From 64533fd863d4c8fe81427d9b13b2448b31bcf6a5 Mon Sep 17 00:00:00 2001 From: William J Edsall Date: Thu, 9 Feb 2017 13:07:21 -0500 Subject: [PATCH 1/3] New example resource_task_network --- resource_task_network/RTN.py | 287 ++++++ .../ResourceTaskNetwork.ipynb | 944 ++++++++++++++++++ resource_task_network/images/recipes.jpg | Bin 0 -> 105654 bytes resource_task_network/images/sched1.jpg | Bin 0 -> 155887 bytes resource_task_network/images/sched2.jpg | Bin 0 -> 155115 bytes resource_task_network/images/sched3.jpg | Bin 0 -> 246896 bytes resource_task_network/images/sched4.jpg | Bin 0 -> 242928 bytes resource_task_network/results.yml | 207 ++++ 8 files changed, 1438 insertions(+) create mode 100755 resource_task_network/RTN.py create mode 100644 resource_task_network/ResourceTaskNetwork.ipynb create mode 100644 resource_task_network/images/recipes.jpg create mode 100644 resource_task_network/images/sched1.jpg create mode 100644 resource_task_network/images/sched2.jpg create mode 100644 resource_task_network/images/sched3.jpg create mode 100644 resource_task_network/images/sched4.jpg create mode 100644 resource_task_network/results.yml diff --git a/resource_task_network/RTN.py b/resource_task_network/RTN.py new file mode 100755 index 0000000..12bf26c --- /dev/null +++ b/resource_task_network/RTN.py @@ -0,0 +1,287 @@ +#!/usr/bin/env python +# -*- coding: utf-8 -*- + +# Import +from pyomo.environ import * + +# Creation of a Concrete Model +model = ConcreteModel() + + +# Set i, hours +model.i = Set(initialize=['1','2','3','4','5','6','7','8','9','10', + '11','12','13','14','15','16','17','18','19', + '20','21','22','23','24'], doc='Hours') +# Set k, tasks +model.k = Set(initialize=['reaction', 'inject', 'cool', 'mix', 'package', 'collide', 'melt'], doc='Tasks') + +# Set m, materials +model.m = Set(initialize=['Plastic_Parts', 'Putty', 'ChemA', 'ChemB', 'Dark_Matter', 'Yogurt_Cups', 'Heat_Cool'], doc='Materials') + + +#Set materials_to_hours +def init_materials_to_hours(model): + return (m+"-"+i for m in model.m for i in model.i) +model.materials_to_hours = Set(dimen=1,initialize=init_materials_to_hours) +print "Materials to Hours Set" +#model.materials_to_hours.pprint() + +#Set tasks_to_hours +def init_tasks_to_hours(model): + return (k+"-"+i for k in model.k for i in model.i) +model.tasks_to_hours = Set(dimen=1,initialize=init_tasks_to_hours) +print "Tasks to Hours Set" +#model.tasks_to_hours.pprint() + +#Bounds on Decision Variables - Prevents schedule overrun +def DecBounds(model, i): + isp = i.split("-") + ii = int( isp[1] ) + ina = isp[0] + + if ina == "Plastic_Parts" and ii > (24-5): return (0,0) + if ina == "Putty" and ii > (24-2): return (0,0) + if ina == "ChemA" and ii > (24-4): return (0,0) + if ina == "ChemB" and ii > (24-8): return (0,0) + if ina == "Dark_Matter" and ii > (24-5): return (0,0) + if ina == "Yogurt_Cups" and ii > (24-4): return (0,0) + if ina == "Heat_Cool" and ii > (24-7): return (0,0) + + return (0,1) +#Binary Decision Variables Deci +def zeros(model, x): + return 0 +model.Deci = Var(model.materials_to_hours, within=Binary, initialize=zeros, bounds=DecBounds) +model.Deci.pprint() + +#Free Variables Task_HRS +model.Task_HRS = Var(model.tasks_to_hours, domain=NonNegativeIntegers) +model.Task_HRS.pprint() + +#Free Variables Resources +model.Resources = Var(model.k, domain=PositiveIntegers) +model.Resources.pprint() + +def mixer_rule(model, i): + ii = int(i) + if ii == 1: + return model.Task_HRS["mix-1"] == model.Resources['mix'] \ + - model.Deci["Putty-1"] - model.Deci["ChemB-1"] + if ii == 2: + return model.Task_HRS["mix-2"] == model.Task_HRS["mix-1"] \ + - model.Deci["Putty-2"] \ + - model.Deci["ChemB-2"] + model.Deci["ChemB-1"] + if ii == 3: + return model.Task_HRS["mix-3"] == model.Task_HRS["mix-2"] \ + - model.Deci["Putty-3"] + model.Deci["Putty-1"] \ + - model.Deci["ChemB-3"] + model.Deci["ChemB-2"] \ + - model.Deci["Dark_Matter-1"] + + return model.Task_HRS["mix-"+i] == model.Task_HRS["mix-"+str(ii-1)] \ + - model.Deci["Putty-"+i] + model.Deci["Putty-"+str(ii-2)] \ + - model.Deci["ChemB-"+i] + model.Deci["ChemB-"+str(ii-1)] \ + - model.Deci["Dark_Matter-"+str(ii-2)] + model.Deci["Dark_Matter-"+str(ii-3)] + +model.mixer_constraint = Constraint(model.i, rule=mixer_rule) + +def melter_rule(model, i): + ii = int(i) + if ii == 1: + return model.Task_HRS["melt-1"] == model.Resources['melt'] \ + - model.Deci["Plastic_Parts-1"] - model.Deci["ChemA-1"] \ + - model.Deci["Yogurt_Cups-1"] - model.Deci["Heat_Cool-1"] + if ii > 1 and ii < 4: + return model.Task_HRS["melt-"+i] == model.Task_HRS["melt-"+str(ii-1)] \ + - model.Deci["Plastic_Parts-"+i] + model.Deci["Plastic_Parts-"+str(ii-1)] \ + - model.Deci["ChemA-"+i] + model.Deci["ChemA-"+str(ii-1)] \ + - model.Deci["Yogurt_Cups-"+i] + model.Deci["Yogurt_Cups-"+str(ii-1)] \ + - model.Deci["Heat_Cool-"+i] + model.Deci["Heat_Cool-"+str(ii-1)] + + return model.Task_HRS["melt-"+i] == model.Task_HRS["melt-"+str(ii-1)] \ + - model.Deci["Plastic_Parts-"+i] + model.Deci["Plastic_Parts-"+str(ii-1)] \ + - model.Deci["ChemA-"+i] + model.Deci["ChemA-"+str(ii-1)] \ + - model.Deci["Yogurt_Cups-"+i] + model.Deci["Yogurt_Cups-"+str(ii-1)] \ + - model.Deci["Heat_Cool-"+i] + model.Deci["Heat_Cool-"+str(ii-1)] \ + - model.Deci["Heat_Cool-"+str(ii-2)] + model.Deci["Heat_Cool-"+str(ii-3)] + +model.melter_constraint = Constraint(model.i, rule=melter_rule) + +def injector_rule(model, i): + ii = int(i) + if ii == 1: + return model.Task_HRS["inject-1"] == model.Resources['inject'] + if ii == 2: + return model.Task_HRS["inject-2"] == model.Task_HRS["inject-1"] - model.Deci["Plastic_Parts-1"] + if ii == 3: + return model.Task_HRS["inject-3"] == model.Task_HRS["inject-2"] - model.Deci["Plastic_Parts-2"] + if ii > 3 and ii < 6: + return model.Task_HRS["inject-"+i] == model.Task_HRS["inject-"+str(ii-1)] \ + - model.Deci["Plastic_Parts-"+str(ii-1)] \ + + model.Deci["Plastic_Parts-"+str(ii-3)] + return model.Task_HRS["inject-"+i] == model.Task_HRS["inject-"+str(ii-1)] \ + - model.Deci["Plastic_Parts-"+str(ii-1)] \ + + model.Deci["Plastic_Parts-"+str(ii-3)] \ + - model.Deci["Heat_Cool-"+str(ii-5)] + +model.injector_constraint = Constraint(model.i, rule=injector_rule) + + +def packager_rule(model, i): + ii = int(i) + if ii == 1: + return model.Task_HRS["package-1"] == model.Resources['package'] + if ii == 2: + return model.Task_HRS["package-2"] == model.Task_HRS["package-1"] \ + - model.Deci["ChemA-1"] \ + - model.Deci["Yogurt_Cups-1"] + if ii == 3: + return model.Task_HRS["package-3"] == model.Task_HRS["package-2"] \ + - model.Deci["Putty-1"] \ + - model.Deci["ChemA-2"] \ + - model.Deci["Yogurt_Cups-2"] + if ii > 3 and ii < 6: + return model.Task_HRS["package-"+i] == model.Task_HRS["package-"+str(ii-1)] \ + - model.Deci["Putty-"+str(ii-2)] + model.Deci["Putty-"+str(ii-3)] \ + - model.Deci["ChemA-"+str(ii-1)] \ + - model.Deci["Yogurt_Cups-"+str(ii-1)] + if ii > 5 and ii < 8: + return model.Task_HRS["package-"+i] == model.Task_HRS["package-"+str(ii-1)] \ + - model.Deci["Putty-"+str(ii-2)] + model.Deci["Putty-"+str(ii-3)] \ + - model.Deci["Plastic_Parts-"+str(ii-5)] \ + - model.Deci["ChemA-"+str(ii-1)] + model.Deci["ChemA-"+str(ii-5)] \ + - model.Deci["Dark_Matter-"+str(ii-5)] \ + - model.Deci["Yogurt_Cups-"+str(ii-1)] + model.Deci["Yogurt_Cups-"+str(ii-5)] + if ii > 7 and ii < 9: + return model.Task_HRS["package-"+i] == model.Task_HRS["package-"+str(ii-1)] \ + - model.Deci["Putty-"+str(ii-2)] + model.Deci["Putty-"+str(ii-3)] \ + - model.Deci["Plastic_Parts-"+str(ii-5)] + model.Deci["Plastic_Parts-"+str(ii-6)] \ + - model.Deci["ChemA-"+str(ii-1)] + model.Deci["ChemA-"+str(ii-5)] \ + - model.Deci["ChemB-"+str(ii-7)] \ + - model.Deci["Dark_Matter-"+str(ii-5)] + model.Deci["Dark_Matter-"+str(ii-6)] \ + - model.Deci["Yogurt_Cups-"+str(ii-1)] + model.Deci["Yogurt_Cups-"+str(ii-5)] \ + - model.Deci["Heat_Cool-"+str(ii-7)] + if ii > 8 and ii < 10: + return model.Task_HRS["package-"+i] == model.Task_HRS["package-"+str(ii-1)] \ + - model.Deci["Putty-"+str(ii-2)] + model.Deci["Putty-"+str(ii-3)] \ + - model.Deci["Plastic_Parts-"+str(ii-5)] + model.Deci["Plastic_Parts-"+str(ii-6)] \ + - model.Deci["ChemA-"+str(ii-1)] + model.Deci["ChemA-"+str(ii-5)] \ + - model.Deci["ChemB-"+str(ii-7)] \ + - model.Deci["Dark_Matter-"+str(ii-5)] + model.Deci["Dark_Matter-"+str(ii-6)] \ + - model.Deci["Yogurt_Cups-"+str(ii-1)] + model.Deci["Yogurt_Cups-"+str(ii-5)] \ + - model.Deci["Heat_Cool-"+str(ii-7)] + model.Deci["Heat_Cool-"+str(ii-8)] + + return model.Task_HRS["package-"+i] == model.Task_HRS["package-"+str(ii-1)] \ + - model.Deci["Putty-"+str(ii-2)] + model.Deci["Putty-"+str(ii-3)] \ + - model.Deci["Plastic_Parts-"+str(ii-5)] + model.Deci["Plastic_Parts-"+str(ii-6)] \ + - model.Deci["ChemA-"+str(ii-1)] + model.Deci["ChemA-"+str(ii-5)] \ + - model.Deci["ChemB-"+str(ii-7)] + model.Deci["ChemB-"+str(ii-9)] \ + - model.Deci["Dark_Matter-"+str(ii-5)] + model.Deci["Dark_Matter-"+str(ii-6)] \ + - model.Deci["Yogurt_Cups-"+str(ii-1)] + model.Deci["Yogurt_Cups-"+str(ii-5)] \ + - model.Deci["Heat_Cool-"+str(ii-7)] + model.Deci["Heat_Cool-"+str(ii-8)] + +model.packager_constraint = Constraint(model.i, rule=packager_rule) + +def collider_rule(model, i): + ii = int(i) + if ii == 1: + return model.Task_HRS["collide-1"] == model.Resources['collide'] - model.Deci["Dark_Matter-1"] + if ii == 2: + return model.Task_HRS["collide-2"] == model.Task_HRS["collide-1"] - model.Deci["Dark_Matter-2"] + + return model.Task_HRS["collide-"+i] == model.Task_HRS["collide-"+str(ii-1)] \ + - model.Deci["Dark_Matter-"+str(ii)] + model.Deci["Dark_Matter-"+str(ii-2)] + +model.collider_constraint = Constraint(model.i, rule=collider_rule) + +def cooler_rule(model, i): + ii = int(i) + if ii == 1: + return model.Task_HRS["cool-1"] == model.Resources['cool'] + if ii == 2: + return model.Task_HRS["cool-1"] == model.Task_HRS["cool-1"] - model.Deci["Heat_Cool-1"] + if ii == 3: + return model.Task_HRS["cool-"+i] == model.Task_HRS["cool-"+str(ii-1)] \ + - model.Deci["Heat_Cool-"+str(ii-1)] + model.Deci["Heat_Cool-"+str(ii-2)] + if ii == 4: + return model.Task_HRS["cool-"+i] == model.Task_HRS["cool-"+str(ii-1)] \ + - model.Deci["Plastic_Parts-"+str(ii-3)] \ + - model.Deci["Heat_Cool-"+str(ii-1)] + model.Deci["Heat_Cool-"+str(ii-2)] \ + - model.Deci["Heat_Cool-"+str(ii-3)] + if ii == 5: + return model.Task_HRS["cool-"+i] == model.Task_HRS["cool-"+str(ii-1)] \ + - model.Deci["Plastic_Parts-"+str(ii-3)] \ + - model.Deci["Dark_Matter-"+str(ii-4)] \ + - model.Deci["Heat_Cool-"+str(ii-1)] + model.Deci["Heat_Cool-"+str(ii-2)] \ + - model.Deci["Heat_Cool-"+str(ii-3)] + model.Deci["Heat_Cool-"+str(ii-4)] + if ii == 6: + return model.Task_HRS["cool-"+i] == model.Task_HRS["cool-"+str(ii-1)] \ + - model.Deci["Plastic_Parts-"+str(ii-3)] + model.Deci["Plastic_Parts-"+str(ii-5)] \ + - model.Deci["Dark_Matter-"+str(ii-4)] + model.Deci["Dark_Matter-"+str(ii-5)] \ + - model.Deci["Heat_Cool-"+str(ii-1)] + model.Deci["Heat_Cool-"+str(ii-2)] \ + - model.Deci["Heat_Cool-"+str(ii-3)] + model.Deci["Heat_Cool-"+str(ii-4)] + if ii == 7: + return model.Task_HRS["cool-"+i] == model.Task_HRS["cool-"+str(ii-1)] \ + - model.Deci["Plastic_Parts-"+str(ii-3)] + model.Deci["Plastic_Parts-"+str(ii-5)] \ + - model.Deci["ChemB-"+str(ii-6)] \ + - model.Deci["Dark_Matter-"+str(ii-4)] + model.Deci["Dark_Matter-"+str(ii-5)] \ + - model.Deci["Heat_Cool-"+str(ii-1)] + model.Deci["Heat_Cool-"+str(ii-2)] \ + - model.Deci["Heat_Cool-"+str(ii-3)] + model.Deci["Heat_Cool-"+str(ii-4)] + + return model.Task_HRS["cool-"+i] == model.Task_HRS["cool-"+str(ii-1)] \ + - model.Deci["Plastic_Parts-"+str(ii-3)] + model.Deci["Plastic_Parts-"+str(ii-5)] \ + - model.Deci["ChemB-"+str(ii-6)] + model.Deci["ChemB-"+str(ii-7)] \ + - model.Deci["Dark_Matter-"+str(ii-4)] + model.Deci["Dark_Matter-"+str(ii-5)] \ + - model.Deci["Heat_Cool-"+str(ii-1)] + model.Deci["Heat_Cool-"+str(ii-2)] \ + - model.Deci["Heat_Cool-"+str(ii-3)] + model.Deci["Heat_Cool-"+str(ii-4)] + +model.cooler_constraint = Constraint(model.i, rule=cooler_rule) + +def reactor_rule(model, i): + ii = int(i) + if ii == 1: + return model.Task_HRS["reaction-1"] == model.Resources['reaction'] + if ii > 1 and ii < 4: + return model.Task_HRS["reaction-"+i] == model.Task_HRS["reaction-"+str(ii-1)] \ + - model.Deci["ChemB-"+str(ii-1)] + if ii > 3 and ii < 5: + return model.Task_HRS["reaction-"+i] == model.Task_HRS["reaction-"+str(ii-1)] \ + - model.Deci["ChemB-"+str(ii-1)] \ + - model.Deci["Dark_Matter-"+str(ii-3)] + if ii > 4 and ii < 7: + return model.Task_HRS["reaction-"+i] == model.Task_HRS["reaction-"+str(ii-1)] \ + - model.Deci["ChemB-"+str(ii-1)] \ + - model.Deci["Dark_Matter-"+str(ii-3)] + model.Deci["Dark_Matter-"+str(ii-4)] + + return model.Task_HRS["reaction-"+i] == model.Task_HRS["reaction-"+str(ii-1)] \ + - model.Deci["ChemB-"+str(ii-1)] + model.Deci["ChemB-"+str(ii-6)] \ + - model.Deci["Dark_Matter-"+str(ii-3)] + model.Deci["Dark_Matter-"+str(ii-4)] + +model.reactor_constraint = Constraint(model.i, rule=reactor_rule) + +#Objective +def objective_rule(model): + return sum(model.Task_HRS[k+"-"+i] for k in model.k for i in model.i) +#return sum(model.resourceAllocation[i,j] for i in model.i for j in model.j) +model.objective = Objective(rule=objective_rule, sense=minimize, doc='Define objective function') + + +## Display of the output ## +# Display x.l, x.m ; +##def pyomo_postprocess(options=None, instance=None, results=None): +## model.Deci.display() +## model.Task_HRS.display() + +# This is an optional code path that allows the script to be run outside of +# pyomo command-line. For example: python transport.py +if __name__ == '__main__': + # This emulates what the pyomo command-line tools does + + from pyomo.opt import SolverFactory + import pyomo.environ + opt = SolverFactory("cplex") + results = opt.solve(model) + #sends results to stdout + + results.write() + print("\nDisplaying Solution\n" + '-'*60) + pyomo_postprocess(None, instance, results) \ No newline at end of file diff --git a/resource_task_network/ResourceTaskNetwork.ipynb b/resource_task_network/ResourceTaskNetwork.ipynb new file mode 100644 index 0000000..2f9e73b --- /dev/null +++ b/resource_task_network/ResourceTaskNetwork.ipynb @@ -0,0 +1,944 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Summary\n", + "Multipurpose batch plants can produce a variety of chemicals and materials. \n", + "Each material may require to follow a task recipe. In this context a resource \n", + "is any piece of equipment or material which is consumed during a task, or created \n", + "as the result of a task.\n", + "\n", + "\n", + "## Problem Statement\n", + "\n", + "This problem can be formulated as a mixed-integer programming problem with binary \n", + "decision variables. Non-negative constraints are used to bound resources to tasks. \n", + "\n", + "### Sets\n", + " $T$ = Time Points $\\forall t \\in (1,2,...,24)$
\n", + " \n", + " $M$ = Materials $\\forall m \\in \n", + " (Plastic\\_Parts, Putty, ChemA, ChemB, Dark\\_Matter, Yogurt\\_Cups, Heat\\_Cool)$
\n", + " \n", + " $K$ = Tasks $\\forall k \\in \n", + " (reaction, inject, cool, mix, package, collide, melt)$
\n", + " \n", + "### Binary Decision Variables\n", + " $N_{m,t}$ = Begin recipe for material m at time t\n", + "\n", + "### Positive Free Variables\n", + " $R_{k,t}$ = Task k availablity at time t\n", + "\n", + "### Positive Nonzero Free Variables\n", + " $E_{e}$ = Amount of resource e\n", + "\n", + "### Objective\n", + "\n", + "Minimize the number of idle tasks:
\n", + "$\\min_{x} z = \\sum_{k \\in K} \\sum_{t \\in T} R_{k,t}$\n", + " \n", + "### Recipes\n", + "A fictitious set of recipes is created to simulate a multipurpose batch plant. \n", + "One objective with the recipes is to create overlapping task requirements between material \n", + "recipes to simulate contention for resources. Some materials have exclusive resources such as \n", + "Dark Matter while most materials share some equipment such as the Packager.\n", + "\n", + "![title](images/recipes.jpg)\n", + "\n", + "\n", + "## Pyomo Formulation\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Initial Setup" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "#!/usr/bin/env python\n", + "# -*- coding: utf-8 -*-\n", + "\n", + "# Import\n", + "from pyomo.environ import *\n", + " \n", + "# Creation of a Concrete Model\n", + "model = ConcreteModel()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "### Sets" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Set i, hours\n", + "model.i = Set(initialize=['1','2','3','4','5','6','7','8','9','10',\n", + " '11','12','13','14','15','16','17','18','19',\n", + " '20','21','22','23','24'], doc='Hours') \n", + "# Set k, tasks\n", + "model.k = Set(initialize=['reaction', 'inject', 'cool', 'mix', 'package', 'collide', 'melt'], doc='Tasks')\n", + "\n", + "# Set m, materials\n", + "model.m = Set(initialize=['Plastic_Parts', 'Putty', 'ChemA', 'ChemB', 'Dark_Matter', 'Yogurt_Cups', 'Heat_Cool'], doc='Materials')\n", + "\n", + "\n", + "#Set materials_to_hours\n", + "def init_materials_to_hours(model):\n", + " return (m+\"-\"+i for m in model.m for i in model.i)\n", + "model.materials_to_hours = Set(dimen=1,initialize=init_materials_to_hours) \n", + "print \"Materials to Hours Set\"\n", + "#model.materials_to_hours.pprint()\n", + "\n", + "#Set tasks_to_hours\n", + "def init_tasks_to_hours(model):\n", + " return (k+\"-\"+i for k in model.k for i in model.i)\n", + "model.tasks_to_hours = Set(dimen=1,initialize=init_tasks_to_hours) \n", + "print \"Tasks to Hours Set\"\n", + "#model.tasks_to_hours.pprint()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Binary Decision Variables\n", + "\n", + "Decision variables are bounded above at a point relative to their recipe length to prevent schedule overruns. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "#Bounds on Decision Variables - Prevents schedule overrun\n", + "def DecBounds(model, i):\n", + " isp = i.split(\"-\")\n", + " ii = int( isp[1] )\n", + " ina = isp[0]\n", + " \n", + " if ina == \"Plastic_Parts\" and ii > (24-5): return (0,0)\n", + " if ina == \"Putty\" and ii > (24-2): return (0,0)\n", + " if ina == \"ChemA\" and ii > (24-4): return (0,0)\n", + " if ina == \"ChemB\" and ii > (24-8): return (0,0)\n", + " if ina == \"Dark_Matter\" and ii > (24-5): return (0,0)\n", + " if ina == \"Yogurt_Cups\" and ii > (24-4): return (0,0)\n", + " if ina == \"Heat_Cool\" and ii > (24-7): return (0,0)\n", + " \n", + " return (0,1)\n", + "#Binary Decision Variables Deci\n", + "def zeros(model, x):\n", + " return 0\n", + "model.Deci = Var(model.materials_to_hours, within=Binary, initialize=zeros, bounds=DecBounds) \n", + "#model.Deci.pprint()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### NonNegativeInteger Free Variables" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "#Free Variables Task_HRS\n", + "model.Task_HRS = Var(model.tasks_to_hours, domain=NonNegativeIntegers) \n", + "#model.Task_HRS.pprint()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# PositiveInteger Free Variables" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "#Free Variables Resources\n", + "model.Resources = Var(model.k, domain=PositiveIntegers) \n", + "model.Resources.pprint()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Constraints\n", + "\n", + "Constraints are the 'magic' behind this RTN problem. Consider the constraints a token system where each resource has a token that may be taken away and perhaps given back at a certain point. Consider also the Putty schedule (Mixing->Mixing->Packaging). If the Putty material were to be started at time t=1, then the mixer would be busy until t=3 when the token would be given back to the mixing task, making it available to other recipes." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def mixer_rule(model, i):\n", + " ii = int(i)\n", + " if ii == 1:\n", + " return model.Task_HRS[\"mix-1\"] == model.Resources['mix'] \\\n", + " - model.Deci[\"Putty-1\"] - model.Deci[\"ChemB-1\"]\n", + " if ii == 2:\n", + " return model.Task_HRS[\"mix-2\"] == model.Task_HRS[\"mix-1\"] \\\n", + " - model.Deci[\"Putty-2\"] \\\n", + " - model.Deci[\"ChemB-2\"] + model.Deci[\"ChemB-1\"] \n", + " if ii == 3:\n", + " return model.Task_HRS[\"mix-3\"] == model.Task_HRS[\"mix-2\"] \\\n", + " - model.Deci[\"Putty-3\"] + model.Deci[\"Putty-1\"] \\\n", + " - model.Deci[\"ChemB-3\"] + model.Deci[\"ChemB-2\"] \\\n", + " - model.Deci[\"Dark_Matter-1\"]\n", + " \n", + " return model.Task_HRS[\"mix-\"+i] == model.Task_HRS[\"mix-\"+str(ii-1)] \\\n", + " - model.Deci[\"Putty-\"+i] + model.Deci[\"Putty-\"+str(ii-2)] \\\n", + " - model.Deci[\"ChemB-\"+i] + model.Deci[\"ChemB-\"+str(ii-1)] \\\n", + " - model.Deci[\"Dark_Matter-\"+str(ii-2)] + model.Deci[\"Dark_Matter-\"+str(ii-3)] \n", + "\n", + "model.mixer_constraint = Constraint(model.i, rule=mixer_rule)\n", + "\n", + "def melter_rule(model, i):\n", + " ii = int(i)\n", + " if ii == 1:\n", + " return model.Task_HRS[\"melt-1\"] == model.Resources['melt'] \\\n", + " - model.Deci[\"Plastic_Parts-1\"] - model.Deci[\"ChemA-1\"] \\\n", + " - model.Deci[\"Yogurt_Cups-1\"] - model.Deci[\"Heat_Cool-1\"]\n", + " if ii > 1 and ii < 4: \n", + " return model.Task_HRS[\"melt-\"+i] == model.Task_HRS[\"melt-\"+str(ii-1)] \\\n", + " - model.Deci[\"Plastic_Parts-\"+i] + model.Deci[\"Plastic_Parts-\"+str(ii-1)] \\\n", + " - model.Deci[\"ChemA-\"+i] + model.Deci[\"ChemA-\"+str(ii-1)] \\\n", + " - model.Deci[\"Yogurt_Cups-\"+i] + model.Deci[\"Yogurt_Cups-\"+str(ii-1)] \\\n", + " - model.Deci[\"Heat_Cool-\"+i] + model.Deci[\"Heat_Cool-\"+str(ii-1)] \n", + " \n", + " return model.Task_HRS[\"melt-\"+i] == model.Task_HRS[\"melt-\"+str(ii-1)] \\\n", + " - model.Deci[\"Plastic_Parts-\"+i] + model.Deci[\"Plastic_Parts-\"+str(ii-1)] \\\n", + " - model.Deci[\"ChemA-\"+i] + model.Deci[\"ChemA-\"+str(ii-1)] \\\n", + " - model.Deci[\"Yogurt_Cups-\"+i] + model.Deci[\"Yogurt_Cups-\"+str(ii-1)] \\\n", + " - model.Deci[\"Heat_Cool-\"+i] + model.Deci[\"Heat_Cool-\"+str(ii-1)] \\\n", + " - model.Deci[\"Heat_Cool-\"+str(ii-2)] + model.Deci[\"Heat_Cool-\"+str(ii-3)] \n", + " \n", + "model.melter_constraint = Constraint(model.i, rule=melter_rule)\n", + "\n", + "def injector_rule(model, i):\n", + " ii = int(i)\n", + " if ii == 1:\n", + " return model.Task_HRS[\"inject-1\"] == model.Resources['inject']\n", + " if ii == 2:\n", + " return model.Task_HRS[\"inject-2\"] == model.Task_HRS[\"inject-1\"] - model.Deci[\"Plastic_Parts-1\"]\n", + " if ii == 3:\n", + " return model.Task_HRS[\"inject-3\"] == model.Task_HRS[\"inject-2\"] - model.Deci[\"Plastic_Parts-2\"] \n", + " if ii > 3 and ii < 6:\n", + " return model.Task_HRS[\"inject-\"+i] == model.Task_HRS[\"inject-\"+str(ii-1)] \\\n", + " - model.Deci[\"Plastic_Parts-\"+str(ii-1)] \\\n", + " + model.Deci[\"Plastic_Parts-\"+str(ii-3)] \n", + " return model.Task_HRS[\"inject-\"+i] == model.Task_HRS[\"inject-\"+str(ii-1)] \\\n", + " - model.Deci[\"Plastic_Parts-\"+str(ii-1)] \\\n", + " + model.Deci[\"Plastic_Parts-\"+str(ii-3)] \\\n", + " - model.Deci[\"Heat_Cool-\"+str(ii-5)] \n", + " \n", + "model.injector_constraint = Constraint(model.i, rule=injector_rule)\n", + "\n", + "\n", + "def packager_rule(model, i):\n", + " ii = int(i)\n", + " if ii == 1:\n", + " return model.Task_HRS[\"package-1\"] == model.Resources['package']\n", + " if ii == 2:\n", + " return model.Task_HRS[\"package-2\"] == model.Task_HRS[\"package-1\"] \\\n", + " - model.Deci[\"ChemA-1\"] \\\n", + " - model.Deci[\"Yogurt_Cups-1\"]\n", + " if ii == 3:\n", + " return model.Task_HRS[\"package-3\"] == model.Task_HRS[\"package-2\"] \\\n", + " - model.Deci[\"Putty-1\"] \\\n", + " - model.Deci[\"ChemA-2\"] \\\n", + " - model.Deci[\"Yogurt_Cups-2\"]\n", + " if ii > 3 and ii < 6: \n", + " return model.Task_HRS[\"package-\"+i] == model.Task_HRS[\"package-\"+str(ii-1)] \\\n", + " - model.Deci[\"Putty-\"+str(ii-2)] + model.Deci[\"Putty-\"+str(ii-3)] \\\n", + " - model.Deci[\"ChemA-\"+str(ii-1)] \\\n", + " - model.Deci[\"Yogurt_Cups-\"+str(ii-1)]\n", + " if ii > 5 and ii < 8:\n", + " return model.Task_HRS[\"package-\"+i] == model.Task_HRS[\"package-\"+str(ii-1)] \\\n", + " - model.Deci[\"Putty-\"+str(ii-2)] + model.Deci[\"Putty-\"+str(ii-3)] \\\n", + " - model.Deci[\"Plastic_Parts-\"+str(ii-5)] \\\n", + " - model.Deci[\"ChemA-\"+str(ii-1)] + model.Deci[\"ChemA-\"+str(ii-5)] \\\n", + " - model.Deci[\"Dark_Matter-\"+str(ii-5)] \\\n", + " - model.Deci[\"Yogurt_Cups-\"+str(ii-1)] + model.Deci[\"Yogurt_Cups-\"+str(ii-5)] \n", + " if ii > 7 and ii < 9:\n", + " return model.Task_HRS[\"package-\"+i] == model.Task_HRS[\"package-\"+str(ii-1)] \\\n", + " - model.Deci[\"Putty-\"+str(ii-2)] + model.Deci[\"Putty-\"+str(ii-3)] \\\n", + " - model.Deci[\"Plastic_Parts-\"+str(ii-5)] + model.Deci[\"Plastic_Parts-\"+str(ii-6)] \\\n", + " - model.Deci[\"ChemA-\"+str(ii-1)] + model.Deci[\"ChemA-\"+str(ii-5)] \\\n", + " - model.Deci[\"ChemB-\"+str(ii-7)] \\\n", + " - model.Deci[\"Dark_Matter-\"+str(ii-5)] + model.Deci[\"Dark_Matter-\"+str(ii-6)] \\\n", + " - model.Deci[\"Yogurt_Cups-\"+str(ii-1)] + model.Deci[\"Yogurt_Cups-\"+str(ii-5)] \\\n", + " - model.Deci[\"Heat_Cool-\"+str(ii-7)] \n", + " if ii > 8 and ii < 10: \n", + " return model.Task_HRS[\"package-\"+i] == model.Task_HRS[\"package-\"+str(ii-1)] \\\n", + " - model.Deci[\"Putty-\"+str(ii-2)] + model.Deci[\"Putty-\"+str(ii-3)] \\\n", + " - model.Deci[\"Plastic_Parts-\"+str(ii-5)] + model.Deci[\"Plastic_Parts-\"+str(ii-6)] \\\n", + " - model.Deci[\"ChemA-\"+str(ii-1)] + model.Deci[\"ChemA-\"+str(ii-5)] \\\n", + " - model.Deci[\"ChemB-\"+str(ii-7)] \\\n", + " - model.Deci[\"Dark_Matter-\"+str(ii-5)] + model.Deci[\"Dark_Matter-\"+str(ii-6)] \\\n", + " - model.Deci[\"Yogurt_Cups-\"+str(ii-1)] + model.Deci[\"Yogurt_Cups-\"+str(ii-5)] \\\n", + " - model.Deci[\"Heat_Cool-\"+str(ii-7)] + model.Deci[\"Heat_Cool-\"+str(ii-8)] \n", + " \n", + " return model.Task_HRS[\"package-\"+i] == model.Task_HRS[\"package-\"+str(ii-1)] \\\n", + " - model.Deci[\"Putty-\"+str(ii-2)] + model.Deci[\"Putty-\"+str(ii-3)] \\\n", + " - model.Deci[\"Plastic_Parts-\"+str(ii-5)] + model.Deci[\"Plastic_Parts-\"+str(ii-6)] \\\n", + " - model.Deci[\"ChemA-\"+str(ii-1)] + model.Deci[\"ChemA-\"+str(ii-5)] \\\n", + " - model.Deci[\"ChemB-\"+str(ii-7)] + model.Deci[\"ChemB-\"+str(ii-9)] \\\n", + " - model.Deci[\"Dark_Matter-\"+str(ii-5)] + model.Deci[\"Dark_Matter-\"+str(ii-6)] \\\n", + " - model.Deci[\"Yogurt_Cups-\"+str(ii-1)] + model.Deci[\"Yogurt_Cups-\"+str(ii-5)] \\\n", + " - model.Deci[\"Heat_Cool-\"+str(ii-7)] + model.Deci[\"Heat_Cool-\"+str(ii-8)]\n", + "\n", + "model.packager_constraint = Constraint(model.i, rule=packager_rule)\n", + "\n", + "def collider_rule(model, i):\n", + " ii = int(i)\n", + " if ii == 1:\n", + " return model.Task_HRS[\"collide-1\"] == model.Resources['collide'] - model.Deci[\"Dark_Matter-1\"]\n", + " if ii == 2:\n", + " return model.Task_HRS[\"collide-2\"] == model.Task_HRS[\"collide-1\"] - model.Deci[\"Dark_Matter-2\"]\n", + " \n", + " return model.Task_HRS[\"collide-\"+i] == model.Task_HRS[\"collide-\"+str(ii-1)] \\\n", + " - model.Deci[\"Dark_Matter-\"+str(ii)] + model.Deci[\"Dark_Matter-\"+str(ii-2)] \n", + "\n", + "model.collider_constraint = Constraint(model.i, rule=collider_rule)\n", + "\n", + "def cooler_rule(model, i):\n", + " ii = int(i)\n", + " if ii == 1:\n", + " return model.Task_HRS[\"cool-1\"] == model.Resources['cool']\n", + " if ii == 2:\n", + " return model.Task_HRS[\"cool-1\"] == model.Task_HRS[\"cool-1\"] - model.Deci[\"Heat_Cool-1\"] \n", + " if ii == 3: \n", + " return model.Task_HRS[\"cool-\"+i] == model.Task_HRS[\"cool-\"+str(ii-1)] \\\n", + " - model.Deci[\"Heat_Cool-\"+str(ii-1)] + model.Deci[\"Heat_Cool-\"+str(ii-2)] \n", + " if ii == 4: \n", + " return model.Task_HRS[\"cool-\"+i] == model.Task_HRS[\"cool-\"+str(ii-1)] \\\n", + " - model.Deci[\"Plastic_Parts-\"+str(ii-3)] \\\n", + " - model.Deci[\"Heat_Cool-\"+str(ii-1)] + model.Deci[\"Heat_Cool-\"+str(ii-2)] \\\n", + " - model.Deci[\"Heat_Cool-\"+str(ii-3)] \n", + " if ii == 5: \n", + " return model.Task_HRS[\"cool-\"+i] == model.Task_HRS[\"cool-\"+str(ii-1)] \\\n", + " - model.Deci[\"Plastic_Parts-\"+str(ii-3)] \\\n", + " - model.Deci[\"Dark_Matter-\"+str(ii-4)] \\\n", + " - model.Deci[\"Heat_Cool-\"+str(ii-1)] + model.Deci[\"Heat_Cool-\"+str(ii-2)] \\\n", + " - model.Deci[\"Heat_Cool-\"+str(ii-3)] + model.Deci[\"Heat_Cool-\"+str(ii-4)]\n", + " if ii == 6:\n", + " return model.Task_HRS[\"cool-\"+i] == model.Task_HRS[\"cool-\"+str(ii-1)] \\\n", + " - model.Deci[\"Plastic_Parts-\"+str(ii-3)] + model.Deci[\"Plastic_Parts-\"+str(ii-5)] \\\n", + " - model.Deci[\"Dark_Matter-\"+str(ii-4)] + model.Deci[\"Dark_Matter-\"+str(ii-5)] \\\n", + " - model.Deci[\"Heat_Cool-\"+str(ii-1)] + model.Deci[\"Heat_Cool-\"+str(ii-2)] \\\n", + " - model.Deci[\"Heat_Cool-\"+str(ii-3)] + model.Deci[\"Heat_Cool-\"+str(ii-4)]\n", + " if ii == 7:\n", + " return model.Task_HRS[\"cool-\"+i] == model.Task_HRS[\"cool-\"+str(ii-1)] \\\n", + " - model.Deci[\"Plastic_Parts-\"+str(ii-3)] + model.Deci[\"Plastic_Parts-\"+str(ii-5)] \\\n", + " - model.Deci[\"ChemB-\"+str(ii-6)] \\\n", + " - model.Deci[\"Dark_Matter-\"+str(ii-4)] + model.Deci[\"Dark_Matter-\"+str(ii-5)] \\\n", + " - model.Deci[\"Heat_Cool-\"+str(ii-1)] + model.Deci[\"Heat_Cool-\"+str(ii-2)] \\\n", + " - model.Deci[\"Heat_Cool-\"+str(ii-3)] + model.Deci[\"Heat_Cool-\"+str(ii-4)]\n", + "\n", + " return model.Task_HRS[\"cool-\"+i] == model.Task_HRS[\"cool-\"+str(ii-1)] \\\n", + " - model.Deci[\"Plastic_Parts-\"+str(ii-3)] + model.Deci[\"Plastic_Parts-\"+str(ii-5)] \\\n", + " - model.Deci[\"ChemB-\"+str(ii-6)] + model.Deci[\"ChemB-\"+str(ii-7)] \\\n", + " - model.Deci[\"Dark_Matter-\"+str(ii-4)] + model.Deci[\"Dark_Matter-\"+str(ii-5)] \\\n", + " - model.Deci[\"Heat_Cool-\"+str(ii-1)] + model.Deci[\"Heat_Cool-\"+str(ii-2)] \\\n", + " - model.Deci[\"Heat_Cool-\"+str(ii-3)] + model.Deci[\"Heat_Cool-\"+str(ii-4)]\n", + " \n", + "model.cooler_constraint = Constraint(model.i, rule=cooler_rule)\n", + "\n", + "def reactor_rule(model, i):\n", + " ii = int(i)\n", + " if ii == 1:\n", + " return model.Task_HRS[\"reaction-1\"] == model.Resources['reaction']\n", + " if ii > 1 and ii < 4:\n", + " return model.Task_HRS[\"reaction-\"+i] == model.Task_HRS[\"reaction-\"+str(ii-1)] \\\n", + " - model.Deci[\"ChemB-\"+str(ii-1)] \n", + " if ii > 3 and ii < 5:\n", + " return model.Task_HRS[\"reaction-\"+i] == model.Task_HRS[\"reaction-\"+str(ii-1)] \\\n", + " - model.Deci[\"ChemB-\"+str(ii-1)] \\\n", + " - model.Deci[\"Dark_Matter-\"+str(ii-3)] \n", + " if ii > 4 and ii < 7:\n", + " return model.Task_HRS[\"reaction-\"+i] == model.Task_HRS[\"reaction-\"+str(ii-1)] \\\n", + " - model.Deci[\"ChemB-\"+str(ii-1)] \\\n", + " - model.Deci[\"Dark_Matter-\"+str(ii-3)] + model.Deci[\"Dark_Matter-\"+str(ii-4)]\n", + " \n", + " return model.Task_HRS[\"reaction-\"+i] == model.Task_HRS[\"reaction-\"+str(ii-1)] \\\n", + " - model.Deci[\"ChemB-\"+str(ii-1)] + model.Deci[\"ChemB-\"+str(ii-6)] \\\n", + " - model.Deci[\"Dark_Matter-\"+str(ii-3)] + model.Deci[\"Dark_Matter-\"+str(ii-4)]\n", + " \n", + "model.reactor_constraint = Constraint(model.i, rule=reactor_rule)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Objective\n", + "\n", + "Our objective in this case is to maximize efficiency of the plant by minimizing task idle time." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "#Objective\n", + "def objective_rule(model):\n", + " return sum(model.Task_HRS[k+\"-\"+i] for k in model.k for i in model.i)\n", + "\n", + "model.objective = Objective(rule=objective_rule, sense=minimize, doc='Define objective function')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Output" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# This is an optional code path that allows the script to be run outside of\n", + "# pyomo command-line. For example: python transport.py\n", + "if __name__ == '__main__':\n", + " # This emulates what the pyomo command-line tools does\n", + " \n", + " from pyomo.opt import SolverFactory\n", + " import pyomo.environ\n", + " opt = SolverFactory(\"cplex\")\n", + " results = opt.solve(model)\n", + " #sends results to stdout\n", + "\n", + " results.write()\n", + " print(\"\\nDisplaying Solution\\n\" + '-'*60)\n", + " pyomo_postprocess(None, instance, results)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### CPLEX vs GLPK\n", + "\n", + "For reasons unknown, note that glpk was attempted but for some reason it was breaking the bounds rules such as in this example below. " + ] + }, + { + "cell_type": "raw", + "metadata": {}, + "source": [ + "Variables:\n", + " Deci : Size=168, Index=materials_to_hours\n", + " Key : Lower : Value : Upper : Fixed : Stale : Domain\n", + " ChemB-23 : 0 : 1 : 0 : False : False : Binary" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Execution Command" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "#!/bin/bash\n", + "\n", + "export PATH=\"/path-to-anaconda/install/bin\":\"/path-to-cplex/bin/x86-64_linux\":${PATH}\n", + "\n", + "pyomo solve RTN.py --solver=cplex --summary" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Solution Summary" + ] + }, + { + "cell_type": "raw", + "metadata": {}, + "source": [ + "==========================================================\n", + "Solution Summary\n", + "==========================================================\n", + "\n", + "Model unknown\n", + "\n", + " Variables:\n", + " Deci : Size=168, Index=materials_to_hours\n", + " Key : Lower : Value : Upper : Fixed : Stale : Domain\n", + " ChemA-1 : 0 : 1.0 : 1 : False : False : Binary\n", + " ChemA-10 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemA-11 : 0 : 1.0 : 1 : False : False : Binary\n", + " ChemA-12 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemA-13 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemA-14 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemA-15 : 0 : 1.0 : 1 : False : False : Binary\n", + " ChemA-16 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemA-17 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemA-18 : 0 : 1.0 : 1 : False : False : Binary\n", + " ChemA-19 : 0 : 1.0 : 1 : False : False : Binary\n", + " ChemA-2 : 0 : 1.0 : 1 : False : False : Binary\n", + " ChemA-20 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemA-21 : 0 : 0.0 : 0 : False : False : Binary\n", + " ChemA-22 : 0 : 0.0 : 0 : False : False : Binary\n", + " ChemA-23 : 0 : 0.0 : 0 : False : False : Binary\n", + " ChemA-24 : 0 : 0.0 : 0 : False : False : Binary\n", + " ChemA-3 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemA-4 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemA-5 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemA-6 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemA-7 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemA-8 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemA-9 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemB-1 : 0 : 1.0 : 1 : False : False : Binary\n", + " ChemB-10 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemB-11 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemB-12 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemB-13 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemB-14 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemB-15 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemB-16 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemB-17 : 0 : 0.0 : 0 : False : False : Binary\n", + " ChemB-18 : 0 : 0.0 : 0 : False : False : Binary\n", + " ChemB-19 : 0 : 0.0 : 0 : False : False : Binary\n", + " ChemB-2 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemB-20 : 0 : 0.0 : 0 : False : False : Binary\n", + " ChemB-21 : 0 : 0.0 : 0 : False : False : Binary\n", + " ChemB-22 : 0 : 0.0 : 0 : False : False : Binary\n", + " ChemB-23 : 0 : 0.0 : 0 : False : False : Binary\n", + " ChemB-24 : 0 : 0.0 : 0 : False : False : Binary\n", + " ChemB-3 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemB-4 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemB-5 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemB-6 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemB-7 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemB-8 : 0 : 0.0 : 1 : False : False : Binary\n", + " ChemB-9 : 0 : 0.0 : 1 : False : False : Binary\n", + " Dark_Matter-1 : 0 : 0.0 : 1 : False : False : Binary\n", + " Dark_Matter-10 : 0 : 1.0 : 1 : False : False : Binary\n", + " Dark_Matter-11 : 0 : 1.0 : 1 : False : False : 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reaction-5 : 0 : 0.0 : None : False : False : NonNegativeIntegers\n", + " reaction-6 : 0 : 0.0 : None : False : False : NonNegativeIntegers\n", + " reaction-7 : 0 : 0.0 : None : False : False : NonNegativeIntegers\n", + " reaction-8 : 0 : 0.0 : None : False : False : NonNegativeIntegers\n", + " reaction-9 : 0 : 0.0 : None : False : False : NonNegativeIntegers\n", + " Resources : Size=7, Index=k\n", + " Key : Lower : Value : Upper : Fixed : Stale : Domain\n", + " collide : 1 : 2.0 : None : False : False : PositiveIntegers\n", + " cool : 1 : 1.0 : None : False : False : PositiveIntegers\n", + " inject : 1 : 1.0 : None : False : False : PositiveIntegers\n", + " melt : 1 : 1.0 : None : False : False : PositiveIntegers\n", + " mix : 1 : 1.0 : None : False : False : PositiveIntegers\n", + " package : 1 : 3.0 : None : False : False : PositiveIntegers\n", + " reaction : 1 : 1.0 : None : False : False : PositiveIntegers\n", + "\n", + " Objectives:\n", + " objective : Size=1, Index=None, Active=True\n", + " Key : Active : Value\n", + " None : True : 54.0" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Optimized Schedule\n", + "\n", + "![title](images/sched3.jpg)\n", + "\n", + "![title](images/sched4.jpg)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### About the Author\n", + "\n", + "William J Edsall is an applied mathematics student graduating with a BA in applied mathematics \n", + "May 2017. This problem was completed as my final project to complete the mathematics program.\n", + "\n", + "https://www.linkedin.com/in/william-edsall-2338b716" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# References\n", + "\n", + "* Problem inspiration: http://pubs.acs.org/doi/abs/10.1021/ie500363p\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/resource_task_network/images/recipes.jpg b/resource_task_network/images/recipes.jpg new file mode 100644 index 0000000000000000000000000000000000000000..fee32dcf4c61057932a72360125846262d7fb680 GIT binary patch literal 105654 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z-(Xhfd>IuaCe7sD!$-O0&Zas=hr~|NL&(G-_y*YwSp+$+C@dV8)rgir&Xc6lL+9!v z(qF+!qIvsR11T)KqwF@vs4;zzJuYmw!yh=y0yTr06C8Tb;5V_Kq~yAu3}^)!oYq@9z=YhLPr3b+zx| zSXeOAeQV-F$hfeYFBIgD_c2VygWSvl3ewGfvP#c<^O@&*$bMtB1p;{kiUlTFW8(~7 zlVhcj{vn+t&0dUwtHs-oN|p(Pn~`k<1l Date: Thu, 9 Feb 2017 13:13:33 -0500 Subject: [PATCH 2/3] New example resource_task_network --- resource_task_network/ResourceTaskNetwork.ipynb | 16 ++++++++++++---- 1 file changed, 12 insertions(+), 4 deletions(-) diff --git a/resource_task_network/ResourceTaskNetwork.ipynb b/resource_task_network/ResourceTaskNetwork.ipynb index 2f9e73b..929371a 100644 --- a/resource_task_network/ResourceTaskNetwork.ipynb +++ b/resource_task_network/ResourceTaskNetwork.ipynb @@ -480,8 +480,12 @@ ] }, { - "cell_type": "raw", - "metadata": {}, + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], "source": [ "Variables:\n", " Deci : Size=168, Index=materials_to_hours\n", @@ -519,8 +523,12 @@ ] }, { - "cell_type": "raw", - "metadata": {}, + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], "source": [ "==========================================================\n", "Solution Summary\n", From 17026587ab82e2e4479f57a0bfd5e1f74cf31b06 Mon Sep 17 00:00:00 2001 From: William J Edsall Date: Thu, 9 Feb 2017 13:30:59 -0500 Subject: [PATCH 3/3] New example resource_task_network --- resource_task_network/ResourceTaskNetwork.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/resource_task_network/ResourceTaskNetwork.ipynb b/resource_task_network/ResourceTaskNetwork.ipynb index 929371a..117f58a 100644 --- a/resource_task_network/ResourceTaskNetwork.ipynb +++ b/resource_task_network/ResourceTaskNetwork.ipynb @@ -39,7 +39,7 @@ "### Objective\n", "\n", "Minimize the number of idle tasks:
\n", - "$\\min_{x} z = \\sum_{k \\in K} \\sum_{t \\in T} R_{k,t}$\n", + "$\\min z = \\sum_{k \\in K} \\sum_{t \\in T} R_{k,t}$\n", " \n", "### Recipes\n", "A fictitious set of recipes is created to simulate a multipurpose batch plant. \n",