{ "metadata": { "name": "sdm_diaper_delivery" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "import pandas" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The system dynamics of diapers with weekly pickup/delivery::\n", "\n", " q +-----+ r +-----+ s\n", " ---->| C |---->| D |---->\n", " ^^ +-----+ +-++--+\n", " || ||\n", " ++= = = = = = = = ++\n", "\n", "$C$ = stock of clean diapers\n", "\n", "$D$ = stock of dirty diapers\n", "\n", "$q$ = in-flow of clean diapers\n", "\n", "$r$ = flow of clean diapers to dirty diapers\n", "\n", "$s$ = out-flow of dirty diapers\n", "\n", "To make this totally precise we need a system of equations relating the stocks and flows. In this case, a system of difference equations with a timestep of one day works fine:\n", "\n", "$C(t+1) = C(t) + q(t) - r(t)$\n", "\n", "$D(t+1) = D(t) + r(t) - s(t)$\n", "\n", "So far this seems like an example from intro applied math, and 100 other subjects. But what makes it truely a system dyamics modeling example is the dashed arrow from compartment $D$ to flow $q$. This signifies feedback, a core feature of SDM. It is actually what makes me _want_ this simulation, because it makes things complicated (especially since I am a new parent, and therefore I am not sleeping much!) The in-flow of clean diapers happens weekly (on Fridays... don't forget to take the dirty ones out on Thursday!), and the number of diapers that flow in is a function of the number of diapers that flow out... a week ago. In equations,\n", "$$q(t) = s(t-7) + A(t) - C(t-7).$$\n", "\n", "I've added something new here, $A(t)$ which is the stock of diapers I ask for. It started out at 70, but I was worried about running out, so I raised\n", "it to 100.\n", "\n", "So what is left to specify? $r(t)$ is up to little Sidney, mostly, and $s(t)$ is equal to $D(t)$ on Thursdays and zero every other day.\n", "\n", "Code that up and we have a system dynamics model." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# what would make this code really cool is if I could use the \"with\" syntax on a pandas.DataFrame\n", "\n", "# that requires a context manager\n", "\n", "from contextlib import contextmanager\n", "\n", "@contextmanager\n", "def columns_in(df):\n", " col_names = df.columns\n", " col_list = [df[col] for col in col_names]\n", " try:\n", " yield tuple(col_list)\n", " finally:\n", " for i, col in enumerate(col_names):\n", " df[col] = col_list[i]\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "T = 120\n", "state = pandas.DataFrame(index=range(-7,T), columns=['C', 'D', 'q', 'r', 's'])\n", "\n", "state.ix[-7:0, ['C']] = 70\n", "state.ix[-7:0, ['D', 'q', 'r', 's']] = 0\n", "\n", "\n", "# simulate\n", "with columns_in(state) as (C,D,q,r,s):\n", " for t in range(T-1):\n", " C[t+1] = C[t] + q[t] - r[t]\n", " if C[t+1] < 0:\n", " C[t+1] = 0\n", "\n", " D[t+1] = D[t] + r[t] - s[t]\n", " \n", " q[t+1] = s[t+1-7] if t % 7 == 6 else 0\n", " # special case, first pickup, need to deliver something\n", " if t == 6:\n", " q[t+1] = 70.\n", " \n", " r[t+1] = 8.\n", " s[t+1] = D[t] if t % 7 == 6 else 0\n", "\n", "t = state.filter(['C','D'])\n", "t.columns = ['Clean', 'Dirty']\n", "t.plot(linewidth=2, alpha=.9, figsize=(11.5, 4.5))\n", "plot(arange(-7,T)[::7], state.ix[::7,'C'], ':o', mec='k', ms=7, color='k', linewidth=2, alpha=.7, label='Weekly minimum')\n", "\n", "axis([-5,60,-10,120])\n", "grid()\n", "legend()\n", "xlabel('Time (Days)')\n", "ylabel('Diapers')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", 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UBcexcw4cAPr2Bb74Qvo8EvJCEkCmoZhlwhzoPikJlYnyoZhcwinhVzurWtW8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hrffvst7ty5g8uXL2Pjxo24d+8eoqKiEBISgocPH2LAgAGI0mXTaQGjUNY5XN5/Oa9TCh988AFs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\nJUHTNLZc3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} ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now I can simulate my nightmare scenario, forgetting to take the dirty diapers out one week" ] }, { "cell_type": "code", "collapsed": false, "input": [ "T = 120\n", "state = pandas.DataFrame(index=range(-7,T), columns=['C', 'D', 'q', 'r', 's'])\n", "\n", "state.ix[-7:0, 'C'] = 70\n", "state.ix[-7:0, ['D', 'q', 'r', 's']] = 0\n", "\n", "\n", "# simulate\n", "with columns_in(state) as (C,D,q,r,s):\n", " for t in range(T-1):\n", " C[t+1] = C[t] + q[t] - r[t]\n", " if C[t+1] < 0:\n", " C[t+1] = 0\n", "\n", " D[t+1] = D[t] + r[t] - s[t]\n", " \n", " q[t+1] = s[t+1-7] if t % 7 == 6 else 0\n", " # special case, first pickup, need to deliver something\n", " if t == 6:\n", " q[t+1] = 70.\n", " \n", " r[t+1] = 8.\n", " s[t+1] = D[t] if t % 7 == 6 else 0\n", " \n", " # special case, forget to take the diapers out\n", " if t == 34:\n", " s[t+1] = 0\n", "\n", "t = state.filter(['C','D'])\n", "t.columns = ['Clean', 'Dirty']\n", "t.plot(linewidth=2, alpha=.9, figsize=(11.5, 4.5))\n", "plot(arange(-7,T)[::7], state.ix[::7,'C'], ':o', mec='k', ms=7, color='k', linewidth=2, alpha=.7, label='Weekly minimum')\n", "\n", "axis([-5,100,-10,130])\n", "grid()\n", "legend()\n", "xlabel('Time (Days)')\n", "ylabel('Diapers')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 4, "text": [ "" ] }, { "output_type": "display_data", "png": 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lthV27NgBmUyGF154QWpTLA7N68rOTq3LbQ7M4WUwGC2S2Av0MWJU3yhVDq45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\nr5n8WvUrTtw8ASeJE2JCYvgOh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 # -*- coding: utf-8 -*- # 3.0 # import pandas # # The system dynamics of diapers with weekly pickup/delivery:: # # q +-----+ r +-----+ s # ---->| C |---->| D |----> # ^^ +-----+ +-++--+ # || || # ++= = = = = = = = ++ # # $C$ = stock of clean diapers # # $D$ = stock of dirty diapers # # $q$ = in-flow of clean diapers # # $r$ = flow of clean diapers to dirty diapers # # $s$ = out-flow of dirty diapers # # To make this totally precise we need a system of equations relating the stocks and flows. In this case, a system of difference equations with a timestep of one day works fine: # # $C(t+1) = C(t) + q(t) - r(t)$ # # $D(t+1) = D(t) + r(t) - s(t)$ # # So far this seems like an example from intro applied math, and 100 other subjects. But what makes it truely a system dyamics modeling example is the dashed arrow from compartment $D$ to flow $q$. This signifies feedback, a core feature of SDM. It is actually what makes me _want_ this simulation, because it makes things complicated (especially since I am a new parent, and therefore I am not sleeping much!) The in-flow of clean diapers happens weekly (on Fridays... don't forget to take the dirty ones out on Thursday!), and the number of diapers that flow in is a function of the number of diapers that flow out... a week ago. In equations, # $$q(t) = s(t-7) + A(t) - C(t-7).$$ # # I've added something new here, $A(t)$ which is the stock of diapers I ask for. It started out at 70, but I was worried about running out, so I raised # it to 100. # # So what is left to specify? $r(t)$ is up to little Sidney, mostly, and $s(t)$ is equal to $D(t)$ on Thursdays and zero every other day. # # Code that up and we have a system dynamics model. # # what would make this code really cool is if I could use the "with" syntax on a pandas.DataFrame # that requires a context manager from contextlib import contextmanager @contextmanager def columns_in(df): col_names = df.columns col_list = [df[col] for col in col_names] try: yield tuple(col_list) finally: for i, col in enumerate(col_names): df[col] = col_list[i] # T = 120 state = pandas.DataFrame(index=range(-7,T), columns=['C', 'D', 'q', 'r', 's']) state.ix[-7:0, ['C']] = 70 state.ix[-7:0, ['D', 'q', 'r', 's']] = 0 # simulate with columns_in(state) as (C,D,q,r,s): for t in range(T-1): C[t+1] = C[t] + q[t] - r[t] if C[t+1] < 0: C[t+1] = 0 D[t+1] = D[t] + r[t] - s[t] q[t+1] = s[t+1-7] if t % 7 == 6 else 0 # special case, first pickup, need to deliver something if t == 6: q[t+1] = 70. r[t+1] = 8. s[t+1] = D[t] if t % 7 == 6 else 0 t = state.filter(['C','D']) t.columns = ['Clean', 'Dirty'] t.plot(linewidth=2, alpha=.9, figsize=(11.5, 4.5)) plot(arange(-7,T)[::7], state.ix[::7,'C'], ':o', mec='k', ms=7, color='k', linewidth=2, alpha=.7, label='Weekly minimum') axis([-5,60,-10,120]) grid() legend() xlabel('Time (Days)') ylabel('Diapers') # # Now I can simulate my nightmare scenario, forgetting to take the dirty diapers out one week # T = 120 state = pandas.DataFrame(index=range(-7,T), columns=['C', 'D', 'q', 'r', 's']) state.ix[-7:0, 'C'] = 70 state.ix[-7:0, ['D', 'q', 'r', 's']] = 0 # simulate with columns_in(state) as (C,D,q,r,s): for t in range(T-1): C[t+1] = C[t] + q[t] - r[t] if C[t+1] < 0: C[t+1] = 0 D[t+1] = D[t] + r[t] - s[t] q[t+1] = s[t+1-7] if t % 7 == 6 else 0 # special case, first pickup, need to deliver something if t == 6: q[t+1] = 70. r[t+1] = 8. s[t+1] = D[t] if t % 7 == 6 else 0 # special case, forget to take the diapers out if t == 34: s[t+1] = 0 t = state.filter(['C','D']) t.columns = ['Clean', 'Dirty'] t.plot(linewidth=2, alpha=.9, figsize=(11.5, 4.5)) plot(arange(-7,T)[::7], state.ix[::7,'C'], ':o', mec='k', ms=7, color='k', linewidth=2, alpha=.7, label='Weekly minimum') axis([-5,100,-10,130]) grid() legend() xlabel('Time (Days)') ylabel('Diapers') #