{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Asset replacement model\n", "\n", "**Randall Romero Aguilar, PhD**\n", "\n", "This demo is based on the original Matlab demo accompanying the Computational Economics and Finance 2001 textbook by Mario Miranda and Paul Fackler.\n", "\n", "Original (Matlab) CompEcon file: **demddp02.m**\n", "\n", "Running this file requires the Python version of CompEcon. This can be installed with pip by running\n", "\n", " !pip install compecon --upgrade\n", "\n", "Last updated: 2021-Oct-01\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## About\n", "\n", "At the beginning of each year, a manufacturer must decide whether to continue to operate an aging physical asset or replace it with a new one. An asset that is $a$ years old yields a profit contribution $p(a)$ up to $n$ years, at which point the asset becomes unsafe and must be\n", "replaced by law. The cost of a new asset is $c$. What replacement policy maximizes profits?\n", "\n", "This is an infinite horizon, deterministic model with time $t$ measured in years." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Initial tasks" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from compecon import DDPmodel" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model Parameters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Assume a maximum asset age of 5 years, asset replacement cost $c = 75$, and annual discount factor $\\delta = 0.9$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "maxage = 5\n", "repcost = 75\n", "delta = 0.9" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### State Space" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The state variable $a \\in \\{1, 2, 3, \\dots, n\\}$ is the age of the asset in years." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "S = np.arange(1, 1 + maxage) # machine age\n", "n = S.size # number of states" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Action Space" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The action variable $x \\in \\{\\text{keep, replace}\\}$ is the hold-replacement decision. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "X = np.array(['keep', 'replace']) # list of actions\n", "m = len(X) # number of actions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Reward Function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The reward function is\n", "\\begin{equation}\n", "f(a, x) = \\begin{cases} p(a), &x = \\text{keep} \\\\\n", " p(0) - c, &x = \\text{replace}\n", "\\end{cases}\n", "\\end{equation}\n", "\n", "Assuming a profit contribution $p(a) = 50 − 2.5a − 2.5a^2$ that is a function of the asset age $a$ in years:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "f = np.zeros((m, n))\n", "f[0] = 50 - 2.5 * S - 2.5 * S ** 2\n", "f[1] = 50 - repcost\n", "f[0, -1] = -np.inf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### State Transition Function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The state transition function is\n", "\\begin{equation}\n", "g(a, x) = \\begin{cases} a + 1, &x = \\text{keep} \\\\\n", " 1, &x = \\text{replace}\n", "\\end{cases}\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "g = np.zeros_like(f)\n", "g[0] = np.arange(1, n + 1)\n", "g[0, -1] = n - 1 # adjust last state so it doesn't go out of bounds" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model Structure" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The value of an asset of age a satisfies the Bellman equation\n", "\\begin{equation}\n", "V(a) = \\max\\{p(a) + \\delta V(a + 1),\\quad p(0) − c + \\delta V(1)\\}\n", "\\end{equation}\n", "\n", "where we set $p(n) = -\\infty$ to enforce replacement of an asset of age $n$. The Bellman equation asserts that if the manufacturer keeps an asset of age $a$, he earns $p(a)$ over the coming year and begins the subsequent year with an asset that is one year older and worth $V(a+1)$; if he replaces the asset, however, he starts the year with a new asset, earns $p(0)−c$ over the year, and begins the subsequent year with an asset that is one year old and worth $V(1)$. Actually, our language is a little loose here. The value $V(a)$ measures not only the current and future net earnings of an asset of age $a$, but also the net earnings of all future assets that replace it." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To solve and simulate this model, use the CompEcon class ```DDPmodel```. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": "A deterministic discrete state, discrete action, dynamic model.\nThere are 2 possible actions over 5 possible states" }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model = DDPmodel(f, g, delta)\n", "model.solve()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "solution = pd.DataFrame({\n", " 'Age of Machine': S,\n", " 'Action': X[model.policy], \n", " 'Value': model.value}).set_index('Age of Machine')\n", "\n", "solution['Action'] = solution['Action'].astype('category')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot Optimal Value\n", "This Figure gives the value of the firm at\n", "the beginning of the period as a function of the asset’s age." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": "
", "image/png": "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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = solution['Value'].plot();\n", "ax.set(title='Optimal Value Function', ylabel='Value', xticks=S);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot Optimal Policy\n", "This Figure gives the optimal action as a function of the asset’s age." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": "
", "image/png": "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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = solution['Action'].cat.codes.plot(marker='o')\n", "ax.set(title='Optimal Replacement Policy', yticks=[0, 1], yticklabels=X, xticks=S);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulate Model\n", "The path was computed by performing a deterministic simulation of 12 years in duration using the ```simulate()``` method." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "sinit, nyrs = S.min() - 1, 12\n", "t = np.arange(1 + nyrs)\n", "spath, xpath = model.simulate(sinit, nyrs)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": " Age of Machine Action\nYear \n0 1 keep\n1 2 keep\n2 3 keep\n3 4 replace\n4 1 keep\n5 2 keep\n6 3 keep\n7 4 replace\n8 1 keep\n9 2 keep\n10 3 keep\n11 4 replace\n12 1 keep", "text/html": "
\n\n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
Age of MachineAction
Year
01keep
12keep
23keep
34replace
41keep
52keep
63keep
74replace
81keep
92keep
103keep
114replace
121keep
\n
" }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simul = pd.DataFrame({\n", " 'Year': t,\n", " 'Age of Machine': S[spath],\n", " 'Action': X[xpath]}).set_index('Year')\n", "\n", "simul['Action'] = pd.Categorical(X[xpath], categories=X)\n", "simul" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot State and Action Paths\n", "Next Figure gives the age of the asset along the optimal path. As can be seen in this figure, the asset is replaced every four years." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": "
", "image/png": "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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(2, 1, sharex=True)\n", "simul['Age of Machine'].plot(ax=axs[0])\n", "axs[0].set(title='Age Path');\n", "\n", "simul['Action'].cat.codes.plot(marker='o', ax=axs[1])\n", "axs[1].set(title='Replacement Path', yticks=[0, 1], yticklabels=X);" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.8.3" } }, "nbformat": 4, "nbformat_minor": 4 }