 1, 'rho': 1.0},\n",
    "        ('Reaction_2', 'Product_1'): {'dur': 2, 'rho': 0.4},\n",
    "        ('Reaction_2', 'Int_AB')   : {'dur': 2, 'rho': 0.6},\n",
    "        ('Reaction_1', 'Int_BC')   : {'dur': 2, 'rho': 1.0},\n",
    "        ('Reaction_3', 'Impure_E') : {'dur': 1, 'rho': 1.0},\n",
    "        ('Separation', 'Int_AB')   : {'dur': 2, 'rho': 0.1},\n",
    "        ('Separation', 'Product_2'): {'dur': 1, 'rho': 0.9},\n",
    "    },\n",
    "    \n",
    "    # unit data indexed by (unit, task)\n",
    "    'UNIT_TASKS': {\n",
    "        ('Heater',    'Heating')   : {'Bmin': 0, 'Bmax': 100, 'Cost': 1, 'vCost': 0, 'Tclean': 0},\n",
    "        ('Reactor_1', 'Reaction_1'): {'Bmin': 0, 'Bmax':  80, 'Cost': 1, 'vCost': 0, 'Tclean': 0},\n",
    "        ('Reactor_1', 'Reaction_2'): {'Bmin': 0, 'Bmax':  80, 'Cost': 1, 'vCost': 0, 'Tclean': 0},\n",
    "        ('Reactor_1', 'Reaction_3'): {'Bmin': 0, 'Bmax':  80, 'Cost': 1, 'vCost': 0, 'Tclean': 0},\n",
    "        ('Reactor_2', 'Reaction_1'): {'Bmin': 0, 'Bmax':  80, 'Cost': 1, 'vCost': 0, 'Tclean': 0},\n",
    "        ('Reactor_2', 'Reaction_2'): {'Bmin': 0, 'Bmax':  80, 'Cost': 1, 'vCost': 0, 'Tclean': 0},\n",
    "        ('Reactor_2', 'Reaction_3'): {'Bmin': 0, 'Bmax':  80, 'Cost': 1, 'vCost': 0, 'Tclean': 0},\n",
    "        ('Still',     'Separation'): {'Bmin': 0, 'Bmax': 200, 'Cost': 1, 'vCost': 0, 'Tclean': 0},\n",
    "    },\n",
    "}\n",
    "\n",
    "STN = Hydrolubes\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "### Setting a time grid\n",
    "\n",
    "The following computations can be done on any time grid, including real-valued time points. TIME is a list of time points commencing at 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "## Creating a Pyomo model\n",
    "\n",
    "The following Pyomo model closely follows the development in Kondili, et al. (1993). In particular, the first step in the model is to process the STN data to create sets as given in Kondili.  \n",
    "\n",
    "One important difference from Kondili is the adoption of a more natural time scale that starts at $t = 0$ and extends to $t = H$ (rather than from 1 to H+1).\n",
    "\n",
    "A second difference is the introduction of an additional decision variable denoted by $Q_{j,t}$ indicating the amount of material in unit $j$ at time $t$. A material balance then reads\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "Q_{jt} & = Q_{j(t-1)} + \\sum_{i\\in I_j}B_{ijt} - \\sum_{i\\in I_j}\\sum_{\\substack{s \\in \\bar{S}_i\\\\s\\ni t-P_{is} \\geq 0}}\\bar{\\rho}_{is}B_{ij(t-P_{is})} \\qquad \\forall j,t\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "Following Kondili's notation, $I_j$ is the set of tasks that can be performed in unit $j$, and $\\bar{S}_i$ is the set of states fed by task $j$. We assume the units are empty at the beginning and end of production period, i.e.,\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "Q_{j(-1)} & = 0 \\qquad \\forall j \\\\\n",
    "Q_{j,H} & = 0 \\qquad \\forall j\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "The unit allocation constraints are written the full backward aggregation method described by Shah (1993).  The allocation constraint reads\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\sum_{i \\in I_j} \\sum_{t'=t}^{t-p_i+1} W_{ijt'} & \\leq 1 \\qquad \\forall j,t\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "Each processing unit $j$ is tagged with a minimum and maximum capacity, $B_{ij}^{min}$ and $B_{ij}^{max}$, respectively, denoting the minimum and maximum batch sizes for each task $i$. A minimum capacity may be needed to cover heat exchange coils in a reactor or mixing blades in a blender, for example. The capacity may depend on the nature of the task being performed.  These constraints are written\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "B_{ij}^{min}W_{ijt} & \\leq B_{ijt} \\leq  B_{ij}^{max}W_{ijt} \\qquad \\forall j, \\forall i\\in I_j, \\forall t\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "### Characterization of tasks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [],
   "source": [
    "STATES = STN['STATES']\n",
    "ST_ARCS = STN['ST_ARCS']\n",
    "TS_ARCS = STN['TS_ARCS']\n",
    "UNIT_TASKS = STN['UNIT_TASKS']\n",
    "TIME = STN['TIME']\n",
    "H = max(TIME)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [],
   "source": [
    "# set of tasks\n",
    "TASKS = set([i for (j,i) in UNIT_TASKS])\n",
    "\n",
    "# S[i] input set of states which feed task i\n",
    "S = {i: set() for i in TASKS}\n",
    "for (s,i) in ST_ARCS:\n",
    "    S[i].add(s)\n",
    "\n",
    "# S_[i] output set of states fed by task i\n",
    "S_ = {i: set() for i in TASKS}\n",
    "for (i,s) in TS_ARCS:\n",
    "    S_[i].add(s)\n",
    "\n",
    "# rho[(i,s)] input fraction of task i from state s\n",
    "rho = {(i,s): ST_ARCS[(s,i)]['rho'] for (s,i) in ST_ARCS}\n",
    "\n",
    "# rho_[(i,s)] output fraction of task i to state s\n",
    "rho_ = {(i,s): TS_ARCS[(i,s)]['rho'] for (i,s) in TS_ARCS}\n",
    "\n",
    "# P[(i,s)] time for task i output to state s \n",
    "P = {(i,s): TS_ARCS[(i,s)]['dur'] for (i,s) in TS_ARCS}\n",
    "\n",
    "# p[i] completion time for task i\n",
    "p = {i: max([P[(i,s)] for s in S_[i]]) for i in TASKS}\n",
    "\n",
    "# K[i] set of units capable of task i\n",
    "K = {i: set() for i in TASKS}\n",
    "for (j,i) in UNIT_TASKS:\n",
    "    K[i].add(j) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "### Characterization of states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [],
   "source": [
    "# T[s] set of tasks receiving material from state s\n",
    "T = {s: set() for s in STATES}\n",
    "for (s,i) in ST_ARCS:\n",
    "    T[s].add(i)\n",
    "\n",
    "# set of tasks producing material for state s\n",
    "T_ = {s: set() for s in STATES}\n",
    "for (i,s) in TS_ARCS:\n",
    "    T_[s].add(i)\n",
    "\n",
    "# C[s] storage capacity for state s\n",
    "C = {s: STATES[s]['capacity'] for s in STATES}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "### Characterization of units"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [],
   "source": [
    "UNITS = set([j for (j,i) in UNIT_TASKS])\n",
    "\n",
    "# I[j] set of tasks performed with unit j\n",
    "I = {j: set() for j in UNITS}\n",
    "for (j,i) in UNIT_TASKS:\n",
    "    I[j].add(i)\n",
    "\n",
    "# Bmax[(i,j)] maximum capacity of unit j for task i\n",
    "Bmax = {(i,j):UNIT_TASKS[(j,i)]['Bmax'] for (j,i) in UNIT_TASKS}\n",
    "\n",
    "# Bmin[(i,j)] minimum capacity of unit j for task i\n",
    "Bmin = {(i,j):UNIT_TASKS[(j,i)]['Bmin'] for (j,i) in UNIT_TASKS}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "### Pyomo model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# ==========================================================\n",
      "# = Solver Results                                         =\n",
      "# ==========================================================\n",
      "# ----------------------------------------------------------\n",
      "#   Problem Information\n",
      "# ----------------------------------------------------------\n",
      "Problem: \n",
      "- Name: unknown\n",
      "  Lower bound: -4870.33333333\n",
      "  Upper bound: -4870.33333333\n",
      "  Number of objectives: 1\n",
      "  Number of constraints: 252\n",
      "  Number of variables: 332\n",
      "  Number of binary variables: 136\n",
      "  Number of integer variables: 136\n",
      "  Number of nonzeros: 136\n",
      "  Sense: maximize\n",
      "# ----------------------------------------------------------\n",
      "#   Solver Information\n",
      "# ----------------------------------------------------------\n",
      "Solver: \n",
      "- Status: ok\n",
      "  User time: -1.0\n",
      "  System time: 2.22\n",
      "  Wallclock time: 2.28\n",
      "  Termination condition: optimal\n",
      "  Termination message: Model was solved to optimality (subject to tolerances), and an optimal solution is available.\n",
      "  Statistics: \n",
      "    Branch and bound: \n",
      "      Number of bounded subproblems: 1476\n",
      "      Number of created subproblems: 1476\n",
      "    Black box: \n",
      "      Number of iterations: 17777\n",
      "  Error rc: 0\n",
      "  Time: 2.296165943145752\n",
      "# ----------------------------------------------------------\n",
      "#   Solution Information\n",
      "# ----------------------------------------------------------\n",
      "Solution: \n",
      "- number of solutions: 0\n",
      "  number of solutions displayed: 0\n"
     ]
    }
   ],
   "source": [
    "TIME = np.array(TIME)\n",
    "\n",
    "model = ConcreteModel()\n",
    "\n",
    "# W[i,j,t] 1 if task i starts in unit j at time t\n",
    "model.W = Var(TASKS, UNITS, TIME, domain=Boolean)\n",
    "\n",
    "# B[i,j,t,] size of batch assigned to task i in unit j at time t\n",
    "model.B = Var(TASKS, UNITS, TIME, domain=NonNegativeReals)\n",
    "\n",
    "# S[s,t] inventory of state s at time t\n",
    "model.S = Var(STATES.keys(), TIME, domain=NonNegativeReals)\n",
    "\n",
    "# Q[j,t] inventory of unit j at time t\n",
    "model.Q = Var(UNITS, TIME, domain=NonNegativeReals)\n",
    "\n",
    "# Objective function\n",
    "\n",
    "# project value\n",
    "model.Value = Var(domain=NonNegativeReals)\n",
    "model.valuec = Constraint(expr = model.Value == sum([STATES[s]['price']*model.S[s,H] for s in STATES]))\n",
    "\n",
    "# project cost\n",
    "model.Cost = Var(domain=NonNegativeReals)\n",
    "model.costc = Constraint(expr = model.Cost == sum([UNIT_TASKS[(j,i)]['Cost']*model.W[i,j,t] +\n",
    "        UNIT_TASKS[(j,i)]['vCost']*model.B[i,j,t] for i in TASKS for j in K[i] for t in TIME])) \n",
    "\n",
    "model.obj = Objective(expr = model.Value - model.Cost, sense = maximize)\n",
    "\n",
    "# Constraints\n",
    "model.cons = ConstraintList()\n",
    "\n",
    "# a unit can only be allocated to one task \n",
    "for j in UNITS:\n",
    "    for t in TIME:\n",
    "        lhs = 0\n",
    "        for i in I[j]:\n",
    "            for tprime in TIME:\n",
    "                if tprime >= (t-p[i]+1-UNIT_TASKS[(j,i)]['Tclean']) and tprime <= t:\n",
    "                    lhs += model.W[i,j,tprime]\n",
    "        model.cons.add(lhs <= 1)\n",
    "    \n",
    "# state capacity constraint\n",
    "model.sc = Constraint(STATES.keys(), TIME, rule = lambda model, s, t: model.S[s,t] <= C[s])\n",
    "\n",
    "# state mass balances\n",
    "for s in STATES.keys():\n",
    "    rhs = STATES[s]['initial']\n",
    "    for t in TIME:\n",
    "        for i in T_[s]:\n",
    "            for j in K[i]:\n",
    "                if t >= P[(i,s)]: \n",
    "                    rhs += rho_[(i,s)]*model.B[i,j,max(TIME[TIME <= t-P[(i,s)]])]             \n",
    "        for i in T[s]:\n",
    "            rhs -= rho[(i,s)]*sum([model.B[i,j,t] for j in K[i]])\n",
    "        model.cons.add(model.S[s,t] == rhs)\n",
    "        rhs = model.S[s,t] \n",
    "    \n",
    "# unit capacity constraints\n",
    "for t in TIME:\n",
    "    for j in UNITS:\n",
    "        for i in I[j]:\n",
    "            model.cons.add(model.W[i,j,t]*Bmin[i,j] <= model.B[i,j,t])\n",
    "            model.cons.add(model.B[i,j,t] <= model.W[i,j,t]*Bmax[i,j]) \n",
    "\n",
    "# unit mass balances\n",
    "for j in UNITS:\n",
    "    rhs = 0\n",
    "    for t in TIME:\n",
    "        rhs += sum([model.B[i,j,t] for i in I[j]])\n",
    "        for i in I[j]:\n",
    "            for s in S_[i]:\n",
    "                if t >= P[(i,s)]:\n",
    "                    rhs -= rho_[(i,s)]*model.B[i,j,max(TIME[TIME <= t-P[(i,s)]])]\n",
    "        model.cons.add(model.Q[j,t] == rhs)\n",
    "        rhs = model.Q[j,t]\n",
    "\n",
    "# unit terminal condition\n",
    "model.tc = Constraint(UNITS, rule = lambda model, j: model.Q[j,H] == 0)\n",
    "\n",
    "SolverFactory('cbc').solve(model).write()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "## Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "### Profitability\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of State Inventories =      4893.33\n",
      "  Cost of Unit Assignments =        23.00\n",
      "             Net Objective =      4870.33\n"
     ]
    }
   ],
   "source": [
    "print(\"Value of State Inventories = {0:12.2f}\".format(model.Value()))\n",
    "print(\"  Cost of Unit Assignments = {0:12.2f}\".format(model.Cost()))\n",
    "print(\"             Net Objective = {0:12.2f}\".format(model.Value() - model.Cost()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "### Unit assignment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Heater</th>\n",
       "      <th>Reactor_1</th>\n",
       "      <th>Reactor_2</th>\n",
       "      <th>Still</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>None</td>\n",
       "      <td>(Reaction_1, 80.0)</td>\n",
       "      <td>(Reaction_1, 80.0)</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(Heating, 100.0)</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>None</td>\n",
       "      <td>(Reaction_1, 80.0)</td>\n",
       "      <td>(Reaction_2, 80.0)</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>None</td>\n",
       "      <td>(Reaction_2, 80.0)</td>\n",
       "      <td>(Reaction_2, 80.0)</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>(Heating, 60.0)</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>None</td>\n",
       "      <td>(Reaction_3, 80.0)</td>\n",
       "      <td>(Reaction_2, 80.0)</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>None</td>\n",
       "      <td>(Reaction_3, 80.0)</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>None</td>\n",
       "      <td>(Reaction_3, 80.0)</td>\n",
       "      <td>(Reaction_2, 80.0)</td>\n",
       "      <td>(Separation, 160.0)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>(Heating, 53.333333)</td>\n",
       "      <td>(Reaction_1, 80.0)</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>(Reaction_3, 80.0)</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>None</td>\n",
       "      <td>(Reaction_2, 53.333333)</td>\n",
       "      <td>(Reaction_2, 80.0)</td>\n",
       "      <td>(Separation, 160.0)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>None</td>\n",
       "      <td>(Reaction_3, 40.0)</td>\n",
       "      <td>(Reaction_3, 80.0)</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>(Separation, 120.0)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  Heater                Reactor_1           Reactor_2  \\\n",
       "0                   None       (Reaction_1, 80.0)  (Reaction_1, 80.0)   \n",
       "1       (Heating, 100.0)                     None                None   \n",
       "2                   None       (Reaction_1, 80.0)  (Reaction_2, 80.0)   \n",
       "3                   None                     None                None   \n",
       "4                   None       (Reaction_2, 80.0)  (Reaction_2, 80.0)   \n",
       "5        (Heating, 60.0)                     None                None   \n",
       "6                   None       (Reaction_3, 80.0)  (Reaction_2, 80.0)   \n",
       "7                   None       (Reaction_3, 80.0)                None   \n",
       "8                   None       (Reaction_3, 80.0)  (Reaction_2, 80.0)   \n",
       "9   (Heating, 53.333333)       (Reaction_1, 80.0)                None   \n",
       "10                  None                     None  (Reaction_3, 80.0)   \n",
       "11                  None  (Reaction_2, 53.333333)  (Reaction_2, 80.0)   \n",
       "12                  None                     None                None   \n",
       "13                  None       (Reaction_3, 40.0)  (Reaction_3, 80.0)   \n",
       "14                  None                     None                None   \n",
       "15                  None                     None                None   \n",
       "16                  None                     None                None   \n",
       "\n",
       "                  Still  \n",
       "0                  None  \n",
       "1                  None  \n",
       "2                  None  \n",
       "3                  None  \n",
       "4                  None  \n",
       "5                  None  \n",
       "6                  None  \n",
       "7                  None  \n",
       "8   (Separation, 160.0)  \n",
       "9                  None  \n",
       "10                 None  \n",
       "11  (Separation, 160.0)  \n",
       "12                 None  \n",
       "13                 None  \n",
       "14  (Separation, 120.0)  \n",
       "15                 None  \n",
       "16                 None  "
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "UnitAssignment = pd.DataFrame({j:[None for t in TIME] for j in UNITS}, index=TIME)\n",
    "\n",
    "for t in TIME:\n",
    "    for j in UNITS:\n",
    "        for i in I[j]:\n",
    "            for s in S_[i]:\n",
    "                if t-p[i] >= 0:\n",
    "                    if model.W[i,j,max(TIME[TIME <= t-p[i]])]() > 0:\n",
    "                        UnitAssignment.loc[t,j] = None               \n",
    "        for i in I[j]:\n",
    "            if model.W[i,j,t]() > 0:\n",
    "                UnitAssignment.loc[t,j] = (i,model.B[i,j,t]())\n",
    "\n",
    "UnitAssignment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "### State inventories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Feed_A</th>\n",
       "      <th>Feed_B</th>\n",
       "      <th>Feed_C</th>\n",
       "      <th>Hot_A</th>\n",
       "      <th>Int_AB</th>\n",
       "      <th>Int_BC</th>\n",
       "      <th>Impure_E</th>\n",
       "      <th>Product_1</th>\n",
       "      <th>Product_2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>500.00000</td>\n",
       "      <td>420.0</td>\n",
       "      <td>420.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>400.00000</td>\n",
       "      <td>420.0</td>\n",
       "      <td>420.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>400.00000</td>\n",
       "      <td>380.0</td>\n",
       "      <td>380.0</td>\n",
       "      <td>68.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>112.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>400.00000</td>\n",
       "      <td>380.0</td>\n",
       "      <td>380.0</td>\n",
       "      <td>68.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>112.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>400.00000</td>\n",
       "      <td>380.0</td>\n",
       "      <td>380.0</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.800000e+01</td>\n",
       "      <td>96.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>32.00000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>340.00000</td>\n",
       "      <td>380.0</td>\n",
       "      <td>380.0</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.800000e+01</td>\n",
       "      <td>96.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>32.00000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>340.00000</td>\n",
       "      <td>380.0</td>\n",
       "      <td>364.0</td>\n",
       "      <td>32.000000</td>\n",
       "      <td>8.000000e+01</td>\n",
       "      <td>48.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>96.00000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>340.00000</td>\n",
       "      <td>380.0</td>\n",
       "      <td>348.0</td>\n",
       "      <td>32.000000</td>\n",
       "      <td>1.600000e+01</td>\n",
       "      <td>48.0</td>\n",
       "      <td>80.0</td>\n",
       "      <td>96.00000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>340.00000</td>\n",
       "      <td>380.0</td>\n",
       "      <td>332.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3.182357e-14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>128.00000</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>286.66667</td>\n",
       "      <td>340.0</td>\n",
       "      <td>292.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6.364715e-14</td>\n",
       "      <td>0.0</td>\n",
       "      <td>80.0</td>\n",
       "      <td>128.00000</td>\n",
       "      <td>144.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>286.66667</td>\n",
       "      <td>340.0</td>\n",
       "      <td>276.0</td>\n",
       "      <td>53.333333</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>80.0</td>\n",
       "      <td>160.00000</td>\n",
       "      <td>144.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>286.66667</td>\n",
       "      <td>340.0</td>\n",
       "      <td>276.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>160.00000</td>\n",
       "      <td>144.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>286.66667</td>\n",
       "      <td>340.0</td>\n",
       "      <td>276.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>160.00000</td>\n",
       "      <td>288.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>286.66667</td>\n",
       "      <td>340.0</td>\n",
       "      <td>252.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>213.33333</td>\n",
       "      <td>288.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>286.66667</td>\n",
       "      <td>340.0</td>\n",
       "      <td>252.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>213.33333</td>\n",
       "      <td>288.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>286.66667</td>\n",
       "      <td>340.0</td>\n",
       "      <td>252.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>213.33333</td>\n",
       "      <td>396.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>286.66667</td>\n",
       "      <td>340.0</td>\n",
       "      <td>252.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.200000e+01</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>213.33333</td>\n",
       "      <td>396.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Feed_A  Feed_B  Feed_C      Hot_A        Int_AB  Int_BC  Impure_E  \\\n",
       "0   500.00000   420.0   420.0   0.000000  0.000000e+00     0.0       0.0   \n",
       "1   400.00000   420.0   420.0   0.000000  0.000000e+00     0.0       0.0   \n",
       "2   400.00000   380.0   380.0  68.000000  0.000000e+00   112.0       0.0   \n",
       "3   400.00000   380.0   380.0  68.000000  0.000000e+00   112.0       0.0   \n",
       "4   400.00000   380.0   380.0   4.000000  4.800000e+01    96.0       0.0   \n",
       "5   340.00000   380.0   380.0   4.000000  4.800000e+01    96.0       0.0   \n",
       "6   340.00000   380.0   364.0  32.000000  8.000000e+01    48.0       0.0   \n",
       "7   340.00000   380.0   348.0  32.000000  1.600000e+01    48.0      80.0   \n",
       "8   340.00000   380.0   332.0   0.000000  3.182357e-14     0.0       0.0   \n",
       "9   286.66667   340.0   292.0   0.000000  6.364715e-14     0.0      80.0   \n",
       "10  286.66667   340.0   276.0  53.333333  0.000000e+00     0.0      80.0   \n",
       "11  286.66667   340.0   276.0   0.000000  0.000000e+00     0.0       0.0   \n",
       "12  286.66667   340.0   276.0   0.000000  0.000000e+00     0.0       0.0   \n",
       "13  286.66667   340.0   252.0   0.000000  0.000000e+00     0.0       0.0   \n",
       "14  286.66667   340.0   252.0   0.000000  0.000000e+00     0.0       0.0   \n",
       "15  286.66667   340.0   252.0   0.000000  0.000000e+00     0.0       0.0   \n",
       "16  286.66667   340.0   252.0   0.000000  1.200000e+01     0.0       0.0   \n",
       "\n",
       "    Product_1  Product_2  \n",
       "0     0.00000        0.0  \n",
       "1     0.00000        0.0  \n",
       "2     0.00000        0.0  \n",
       "3     0.00000        0.0  \n",
       "4    32.00000        0.0  \n",
       "5    32.00000        0.0  \n",
       "6    96.00000        0.0  \n",
       "7    96.00000        0.0  \n",
       "8   128.00000        0.0  \n",
       "9   128.00000      144.0  \n",
       "10  160.00000      144.0  \n",
       "11  160.00000      144.0  \n",
       "12  160.00000      288.0  \n",
       "13  213.33333      288.0  \n",
       "14  213.33333      288.0  \n",
       "15  213.33333      396.0  \n",
       "16  213.33333      396.0  "
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame([[model.S[s,t]() for s in STATES.keys()] for t in TIME], columns = STATES.keys(), index = TIME)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x432 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "for (s,idx) in zip(STATES.keys(),range(0,len(STATES.keys()))):\n",
    "    plt.subplot(ceil(len(STATES.keys())/3),3,idx+1)\n",
    "    tlast,ylast = 0,STATES[s]['initial']\n",
    "    for (t,y) in zip(list(TIME),[model.S[s,t]() for t in TIME]):\n",
    "        plt.plot([tlast,t,t],[ylast,ylast,y],'b')\n",
    "        #plt.plot([tlast,t],[ylast,y],'b.',ms=10)\n",
    "        tlast,ylast = t,y\n",
    "    plt.ylim(0,1.1*C[s])\n",
    "    plt.plot([0,H],[C[s],C[s]],'r--')\n",
    "    plt.title(s)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "### Unit batch inventories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Heater</th>\n",
       "      <th>Reactor_1</th>\n",
       "      <th>Reactor_2</th>\n",
       "      <th>Still</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>80.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>80.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>80.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>80.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>80.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>60.000000</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>80.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>80.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>80.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>80.0</td>\n",
       "      <td>160.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>53.333333</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>80.0</td>\n",
       "      <td>16.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>80.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>53.333333</td>\n",
       "      <td>80.0</td>\n",
       "      <td>160.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>53.333333</td>\n",
       "      <td>80.0</td>\n",
       "      <td>16.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>40.000000</td>\n",
       "      <td>80.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>120.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>12.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Heater  Reactor_1  Reactor_2  Still\n",
       "0     0.000000  80.000000       80.0    0.0\n",
       "1   100.000000  80.000000       80.0    0.0\n",
       "2     0.000000  80.000000       80.0    0.0\n",
       "3     0.000000  80.000000       80.0    0.0\n",
       "4     0.000000  80.000000       80.0    0.0\n",
       "5    60.000000  80.000000       80.0    0.0\n",
       "6     0.000000  80.000000       80.0    0.0\n",
       "7     0.000000  80.000000       80.0    0.0\n",
       "8     0.000000  80.000000       80.0  160.0\n",
       "9    53.333333  80.000000       80.0   16.0\n",
       "10    0.000000  80.000000       80.0    0.0\n",
       "11    0.000000  53.333333       80.0  160.0\n",
       "12    0.000000  53.333333       80.0   16.0\n",
       "13    0.000000  40.000000       80.0    0.0\n",
       "14    0.000000   0.000000        0.0  120.0\n",
       "15    0.000000   0.000000        0.0   12.0\n",
       "16    0.000000   0.000000        0.0    0.0"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame([[model.Q[j,t]() for j in UNITS] for t in TIME], columns = UNITS, index = TIME)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "### Gannt chart"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,6))\n",
    "\n",
    "gap = H/500\n",
    "idx = 1\n",
    "lbls = []\n",
    "ticks = []\n",
    "for j in sorted(UNITS):\n",
    "    idx -= 1\n",
    "    for i in sorted(I[j]):\n",
    "        idx -= 1\n",
    "        ticks.append(idx)\n",
    "        lbls.append(\"{0:s} -> {1:s}\".format(j,i))\n",
    "        plt.plot([0,H],[idx,idx],lw=20,alpha=.3,color='y')\n",
    "        for t in TIME:\n",
    "            if model.W[i,j,t]() > 0:\n",
    "                plt.plot([t+gap,t+p[i]-gap], [idx,idx],'b', lw=20, solid_capstyle='butt')\n",
    "                txt = \"{0:.2f}\".format(model.B[i,j,t]())\n",
    "                plt.text(t+p[i]/2, idx, txt, color='white', weight='bold', ha='center', va='center')\n",
    "plt.xlim(0,H)\n",
    "plt.gca().set_yticks(ticks)\n",
    "plt.gca().set_yticklabels(lbls);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "## Trace of events and states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "Starting Conditions\n",
      "    Initial Inventories:\n",
      "        Feed_A       500.0 kg\n",
      "        Feed_B       500.0 kg\n",
      "        Feed_C       500.0 kg\n",
      "        Hot_A          0.0 kg\n",
      "        Int_AB         0.0 kg\n",
      "        Int_BC         0.0 kg\n",
      "        Impure_E       0.0 kg\n",
      "        Product_1      0.0 kg\n",
      "        Product_2      0.0 kg\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "Time = 0 hr\n",
      "    Instructions:\n",
      "        Assign Reactor_2 with capacity 80 kg to task Reaction_1 for 2 hours\n",
      "        Transfer 40.0 kg from Feed_C to Reactor_2\n",
      "        Transfer 40.0 kg from Feed_B to Reactor_2\n",
      "        Assign Reactor_1 with capacity 80 kg to task Reaction_1 for 2 hours\n",
      "        Transfer 40.0 kg from Feed_C to Reactor_1\n",
      "        Transfer 40.0 kg from Feed_B to Reactor_1\n",
      "        Assign Heater with capacity 100 kg to task Heating for 1 hours\n",
      "        Transfer 6.6666667 kg from Feed_A to Heater\n",
      "\n",
      "    Inventories are now:\n",
      "        Feed_A       493.3 kg\n",
      "        Feed_B       420.0 kg\n",
      "        Feed_C       420.0 kg\n",
      "        Hot_A          0.0 kg\n",
      "        Int_AB         0.0 kg\n",
      "        Int_BC         0.0 kg\n",
      "        Impure_E       0.0 kg\n",
      "        Product_1      0.0 kg\n",
      "        Product_2      0.0 kg\n",
      "\n",
      "    Unit Assignments are now:\n",
      "        Reactor_2 performs the Reaction_1 task with a 80.00 kg batch for hour 1.000000 of 2.000000\n",
      "        Reactor_1 performs the Reaction_1 task with a 80.00 kg batch for hour 1.000000 of 2.000000\n",
      "        Heater performs the Heating task with a 6.67 kg batch for hour 1.000000 of 1.000000\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "Time = 1 hr\n",
      "    Instructions:\n",
      "        Transfer 6.6666667 kg from Heater to Hot_A\n",
      "        Release Heater from Heating\n",
      "        Assign Heater with capacity 100 kg to task Heating for 1 hours\n",
      "        Transfer 100.0 kg from Feed_A to Heater\n",
      "\n",
      "    Inventories are now:\n",
      "        Feed_A       393.3 kg\n",
      "        Feed_B       420.0 kg\n",
      "        Feed_C       420.0 kg\n",
      "        Hot_A          6.7 kg\n",
      "        Int_AB         0.0 kg\n",
      "        Int_BC         0.0 kg\n",
      "        Impure_E       0.0 kg\n",
      "        Product_1      0.0 kg\n",
      "        Product_2      0.0 kg\n",
      "\n",
      "    Unit Assignments are now:\n",
      "        Reactor_2 performs the Reaction_1 task with a 80.00 kg batch for hour 2.000000 of 2.000000\n",
      "        Reactor_1 performs the Reaction_1 task with a 80.00 kg batch for hour 2.000000 of 2.000000\n",
      "        Heater performs the Heating task with a 100.00 kg batch for hour 1.000000 of 1.000000\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "Time = 2 hr\n",
      "    Instructions:\n",
      "        Transfer 80.0 kg from Reactor_2 to Int_BC\n",
      "        Transfer 80.0 kg from Reactor_1 to Int_BC\n",
      "        Transfer 100.0 kg from Heater to Hot_A\n",
      "        Release Reactor_2 from Reaction_1\n",
      "        Assign Reactor_2 with capacity 80 kg to task Reaction_2 for 2 hours\n",
      "        Transfer 48.0 kg from Int_BC to Reactor_2\n",
      "        Transfer 32.0 kg from Hot_A to Reactor_2\n",
      "        Release Reactor_1 from Reaction_1\n",
      "        Assign Reactor_1 with capacity 80 kg to task Reaction_2 for 2 hours\n",
      "        Transfer 48.0 kg from Int_BC to Reactor_1\n",
      "        Transfer 32.0 kg from Hot_A to Reactor_1\n",
      "        Release Heater from Heating\n",
      "\n",
      "    Inventories are now:\n",
      "        Feed_A       393.3 kg\n",
      "        Feed_B       420.0 kg\n",
      "        Feed_C       420.0 kg\n",
      "        Hot_A         42.7 kg\n",
      "        Int_AB         0.0 kg\n",
      "        Int_BC        64.0 kg\n",
      "        Impure_E       0.0 kg\n",
      "        Product_1      0.0 kg\n",
      "        Product_2      0.0 kg\n",
      "\n",
      "    Unit Assignments are now:\n",
      "        Reactor_2 performs the Reaction_2 task with a 80.00 kg batch for hour 1.000000 of 2.000000\n",
      "        Reactor_1 performs the Reaction_2 task with a 80.00 kg batch for hour 1.000000 of 2.000000\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "Time = 3 hr\n",
      "    Instructions:\n",
      "\n",
      "    Inventories are now:\n",
      "        Feed_A       393.3 kg\n",
      "        Feed_B       420.0 kg\n",
      "        Feed_C       420.0 kg\n",
      "        Hot_A         42.7 kg\n",
      "        Int_AB         0.0 kg\n",
      "        Int_BC        64.0 kg\n",
      "        Impure_E       0.0 kg\n",
      "        Product_1      0.0 kg\n",
      "        Product_2      0.0 kg\n",
      "\n",
      "    Unit Assignments are now:\n",
      "        Reactor_2 performs the Reaction_2 task with a 80.00 kg batch for hour 2.000000 of 2.000000\n",
      "        Reactor_1 performs the Reaction_2 task with a 80.00 kg batch for hour 2.000000 of 2.000000\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "Time = 4 hr\n",
      "    Instructions:\n",
      "        Transfer 48.0 kg from Reactor_2 to Int_AB\n",
      "        Transfer 32.0 kg from Reactor_2 to Product_1\n",
      "        Transfer 48.0 kg from Reactor_1 to Int_AB\n",
      "        Transfer 32.0 kg from Reactor_1 to Product_1\n",
      "        Release Reactor_2 from Reaction_2\n",
      "        Assign Reactor_2 with capacity 80 kg to task Reaction_3 for 1 hours\n",
      "        Transfer 32.0 kg from Int_AB to Reactor_2\n",
      "        Transfer 8.0 kg from Feed_C to Reactor_2\n",
      "        Release Reactor_1 from Reaction_2\n",
      "        Assign Reactor_1 with capacity 80 kg to task Reaction_3 for 1 hours\n",
      "        Transfer 64.0 kg from Int_AB to Reactor_1\n",
      "        Transfer 16.0 kg from Feed_C to Reactor_1\n",
      "\n",
      "    Inventories are now:\n",
      "        Feed_A       393.3 kg\n",
      "        Feed_B       420.0 kg\n",
      "        Feed_C       396.0 kg\n",
      "        Hot_A         42.7 kg\n",
      "        Int_AB         0.0 kg\n",
      "        Int_BC        64.0 kg\n",
      "        Impure_E       0.0 kg\n",
      "        Product_1     64.0 kg\n",
      "        Product_2      0.0 kg\n",
      "\n",
      "    Unit Assignments are now:\n",
      "        Reactor_2 performs the Reaction_3 task with a 40.00 kg batch for hour 1.000000 of 1.000000\n",
      "        Reactor_1 performs the Reaction_3 task with a 80.00 kg batch for hour 1.000000 of 1.000000\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "Time = 5 hr\n",
      "    Instructions:\n",
      "        Transfer 40.0 kg from Reactor_2 to Impure_E\n",
      "        Transfer 80.0 kg from Reactor_1 to Impure_E\n",
      "        Release Reactor_2 from Reaction_3\n",
      "        Assign Reactor_2 with capacity 80 kg to task Reaction_2 for 2 hours\n",
      "        Transfer 48.0 kg from Int_BC to Reactor_2\n",
      "        Transfer 32.0 kg from Hot_A to Reactor_2\n",
      "        Assign Still with capacity 200 kg to task Separation for 2 hours\n",
      "        Transfer 120.0 kg from Impure_E to Still\n",
      "        Release Reactor_1 from Reaction_3\n",
      "        Assign Reactor_1 with capacity 80 kg to task Reaction_2 for 2 hours\n",
      "        Transfer 16.0000002 kg from Int_BC to Reactor_1\n",
      "        Transfer 10.666666800000002 kg from Hot_A to Reactor_1\n",
      "\n",
      "    Inventories are now:\n",
      "        Feed_A       393.3 kg\n",
      "        Feed_B       420.0 kg\n",
      "        Feed_C       396.0 kg\n",
      "        Hot_A          0.0 kg\n",
      "        Int_AB         0.0 kg\n",
      "        Int_BC         0.0 kg\n",
      "        Impure_E       0.0 kg\n",
      "        Product_1     64.0 kg\n",
      "        Product_2      0.0 kg\n",
      "\n",
      "    Unit Assignments are now:\n",
      "        Reactor_2 performs the Reaction_2 task with a 80.00 kg batch for hour 1.000000 of 2.000000\n",
      "        Still performs the Separation task with a 120.00 kg batch for hour 1.000000 of 2.000000\n",
      "        Reactor_1 performs the Reaction_2 task with a 26.67 kg batch for hour 1.000000 of 2.000000\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "Time = 6 hr\n",
      "    Instructions:\n",
      "        Transfer 108.0 kg from Still to Product_2\n",
      "\n",
      "    Inventories are now:\n",
      "        Feed_A       393.3 kg\n",
      "        Feed_B       420.0 kg\n",
      "        Feed_C       396.0 kg\n",
      "        Hot_A          0.0 kg\n",
      "        Int_AB         0.0 kg\n",
      "        Int_BC         0.0 kg\n",
      "        Impure_E       0.0 kg\n",
      "        Product_1     64.0 kg\n",
      "        Product_2    108.0 kg\n",
      "\n",
      "    Unit Assignments are now:\n",
      "        Reactor_2 performs the Reaction_2 task with a 80.00 kg batch for hour 2.000000 of 2.000000\n",
      "        Still performs the Separation task with a 12.00 kg batch for hour 2.000000 of 2.000000\n",
      "        Reactor_1 performs the Reaction_2 task with a 26.67 kg batch for hour 2.000000 of 2.000000\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "Time = 7 hr\n",
      "    Instructions:\n",
      "        Transfer 48.0 kg from Reactor_2 to Int_AB\n",
      "        Transfer 32.0 kg from Reactor_2 to Product_1\n",
      "        Transfer 12.0 kg from Still to Int_AB\n",
      "        Transfer 16.0000002 kg from Reactor_1 to Int_AB\n",
      "        Transfer 10.666666800000002 kg from Reactor_1 to Product_1\n",
      "        Release Reactor_2 from Reaction_2\n",
      "        Assign Reactor_2 with capacity 80 kg to task Reaction_3 for 1 hours\n",
      "        Transfer 64.0 kg from Int_AB to Reactor_2\n",
      "        Transfer 16.0 kg from Feed_C to Reactor_2\n",
      "        Release Still from Separation\n",
      "        Release Reactor_1 from Reaction_2\n",
      "        Assign Reactor_1 with capacity 80 kg to task Reaction_3 for 1 hours\n",
      "        Transfer 12.0 kg from Int_AB to Reactor_1\n",
      "        Transfer 3.0 kg from Feed_C to Reactor_1\n",
      "\n",
      "    Inventories are now:\n",
      "        Feed_A       393.3 kg\n",
      "        Feed_B       420.0 kg\n",
      "        Feed_C       377.0 kg\n",
      "        Hot_A          0.0 kg\n",
      "        Int_AB         0.0 kg\n",
      "        Int_BC         0.0 kg\n",
      "        Impure_E       0.0 kg\n",
      "        Product_1    106.7 kg\n",
      "        Product_2    108.0 kg\n",
      "\n",
      "    Unit Assignments are now:\n",
      "        Reactor_2 performs the Reaction_3 task with a 80.00 kg batch for hour 1.000000 of 1.000000\n",
      "        Reactor_1 performs the Reaction_3 task with a 15.00 kg batch for hour 1.000000 of 1.000000\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "Time = 8 hr\n",
      "    Instructions:\n",
      "        Transfer 80.0 kg from Reactor_2 to Impure_E\n",
      "        Transfer 15.0 kg from Reactor_1 to Impure_E\n",
      "        Release Reactor_2 from Reaction_3\n",
      "        Assign Still with capacity 200 kg to task Separation for 2 hours\n",
      "        Transfer 95.0 kg from Impure_E to Still\n",
      "        Release Reactor_1 from Reaction_3\n",
      "\n",
      "    Inventories are now:\n",
      "        Feed_A       393.3 kg\n",
      "        Feed_B       420.0 kg\n",
      "        Feed_C       377.0 kg\n",
      "        Hot_A          0.0 kg\n",
      "        Int_AB         0.0 kg\n",
      "        Int_BC         0.0 kg\n",
      "        Impure_E       0.0 kg\n",
      "        Product_1    106.7 kg\n",
      "        Product_2    108.0 kg\n",
      "\n",
      "    Unit Assignments are now:\n",
      "        Still performs the Separation task with a 95.00 kg batch for hour 1.000000 of 2.000000\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "Time = 9 hr\n",
      "    Instructions:\n",
      "        Transfer 85.5 kg from Still to Product_2\n",
      "\n",
      "    Inventories are now:\n",
      "        Feed_A       393.3 kg\n",
      "        Feed_B       420.0 kg\n",
      "        Feed_C       377.0 kg\n",
      "        Hot_A          0.0 kg\n",
      "        Int_AB         0.0 kg\n",
      "        Int_BC         0.0 kg\n",
      "        Impure_E       0.0 kg\n",
      "        Product_1    106.7 kg\n",
      "        Product_2    193.5 kg\n",
      "\n",
      "    Unit Assignments are now:\n",
      "        Still performs the Separation task with a 9.50 kg batch for hour 2.000000 of 2.000000\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "Time = 10 hr\n",
      "    Instructions:\n",
      "        Transfer 9.5 kg from Still to Int_AB\n",
      "        Release Still from Separation\n",
      "\n",
      "    Inventories are now:\n",
      "        Feed_A       393.3 kg\n",
      "        Feed_B       420.0 kg\n",
      "        Feed_C       377.0 kg\n",
      "        Hot_A          0.0 kg\n",
      "        Int_AB         9.5 kg\n",
      "        Int_BC         0.0 kg\n",
      "        Impure_E       0.0 kg\n",
      "        Product_1    106.7 kg\n",
      "        Product_2    193.5 kg\n",
      "\n",
      "    Unit Assignments are now:\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "Final Conditions\n",
      "    Final Inventories:\n",
      "        Feed_A       393.3 kg\n",
      "        Feed_B       420.0 kg\n",
      "        Feed_C       377.0 kg\n",
      "        Hot_A          0.0 kg\n",
      "        Int_AB         9.5 kg\n",
      "        Int_BC         0.0 kg\n",
      "        Impure_E       0.0 kg\n",
      "        Product_1    106.7 kg\n",
      "        Product_2    193.5 kg\n"
     ]
    }
   ],
   "source": [
    "sep = '\\n--------------------------------------------------------------------------------------------\\n'\n",
    "print(sep)\n",
    "print(\"Starting Conditions\")\n",
    "print(\"    Initial Inventories:\")            \n",
    "for s in STATES.keys():\n",
    "        print(\"        {0:10s}  {1:6.1f} kg\".format(s,STATES[s]['initial']))\n",
    "        \n",
    "units = {j:{'assignment':'None', 't':0} for j in UNITS}\n",
    "\n",
    "for t in TIME:\n",
    "    print(sep)\n",
    "    print(\"Time =\",t,\"hr\")\n",
    "    print(\"    Instructions:\")\n",
    "    for j in UNITS:\n",
    "        units[j]['t'] += 1\n",
    "        # transfer from unit to states\n",
    "        for i in I[j]:  \n",
    "            for s in S_[i]:\n",
    "                if t-P[(i,s)] >= 0:\n",
    "                    amt = rho_[(i,s)]*model.B[i,j,max(TIME[TIME <= t - P[(i,s)]])]()\n",
    "                    if amt > 0:\n",
    "                        print(\"        Transfer\", amt, \"kg from\", j, \"to\", s)\n",
    "    for j in UNITS:\n",
    "        # release units from tasks\n",
    "        for i in I[j]:\n",
    "            if t-p[i] >= 0:\n",
    "                if model.W[i,j,max(TIME[TIME <= t-p[i]])]() > 0:\n",
    "                    print(\"        Release\", j, \"from\", i)\n",
    "                    units[j]['assignment'] = 'None'\n",
    "                    units[j]['t'] = 0\n",
    "        # assign units to tasks             \n",
    "        for i in I[j]:\n",
    "            if model.W[i,j,t]() > 0:\n",
    "                print(\"        Assign\", j, \"with capacity\", Bmax[(i,j)], \"kg to task\",i,\"for\",p[i],\"hours\")\n",
    "                units[j]['assignment'] = i\n",
    "                units[j]['t'] = 1\n",
    "        # transfer from states to starting tasks\n",
    "        for i in I[j]:\n",
    "            for s in S[i]:\n",
    "                amt = rho[(i,s)]*model.B[i,j,t]()\n",
    "                if amt > 0:\n",
    "                    print(\"        Transfer\", amt,\"kg from\", s, \"to\", j)\n",
    "    print(\"\\n    Inventories are now:\")            \n",
    "    for s in STATES.keys():\n",
    "        print(\"        {0:10s}  {1:6.1f} kg\".format(s,model.S[s,t]()))\n",
    "    print(\"\\n    Unit Assignments are now:\")\n",
    "    for j in UNITS:\n",
    "        if units[j]['assignment'] != 'None':\n",
    "            fmt = \"        {0:s} performs the {1:s} task with a {2:.2f} kg batch for hour {3:f} of {4:f}\"\n",
    "            i = units[j]['assignment']\n",
    "            print(fmt.format(j,i,model.Q[j,t](),units[j]['t'],p[i]))\n",
    "            \n",
    "print(sep)\n",
    "print('Final Conditions')\n",
    "print(\"    Final Inventories:\")            \n",
    "for s in STATES.keys():\n",
    "        print(\"        {0:10s}  {1:6.1f} kg\".format(s,model.S[s,H]()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}