1-3-News-continuous.ipynb

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    "# The Newsvendor Model - Section 3: Continuous Demand\n",
    "\n",
    "In Sections 1 and 2 we explored the basic ideas of the Newsvendor Problem through numerical simulation and mathematical analysis.  By the end of Section 2, you had derived formulas for the expected profit in terms of the order quantity for any retail price $p$, wholesale cost $c$, and demand distribution $D \\sim \\text{Uniform}\\{0,\\dots,d\\}$.\n",
    "\n",
    "Here we will show that this analysis extends to continuous demand distributions.  $D \\sim \\text{Exponential}(\\lambda)$.  We will derive everything analytically and use some Python at the end to help with visualizations.\n",
    "\n",
    "The cumulative distribution function (cdf) and probability density function (pdf) of this distribution are:\n",
    "\n",
    "$$ F(x) = \\mathsf{P}(D \\leq x) = 1 - e^{-\\lambda x} \\qquad f(x) = \\frac{d F(x)}{dx} = \\lambda e^{-\\lambda x} $$"
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    "## Formulas\n",
    "\n",
    "You may have already noticed that the formulas for sales, revenue, cost, and profit you came up with back in Section 1 Exercise 1.3 hold true for any demand random variable $D$ that has a non-negative probability distribution:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "    \\text{sales} &= \\min\\{y, D\\} \\\\\n",
    "    \\text{revenue} &= p \\min\\{y, D\\} \\\\\n",
    "    \\text{cost} &= c y \\\\\n",
    "    \\text{profit} &= p \\min\\{y, D\\} - c y\n",
    "  \\end{aligned} $$\n",
    "\n",
    "However, the formulas for the *expected* sales, revenue, and profit, will change depending on the demand distribution (and therefore, so will the optimal order quantity that maximizes expected profit)."
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    "## Expected Sales\n",
    "\n",
    "Recall that our basic recipe consisted of the following:\n",
    "\n",
    "1. Find a formula for $\\mathsf{E}[\\text{profit}]$ as a function of order quantity $y$.\n",
    "1. Maximize $\\mathsf{E}[\\text{profit}]$ with respect to order quantity $y$.\n",
    "\n",
    "\n",
    "Finding a formula for expected profit as a function of order quantity is is really about finding a formula for expected sales, $\\mathsf{E}[\\text{sales}] = \\mathsf{E}[\\min\\{y, D\\}]$.  Since $\\mathsf{E}[\\text{profit}] = p \\mathsf{E}[\\text{sales}] - c y$.\n",
    "\n",
    "### Exercise 3.1\n",
    "\n",
    "Show that $\\displaystyle\\mathsf{E}[\\text{sales}] = \\frac{1}{\\lambda} \\left(1 - e^{-\\lambda y}\\right)$.\n",
    "\n",
    "*Hint:* The hint for Exercise 2.1 can be translated to a continuous distribution:\n",
    "$$\\begin{aligned}\n",
    "    \\mathsf{E}[\\text{sales}] = \\mathsf{E}[\\min\\{y, D\\}] &= \\int_0^\\infty \\min\\{y, x\\} f(x)\\ dx = \\int_0^y x f(x)\\ dx + \\int_y^\\infty y f(x)\\ dx\n",
    "  \\end{aligned}$$\n",
    "where $f(x)$ is the pdf of the distribution.  Remember to use [integration by parts](https://en.wikipedia.org/wiki/Integration_by_parts) to evaluate the first integral.\n",
    "\n",
    "### Exercise 3.2\n",
    "\n",
    "Show that the optimal order quantity (that maximizes expected profit) is given by the formula:\n",
    "\n",
    "$$ y^* = \\frac{1}{\\lambda} \\log\\left(\\frac{p}{c}\\right) $$\n",
    "\n",
    "### Exercise 3.3\n",
    "\n",
    "Derive a formula for the optimal order quantity assuming $D \\sim \\text{Uniform}[0,d]$.\n",
    "\n",
    "### Exercise 3.4\n",
    "\n",
    "Derive a formula for the optimal order quantity for **any** demand distribution that is continuous and non-negative.  Denote its cdf as $F(x)$ and its pdf as $f(x)$.\n",
    "\n",
    "To get a guess for the general formula, try rewriting the formulas you derived in Exercises 3.2 and 3.3 as $F(y^*) = \\dots$\n",
    "\n",
    "*Hints:* This simply combines [integration by parts](https://en.wikipedia.org/wiki/Integration_by_parts) with the [fundamental theorem of calculus](https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus).\n",
    "$$\\begin{aligned}\n",
    "    \\int_0^y x f(x) dx &= y F(y) - \\int_0^y F(x) dx \\\\\n",
    "    \\int_y^\\infty f(x) dx &= 1 - F(y) \\\\\n",
    "    \\frac{d}{dy} \\left(\\int_0^y F(x) dx\\right) &= F(y)\n",
    "  \\end{aligned}$$"
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    "## Setup\n",
    "\n",
    "The following Python code imports the necessary Python packages and specifies the problem parameters for the remainder of this notebook.  You can change the parameters if you'd like and all the code should still work, but their output may be mismatched with the written text."
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Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"1001\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };var element = document.getElementById(\"1001\");\n  if (element == null) {\n    console.error(\"Bokeh: ERROR: autoload.js configured with elementid '1001' but no matching script tag was found. \")\n    return false;\n  }\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  var js_urls = [\"https://cdn.pydata.org/bokeh/release/bokeh-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-tables-1.3.4.min.js\", \"https://cdn.pydata.org/bokeh/release/bokeh-gl-1.3.4.min.js\"];\n  var css_urls = [];\n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    \n    function(Bokeh) {\n      \n    },\n    function(Bokeh) {} // ensure no trailing comma for IE\n  ];\n\n  function run_inline_js() {\n    \n    if ((root.Bokeh !== undefined) || (force === true)) {\n      for (var i = 0; i < inline_js.length; i++) {\n        inline_js[i].call(root, root.Bokeh);\n      }if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"1001\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import Python packages\n",
    "import newsvendor\n",
    "import news_plot\n",
    "\n",
    "# Default exponential distribution has parameter lambda = 0.1\n",
    "# Default model parameters are wholesale_cost = 1, retail_price = 2.\n",
    "news = newsvendor.Newsvendor('exponential')\n",
    "\n",
    "# Simulate demand\n",
    "news.sim_data(num_days=365)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b30540e7a6024e1493eee4ac517a6b94",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=15, description='Order Qty', max=20), Output()), _dom_classes=('widget-i…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"b1d9d552-dadb-4ec1-bbc1-5db6d2cf93b7\" data-root-id=\"1168\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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       "  function embed_document(root) {\n",
       "    \n",
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":\"1007\",\"type\":\"LinearScale\"},{\"attributes\":{\"below\":[{\"id\":\"1043\",\"type\":\"LinearAxis\"}],\"center\":[{\"id\":\"1047\",\"type\":\"Grid\"},{\"id\":\"1052\",\"type\":\"Grid\"}],\"left\":[{\"id\":\"1048\",\"type\":\"LinearAxis\"}],\"plot_height\":300,\"plot_width\":300,\"renderers\":[{\"id\":\"1115\",\"type\":\"GlyphRenderer\"}],\"title\":{\"id\":\"1117\",\"type\":\"Title\"},\"toolbar\":{\"id\":\"1059\",\"type\":\"Toolbar\"},\"toolbar_location\":null,\"x_range\":{\"id\":\"1035\",\"type\":\"DataRange1d\"},\"x_scale\":{\"id\":\"1039\",\"type\":\"LinearScale\"},\"y_range\":{\"id\":\"1037\",\"type\":\"DataRange1d\"},\"y_scale\":{\"id\":\"1041\",\"type\":\"LinearScale\"}},\"id\":\"1034\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{},\"id\":\"1009\",\"type\":\"LinearScale\"},{\"attributes\":{\"tools\":[{\"id\":\"1021\",\"type\":\"PanTool\"},{\"id\":\"1022\",\"type\":\"WheelZoomTool\"},{\"id\":\"1023\",\"type\":\"BoxZoomTool\"},{\"id\":\"1024\",\"type\":\"SaveTool\"},{\"id\":\"1025\",\"type\":\"ResetTool\"},{\"id\":\"1026\",\"type\":\"HelpTool\"},{\"id\":\"1053\",\"type\":\"PanTool\"},{\"id\":\"1054\",\"type\":\"WheelZoomTool\"},{\"id\":\"1055\",\"type\":\"BoxZoomTool\"},{\"id\":\"1056\",\"type\":\"SaveTool\"},{\"id\":\"1057\",\"type\":\"ResetTool\"},{\"id\":\"1058\",\"type\":\"HelpTool\"},{\"id\":\"1085\",\"type\":\"PanTool\"},{\"id\":\"1086\",\"type\":\"WheelZoomTool\"},{\"id\":\"1087\",\"type\":\"BoxZoomTool\"},{\"id\":\"1088\",\"type\":\"SaveTool\"},{\"id\":\"1089\",\"type\":\"ResetTool\"},{\"id\":\"1090\",\"type\":\"HelpTool\"}]},\"id\":\"1166\",\"type\":\"ProxyToolbar\"},{\"attributes\":{\"ticker\":{\"id\":\"1012\",\"type\":\"BasicTicker\"}},\"id\":\"1015\",\"type\":\"Grid\"},{\"attributes\":{\"axis_label\":\"demand\",\"formatter\":{\"id\":\"1140\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"1012\",\"type\":\"BasicTicker\"}},\"id\":\"1011\",\"type\":\"LinearAxis\"},{\"attributes\":{},\"id\":\"1012\",\"type\":\"BasicTicker\"}],\"root_ids\":[\"1168\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.4\"}};\n",
       "  var render_items = [{\"docid\":\"b2bb9cd8-9d1f-4445-967c-a24a37de3eeb\",\"notebook_comms_target\":\"1196\",\"roots\":{\"1168\":\"b1d9d552-dadb-4ec1-bbc1-5db6d2cf93b7\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1168"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = int(max(news.data['demand'])-min(news.data['demand'])+1)\n",
    "fields = ['demand', 'sales', 'profit']\n",
    "hist_func = lambda n: news_plot.hist_glyphs(news.data, bins=bins)\n",
    "labels = {field: {'x': field, 'y': 'count', 'title': field + ' histogram'} for field in fields}\n",
    "newsvendor.interact_gridplot(news_plot.figures(fields), hist_func, news, labels=labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "156e317b0a174ca29084fe1f55de9c3c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=15, description='Order Qty', max=20), Output()), _dom_classes=('widget-i…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"017260a2-4357-4dc8-936e-581d75aa03de\" data-root-id=\"1525\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
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       "  var render_items = [{\"docid\":\"4b3e21cc-bc70-432b-bf87-a3acdd855c59\",\"notebook_comms_target\":\"1580\",\"roots\":{\"1525\":\"017260a2-4357-4dc8-936e-581d75aa03de\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1525"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fields = ['sales', 'revenue', 'profit']\n",
    "labels = {field: {'x': 'demand', 'y': field, 'title': field} for field in fields}\n",
    "scatter_func = lambda n: news_plot.scatter_glyphs(n.data, 'demand')\n",
    "newsvendor.interact_gridplot(news_plot.figures(fields), scatter_func, news, labels=labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e4e387db8c894042a69bc9fbfafaae56",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=15, description='Order Qty', max=20), Output()), _dom_classes=('widget-i…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Table of expected values with order quantity slider\n",
    "fields = ['demand', 'sales', 'profit']\n",
    "newsvendor.order_qty_interact(lambda y: news.exp_vals([y])[fields].style.hide_index(), news)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "701ebaf531bf460691b5d02d12661d8f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=15, description='Order Qty', max=20), Output()), _dom_classes=('widget-i…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"062cc998-f134-405b-9cd7-c396f1e30fd9\" data-root-id=\"1990\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  var docs_json = 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revenue\",\"formatter\":{\"id\":\"1954\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"1790\",\"type\":\"BasicTicker\"}},\"id\":\"1789\",\"type\":\"LinearAxis\"},{\"attributes\":{\"data_source\":{\"id\":\"1883\",\"type\":\"ColumnDataSource\"},\"glyph\":{\"id\":\"1884\",\"type\":\"Line\"},\"hover_glyph\":null,\"muted_glyph\":null,\"view\":{\"id\":\"1894\",\"type\":\"CDSView\"}},\"id\":\"1893\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"1794\",\"type\":\"PanTool\"},{\"attributes\":{\"text\":\"sales\"},\"id\":\"1889\",\"type\":\"Title\"},{\"attributes\":{\"axis_label\":\"order qty\",\"formatter\":{\"id\":\"1968\",\"type\":\"BasicTickFormatter\"},\"ticker\":{\"id\":\"1817\",\"type\":\"BasicTicker\"}},\"id\":\"1816\",\"type\":\"LinearAxis\"},{\"attributes\":{\"below\":[{\"id\":\"1848\",\"type\":\"LinearAxis\"}],\"center\":[{\"id\":\"1852\",\"type\":\"Grid\"},{\"id\":\"1857\",\"type\":\"Grid\"}],\"left\":[{\"id\":\"1853\",\"type\":\"LinearAxis\"}],\"plot_height\":350,\"plot_width\":350,\"renderers\":[{\"id\":\"1896\",\"type\":\"GlyphRenderer\"},{\"id\":\"1921\",\"type\":\"GlyphRenderer\"}],\"title\":{\"id\":\"1898\",\"type\":\"Title\"},\"toolbar\":{\"id\":\"1864\",\"type\":\"Toolbar\"},\"toolbar_location\":null,\"x_range\":{\"id\":\"1840\",\"type\":\"DataRange1d\"},\"x_scale\":{\"id\":\"1844\",\"type\":\"LinearScale\"},\"y_range\":{\"id\":\"1842\",\"type\":\"DataRange1d\"},\"y_scale\":{\"id\":\"1846\",\"type\":\"LinearScale\"}},\"id\":\"1839\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{},\"id\":\"1814\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"1762\",\"type\":\"PanTool\"}],\"root_ids\":[\"1990\"]},\"title\":\"Bokeh Application\",\"version\":\"1.3.4\"}};\n",
       "  var render_items = [{\"docid\":\"ed809252-fe59-42b6-b0b9-284c853e1b7d\",\"notebook_comms_target\":\"2089\",\"roots\":{\"1990\":\"062cc998-f134-405b-9cd7-c396f1e30fd9\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    var attempts = 0;\n",
       "    var timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        embed_document(root);\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "      attempts++;\n",
       "      if (attempts > 100) {\n",
       "        console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        clearInterval(timer);\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1990"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fields = ['sales', 'revenue', 'cost', 'profit']\n",
    "labels = {field: {'x': 'order qty', 'y': 'expected ' + field, 'title': field} for field in fields}\n",
    "ev_func = lambda n: news_plot.line_glyphs(n.exp_vals(), 'order qty')\n",
    "ev_sources, ev_plots = newsvendor.news_gridplot(news_plot.figures(fields, plot_width=350, plot_height=350), ev_func, news, labels=labels)\n",
    "circle_func = lambda n: news_plot.circle_markers(n.exp_vals([n.order_qty]))\n",
    "newsvendor.interact_gridplot({field: ev_plots[field] for field in fields}, circle_func, news, ncols=2)"
   ]
  }
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