hse2021task8.ipynb

{
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   "source": [
    "# Inventory dynamics problem with stochastic demand\n",
    "\n",
    "Using bus engine replacement model as an analogy, in this exercise you’ll continue developing the inventory model from the first lecture on dynamic programming (video 27),\n",
    "and extend it to the infinite horizon case with stochastic demand."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inventory dynamics model\n",
    "\n",
    "Recall the inventory management problem in discrete time and finite horizon $ t=0,\\dots,T $\n",
    "\n",
    "The notation is:\n",
    "\n",
    "- $ x_t\\ge 0 $ is inventory at period $ t $  \n",
    "- $ d_t\\ge 0 $ is *stochastic* demand at period $ t $  \n",
    "- $ q_t\\ge 0 $ is the order of new inventory  \n",
    "- $ p $ is the profit per one unit of (supplied) good  \n",
    "- $ c $ is the fixed cost of ordering any amount of new inventory  \n",
    "- $ r $ is the cost of storing one unit of good  \n",
    "\n",
    "\n",
    "The sales in period $ t $ are given by $ s_t = \\min\\{x_t,d_t\\} $.\n",
    "\n",
    "Inventory to be stored till next period is given by $ k_t = \\max\\{x_t-d_t,0\\} + q_t = x_{t+1} $.\n",
    "\n",
    "The profit in period $ t $ is given by\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "\\pi_t & = & p \\cdot \\text{sales}_t - r \\cdot x_{t+1} - c \\cdot (\\text{order made in period }t) \\\\\n",
    "& = & s_t p - k_t r - c \\mathbb{1}\\{q_t>0\\}\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "\n",
    "Assuming all $ q_t \\ge 0 $, let $ \\sigma =  \\{q_t\\}_{t=1,\\dots,T} $ denote a feasible inventory policy.\n",
    "\n",
    "If $ d_t $ is stochastic the policy becomes a function of the period $ t $ inventory $ x_t $.\n",
    "\n",
    "The expected profit maximizing problem is given by\n",
    "\n",
    "$$\n",
    "{\\max}_{\\sigma} \\mathbb{E}\\Big[ \\sum_{t=0}^{T} \\beta^t \\pi_t \\Big],\n",
    "$$\n",
    "\n",
    "where $ \\beta $ is discount factor."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bellman equation for the problem\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "V(x_t,d_t) &=& \\max_{q_t \\ge 0} \\Big\\{ \\pi_t + \\beta \\mathbb{E}\\Big[ V\\big(x_{t+1} , d_{t+1} \\big) \\Big| x_t,d_t,q_t \\Big] \\Big\\} \\\\\n",
    "&=& \\max_{q_t \\ge 0} \\Big\\{ s_t p - k_t r - c \\mathbb{1}\\{q_t>0\\}\n",
    "+ \\beta \\mathbb{E}\\Big[ V\\big( k_t, d_{t+1} \\big) \\Big] \\Big\\}\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "s_t &=& \\min\\{x_t,d_t\\} \\\\\n",
    "k_t &=& \\max\\{x_t-d_t,0\\} + q_t\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "\n",
    "The expectation in the Bellman equation is taken over the distribution of the next period demand $ d_{t+1} $, which according to the problem is independent of any other variables (idiosyncratic), thus the conditioning on $ (x_t,d_t,q_t) $ can be meaningfully dropped.  Expectation can be written as an integral over the distribution of demand $ F(d) $.\n",
    "\n",
    "$$\n",
    "V(x_t,d_t)\n",
    "= \\max_{q_t \\ge 0} \\Big\\{ s_t p - k_t r - c \\mathbb{1}\\{q_t>0\\}\n",
    "+ \\beta \\int V\\big( k_t, d \\big) \\partial F(d)  \\Big\\}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dropping the time subscripts\n",
    "\n",
    "Because we’ll be solving the problem in infinite horizon, the time subscripts can be dropped, and we can just have current period variables $ x,d,q,s,k $, and next period variables denoted by prime, i.e. $ x' $\n",
    "\n",
    "The Bellman equation is then\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "V(x,d) &=& \\max_{q \\ge 0} \\Big\\{ \\pi + \\beta \\mathbb{E}\\Big[ V\\big(x', d' \\big) \\Big| x,d,q \\Big] \\Big\\} \\\\\n",
    "&=& \\max_{q \\ge 0} \\Big\\{ s\\cdot p - k\\cdot  r - c \\mathbb{1}\\{q>0\\}\n",
    "+ \\beta \\mathbb{E}\\Big[ V\\big( k, d' \\big) \\Big] \\Big\\}\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "s &=& \\min\\{x,d\\} \\\\\n",
    "k &=& \\max\\{x-d,0\\} + q\n",
    "\\end{eqnarray}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bellman equation in expected value function space\n",
    "\n",
    "Note that similar to the bus engine replacement model, the inventory model features random variable which distribution does not depend on the previous period variables (it is *idiosyncratic*).\n",
    "\n",
    "In this case it is possible to reduce the dimensionality of the fixed point problem by rewriting the Bellman operator in expected value function terms.\n",
    "\n",
    "$$\n",
    "EV(x') =  \\mathbb{E}\\Big[ V\\big(x', d' \\big) \\Big| x,d,q \\Big] =  \\mathbb{E}\\Big[ V\\big(x', d' \\big) \\Big],\n",
    "$$\n",
    "\n",
    "where the expectation is taken over the distribution of the next period demand $ d' $.\n",
    "The conditioning on $ x,d,q $ can be dropped exactly because $ d' $ is idiosyncratic.\n",
    "\n",
    "We can then write the Bellman equation as\n",
    "\n",
    "$$\n",
    "V(x,d) = \\max_{q \\ge 0} \\Big\\{ s\\cdot p - k\\cdot  r - c \\mathbb{1}\\{q>0\\}\n",
    "+ \\beta EV(k) \\Big\\}\n",
    "$$\n",
    "\n",
    "$$\n",
    "V(x,d) = \\max_{q \\ge 0} \\Big\\{ p \\min\\{x,d\\} - r ( \\max\\{x-d,0\\} + q ) - c \\mathbb{1}\\{q>0\\}\n",
    "+ \\beta EV(\\max\\{x-d,0\\} + q) \\Big\\}\n",
    "$$\n",
    "\n",
    "Taking the expectation with respect to $ d $ on both sides, we get\n",
    "\n",
    "$$\n",
    "EV(x) = \\mathbb{E}\\Big[ \\max_{q \\ge 0} \\Big\\{ p \\min\\{x,d\\} - r ( \\max\\{x-d,0\\} + q ) - c \\mathbb{1}\\{q>0\\}\n",
    "+ \\beta EV(\\max\\{x-d,0\\} + q) \\Big\\} \\Big]\n",
    "$$\n",
    "\n",
    "By assumption the inventory is discrete, and so it is natural to assume that the demand is also represented as a discrete random variable.  Then the expectation can be written as a sum weighted with\n",
    "the corresponding probabilities $ pr(d) $, as\n",
    "\n",
    "$$\n",
    "EV(x) = \\sum_{d} \\Big[ \\max_{q \\ge 0} \\Big\\{ p \\min\\{x,d\\} - r ( \\max\\{x-d,0\\} + q ) - c \\mathbb{1}\\{q>0\\}\n",
    "+ \\beta EV(\\max\\{x-d,0\\} + q) \\Big\\} \\Big] pr(d)\n",
    "$$\n",
    "\n",
    "This is functional equation in $ EV $ which is also a contraction mapping!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Specification of stochastic demand\n",
    "\n",
    "Assume that $ d(t) $ is stochastic and follows a truncated geometric distribution with the support\n",
    "$ k \\in \\{0,1,2,\\dots\\} $  and corresponding probabilities $ P(k)=(1-p)^k p $, where $ p $ is a fixed parameter.  Implement this distribution with the probability mass from the tail collected at the upper bound, assuming the maximum value of the demand is the same as the maximum inventory."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tasks\n",
    "\n",
    "1. Copy the implementation of the inventory model from the lecture notebook (27) to serve the starter code  \n",
    "1. Add `demand_pr()` method to compute the probabilities for the random demand (modelling demand as discrete random variable with support the same as the inventory grid). Include the functionality to plot these probabilities.  \n",
    "1. Implement Bellman equation similar to the Rust bus engine model, as class method  \n",
    "1. Implement VFI solver for the infinite horizon stochastic inventory problem, also as class method  \n",
    "1. Initialize the model using reasonable parameter values, plot demand distribution  \n",
    "1. Solve the model with VFI and make nice plots to illustrate convergence of the value and the policy functions to the solution.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "hide-output": false,
    "scrolled": false
   },
   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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r3X6zMcRfOHpQBXmdTJ6N9LAO19YvAyJCeKEOQIwRfgOw0u3XZh3WYKPnF+R10smdTjZ6OgC0AC/UAYg5wm9ABitfCy9ZaPJs+n0RF9TBNc+6TUIybpRIwAt1ANKN8AsgENTBNc+6TUJiUAcANIfwCyAQYdXBxZl1m4REo0S2rOvUqFIDoovwCwBIFes6NarUgGhLfPi98MBKnX/wWdtBFEf2S/md7Z4P4CMMAkFbWdepUaUGtFz//v3VpUsXtW/fXnl5eVqzZo3ZWokPv+cffFb9j2yRdKbdIvmdpc497Z4PQJL9veK43ykGgDh79tln1aNHD/N1Eh9+JWlrh4E6bfpTdgtwxy7nXntuu15fXW26xqBzeum0z9lPn0Lj6CrOjnWjhGmbhGTfIyzRJQykWCrCb9xtyxuk7XkD9fJdL+d6K5H13ht7JUm9T+1m8vyailpJIvymQNyvVVg3Spi3SVj3CEt0CQNNeG7p66p5tzbQZ/Y4pVCfmzyoyZ/jnNPFF18s55yuv/56zZo1K9A9NET4jYHteQO1r113dcz1RiKs96ndTE9mn7jrZdVU1OoJ4z+AcLqcW0m4VmHdKGHeJmHdIyzRJQxE0PPPP6/evXtrx44duuiiizRkyBCNGTPGZC3Cb0x0/XC3Jn79klxvI7UGndPLfA1Ol3OPaxUIinWVmkSdGmw0d0JrpXfv3pKkoqIiTZw4UatXryb8Arl02uf6mIfSME6XOVkG7FlXqUnUqSFZ9u/frw8//FBdunTR/v379bvf/U7f+c53zNYj/AbgjD9Va+hLNWZjiD/8cIzaFRSYPBvRYX26/N4be/XeG3tNXwwkXKdD7F+oM2ZdpSZRp4Zkqa6u1sSJEyVJR48e1VVXXaVLLrH7227CbwCGvlSjou0HpO42z29XUKC8k0+2eTgiw/p02boRg2sb6RD7F+oARM7AgQP1l7/8JbT1Eh9+O+eH86+4o0+BznzoQZNn0/KAIFiHa+uXAZPCuk1Csm2UiP0LdfWs69SoUgMiK/Hht//JTF4DEA3WbRISgzqyYl2nRpUaEGmJD78AEBXWbRISjRJZsa5To0oNiDTCL4DA0IUMAIi6xIffR1WrlW6/6QjiLxw9qIK8TmbPB+KALmQAQBwkPvyudPu1WYc12HCNgrxOOrkTbQxIt7C6kJF81lVqUvzr1CT7QRoM0UBSZRV+nXPdJP1C0nBJXtIMSZslLZHUX9JWSZO993tMdtlGg5WvhZcsNHu+Vb8vALSGdaOEZZuEdZWalIw6NetBGgzRQNj27t2rr3zlK1q/fr2cc3rggQd03nnnmayV7cnv3ZKe9t5Pcs7lSyqQdLOkVd77Bc65uZLmSppjsksAyGAKXtOsGyWs2ySsq9SkkOrUjKvUrpJ01Vl2dWoM0UDYbrjhBl1yySV67LHHdPjwYR04cMBsrWbDr3Ouq6QxkqZJkvf+sKTDzrkJksZmftoiSeUi/AIwZH2vOAl3iq0bJWiTyIJ1lZpEnRoSZd++ffrDH/6gX/7yl5Kk/Px85efnm62XzcnvQEk7JS10zp0h6SVJN0jq5b2vlCTvfaVzrshslwAgBnUgJqyr1CTq1GDm2V/eqx3btgT6zKJ+A/X302Y1+uNbtmxRz549NX36dP3lL3/RWWedpbvvvludO9vMasgm/OZJGiXpq977F5xzd6vuikNWnHOzJM2SpL59uTsEG6/+/mltfL7cdI2h54/V6Z+3mzWOaOBaBQCE6+jRo3r55Zf1k5/8RKNHj9YNN9ygBQsW6LbbbjNZL5vwWyGpwnv/Qubjx1QXfqudcyWZU98SSTuO94u99/dKuleSysrKfAB7bpn8+E9427djjWp3vaol85bmeiuRVbFhvSSpdNhwk+fv3Pq2JBF+E45rFdmJ8wt1AJrW1AmtldLSUpWWlmr06NGSpEmTJmnBggVm6zUbfr33Vc65d51zg733myVdKGlD5p9rJS3IfLvMbJdt0X1grnfQZrW7XtXhA1WSPpvrrURW6bDhpiezS+bN1c6tb2vJvKz/0qNVOF3OLa5VNC/uL9QBiJ7i4mKdcsop2rx5swYPHqxVq1Zp2LBhZutl2/bwVUm/zjQ9bJE0XVI7SUudczMlvSMpvp0xbbQtb5C25w3Uy0b/x3bkg2PKLyjWlbfY/SkITRt6/ljzNThdRhwk5YU66y7hJPQIA2H6yU9+oquvvlqHDx/WwIEDtXChXUVtVuHXe79WUtlxfujCYLcTT9vzBmpfu+7qaPT8Die0V6cudm89onmnf/4S81AaxukyJ8uAfZdwEnqEJYZoIFwjR47UmjVrQlkr8RPewtL1w92a+HWrv3Lnrm8aWJ8uV2xYr4oN601fDCRcIw6su4RD6RE2xhANJBnhF4gI69Nl60YMrm1kx7pNQqJRIjUMB2kwRANJlvjwe8afqjX0pRrTEcQffjhG7QoKzJ4PBME6XFu/DJgE1m0SUnIaJdAM60EaDNFAgiU+/A59qUZF2w9I3e3WaFdQoLyTT7ZbAEAiWLdJSMlolEAWrAdpMEQDCZb48CtJO/oU6MyHHjR7vlXLAxA31MEhCNY9wpJ9l7B1m4REowTQWqkIvwDsUQeHIFj3CEv2XcLWbRJScholgFwg/AIIRFh1cEg26x5hyb5L2LpNQkpGowRQb/Pmzbryyis/+njLli367ne/qxtvvNFkPcIvACSMdaMEbRIIgnWPsESXcFwMHjxYa9eulSQdO3ZMffr00cSJE83WI/wCQIJYN0rQJoEgWPcIS3QJx9WqVav0mc98Rv369TNbI/Hht6ADFWRAkjAFr2nWjRK0SSAIV43uax5K6RJunb1PvqXD7+0P9Jn5vTur2+WfyernPvLII5oyZUqg639S4sNv3y78iQ9ICuuX6nihDmjAcIiGpLquYnqE0cDhw4e1fPlyzZ8/33SdxIdfAMnBoI5oSMKdYus6NesqNXMM0UitbE9oLfzmN7/RqFGj1KuX7fUtwi8ANMC1iqYl4U6xdZ2adZVaKBiigRxYvHix+ZUHifALAB/hWkXzknCn2LpOzbpKrZ71IA2GaCBMBw4c0DPPPKN77rnHfC3CLxKh9oVKHVi703SNgpE9VTi6xHQN5BbXKhAX1oM0GKKBsBUUFGjXrl2hrEX4DcC+HWtUu+tVLZm31OT5BdUFGtjtdO2451WT5yfB4bf/KknKH3CiyfOPVNbqgET4BRAJ1oM0GKKBJCP8BqB216s6fKBK0mdNnj+w2+nq0q67ybOTIn/AiaYnszvueVVHKmvN/wDC6TIAALYIvwHJLyjWlbcsMHl2feAquv50k+ejeQUje+qA8RqcLgNAsKynyDFBLp4SH3635Q3S9ryBetnwJYojHxxThxPamz0fuVc4usQ8lIZxuszJcu5Zt0lI8W+USALrKjUpAXVqxj3CP/7gkJad+P9plWzuRzNBLr4SH3635w3Uvnbd1dFwjQ4ntFenLvmGKyANrE+XD7/9Vx1++6+mLwYSrptm3SYhJaNRwrpHWLLtErauUpMSUKdm3SMsqdf+NzSruKNmTb/N5PlMkIuvxIdfSer64W5N/LrlG9w2L7ohXaxPl60bMbi20TzrNgkp/o0S1j3Ckn2XsHWVmhRenZoZ6x5hiS5hNCoV4ReAfbimjQRBsO4RlsLpEgbQMj/84Q/1i1/8Qs45jRgxQgsXLlTHjjZ/b5/48NuuoCDXWwAAIHYYooGwbN++XT/+8Y+1YcMGderUSZMnT9YjjzyiadOmmayX+PCb35eL6EBYqIOLBkY0o60YooGwHT16VAcPHlSHDh104MAB9e7d22ytxIdfAOGgDi4aGNGMIDBEI71+85vfqKqqKtBnFhcX69JLL230x/v06aObbrpJffv2VadOnXTxxRfr4osvDnQPDRF+AQQirDo4NI0RzQDiZs+ePVq2bJnefvttdevWTVdccYV+9atf6ctf/rLJeoRfAEDqWNepWVapAZaaOqG18vvf/14DBgxQz549JUlf/OIX9ac//YnwCwCS/b1i7hQnn3WdmnWVWj3rQRqxH6IRAibIBaNv37767//+bx04cECdOnXSqlWrVFZWZrYe4RdAbFjfK+ZOcXbi/kKddZ1aGFVq1oM0Yj9Eo57hFDkmyAVn9OjRmjRpkkaNGqW8vDydeeaZmjVrltl6hF8AsUFXce7xQl00WA/SiP0QDcl8ihwT5II1b948zZs3L5S1CL8A0ADXKprGC3UIinWPsCSNO3+aXWsFE+Rii/ALABlcqwDCYd0jLNEljMYRfgEgg2sVQDise4QluoTROMIvAAABs65Sk6hTA1qL8BuAXkdPUc9jfcxOdY5U1qpDSaHJswEAwbKuUpPCq1MDkijx4XffjjWq3fWqlsxbarbG4P0j1Tm/q9nzO5QUqmBkT7PnJ8GaNWu0bt060zVGjBhh2jsIIBmsq9SkcOrUgKRKfPit3fWqDh+okvRZszU6dOwo37Wdiq4/3eT5dcHuaWmDyeMTYdu2bZKkfv36mTy/fs454RdtZd0mIcW/UcK6R1iy7xJOAoZoIEx333237rvvPnnvdd111+nGG280Wyvx4VeS8guKdeUtC8yeb/1/ZOvWrVNVVZWKi4tN14mzfv36mZ7MLly4UFVVVVq4cKHJ8+txupxs1m0SUvwbJax7hCW6hLPBEI1osJ4gJ9VNkTvT7i+vs7J+/Xrdd999Wr16tfLz83XJJZfosssu06mnnmqyXuLDb4cT2ud6C4EoLi7W9Om8uZorI0aMMF+D0+Xks26TkOLfKGHdIyzRJZwNhmhkKcYT5KSPp8idOaab2RrZ2Lhxo84991wVFBRIkv7u7/5OTzzxhL75zW+arJf48HtiUadcbwEJUFZWZh5Kwzhd5mQZAAIS8wly0vGnyL3++m16v3ZjoOt0KRyqQYO+3eiPDx8+XN/61re0a9cuderUSStXrjT9/6rEh18gLqxPl7dt26Zt27aZvhhIuAYQJdZT5JggF4yhQ4dqzpw5uuiii1RYWKgzzjhDeXl2EZXwC0SE9emydSMG1zYARIn1FLmkTpBr6oTW0syZMzVz5kxJ0s0336zS0lKztQi/QEpYh2vrlwGRPetGibi3SSSF9SCNuA/RsJ4ixwS5YO3YsUNFRUV655139Pjjj+vPf7Z70Y/wCwAJYt0oEfc2iXrWdWrWVWrWgzQYooGwfelLX9KuXbvUoUMH/exnP9NJJ51kthbhF0BgqIPLPetGibi3SUj2dWphVKlZD9IIY4iGdY+wRJdwnDz33HOhrZVV+HXObZX0vqRjko5678ucc90lLZHUX9JWSZO993tstgkg6qiDQ1xY16lRpdY86x5hiS5hNK4lJ79/772vafDxXEmrvPcLnHNzMx/PCXR3AGIjrDo4APFn3SMsJahLGIFry7WHCZLGZr6/SFK5CL8AkHi8UAcgzrINv17S75xzXtI93vt7JfXy3ldKkve+0jlXZLVJAKjHIJDc4oU6IESGE+Qk6Tu7/qrHDp+nne9frfydtSZrdOrQXr27RWvgWLbh93zv/XuZgPuMc25Ttgs452ZJmiVJffv2bcUWAaCO9b1i7hQ3jxfqgJAYT5CTpFM/3KpJ+dIuXW2+VpRkFX699+9lvt3hnHtC0jmSqp1zJZlT3xJJOxr5tfdKuleSysrKfDDbBpBGdBUjLqyr1CT7OjXkWNn0un8M5S+8TKdJ2tjlBH2mZ6HpWlHSbPh1znWW1M57/37m+xdL+q6k5ZKulbQg8+0yy40CQBi4VoG2sq5Sk8KpU2OIRvPMxycPHJe4CXKNmTFjhlasWKGioiKtX79ekrR7925deeWV2rp1q/r376+lS5cG0v+bzclvL0lPOOfqf/7D3vunnXMvSlrqnJsp6R1J6fjqAEgsrlUgCNZVapJ9nRpDNJrH+ORgTZs2TbNnz9bUqR+3dCxYsEAXXnih5s6dqwULFmjBggW6884727xWs+HXe79F0hnH+fwuSRe2eQfGeh09RT2P9TG9R3akslYdStLz1wVAUnGtAqiThCEa1hifHKwxY8Zo69atf/O5ZcuWqby8XJJ07bXXauzYseGE37jreayPOn/Y1XSNDiWFKhjZ03QNAADQMtZT5JI4Qe7bb1RofaepXZwAACAASURBVO3BQJ85vLCTbju1tMW/rrq6WiUldS/YlpSUaMeO475e1mKJD78dTuiowzqs/tefbrbGmjVrtG7d09IGm+dXVVWpuLjY5uEAEDHWPcISXcJpYD1Fjgly8ZX48NutuLf5GuvWrTMNqMXFxaGMjgWAXLPuEZboEk4L6ylySZ0g15oTWiu9evVSZWWlSkpKVFlZqaKiYEZKJD78hqW4uFjTp6frfg6AlrNuk5Di3Shh3SMs0SUMxMUXvvAFLVq0SHPnztWiRYs0YcKEQJ5L+EUibN++WFXVT5quUdzrcvXpM8V0DSRbGH+DQ6MEgDiaMmWKysvLVVNTo9LSUs2bN09z587V5MmTdf/996tv37569NFHA1mL8BsDYQS7uNu79wVJUrduo02eX1u7QVUS4RdtYt0mIdEokSbWgzSsh2hY9whLyegSNle1TqrdIdUYRcIOnaQTm79KsXjx4uN+ftWqVUHviPAbB1XVT6q2doMKC4fleiuR1a3baNOT2Zdevkq1tRv00stXmTy/HqfLALJhPUjDeoiGdY+wlIwuYeshGir8UOOKB2i43QqRRPiNicLCYTpr1MO53kZqFfe6XFXGa3C6DCBb1oM0rIdoWPcIS/HvErYeoiFJm4/8VSoZrOGFRVKPU83XiwrCL5CFPn2mmIfSME6XOVkG6ljXqVGlhrayHqIhpW+QRj3CLxAR1qfLe/e+oL17XzC9P064jgbrRok4t0lI9nVqVKkB0Ub4BSLC+nTZ+sVJrm1Eg3WjRBLaJKzr1KhSSw8myMUT4RdICetwbf0yILJj3ShBmwRQhwly8UX4BQAAaCEmyAVrxowZWrFihYqKirR+/XpJ0qOPPqpbb71VGzdu1OrVqwP7gz3hF0BgqIMDALTGtGnTNHv2bE2d+nHoHz58uB5//HFdf/31ga5F+AUQCOrg0oMX6tIh7kM0EC9jxozR1q1b/+ZzQ4cONVmL8AsgEGHVwSG3eKEuO9ZVapJtnVrch2jUs54il8QJcvOefE0b3tsX6DOH9e6qWy4/LdBntgXhFwCQNV6oa551lZpkX6cW9yEakv0UuSRMkEsrwi+AWGEQCKLOukpNok4tG9ZT5OI+Qa4xUTqhtUL4BRAb1veKuVMMIG02796smqIavf3Xt02e3zGvo0o6R2vgS+LDb37vzrneAoCA0FUMAMEZN3BcrrfwkSlTpqi8vFw1NTUqLS3VvHnz1L17d331q1/Vzp07ddlll2nkyJH67W9/2+a1Eh9+3yzZo3Xr1kkL/2C2RlVVlYqLi82eDyA8XKsAEBXWE+TOkfT58eNV1a+HBpw4wGydbCxevPi4n584cWLgayU+/K5bt848nBYXF5u/AQ3AHtcqAESF9QQ56eMpcjo9XRkm8eFXqgun06dPz/U2AEQc1yqiwbpHWKJLOAqse4SleHcJW0+Qk9I3Ra5eKsIvACAewvhbtKR0CceZdY+wFF6XMOKH8BuA7dsXq6r6SbPn19ZuUGHhMLPnA0BUWPcIS8noEpbsB2lYDtGw7hGWwukSRjy1y/UGkqCq+knV1m4we35h4TAV97rc7PkAgHgpGNlTHUoKzZ5/pLJWB9buNHs+kEuc/AaksHCYzhr1cK63ASDirNskJBol0sB6kAZDNLLD+OR44uQXAEJS3Oty8ytMtbUbTK9hAagz6Jxe6lFqd/peU1Gr11dXmz0/ambMmKGioiINHz78o8994xvf0JAhQ3T66adr4sSJ2rt3byBrcfILACGxbpOQaJQAwsL45GBNmzZNs2fP1tSpHzdQXHTRRZo/f77y8vI0Z84czZ8/X3feeWeb1yL8AgBSx7pOjSo1oGXGjBmjrVu3/s3nLr744o++f+655+qxxx4LZC3CLxLhofdq9Hj1HtM1vtjrJF3Tu4fpGgDsWdepUaWGWPvNXKlqXbDPLB4hXbqgTY944IEHdOWVVwayHcJvDIQR7OLuz3v3S5LO69bZ5Pmv1R6UJMIvkADWdWpJqVJDOhzatElHa2r0wZa6XuT2+/6qdocOBrdAu3ZtfsHs9ttvV15enq6++upAtkT4jYHHq/fotdqDOq2wU663ElnndetsejI78ZU39FrtQU185Q2T59fjdBlBsG6UoE0CcWE9RS7OE+Skj0coH27wuWNnf1PHAlyjXaeOalfS+maSRYsWacWKFVq1apWcc4HsifAbE6cVdtITZ56a622k1hd7nWS+BqfLCEJxr8tVZfj82toNqpIIvykQ5yEakv0UuSRMkKsfobxx40adMHBArrfzKU8//bTuvPNO/dd//ZcKCgoCey7hF8jCNb17mIfSME6XOVlOPutGCdok0qFgZE8dMHz+kcpaHZBMw6/1FDkmyAVrypQpKi8vV01NjUpLSzVv3jzNnz9fH3zwgS666CJJdS+9/fznP2/zWoRfICKsT5f/vHe//rx3v+n9ccI1kAwM0YgG6yEaUl1fcbsI/Gd78eLFn/rczJkzTdYi/AIRYX26bP3iJNc2gI9ZV6lJ1Kkl3aBzepmvUVNRK0kaMi5d7xQRfoGUsA7X1i8DIjp4oa5p1lVqEnVqaWA9RENK3yCNeoRfAEDWeKGuedZVahJ1akBbEH4BBIY6uOTjhToAcZf48FtcXJzrLQCpQB0cACAOEh9+L7300lxvAUiFsOrgACSDdY+wZN8ljHhKfPgFAADRYt0jLIXTJcwEueDMmDFDK1asUFFRkdavXy9J+va3v61ly5apXbt2Kioq0i9/+Uv17t27zWslPvxu375YVdVPmq5RW7tBhYXDTNcAUIdBIED8WfcIS/ZdwkyQC9a0adM0e/ZsTZ069aPPfeMb39Btt90mSfrxj3+s7373uwy5yEZV9ZPm4bSwcJiKe11u9nwAdazvFXOnGEC2mCAXrDFjxmjr1q1/87muXbt+9P39+/fLORfIWokPv1JdOD1r1MO53gaANqKrOB2se4Sl+HcJS/aDNBiikU53rr5Tm3ZvCvSZQ7oP0Zxz5rTq137rW9/Sgw8+qBNPPFHPPvtsIPvJOvw659pLWiNpu/d+vHNugKRHJHWX9LKka7z3hwPZFQDkCNcqcsu6R1hKRpew9SANhmikR01FrQ7sa689VfslSYf2H9HRw8cCe75r17bT2ttvv12333675s+fr5/+9KeaN29em/fUkpPfGyRtlFR/Bn2npB967x9xzv1c0kxJ/97mHQFAjnCtIvese4SlZHQJWw/SYIhGOhxvhPL/Hvq1QNfIy2+vLt07tvk5V111lS677LLwwq9zrlTSZZJul/Qvru7SxT9Iqv8vyCJJt4rwCyDGuFYBIE3qRyhv3LhRJxV3zvV2PuWNN97QqaeeKklavny5hgwZEshzsz35/ZGkb0rqkvn4ZEl7vfdHMx9XSLIdQA0AAIBEmjJlisrLy1VTU6PS0lLNmzdPK1eu1ObNm9WuXTv169cvkKYHKYvw65wbL2mH9/4l59zY+k8f56f6Rn79LEmzJKlv376t3Ga0PfRejR6v3mP2/NdqD+q0wk5mzwcAAMilxYsXf+pzM2fONFkrm5Pf8yV9wTk3TlJH1d35/ZGkbs65vMzpb6mk9473i73390q6V5LKysqOG5Dj7vHqPaYB9bTCTqGMjgUAIEmsp8gxQS6emg2/3vt/lfSvkpQ5+b3Je3+1c+5RSZNU1/hwraRlhvuMvNMKO+mJM0/N9TYARJx1m4REo0Q2rOvUklClFnfWU+SSMEFOqhvW0aFPP9M1oqYtPb9zJD3inPs3Sa9Iuj+YLQFAMoXxNzg0SjTPuk4tCVVqSWA9RS7uE+SkBlPkJl9rvlaUtCj8eu/LJZVnvr9F0jnBbwkAksm6TUKiUSIb1nVqSahSkxiikWvWE+Sk9E2Rq5eKCW8AACB7DNFAkhF+AQDA32CIBpKsXa43AAAAgHSbMWOGioqKNHz48E/92Pe//30551RTUxPIWpz8IhEefuEdLVu73XSNCSP76KrRyeyqRrJYN0rQJgEgaNOmTdPs2bM1derUv/n8u+++q2eeeSbQWRGEXyTCsrXbtaFyn4aVdDV5/obKfZJE+EXkWTdK0CaRHesqNYk6NSTLmDFjtHXr1k99/mtf+5q+973vacKECYGtRfiNgTBONeOuPvguuf48k+dfec+ftaFyn668588mz6/H6TLayrpRgjaJ5llXqUnUqcFO1R136IONmwJ95glDh6j45ptb/OuWL1+uPn366Iwzzgh0P4TfGLA+1UyCYSVdNWFkH7PnWz67HqfLQDJYV6lJyalTizsmyNk5cOCAbr/9dv3ud78L/NmE35iwPNVE864a3dc8lFqfKgNAlFj3CEu2XcJJmCB3PK05obXw1ltv6e233/7o1LeiokKjRo3S6tWrVVxc3KZnJz78dikcmustAFmzvlrBtQoEgRfq0FbWPcKSfZdw3CfI1du59W3t37tHu9+rMHl+Xv4J6tqjZ4t/3YgRI7Rjx46PPu7fv7/WrFmjHj3a/t+GxIffQYO+nestAFmxvlrxwtu79cLbu03vjxOuk48X6hAE6x5hiS7hbIQxQjlbU6ZMUXl5uWpqalRaWqp58+Zp5syZJmslPvwCcWF9tcL6xUnuLKcDL9QByVE/Qnnjxo3q3rs0p3tZvHhxkz9+vCaI1iL8AilhHa65swwAiAMmvAEAACA1OPkFEBi6kIHwWA/SYIgGkirx4feh92r0ePUe0zVeqz2o0wo7ma4BRB1dyEB4rAdpMEQDSZb48Pt49R7zcHpaYSfzN6CBqKMLGQiP9SANhmggyRIffqW6cPrEmafmehsAgCxY9whLdAkjHqwnyEl1wzqUsgGyqQi/AJKDQSDJFsbfotElnB7WU+TiPEFO+niKnMZ0MF6peTNmzNCKFStUVFSk9evXS5JuvfVW3XffferZs25Ixh133KFx48a1eS3CL4DYsL5XzJ3i3LPuEZboEk4L6ylycZ8gJ4U3RS4b06ZN0+zZszV16tS/+fzXvvY13XTTTYGuRfgFEBt0FQPIlvUUOSbIBWvMmDGBDrJoCuEXABrgWgWANHtu6euqebc20Gf2OKVQn5s8qFW/9qc//akefPBBlZWV6a677tJJJ7X9ahRDLgAgY8LIPhpWYvfmx4bKfaYjpgEgSf7pn/5Jb731ltauXauSkhJ9/etfD+S5nPwCQAbXKoCPMUQjnVp7QmuhV69eH33/uuuu0/jx4wN5LuEXAJA61nVqca9SY4gGoqCyslIlJXUv/T3xxBMaPnx4IM8l/Abg4RfeMf2rzA2V+0z/KhYA0sS6Ti0JVWoM0UDYpkyZovLyctXU1Ki0tFTz5s1TeXm51q5dK+ec+vfvr3vuuSeQtQi/AVi2drtpQB1W0jWU0bEAkAbWdWpUqQEtt3jx4k99bubMmSZrEX4DMqykq5Zcf16utwEg4qzbJCQaJQCgKYRfAAhJGH+Dw6AOIDxxniBX70hlrY6931lHdtrMk3Md2imvW0eTZ7cW4RcAQmLdJiHRKAGEJe4T5KSGI5S92RpRRPgFAABooSRMkKsfobxr40bl9egk55z5mkHzvuXBnfALAEDArKvUpPjXqVn3CEt0CWerY8eO2rVrl04++eRYBWDvvXbt2qWOHVt2rYLwCwBAgKyr1KT416lZ9whLdAm3RGlpqSoqKrRz585cb6XFOnbsqNLS0hb9GsIvACSMdaMEbRJNs65Sk+Jfp2bdIyzRJdwSHTp00IABA3K9jdAQfgEgQawbJWiTABB3iQ+/wws75XoLABAa60YJ2iQAxF3iw+9tp7bsHghias1Cad1jtmuMmCSVTbddAwAAmEp8+E2EMIJd3G37Y923/S6weX7VurpvCb8AAMQa4TcO1j1WF76KbQu1Y63fBbYnswsvq/saLLzM5vn1OF1GDPBCHRAO6wlyUjhT5KKG8BsXxSOk6U/lehfpNWKS/RqcLiMGeKEOCIf1BDkpnClyUUT4BbJRNt0+lIZxuszJMtqIF+qAcFhPkJPCmSIXRYRfICqsT5e3/bHuH8v744RrIDTWU+TiPkEOaAzhF4gK69Nl6xcnubYBhMZ6ilzcJ8jVsx6hzPjkeCL8AmlhHa6tXwYE8BHrKXJxnyAn2Y9QZnxyfCU+/D78wjtatna76RobKvdpWElX0zUAAED2rEcoMz45vtrlegPWlq3d/tHbw1aGlXQ1fwMaAAAAbZf4k1+pLpwuuf68XG8DSD66kAEAEdds+HXOdZT0B0knZH7+Y977W5xzAyQ9Iqm7pJclXeO9P2y5WQARRhcyAmI9RENikAaQZtmc/H4g6R+897XOuQ6S/uic+42kf5H0Q+/9I865n0uaKenfDfcKIMrC6kJGooVxhYxBGkC6NRt+vfdeUm3mww6Zf7ykf5BUf9t7kaRbRfgFALSB9RANiUEaQNpldefXOdde0kuSPivpZ5LekrTXe38081MqJB33j+vOuVmSZklS3778KRtAGzEFDwACU1VVZTrprbi4WJdeeqnZ81sjq/DrvT8maaRzrpukJyQNPd5Pa+TX3ivpXkkqKys77s8BgKxY3yvmTjHwESbIJd+IESNyvYWcaFHbg/d+r3OuXNK5kro55/Iyp7+lkt4z2B8AfIxBHUAomCCXDmVlZSorK8v1NkKXTdtDT0lHMsG3k6TPS7pT0rOSJqmu8eFaScssNwoAoeBaBcAEOSRaNie/JZIWZe79tpO01Hu/wjm3QdIjzrl/k/SKpPsN9wkA9rhWAaAFams3mE56K+51OeOTDWTT9vCqpDOP8/ktks6x2BQA5ATXKgBkqbjX5aoyfH5t7QZVSYRfA6mY8AYAQEPWgzQYopF8ffpMMQ2mlifKaUf4DcKahdK6x+yeX7VOKk7nG5kAEDTrQRoM0QCijfAbhHWP2QbU4hHhjI4FgBSwHqTBEA0g2gi/QSkeIU1/Kte7AAAAQBMIvwAQJusqNYk6NQBoAuEXAMISxvUl6tQQE9YT5CSmyOH4CL8AEBbrKjWJOjXEgvUEOYkpcmgc4RcAAITKeoKcxBQ5NC7x4XdY76653gIAIGWse4QluoSB1kp8+L3l8tNyvQUAQIpY9whLdAmnhfX4ZCmdI5QTH34BAAiTdY+wRJdwGliPT5bSO0KZ8AsAABAx1uOTpfSOUCb8AkDSWHcJ0yMMIMYIvwCQJNZdwvQIA4g5wi8AJIl1lzA9wgBijvCLRHj09Ue1cstK0zXGDRynKwZdYboGAACwRfhFIqzcslKbd2/W4O6DTZ6/efdmSSL8AkCMWI9QZnxyPBF+YyCMU824qw++Cy9ZaPL86U9zvxFAtFgP0oj7EA3rEcqMT44vwm8MWJ9qJsHg7oM1buA40zU2795sHoK5WgEgG9aDNJIwRMN6hDLjk+OL8BsTlqeaaJ51sJa4WoEYoUot56wHaTBEA0mW/PC7ZqG07jHbNarWScUjbNdATl0x6ArzUDr96enmp8ucLKPNqFIDEsV6hHKXwqEaNOjbZs9vjeSH33WP2YfT4hH2/4eAxLM+XV5TvUZrqteY3h8nXKcAVWpAYoQxQjmKkh9+pbpwOv2pXO8CaJL16bL1i5Nc2wCAeAljhHIUpSP8AjAP1zRiAADioF2uNwAAAACEhfALAACA1ODaAwAA+BSGaDSPCXLxRPgFEBgGgSAQ1j3CEl3CzWCIRvOYIBdfhF8AgWAQCAIRRm0kXcLNYohG85ggF1+EXwCBCGsQCBLOukdYoksYSDleeAMAAEBqEH4BAACQGoRfAAAApAZ3fgHEinWjBG0SAJBshF8AsWHdKEGbRIpY16lRpQZEFuEXQGxYN0rQJpES1nVqVKllxXqIhpSMQRoIHuE3AI++/qhWbllp9vzNuzdrcPfBZs8HgFSxrlOjSq1Z1kM0pGQM0rCeICelc4oc4TcAK7esNA2og7sPDmWAAAAAYbAeoiHFf5CG9QQ5Kb1T5Ai/ARncfbAWXrIw19sA0Ea8UAcgCqwnyEnpnSJH+AWADF6oA4DkS374LR6R6x0AiAleqAOA5Et++L10Qa53AAAAgIhIfvgFACBs1j3CEl3CQCsRfgEACJJ1j7BElzDQBoRfAAiRdZuERKNEzln3CEt0CWfJepAGQzTiqdnw65w7RdKDkoolfSjpXu/93c657pKWSOovaaukyd77PXZbBYB4C6Ovm0YJoI71II0kDNFIq2xOfo9K+rr3/mXnXBdJLznnnpE0TdIq7/0C59xcSXMlzbHbKgDEm3WbhESjBFDPepBG3Ido1LOeIje8sJNuO7XU7Pmt0Wz49d5XSqrMfP9959xGSX0kTZA0NvPTFkkqF+EXAAAgFsKYIhdFLbrz65zrL+lMSS9I6pUJxvLeVzrnigLfHQAAAEyEMUUuirIOv865Qkn/IelG7/0+51y2v26WpFmS1Lcv92IAAAiEdZ0aVWpIqKzCr3Oug+qC76+9949nPl3tnCvJnPqWSNpxvF/rvb9X0r2SVFZW5gPYMwCgCdaNErRJRIB1nRpVakiwbNoenKT7JW303v+gwQ8tl3StpAWZb5eZ7BAAkDXrRgnaJCLCuk6NKjUkWDYnv+dLukbSOufc2sznblZd6F3qnJsp6R1J/JcQAHLMulGCNgkAcZdN28MfJTV2wffCYLcDAAAQDwzRiCcmvAEAALQQQzTiK/Hh99HXH9XKLStN19i8e7MGdx9sugaatmfJUu1bscJ0ja7jx+ukKyebrgEAiAeGaMRX4sPvyi0rzcPp4O6DTV8yCSPYxd2BF1+UJBWcfbbJ8w9t2iRJhF9AtEkAiLfEh1+pLpwuvGRhrrfRavtWrNChTZvUcciQXG8lsgrOPtv0ZHbbNVNNngvEDW0SKUKPMBIqFeE3CToOGaJ+Dz2Y620ASDnaJFKCHmEkGOEXyNKhTZvMT4C5VwwgEugRRoIRfoEsdB0/3nwN7hUDAGCP8Atk4aQrJ5uHUu4VAwBgj/ALAIgU6zYJiUYJxIP1EA0pnYM0CL9AhFjfK+ZOMaLOuk1ColEC8WA9RENK7yANwi8QEdb3irlTjDiwbpOQaJSIDOsqNSnWdWrWQzSk9A7SIPwCEWF9r5g7xQAiw7pKTaJODY0i/AIAgHBZV6lJ1KmhUYRfIEW4UwwASDvCL5AS3CkGPmbdKEGbBBBdhF8gJbhTDNSxbpSgTQKINsIvACBVrBslaJMAoo3wCyAw1neKJe4VA0CQrAdpDOvdVbdcfprZ81uD8AsgENZ3iiXuFQNoIesu4Rj3CEvhDNKIIsIvgEBY3ymWuFcMoAWsu4QT0CMcxiCNKCL8AgAQMOs2CYlGiWZZdwnTIxxbiQ+/Q7oPMV9jz5Kl2rdihdnzD23apI5D7P89gDigqxhRZ90mIdEoAbRF4sPvnHPmmK+xb8UK04DacciQUO5TAlFHVzHiwLpNQqJRAmiLxIffsHQcMkT9Hnow19sAEo2uYgBAW7XL9QYAAACAsHDyCwAA0BpUqcUS4RcAGuCFOsSFdaMEbRLNoEottgi/AJDBC3WIC+tGCdokskCVWmwRfgEggxfqEBfWjRK0SSDJeOENAAAAqcHJLwCEyPpOscS9YgBoCuEXAEISxrAa7hUDQNMIvwAQEus7xRL3ihEc2iSQVIRfAADwN2iTiAjrHmEplV3ChF8ASBi6itFWtElEgHWPsJTaLmHCLwAkCF3FQEJY9whLqe0SJvwCQILQVQwATaPnFwAAAKnByS8AoEW4U4wgWLdJSDRK4PgIvwCArHGnGEGwbpOQaJRA4xIffvcsWap9K1aYrnFo0yZ1HDLEdA0AiALuFCMI1m0SEo0SWbOuUyseIV26wO75rZD4O7/7Vqz46CTBSschQ0KZ3AQAABCYEZPqwmnKJP7kV6oLp/0eejDX2wAAZMH6TrHEvWJAUjh1ahGUivALAIiHMP4WjXvFQLoRfgEAkWF9p1jiXnGaWDdK0CYRT4RfAACQONaNErRJxFez4dc594Ck8ZJ2eO+HZz7XXdISSf0lbZU02Xu/x26b6fbac9v1+upq0zUGndNLp32uj+kaABAVdBUnn3WjBG0S8ZVN28MvJV3yic/NlbTKe3+qpFWZj2Hk9dXVqqmoNXt+TUWtebgGgKjoOn68aT3loU2bzCs2AbResye/3vs/OOf6f+LTEySNzXx/kaRySXMC3Bc+oUdpoSZ+fZTJs5+462XVVNTqibteNnl+PU6XAUQBXcVAurX2zm8v732lJHnvK51zRY39ROfcLEmzJKlv376tXA6WBp3Ty3yN+pNrwi8AAMgl8xfevPf3SrpXksrKyrz1emi50z7XxzyUhnG6zMkygKigqzgdaJOIp9aG32rnXEnm1LdE0o4gN4XksT5d5mQZQFTQVZwOtEnEV2vD73JJ10pakPl2WWA7QiJZny5zsgwgKugqTgfaJOIrm6qzxap7ua2Hc65C0i2qC71LnXMzJb0jiT+WIKc4WQYAANnIpu1hSiM/dGHAewFaLQknyxKnywAAWGPCG5AFGjEARA2DOpLP+oU6KZ0v1RF+gSyE1YgBANmwfqmOF+pyz/qFOim9L9URfoEI4aU9ANlgUEfyWb9QJ6X3pTrCLxARvLQHAIA9wi8QEUl4aY+TZSA5uFOMpEp8+D1h6JBcbwGIBE6WAWSLO8VIssSH3+Kbb871FoBISMLJssTpMhAG7hSnh3WjxJDuQzTnnDlmz2+NxIdfAOGgDg4A4iWMRokoIvwCCERYdXDcWwaSwfpOscS94uaE0SgRRYRfALHBvWUgGazvFEvcK0bjCL8BeO257Xp9dbXZ82sqatWjtNDs+UBcJOHeMifLgP2dYol7xWhcu1xvIAleX1390YmRhR6lhaHcpwTSbtA5vUz/oFlTUWv6B2UAQPM4+Q1Ij9JCTfz6qFxvA0AbhHGyDCA8dBXjeAi/ABAi6uCAcNBVjMYQfgEgJNTBAeGhqxiNIfwCQEiogwOA3CP8AkCCUAcHhIc7xfFECIoDUAAABnFJREFU+AWABKEODggHd4rji/ALAMgaJ8tAHe4UxxfhFwCQtSScLEucLgNpRvgFAEQGjRjAx6zvFEvpvFdM+AUARAaNGEAd6zvFUnrvFRN+AQCpwr1lxIH1nWIpvfeKCb8AgFTh3jKQboRfAAACxL1lINoIvwAABCise8tAEKxfqjth6BAV33yz2fNbg/ALAEAM8dIe2iqMl+qiiPALAEDM8NIeghDGS3VRRPgFACBmkvDSHifLyJXEh9/Xntuu11dXm65RU1GrHqWFpmsAABAWTpaRZIkPv6+vrjYPpz1KC0N5uxcAgDAk4WRZ4nQZx5f48CvVhdOJXx+V620AAABRB4fcSkX4BQAA0cEYa+QS4RcAACQO95bRGMIvAABInCTcW+Zk2QbhFwAAoIU4WY4vwi8AAEALhXGyDBuEXwAAgAiiDs4G4RcAACBiqIOzQ/gFAACImKTUwfU4pVCfmzzI7PmtQfgFAABIobROpyX8AgAApFAYp8tR1C7XGwAAAADCQvgFAABAahB+AQAAkBptCr/OuUucc5udc2865+YGtSkAAADAQqvDr3OuvaSfSbpU0jBJU5xzw4LaGAAAABC0tpz8niPpTe/9Fu/9YUmPSJoQzLYAAACA4LUl/PaR9G6DjysynwMAAAAiqS09v+44n/Of+knOzZI0S5L69u3bhuVap8cphaGvCQAAgGhqS/itkHRKg49LJb33yZ/kvb9X0r2SVFZW9qlwbC1qI/UAAACQO2259vCipFOdcwOcc/mS/lHS8mC2BQAAAASv1Se/3vujzrnZkn4rqb2kB7z3rwW2MwAAACBgbbn2IO/9SkkrA9oLAAAAYIoJbwAAAEgNwi8AAABSg/ALAACA1CD8AgAAIDUIvwAAAEgNwi8AAABSg/ALAACA1CD8AgAAIDUIvwAAAEgNwi8AAABSg/ALAACA1CD8AgAAIDUIvwAAAEgNwi8AAABSg/ALAACA1HDe+/AWc26npG2hLfixHpJqcrAuwsXXOR34OicfX+N04OucDrn6Ovfz3vc83g+EGn5zxTm3xntflut9wBZf53Tg65x8fI3Tga9zOkTx68y1BwAAAKQG4RcAAACpkZbwe2+uN4BQ8HVOB77OycfXOB34OqdD5L7OqbjzCwAAAEjpOfkFAAAAkh9+nXOXOOc2O+fedM7NzfV+YMM5t9U5t845t9Y5tybX+0EwnHMPOOd2OOfWN/hcd+fcM865NzLfnpTLPaJtGvka3+qc2575/bzWOTcul3tE2znnTnHOPeuc2+ice805d0Pm8/x+TogmvsaR+/2c6GsPzrn2kl6XdJGkCkkvSprivd+Q040hcM65rZLKvPd0RiaIc26MpFpJD3rvh2c+9z1Ju733CzJ/oD3Jez8nl/tE6zXyNb5VUq33/vu53BuC45wrkVTivX/ZOddF0kuS/qekaeL3cyI08TWerIj9fk76ye85kt703m/x3h+W9IikCTneE4Asee//IGn3Jz49QdKizPcXqe4/roipRr7GSBjvfaX3/uXM99+XtFFSH/H7OTGa+BpHTtLDbx9J7zb4uEIR/UKgzbyk3znnXnLOzcr1ZmCql/e+Uqr7j62kohzvBzZmO+dezVyL4K/CE8Q511/SmZJeEL+fE+kTX2MpYr+fkx5+3XE+l9x7Hul2vvd+lKRLJf1z5q9SAcTTv0v6jKSRkiol3ZXb7SAozrlCSf8h6Ubv/b5c7wfBO87XOHK/n5MefiskndLg41JJ7+VoLzDkvX8v8+0OSU+o7soLkqk6c7es/o7ZjhzvBwHz3ld774957z+UdJ/4/ZwIzrkOqgtFv/beP575NL+fE+R4X+Mo/n5Oevh9UdKpzrkBzrl8Sf8oaXmO94SAOec6Zy7XyznXWdLFktY3/asQY8slXZv5/rWSluVwLzBQH4YyJorfz7HnnHOS7pe00Xv/gwY/xO/nhGjsaxzF38+JbnuQpEylxo8ktZf0gPf+9hxvCQFzzg1U3WmvJOVJepivczI45xZLGiuph6RqSbdI+r+SlkrqK+kdSVd473lhKqYa+RqPVd1fkXpJWyVdX38vFPHknLtA0nOS1kn6MPPpm1V3J5TfzwnQxNd4iiL2+znx4RcAAACol/RrDwAAAMBHCL8AAABIDcIvAAAAUoPwCwAAgNQg/AIAACA1CL8AAABIDcIvAAAAUoPwCwAAgNT4f1hNKTUiDXUsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(array([52.25809537, 54.88309537, 56.85184537, 58.32840787, 59.43582974,\n",
       "        60.26639615, 60.93522182, 61.45344021, 61.82590961, 62.05733162,\n",
       "        62.15225614, 62.11508633, 61.95008328, 61.66137065, 61.25293908,\n",
       "        60.72865046, 60.09224212, 59.34733082, 58.49741666, 57.54588682,\n",
       "        56.49601924, 55.3509861 , 54.11385725, 52.78760353, 51.37509993,\n",
       "        49.8791287 ]),\n",
       " None)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = [12, 8]\n",
    "\n",
    "class inventory_model:\n",
    "    '''Small class to hold model fundamentals and its solution'''\n",
    "\n",
    "    def __init__(self,label='noname',\n",
    "                 max_inventory=10,  # upper bound on the state space\n",
    "                 c = 3.2,            # fixed cost of order\n",
    "                 p = 2.5,           # profit per unit of good\n",
    "                 r = 0.5,           # storage cost per unit of good\n",
    "                 β = 0.95,          # discount factor\n",
    "                 dp = 0.5,          # parameter in geometric distribution of demand\n",
    "                 demand = 4         # fixed demand\n",
    "                 ):\n",
    "        '''Create model with default parameters'''\n",
    "        self.label=label # label for the model instance\n",
    "        self.c, self.p, self.r, self.β, self.dp= c, p, r, β, dp\n",
    "        self.demand = demand\n",
    "        # created dependent attributes (it would be better to have them updated when underlying parameters change)\n",
    "        self.n = max_inventory+1    # number of inventory levels\n",
    "        self.upper = max_inventory  # upper boundary on inventory\n",
    "        self.x = np.arange(self.n)  # all possible values of inventory and demand (state space)\n",
    "\n",
    "    def __repr__(self):\n",
    "        '''String representation of the model'''\n",
    "        return 'Inventory model labeled \"{}\"\\nParamters (c,p,r,β) = ({},{},{},{})\\nDemand={}\\nUpper bound on inventory {}' \\\n",
    "               .format (self.label,self.c,self.p,self.r,self.β,self.demand,self.upper)\n",
    "\n",
    "    def sales(self,x,d):\n",
    "        '''Sales in given period'''\n",
    "        return np.minimum(x,d)\n",
    "\n",
    "    def next_x(self,x,d,q):\n",
    "        '''Inventory to be stored, becomes next period state'''\n",
    "        return x - self.sales(x,d) + q\n",
    "\n",
    "    def profit(self,x,d,q):\n",
    "        '''Profit in given period'''\n",
    "        return self.p * self.sales(x,d) - self.r * self.next_x(x,d,q) - self.c * (q>0)\n",
    "\n",
    "    def demand_pr(self,plot=False):\n",
    "        '''Computes stochastic demand probs'''\n",
    "        k = np.arange(self.n)  # all possible values of demand\n",
    "        pr = (1-self.dp)**k *self.dp\n",
    "        pr[-1] = 1 - pr[:-1].sum()  # update last prob to ensure sum=1\n",
    "        if plot:\n",
    "            plt.step(self.x,pr,where='mid')\n",
    "            plt.title('Distribution of demand')\n",
    "            plt.show()\n",
    "        return pr\n",
    "\n",
    "def bellman(m,v0):\n",
    "    '''Bellman equation for inventory model\n",
    "       Inputs: model object\n",
    "               next period value function\n",
    "    '''\n",
    "    # create the grid of choices (same as x), column-vector\n",
    "    q = m.x[:,np.newaxis]\n",
    "    # compute current period profit (relying on numpy broadcasting to get the matrix with choices in rows)\n",
    "    p = m.profit(m.x,m.demand,q)\n",
    "    # indexes for next period value with extrapolation using last value\n",
    "    i = np.minimum(m.next_x(m.x,m.demand,q),m.upper)\n",
    "    # compute the Bellman maximand\n",
    "    vm = p + m.β*v0[i]\n",
    "    # find max and argmax\n",
    "    v1 = np.amax(vm,axis=0)   # maximum in every column\n",
    "    q1 = np.argmax(vm,axis=0) # arg-maximum in every column = order volume\n",
    "    return v1, q1\n",
    "\n",
    "def solver_backwards_induction(m,T=10,verbose=False):\n",
    "    '''Backwards induction solver for the finite horizon case'''\n",
    "    # solution is time dependent\n",
    "    m.value  = np.zeros((m.n,T))\n",
    "    m.policy = np.zeros((m.n,T))\n",
    "    # main DP loop (from T to 1)\n",
    "    for t in range(T,0,-1):\n",
    "        if verbose:\n",
    "            print('Time period %d\\n'%t)\n",
    "        j = t-1 # index of value and policy functions for period t\n",
    "        if t==T:\n",
    "            # terminal period: ordering zero is optimal\n",
    "            m.value[:,j] = m.profit(m.x,m.demand,np.zeros(m.n))\n",
    "            m.policy[:,j] = np.zeros(m.n)\n",
    "        else:\n",
    "            # all other periods\n",
    "            m.value[:,j], m.policy[:,j] = bellman(m,m.value[:,j+1]) # next period to Bellman\n",
    "        if verbose:\n",
    "            print(m.value,'\\n')\n",
    "    # return model with updated value and policy functions\n",
    "    return m\n",
    "\n",
    "def plot_solution(model):\n",
    "    plt.step(model.x,model.value)\n",
    "    plt.legend([f'{i+1}' for i in range(model.value.shape[1])])\n",
    "    plt.title('Value function')\n",
    "    plt.show()\n",
    "    plt.step(model.x,model.policy)\n",
    "    plt.legend([f'{i+1}' for i in range(model.policy.shape[1])])\n",
    "    plt.title('Policy function (optimal order sizes)')\n",
    "    plt.show()\n",
    "\n",
    "def bellman_ev(m,ev0):\n",
    "    '''Bellman equation for inventory model\n",
    "       Inputs: model object\n",
    "               next period EXPECTED value function\n",
    "    '''\n",
    "    pr = m.demand_pr()\n",
    "    ev1 = np.zeros(shape=m.x.shape)\n",
    "    for j,d in enumerate(m.x):  # over all values of demand\n",
    "        # create the grid of choices (same as x), column-vector\n",
    "        q = m.x[:,np.newaxis]\n",
    "        # compute current period profit (relying on numpy broadcasting to get the matrix with choices in rows)\n",
    "        p = m.profit(m.x,d,q)\n",
    "        # indexes for next period value with extrapolation using last value\n",
    "        i = np.minimum(m.next_x(m.x,d,q),m.upper)\n",
    "        # compute the Bellman maximand\n",
    "        vm = p + m.β*ev0[i]\n",
    "        # find max and argmax\n",
    "        v1 = np.amax(vm,axis=0)  # maximum in every column\n",
    "        ev1 = ev1 + pr[j]*v1\n",
    "#     q1 = np.argmax(vm,axis=0) # arg-maximum in every column = order volume\n",
    "    q1 = None\n",
    "    return ev1, q1\n",
    "\n",
    "def solve_vfi(self,tol=1e-6,maxiter=500,callback=None):\n",
    "    '''Solves the Rust model using value function iterations\n",
    "    '''\n",
    "    ev0 = np.zeros(self.n) # initial point for VFI\n",
    "    for i in range(maxiter):  # main loop\n",
    "        ev1, q1 = bellman_ev(self,ev0)  # update approximation\n",
    "        err = np.amax(np.abs(ev0-ev1))\n",
    "        if callback != None: callback(iter=i,err=err,ev1=ev1,ev0=ev0,q1=q1,model=self)\n",
    "        if err<tol:\n",
    "            break  # break out if converged\n",
    "        ev0 = ev1  # get ready to the next iteration\n",
    "    else:\n",
    "        raise RuntimeError('Failed to converge in %d iterations'%maxiter)\n",
    "    return ev1, q1\n",
    "\n",
    "def solve_show(self,maxiter=1000,tol=1e-6,**kvargs):\n",
    "    '''Illustrate solution'''\n",
    "    fig1, (ax1,ax2) = plt.subplots(1,2,figsize=(14,8))\n",
    "    ax1.grid(b=True, which='both', color='0.65', linestyle='-')\n",
    "    ax2.grid(b=True, which='both', color='0.65', linestyle='-')\n",
    "    ax1.set_xlabel('Inventory')\n",
    "    ax2.set_xlabel('Inventory')\n",
    "    ax1.set_title('Value function')\n",
    "    ax2.set_title('Optimal new orders')\n",
    "    def callback(**argvars):\n",
    "        mod, ev, q = argvars['model'],argvars['ev1'],argvars['q1']\n",
    "        ax1.step(mod.x,ev,color='k',alpha=0.25,where='mid')\n",
    "#         ax2.plot(mod.x,q,color='k',alpha=0.25)\n",
    "    ev,pk = solve_vfi(self,maxiter=maxiter,tol=tol,callback=callback,**kvargs)\n",
    "    # add solutions\n",
    "    ax1.step(self.x,ev,color='r',linewidth=2.5,where='mid')\n",
    "#     ax2.plot(self.x,pk,color='r',linewidth=2.5)\n",
    "    plt.show()\n",
    "    return ev,pk\n",
    "\n",
    "mod = inventory_model(label='production',max_inventory=25)\n",
    "mod.dp=.25\n",
    "mod.demand = int((1-mod.dp)/mod.dp)\n",
    "mod.c = .25\n",
    "mod.p = 3.5\n",
    "mod.r = 0.4\n",
    "mod.β = 0.9\n",
    "mod.demand_pr(plot=True)\n",
    "mod = solver_backwards_induction(mod,T=15)\n",
    "plot_solution(mod)\n",
    "\n",
    "solve_vfi(mod)\n",
    "solve_show(mod)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal orders of new inventory for d,x:\n",
      "(d in rows, x in columns)\n",
      "[[7 6 5 4 3 2 0 0 0 0 0 0 0 0 0 0]\n",
      " [7 7 6 5 4 3 2 0 0 0 0 0 0 0 0 0]\n",
      " [7 7 7 6 5 4 3 2 0 0 0 0 0 0 0 0]\n",
      " [7 7 7 7 6 5 4 3 2 0 0 0 0 0 0 0]\n",
      " [7 7 7 7 7 6 5 4 3 2 0 0 0 0 0 0]\n",
      " [7 7 7 7 7 7 6 5 4 3 2 0 0 0 0 0]\n",
      " [7 7 7 7 7 7 7 6 5 4 3 2 0 0 0 0]\n",
      " [7 7 7 7 7 7 7 7 6 5 4 3 2 0 0 0]\n",
      " [7 7 7 7 7 7 7 7 7 6 5 4 3 2 0 0]\n",
      " [7 7 7 7 7 7 7 7 7 7 6 5 4 3 2 0]\n",
      " [7 7 7 7 7 7 7 7 7 7 7 6 5 4 3 2]\n",
      " [7 7 7 7 7 7 7 7 7 7 7 7 6 5 4 3]\n",
      " [7 7 7 7 7 7 7 7 7 7 7 7 7 6 5 4]\n",
      " [7 7 7 7 7 7 7 7 7 7 7 7 7 7 6 5]\n",
      " [7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6]\n",
      " [7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7]]\n"
     ]
    }
   ],
   "source": [
    "def optimal_policy(m,ev):\n",
    "    '''Computes the optimal policy function for the stochastic\n",
    "    inventory dynamics model for given EV function'''\n",
    "    # idea: 3-dim array with q in axes 0, d in axis 1 and x in axis 2\n",
    "    q = m.x[:,np.newaxis,np.newaxis]  # choices\n",
    "    d = m.x[np.newaxis,:,np.newaxis]  # demand\n",
    "    x = m.x[np.newaxis,np.newaxis,:]  # inventories\n",
    "    # compute current period profit (relying on numpy broadcasting to get the matrix with choices in rows)\n",
    "    p = m.profit(x,d,q)  # 3-dim array\n",
    "    # indexes for next period value with extrapolation using last value\n",
    "    i = np.minimum(m.next_x(x,d,q),m.upper)\n",
    "    # compute the Bellman maximand\n",
    "    vm = p + m.β*ev[i]\n",
    "    # find argmax and argmax\n",
    "    return np.argmax(vm,axis=0)  # maximum in every column\n",
    "\n",
    "mod = inventory_model(max_inventory=15)\n",
    "mod.dp=.25\n",
    "mod.demand = int((1-mod.dp)/mod.dp)\n",
    "mod.c = .25\n",
    "mod.p = 3.5\n",
    "mod.r = 0.4\n",
    "mod.β = 0.9\n",
    "ev,q = solve_vfi(mod)\n",
    "q = optimal_policy(mod,ev)\n",
    "print('Optimal orders of new inventory for d,x:\\n(d in rows, x in columns)')\n",
    "print(q)\n",
    "# Note the symmetry in the optimal policy!\n",
    "# This implies that knowing both x and d is not necessary for the\n",
    "# optional new order, it's enough to condition on the inventory\n",
    "# remaining after sales, i.e. x-min(x,d) = max(0,x-d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "hide-output": false
   },
   "outputs": [],
   "source": [
    "# Solution video: https://youtu.be/JSdjTmaXr0w"
   ]
  }
 ],
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  "title": "Inventory dynamics problem with stochastic demand"
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