From 3dd2cecfaae8f5b7e2cc8f7f5fc711c6ae40a750 Mon Sep 17 00:00:00 2001 From: Alessandro Zocca Date: Thu, 19 Oct 2023 16:42:55 +0200 Subject: [PATCH] Fix extra notebooks from chapter 3 + LP relaxation notation convention --- notebooks/02/bim-rawmaterialplanning.ipynb | 2 +- notebooks/03/bim-production-revisited.ipynb | 6 +- notebooks/03/cryptarithms.ipynb | 38 +- notebooks/03/maintenance-planning.ipynb | 171 ++-- notebooks/03/strip-packing.ipynb | 889 +++++++++++--------- notebooks/08/bim-robust-optimization.ipynb | 51 +- notebooks/09/seafood.ipynb | 34 +- python/helper.py | 242 ------ 8 files changed, 606 insertions(+), 827 deletions(-) delete mode 100644 python/helper.py diff --git a/notebooks/02/bim-rawmaterialplanning.ipynb b/notebooks/02/bim-rawmaterialplanning.ipynb index f59f329b..7120cddf 100644 --- a/notebooks/02/bim-rawmaterialplanning.ipynb +++ b/notebooks/02/bim-rawmaterialplanning.ipynb @@ -659,7 +659,7 @@ "\n", "where $(\\Omega_p)_{p \\in P}$ is the vector with the desired end inventories.\n", "\n", - "Here is the Pyomo implementation of this LP." + "Here is the Pyomo implementation of this linear problem." ] }, { diff --git a/notebooks/03/bim-production-revisited.ipynb b/notebooks/03/bim-production-revisited.ipynb index 51d1f4a4..dda21a6f 100644 --- a/notebooks/03/bim-production-revisited.ipynb +++ b/notebooks/03/bim-production-revisited.ipynb @@ -57,7 +57,7 @@ " \n", "else:\n", " from pyomo.environ import SolverFactory\n", - " SOLVER = SolverFactory('appsi_highs')\n", + " SOLVER = SolverFactory('cbc')\n", "\n", "assert SOLVER.available(), f\"Solver {SOLVER} is not available.\"" ] @@ -574,7 +574,7 @@ " unitary_products,\n", " unitary_holding_costs,\n", "):\n", - " m = pyo.ConcreteModel(\"Product acquisition and inventory with sophisticated prices\")\n", + " m = pyo.ConcreteModel(\"BIM product acquisition and inventory problem\")\n", "\n", " periods = demand.columns\n", " products = demand.index\n", @@ -2829,7 +2829,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.11.2" + "version": "3.10.10" } }, "nbformat": 4, diff --git a/notebooks/03/cryptarithms.ipynb b/notebooks/03/cryptarithms.ipynb index fb78e463..78964bbb 100644 --- a/notebooks/03/cryptarithms.ipynb +++ b/notebooks/03/cryptarithms.ipynb @@ -72,9 +72,9 @@ "\n", "There are several possible approaches to modeling this puzzle in Pyomo. \n", "\n", - "[One approach](https://stackoverflow.com/questions/67456379/pyomo-model-constraint-programming-for-sendmore-money-task) would be to using a matrix of binary variables $x_{a,d}$ indexed by letter $a$ and digit $d$ such that $x_{a,d} = 1$ designates the corresponding assignment. The problem constraints can then be implemented by summing the binary variables along the two axes. The arithmetic constraint becomes a more challenging.\n", + "[One approach](https://stackoverflow.com/questions/67456379/pyomo-model-constraint-programming-for-sendmore-money-task) would be to using a matrix of binary variables $x_{a,d}$ indexed by letter $a$ and digit $d$ such that $x_{a,d} = 1$ designates the corresponding assignment. The problem constraints can then be implemented by summing the binary variables along the two axes. The arithmetic constraint becomes a more challenging.\n", "\n", - "[Another approach](https://www.gecode.org/doc/6.0.1/MPG.pdf) is to use Pyomo integer variables indexed by letters, then setup an linear expression to represent the puzzle. If we use the notation $n_a$ to represent the digit assigned to letter $a$, the algebraic constraint becomes\n", + "[Another approach](https://www.gecode.org/doc/6.0.1/MPG.pdf) is to use Pyomo integer variables indexed by letters, then set up a linear expression to represent the puzzle. If we use the notation $n_a$ to represent the digit assigned to letter $a$, the algebraic constraint becomes\n", "\n", "$$\n", "\\begin{align*}\n", @@ -97,7 +97,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 11, "metadata": { "colab": { "base_uri": "https://localhost:8080/" @@ -121,6 +121,17 @@ "name": "stdout", "output_type": "stream", "text": [ + "The solution of the puzzle is:\n", + "S = 9\n", + "E = 5\n", + "N = 6\n", + "D = 7\n", + "M = 1\n", + "O = 0\n", + "R = 8\n", + "Y = 2\n", + "\n", + "\n", " 9 5 6 7\n", " + 1 0 8 5\n", " ----------\n", @@ -132,7 +143,7 @@ "import pyomo.environ as pyo\n", "import pyomo.gdp as gdp\n", "\n", - "m = pyo.ConcreteModel()\n", + "m = pyo.ConcreteModel(\"Cryptarithms Problem\")\n", "\n", "m.LETTERS = pyo.Set(initialize=[\"S\", \"E\", \"N\", \"D\", \"M\", \"O\", \"R\", \"Y\"])\n", "m.PAIRS = pyo.Set(initialize=m.LETTERS * m.LETTERS, filter=lambda m, a, b: a < b)\n", @@ -170,21 +181,25 @@ " return [m.n[a] >= m.n[b] + 1, m.n[b] >= m.n[a] + 1]\n", "\n", "\n", - "# assign a \"dummy\" objective to avoid solver errors\n", + "# assign a \"dummy\" constant objective to avoid solver errors\n", "@m.Objective()\n", "def dummy_objective(m):\n", - " return m.n[\"M\"]\n", + " return 0\n", "\n", "\n", "pyo.TransformationFactory(\"gdp.bigm\").apply_to(m)\n", "SOLVER.solve(m)\n", "\n", + "print(\"The solution of the puzzle is:\")\n", + "for l in m.LETTERS:\n", + " print(f\"{l} = {int(m.n[l]())}\")\n", + "\n", "\n", "def letters2num(s):\n", " return \" \".join(map(lambda s: f\"{int(m.n[s]())}\", list(s)))\n", "\n", "\n", - "print(\" \", letters2num(\"SEND\"))\n", + "print(\"\\n\\n \", letters2num(\"SEND\"))\n", "print(\" + \", letters2num(\"MORE\"))\n", "print(\" ----------\")\n", "print(\"= \", letters2num(\"MONEY\"))" @@ -202,13 +217,6 @@ "\n", "2. There are [many more examples](http://cryptarithms.awardspace.us/puzzles.html) of cryptarithm puzzles. Refactor this code and create a function that can be used to solve generic puzzles of this type." ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { @@ -233,7 +241,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.16" + "version": "3.10.10" } }, "nbformat": 4, diff --git a/notebooks/03/maintenance-planning.ipynb b/notebooks/03/maintenance-planning.ipynb index 5195b6e3..e4f16067 100644 --- a/notebooks/03/maintenance-planning.ipynb +++ b/notebooks/03/maintenance-planning.ipynb @@ -26,8 +26,7 @@ "source": [ "## Problem statement\n", "\n", - "\n", - "A process unit is operating over a maintenance planning horizon from $1$ to $T$ days. On day $t$ the unit makes a profit $c[t]$ which is known in advance. The unit needs to shut down for $P$ maintenance periods during the planning period. Once started, a maintenance period takes $M$ days to finish.\n", + "A process unit is operating over a maintenance planning horizon from $1$ to $T$ days. On day $t$ the unit makes a profit $c_t$ which is known in advance. The unit needs to shut down for $P$ maintenance periods during the planning period. Once started, a maintenance period takes $M$ days to finish.\n", "\n", "Find a maintenance schedule that allows the maximum profit to be produced." ] @@ -96,7 +95,7 @@ "source": [ "## Modeling with disjunctive constraints\n", "\n", - "The model is comprised of two sets of the binary variables indexed 1 to $T$. Binary variables $x_t$ correspond to the operating mode of the process unit, with $x_t=1$ indicating the unit is operating on day $t$ and able to earn a profit $c_t$. Binary variable $y_t=1$ indicates the first day of a maintenance period during which the unit is not operating and earning $0$ profit." + "The model comprises two sets of the binary variables indexed by the day $t$, with $t=1,\\dots,T$. Binary variables $x_t$ correspond to the operating mode of the process unit, with $x_t=1$ indicating the unit is operating on day $t$ and able to earn a profit $c_t$. Binary variable $y_t=1$ indicates the first day of a maintenance period during which the unit is not operating and earning $0$ profit." ] }, { @@ -108,15 +107,13 @@ "source": [ "### Objective\n", "\n", - "The planning objective is to maximize profit realized during the days the plant is operational. \n", + "The planning objective is to maximize profit realized during the $T$ days the plant is operational. This is achieved by maximizing the sum of the products of the profit per day $c_t$ and the binary variable $x_t$ indicating the unit is operating on that day.\n", "\n", "$$\n", "\\begin{align*}\n", - "\\mbox{Profit} & = \\max_{x, y} \\sum_{t=1}^T c_t x_t\n", + "\\text{Profit} & = \\sum_{t=1}^T c_t x_t\n", "\\end{align*}\n", - "$$\n", - "\n", - "subject to completing $P$ maintenance periods. " + "$$" ] }, { @@ -140,11 +137,11 @@ "\n", "**Maintenance periods do not overlap.**\n", "\n", - "No more than one maintenance period can start in any consecutive set of M days.\n", + "No more than one maintenance period can start in any consecutive set of $M$ days.\n", "\n", "$$\n", "\\begin{align*}\n", - "\\sum_{s=0}^{M-1}y_{t+s} & \\leq 1 \\qquad \\forall t = 1, 2, \\ldots, T-M+1\n", + "\\sum_{s=0}^{M-1}y_{t+s} & \\leq 1 \\qquad \\forall \\, t = 1, 2, \\ldots, T-M+1\n", "\\end{align*}\n", "$$\n", "\n", @@ -152,51 +149,22 @@ "\n", "**The unit must shut down for M days following a maintenance start.**\n", "\n", - "The final requirement is a disjunctive constraint that says either $y_t = 0$ or the sum $\\sum_{s}^{M-1}x_{t+s} = 0$, but not both. Mathematically, this forms a set of constraints reading\n", + "The final requirement is a disjunctive constraint that says either $y_t = 0$ or the sum $\\sum_{s=0}^{M-1}x_{t+s} = 0$, but not both. Mathematically, this forms a set of constraints reading\n", "\n", "$$\n", "\\begin{align*}\n", - "\\left(y_t = 0\\right) \\veebar \\left(\\sum_{s=0}^{M-1}x_{t+s} = 0\\right)\\qquad \\forall t = 1, 2, \\ldots, T-M+1\n", + "\\left(y_t = 0\\right) \\veebar \\left(\\sum_{s=0}^{M-1}x_{t+s} = 0\\right)\\qquad \\forall \\, t = 1, 2, \\ldots, T-M+1\n", "\\end{align*}\n", "$$\n", "\n", - "where $\\veebar$ denotes an exclusive or condition." + "where $\\veebar$ denotes an exclusive OR condition." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Pyomo solution" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "Bae6-dR_lYkm" - }, - "source": [ - "### Parameter values" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "L5TaVPbkEPZ0" - }, - "outputs": [], - "source": [ - "# problem parameters\n", - "T = 90 # planning period from 1..T\n", - "M = 3 # length of maintenance period\n", - "P = 4 # number of maintenance periods\n", - "\n", - "# daily profits\n", - "c = {k: np.random.uniform() for k in range(1, T + 1)}" + "## Pyomo implementation" ] }, { @@ -213,7 +181,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": { "colab": { "base_uri": "https://localhost:8080/", @@ -237,9 +205,9 @@ "outputs": [ { "data": { - "image/png": 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ks3XrVpf2F1980TRp0qTQdeLj440kJiYmJiYmJiYmJiYmpt9MR44cKTaDuXWFrW7duvLy8ipwNS0zM7PAVberpk+frri4OOe8w+HQmTNnFBwcLJvN5s7uAUvLzs5WeHi4jhw5osDAwIouByhzjHFUdoxxVGaMb+sxxignJ0dhYWHF9nMrsPn4+KhNmzZKSUlR//79ne0pKSl64IEHCl3HbrfLbre7tNWqVcud3QIeJTAwkDdCVGqMcVR2jHFUZoxvawkKCrpmH7cf6x8XF6eRI0cqJiZG7du316pVq3T48GGNGzeuVEUCAAAAAArndmAbMmSITp8+rdmzZ+v48eNq0aKFPvzwQzVq1Kg86gMAAACAKsvtwCZJ48eP1/jx48u6FsCj2e12xcfHF7gFGKgsGOOo7BjjqMwY357LZq75HEkAAAAAQEWoVtEFAAAAAAAKR2ADAAAAAIsisAEAAACARRHYADckJiaqbdu2CggIUP369dWvXz999913Ln2MMZo5c6bCwsLk5+enrl27at++fRVUMXB9EhMTZbPZNHnyZGcbYxye7ujRoxoxYoSCg4Pl7++v1q1ba8eOHc7ljHF4qvz8fD333HOKjIyUn5+fGjdurNmzZ8vhcDj7ML49D4ENcENqaqomTJigL7/8UikpKcrPz1fPnj2Vm5vr7DNv3jwtWrRIy5YtU1pamkJDQ9WjRw/l5ORUYOWA+9LS0rRq1Sq1bNnSpZ0xDk929uxZdezYUdWrV9dHH32k/fv3a+HChapVq5azD2Mcnuqll17SypUrtWzZMn3zzTeaN2+e5s+fr6VLlzr7ML49kAFQapmZmUaSSU1NNcYY43A4TGhoqJk7d66zz8WLF01QUJBZuXJlRZUJuC0nJ8dERUWZlJQU06VLFzNp0iRjDGMcnm/q1KkmNja2yOWMcXiyPn36mLFjx7q0DRgwwIwYMcIYw/j2VFxhA65DVlaWJKlOnTqSpIMHDyojI0M9e/Z09rHb7erSpYu2bt1aITUCpTFhwgT16dNH9957r0s7Yxyebv369YqJidGgQYNUv3593XHHHXr11Vedyxnj8GSxsbHatGmTDhw4IEnavXu3tmzZot69e0tifHuqUv3jbAD/uQc8Li5OsbGxatGihSQpIyNDkhQSEuLSNyQkRD/99NMNrxEojbfffls7d+5UWlpagWWMcXi6H3/8UStWrFBcXJyeffZZbd++XU8++aTsdrtGjRrFGIdHmzp1qrKystS0aVN5eXnpypUrmjNnjoYNGyaJ93BPRWADSmnixInas2ePtmzZUmCZzWZzmTfGFGgDrOjIkSOaNGmSPv30U/n6+hbZjzEOT+VwOBQTE6OEhARJ0h133KF9+/ZpxYoVGjVqlLMfYxyeaO3atVq9erXWrFmj5s2bKz09XZMnT1ZYWJhGjx7t7Mf49izcEgmUwhNPPKH169dr8+bNatiwobM9NDRU0v99gnVVZmZmgU+zACvasWOHMjMz1aZNG3l7e8vb21upqal6+eWX5e3t7RzHjHF4qgYNGqhZs2YubdHR0Tp8+LAk3sfh2Z5++mlNmzZNQ4cO1e23366RI0dqypQpSkxMlMT49lQENsANxhhNnDhRycnJ+uyzzxQZGemyPDIyUqGhoUpJSXG2Xbp0SampqerQocONLhdwW/fu3bV3716lp6c7p5iYGD300ENKT09X48aNGePwaB07dizw71gOHDigRo0aSeJ9HJ7twoULqlbN9c97Ly8v52P9Gd+eiVsiATdMmDBBa9as0fvvv6+AgADnJ1RBQUHy8/Nz/r+qhIQERUVFKSoqSgkJCfL399fw4cMruHrg2gICApzfybyqRo0aCg4OdrYzxuHJpkyZog4dOighIUGDBw/W9u3btWrVKq1atUqSeB+HR+vbt6/mzJmjiIgINW/eXLt27dKiRYs0duxYSYxvj1WRj6gEPI2kQqfXX3/d2cfhcJj4+HgTGhpq7Ha76dy5s9m7d2/FFQ1cp18/1t8Yxjg834YNG0yLFi2M3W43TZs2NatWrXJZzhiHp8rOzjaTJk0yERERxtfX1zRu3NjMmDHD5OXlOfswvj2PzRhjKjIwAgAAAAAKx3fYAAAAAMCiCGwAAAAAYFEENgAAAACwKAIbAAAAAFgUgQ0AAAAALIrABgAAAAAWRWADAAAAAIsisAEAAACARRHYAAAAAMCiCGwAAAAAYFEENgAAAACwKAIbAAAAAFgUgQ0AAAAALIrABgAAAAAWRWADAAAAAIsisAEAAACARRHYAAAAAMCiCGwAAAAAYFEENgAAAACwKAIbAFhYUlKSbDabDh06JEnaunWrZs6cqXPnzlVoXTdKccf723PjiWbOnCmbzaZTp07dkP2UVmU41wDgqQhsAGBhffr00bZt29SgQQNJ/wkws2bNqlKBrajj/e25AQCgMvKu6AIAAEWrV6+e6tWrV9FllJkLFy7I39+/TLZV2c4NAACF4QobAJSRhx9+WDfffHOB9t/ejnZ1ft++fRo2bJiCgoIUEhKisWPHKisry2XdX9+KNnPmTD399NOSpMjISNlsNtlsNn3++efF1rVlyxZ1795dAQEB8vf3V4cOHbRx48ZCa9y1a5cGDBigwMBABQUFacSIETp58mSBbX7//fcaPny46tevL7vdrujoaL3yyiuFbnPnzp168MEHVbt2bd1yyy2SpB9++EFjxoxRVFSU/P39ddNNN6lv377au3evy/rFHe9vb9Nz57xK0vvvv6+WLVvKbrercePGWrJkSYlvHTx58qT++Mc/Kjw8XHa7XfXq1VPHjh31j3/8w9nn22+/1bBhwxQSEiK73a6IiAiNGjVKeXl5BbZ34sSJa9ZcknMuSRs3blTr1q1lt9sVGRmpBQsWFHoMJR2vRSlpPYU5fvy4atasqaFDh7q0f/DBB6pevbpmzJhRou0AQFXAFTYAqCADBw7UkCFD9Mgjj2jv3r2aPn26JOm1114rtP+jjz6qM2fOaOnSpUpOTnbeCtisWbMi95GamqoePXqoZcuW+utf/yq73a7ly5erb9++euuttzRkyBCX/v3799fgwYM1btw47du3T88//7z279+vr776StWrV5ck7d+/Xx06dFBERIQWLlyo0NBQffLJJ3ryySd16tQpxcfHu2xzwIABGjp0qMaNG6fc3FxJ0rFjxxQcHKy5c+eqXr16OnPmjN544w21a9dOu3btUpMmTUp1vCU9rx9//LEGDBigzp07a+3atcrPz9eCBQt04sSJYrd91ciRI7Vz507NmTNHt912m86dO6edO3fq9OnTkqTdu3crNjZWdevW1ezZsxUVFaXjx49r/fr1unTpkux2u1s1l/Scb9q0SQ888IDat2+vt99+W1euXNG8efNKfFwl5e4Y+K0GDRromWeecYbyNm3a6PPPP9egQYP0+OOPa86cOWVaLwB4NAMAKBOjR482jRo1KtAeHx9vfv12e3V+3rx5Lv3Gjx9vfH19jcPhcLa9/vrrRpI5ePCgMcaY+fPnu8xfy913323q169vcnJynG35+fmmRYsWpmHDhs59Xa1pypQpLuu/+eabRpJZvXq1s+2+++4zDRs2NFlZWS59J06caHx9fc2ZM2dctvmnP/3pmnXm5+ebS5cumaioKJcaijve354bd85r27ZtTXh4uMnLy3O25eTkmODgYFOSX401a9Y0kydPLnL5PffcY2rVqmUyMzOL3U5Jay7pOW/Xrp0JCwszv/zyi7NPdna2qVOnToHjKul4NabguS5pPcXJzc01YWFhpnv37mb79u0mICDAjBkzxuV1cjgcJiAgwBw/fvya2wOAyopbIgGggvz+9793mW/ZsqUuXryozMzMMtl+bm6uvvrqKz344IOqWbOms93Ly0sjR47Uzz//rO+++85lnYceeshlfvDgwfL29tbmzZslSRcvXtSmTZvUv39/+fv7Kz8/3zn17t1bFy9e1JdffumyjYEDBxaoLT8/XwkJCWrWrJl8fHzk7e0tHx8fff/99/rmm2+u67ivdV5zc3P19ddfq1+/fvLx8XH2q1mzpvr27Vuifdx1111KSkrSiy++qC+//FKXL192Lrtw4YJSU1M1ePDgEn/HrriaS3rOc3NzlZaWpgEDBsjX19e5rYCAgBIfV0mUZgwUxt/fXy+++KI2bdqkbt26qVevXnr11Vddbsc8dOiQ7Ha7QkNDy6x+APA0BDYAqCDBwcEu81dvk/vll1/KZPtnz56VMabQpyiGhYVJkvMWvqt++4ext7e3goODnf1Onz6t/Px8LV26VNWrV3eZevfuLUkFHlFf2P7j4uL0/PPPq1+/ftqwYYO++uorpaWlqVWrVtd9/Nc6r1fPS0hISIF1C2srzNq1azV69Gj95S9/Ufv27VWnTh2NGjVKGRkZOnv2rK5cuaKGDRuWSc0lPednz56Vw+EoNNyUZeApzRgoym233SZJstlsSkpKkpeXl3PZ/v37FR0drbNnz6pmzZpq06ZNmR0DAHgSvsMGAGXE19e30AdKlPf/2CpK7dq1Va1aNR0/frzAsmPHjkmS6tat69KekZGhm266yTmfn5+v06dPOwNF7dq1nVfoJkyYUOh+IyMjXeYLe4DF6tWrNWrUKCUkJLi0nzp1SrVq1br2wV2H2rVry2azFfq9royMjBJto27dulq8eLEWL16sw4cPa/369Zo2bZoyMzP13nvvycvLSz///HOZ1VuSc+7r6yubzVboMRTWVtrxWpoxUJj09HTdf//96tixo/71r3/ptddec9les2bNNHv2bB06dEjLly+/5vYAoLIisAFAGbn55puVmZmpEydOOK/UXLp0SZ988kmZ7cOdq3A1atRQu3btlJycrAULFsjPz0+S5HA4tHr1ajVs2NB5heOqN9980+VKxjvvvKP8/Hx17dpV0n9uY+vWrZt27dqlli1butxS6A6bzVbgwRsbN27U0aNHdeutt5bqeEuqRo0aiomJ0bp167RgwQLnMZw/f14ffPCB29uLiIjQxIkTtWnTJv3rX/+Sn5+funTponfffVdz5swpEIrd5c45v+uuu5ScnKz58+c7b4vMycnRhg0bCvQt7XgtizHw3Xff6b777lP79u31/vvva9CgQZo5c6ZGjBihoKAgZ789e/aoU6dObm8fACoTbokEgDIyZMgQeXl5aejQofrwww+VnJysnj176sqVK2W2j9tvv12StGTJEm3btk1ff/21cnJyiuyfmJio06dPq1u3bvrb3/6m9evXq3fv3vr3v/+tBQsWFLj6lZycrGeeeUYpKSlavHixHnvsMbVq1UqDBw929lmyZIkOHz6sTp06KSkpSZ9//rk2bNig//qv/9I999xTouO4//77lZSUpMWLF+uzzz7T/PnzNWbMmAK3Ebp7vCU1e/ZsHT16VPfdd5/WrVunv//977r33ntVs2bNaz7SPisrS3feeacWLFigDz74QKmpqVqwYIE+/vhj9ejRQ5K0aNEiXb58We3atdOrr76qzZs36+2339bw4cNLVX9Jz/kLL7ygjIwM9ejRw3lc3bt3V40aNQps83rG6/WMgUOHDunee+9VkyZN9Pe//13Vq1fX3Llzdfbs2QJXXHfv3q1WrVqV8CwBQCVV0U89AYDK5MMPPzStW7c2fn5+pnHjxmbZsmVFPiXy5MmTLuv+9kl8RbVNnz7dhIWFmWrVqhlJZvPmzcXW9MUXX5h77rnH1KhRw/j5+Zm7777bbNiwwaXP1Zp27Nhh+vbta2rWrGkCAgLMsGHDzIkTJwps8+DBg2bs2LHmpptuMtWrVzf16tUzHTp0MC+++OI1j9MYY86ePWseeeQRU79+fePv729iY2PNF198Ybp06WK6dOni0reo4y3qKZElOa/GGPPee++Z22+/3fj4+JiIiAgzd+5c8+STT5ratWsXez4vXrxoxo0bZ1q2bGkCAwONn5+fadKkiYmPjze5ubnOfvv37zeDBg0ywcHBzn08/PDD5uLFi9c8R4XVXJJzbowx69evNy1btnQ5rsKe/GhMycbr9dbza8eOHTO33HKLufPOOws8YfIPf/iDsdvtzn3k5eUZHx8fc/78+SK3BwBVgc0YY258TAQAWMnMmTM1a9YsnTx58rpv4fNUly9fVuvWrXXTTTfp008/rehyqrzTp0+rQYMGOnHihGrXrl3R5QBAheE7bACAKumRRx5Rjx491KBBA2VkZGjlypX65ptvtGTJkoouDfrPkzOHDx+uiIgIRUdHa/v27RVdEgBUCAIbAKBKysnJ0VNPPaWTJ0+qevXquvPOO/Xhhx/q3nvvrejS8P9LSkpSUlJSRZcBABWKWyIBAAAAwKJ4SiQAAAAAWBSBDQAAAAAsisAGAAAAABbldmD75z//qb59+yosLEw2m03r1q0rh7IAAAAAAG4/JTI3N1etWrXSmDFjNHDgQLd36HA4dOzYMQUEBMhms7m9PgAAAAB4OmOMcnJyFBYWpmrVir6O5nZg69Wrl3r16lXqwo4dO6bw8PBSrw8AAAAAlcWRI0fUsGHDIpff8P/DFhAQIOk/hQUGBt7o3QMAAABAhcvOzlZ4eLgzHxWl3ANbXl6e8vLynPM5OTmSpMDAQAIbAAAAgCrtWl8TK/fAlpiYqFmzZhXb5+ZpG4tdfmhunxL1uda2yqqPFWtyp24r1mSluq1YE69v5a6J17dy1+Tu62s1VjqXV/tZqSYr//xaEa+v5/6sWJGnvr7uKvfH+k+fPl1ZWVnO6ciRI+W9SwAAAACoFMr9Cpvdbpfdbi/v3QAAAABApeN2YDt//rx++OEH5/zBgweVnp6uOnXqKCIiokyLAwAAAICqzO3A9vXXX6tbt27O+bi4OEnS6NGjlZSUVGaFAQAAAEBV53Zg69q1q4wx5VELAAAAAOBXyv2hIwAAAACA0iGwAQAAAIBFEdgAAAAAwKIIbAAAAABgUQQ2AAAAALAoAhsAAAAAWBSBDQAAAAAsisAGAAAAABZFYAMAAAAAiyKwAQAAAIBFEdgAAAAAwKIIbAAAAABgUQQ2AAAAALAoAhsAAAAAWBSBDQAAAAAsisAGAAAAABZFYAMAAAAAiyKwAQAAAIBFEdgAAAAAwKIIbAAAAABgUQQ2AAAAALAoAhsAAAAAWBSBDQAAAAAsisAGAAAAABZFYAMAAAAAiyKwAQAAAIBFEdgAAAAAwKIIbAAAAABgUQQ2AAAAALAoAhsAAAAAWBSBDQAAAAAsisAGAAAAABZFYAMAAAAAiyKwAQAAAIBFEdgAAAAAwKIIbAAAAABgUQQ2AAAAALAoAhsAAAAAWBSBDQAAAAAsisAGAAAAABZFYAMAAAAAiyKwAQAAAIBFEdgAAAAAwKIIbAAAAABgUQQ2AAAAALAoAhsAAAAAWBSBDQAAAAAsisAGAAAAABZFYAMAAAAAiyKwAQAAAIBFEdgAAAAAwKIIbAAAAABgUQQ2AAAAALCoUgW25cuXKzIyUr6+vmrTpo2++OKLsq4LAAAAAKo8twPb2rVrNXnyZM2YMUO7du1Sp06d1KtXLx0+fLg86gMAAACAKsvtwLZo0SI98sgjevTRRxUdHa3FixcrPDxcK1asKI/6AAAAAKDKciuwXbp0STt27FDPnj1d2nv27KmtW7eWaWEAAAAAUNV5u9P51KlTunLlikJCQlzaQ0JClJGRUeg6eXl5ysvLc85nZWVJkrKzs51tjrwLxe43Ozu7RH2uta2y6mPFmtyp24o1WaluK9bE61u5a+L1rdw1ufv6Wo2VzuXVflaqyco/v1bE6+u5PytW5Kmv72/njTHF7l/GDUePHjWSzNatW13aX3zxRdOkSZNC14mPjzeSmJiYmJiYmJiYmJiYmH4zHTlypNgM5tYVtrp168rLy6vA1bTMzMwCV92umj59uuLi4pzzDodDZ86cUXBwsGw2mzu7BywtOztb4eHhOnLkiAIDAyu6HKDMMcZR2THGUZkxvq3HGKOcnByFhYUV28+twObj46M2bdooJSVF/fv3d7anpKTogQceKHQdu90uu93u0larVi13dgt4lMDAQN4IUakxxlHZMcZRmTG+rSUoKOiafdwKbJIUFxenkSNHKiYmRu3bt9eqVat0+PBhjRs3rlRFAgAAAAAK53ZgGzJkiE6fPq3Zs2fr+PHjatGihT788EM1atSoPOoDAAAAgCrL7cAmSePHj9f48ePLuhbAo9ntdsXHxxe4BRioLBjjqOwY46jMGN+ey2au+RxJAAAAAEBFcOsfZwMAAAAAbhwCGwAAAABYFIENAAAAACyKwAYAAAAAFkVgA9yQmJiotm3bKiAgQPXr11e/fv303XffufQxxmjmzJkKCwuTn5+funbtqn379lVQxcD1SUxMlM1m0+TJk51tjHF4uqNHj2rEiBEKDg6Wv7+/WrdurR07djiXM8bhqfLz8/Xcc88pMjJSfn5+aty4sWbPni2Hw+Hsw/j2PAQ2wA2pqamaMGGCvvzyS6WkpCg/P189e/ZUbm6us8+8efO0aNEiLVu2TGlpaQoNDVWPHj2Uk5NTgZUD7ktLS9OqVavUsmVLl3bGODzZ2bNn1bFjR1WvXl0fffSR9u/fr4ULF6pWrVrOPoxxeKqXXnpJK1eu1LJly/TNN99o3rx5mj9/vpYuXersw/j2QAZAqWVmZhpJJjU11RhjjMPhMKGhoWbu3LnOPhcvXjRBQUFm5cqVFVUm4LacnBwTFRVlUlJSTJcuXcykSZOMMYxxeL6pU6ea2NjYIpczxuHJ+vTpY8aOHevSNmDAADNixAhjDOPbU3GFDbgOWVlZkqQ6depIkg4ePKiMjAz17NnT2cdut6tLly7aunVrhdQIlMaECRPUp08f3XvvvS7tjHF4uvXr1ysmJkaDBg1S/fr1dccdd+jVV191LmeMw5PFxsZq06ZNOnDggCRp9+7d2rJli3r37i2J8e2pvCu6AMBTGWMUFxen2NhYtWjRQpKUkZEhSQoJCXHpGxISop9++umG1wiUxttvv62dO3cqLS2twDLGODzdjz/+qBUrViguLk7PPvustm/frieffFJ2u12jRo1ijMOjTZ06VVlZWWratKm8vLx05coVzZkzR8OGDZPEe7inIrABpTRx4kTt2bNHW7ZsKbDMZrO5zBtjCrQBVnTkyBFNmjRJn376qXx9fYvsxxiHp3I4HIqJiVFCQoIk6Y477tC+ffu0YsUKjRo1ytmPMQ5PtHbtWq1evVpr1qxR8+bNlZ6ersmTJyssLEyjR4929mN8exZuiQRK4YknntD69eu1efNmNWzY0NkeGhoq6f8+wboqMzOzwKdZgBXt2LFDmZmZatOmjby9veXt7a3U1FS9/PLL8vb2do5jxjg8VYMGDdSsWTOXtujoaB0+fFgS7+PwbE8//bSmTZumoUOH6vbbb9fIkSM1ZcoUJSYmSmJ8eyoCG+AGY4wmTpyo5ORkffbZZ4qMjHRZHhkZqdDQUKWkpDjbLl26pNTUVHXo0OFGlwu4rXv37tq7d6/S09OdU0xMjB566CGlp6ercePGjHF4tI4dOxb4dywHDhxQo0aNJPE+Ds924cIFVavm+ue9l5eX87H+jG/PxC2RgBsmTJigNWvW6P3331dAQIDzE6qgoCD5+fk5/19VQkKCoqKiFBUVpYSEBPn7+2v48OEVXD1wbQEBAc7vZF5Vo0YNBQcHO9sZ4/BkU6ZMUYcOHZSQkKDBgwdr+/btWrVqlVatWiVJvI/Do/Xt21dz5sxRRESEmjdvrl27dmnRokUaO3asJMa3x6rIR1QCnkZSodPrr7/u7ONwOEx8fLwJDQ01drvddO7c2ezdu7fiigau068f628MYxyeb8OGDaZFixbGbrebpk2bmlWrVrksZ4zDU2VnZ5tJkyaZiIgI4+vraxo3bmxmzJhh8vLynH0Y357HZowxFRkYAQAAAACF4ztsAAAAAGBRBDYAAAAAsCgCGwAAAABYFIENAAAAACyKwAYAAAAAFkVgAwAAAACLIrABAAAAgEUR2AAAAADAoghsAAAAAGBRBDYAAAAAsCgCGwAAAABYFIENAAAAACyKwAYAAAAAFkVgAwAAAACLIrABAAAAgEUR2AAAAADAoghsAAAAAGBRBDYAAAAAsCgCGwAAAABYFIENACrYX/7yF9lsNtWsWbOiS3GRlJQkm82mQ4cOub3u1q1bNXPmTJ07d67M66pKyvM88hoBgGcgsAFABTp69KieeuophYWFVXQpBfTp00fbtm1TgwYN3F5369atmjVrFmHgOpXneeQ1AgDPQGADgAo0btw4de7cWT169KjoUgqoV6+e7r77btnt9oouBWXowoULFV0CAMANBDYAqCCrV69Wamqqli9fXuJ1Zs6cKZvNpj179mjQoEEKCgpSnTp1FBcXp/z8fH333Xf63e9+p4CAAN18882aN29egW388MMPGjNmjKKiouTv76+bbrpJffv21d69e136/faWyKv73rdvn4YNG6agoCCFhIRo7NixysrKcqnx6aefliRFRkbKZrPJZrPp888/d/b5/vvvNXz4cNWvX192u13R0dF65ZVXCj3Wa+2vpMfjzjYl6dtvv9WwYcMUEhIiu92uiIgIjRo1Snl5eW4dR1FOnjypP/7xjwoPD5fdble9evXUsWNH/eMf/7jmeSzpMV893p07d+rBBx9U7dq1dcstt1zzNbpWbUUZMGCAGjZsWKA9Pz9frVu3tuQHEwBgdd4VXQAAVEWZmZmaPHmy5s6dW+gfuNcyePBgjRgxQo899phSUlI0b948Xb58Wf/4xz80fvx4PfXUU1qzZo2mTp2qW2+9VQMGDHCue+zYMQUHB2vu3LmqV6+ezpw5ozfeeEPt2rXTrl271KRJk2L3PXDgQA0ZMkSPPPKI9u7dq+nTp0uSXnvtNUnSo48+qjNnzmjp0qVKTk523lLZrFkzSdL+/fvVoUMHRUREaOHChQoNDdUnn3yiJ598UqdOnVJ8fLxb+yvN8Vxrm7t371ZsbKzq1q2r2bNnKyoqSsePH9f69et16dIl2e12t4/jt0aOHKmdO3dqzpw5uu2223Tu3Dnt3LlTp0+fvuZ5TE9Pd+uYBwwYoKFDh2rcuHHKzc1VmzZtin2NrlVbUTp37qz33ntPP/30kxo1auRsX7Rokb799lu9++67xa4PACiEAQDccAMHDjQdOnQwDofDGGPM6NGjTY0aNa65Xnx8vJFkFi5c6NLeunVrI8kkJyc72y5fvmzq1atnBgwYUOw28/PzzaVLl0xUVJSZMmWKs/311183kszBgwdd9j1v3jyX9cePH298fX2dx2KMMfPnz3dZ99fuu+8+07BhQ5OVleXSPnHiROPr62vOnDnj9v5KcjzubPOee+4xtWrVMpmZmYXuw53jKErNmjXN5MmTi+1T3Hn8taKO+erx/ulPf3Jr2yWprTA7duwwksyaNWucbT/++KPx9/c3s2fPdrY5HA4TEBBgjh8/7vY+AKCq4ZZIALjB/v73v2vDhg169dVXZbPZSrWN+++/32U+OjpaNptNvXr1crZ5e3vr1ltv1U8//eTSNz8/XwkJCWrWrJl8fHzk7e0tHx8fff/99/rmm2+uue/f//73LvMtW7bUxYsXlZmZec11L168qE2bNql///7y9/dXfn6+c+rdu7cuXryoL7/80q39leZ4itvmhQsXlJqaqsGDB6tevXpldhy/dddddykpKUkvvviivvzyS12+fLnY/r/m7jEPHDiwxNu+ntpat26twMBA/etf/3K2Pf744woPD9fUqVOdbYcOHZLdbldoaKhbdQFAVURgA4Ab6Pz585owYYKeeOIJhYWF6dy5czp37pwuXbokSTp37pxyc3OvuZ06deq4zPv4+Mjf31++vr4F2i9evOjSFhcXp+eff179+vXThg0b9NVXXyktLU2tWrXSL7/8cs19BwcHu8xffShJSdY9ffq08vPztXTpUlWvXt1l6t27tyTp1KlTbu2vNMdT3DbPnj2rK1euFHurammO47fWrl2r0aNH6y9/+Yvat2+vOnXqaNSoUcrIyCh2vdIcs7tP+ixtbdWqVVOHDh20detWSdKbb76pTz75RCtXrpSPj4+k/9wSGx0drbNnz6pmzZpq06aNW7UBQFXDd9gA4AY6deqUTpw4oYULF2rhwoUFlteuXVsPPPCA1q1bV241rF69WqNGjVJCQkKB2mrVqlVu+5X+c3xeXl4aOXKkJkyYUGifyMhIt7ZZ1sdTp04deXl56eeffy6yT1kcR926dbV48WItXrxYhw8f1vr16zVt2jRlZmbq448/LnZdd4/Z3Su511Nb586d9fzzz+vw4cOKi4vT6NGj1bVrV+fyZs2aafbs2Tp06JBbD9wBgKqKwAYAN1BoaKg2b95coH3u3LlKTU3VRx99pLp165ZrDTabrcCj+jdu3KijR4/q1ltvLZN9FHXVzd/fX926ddOuXbvUsmVL51WX61HWx+Pn56cuXbro3Xff1Zw5cwp9Pcr6OCIiIjRx4kRt2rTJ5XbCos5jWRxzSa+MFlVbUTp37qwrV67o/vvv15UrV7RgwYICffbs2aNOnTqVqE4AqOoIbABwA/n6+rpcbbgqKSlJXl5ehS4ra/fff7+SkpLUtGlTtWzZUjt27ND8+fNL9bTKotx+++2SpCVLlmj06NGqXr26mjRpooCAAC1ZskSxsbHq1KmTHn/8cd18883KycnRDz/8oA0bNuizzz6r8ONZtGiRYmNj1a5dO02bNk233nqrTpw4ofXr1+vPf/7zdR9HVlaWunXrpuHDh6tp06YKCAhQWlqaPv74Y5cnehZ1HsvimIvatsPhKFFtRWnbtq38/Py0d+9evfbaa4UG3t27d2vixIklrhUAqjICGwBUMUuWLFH16tWVmJio8+fP684771RycrKee+65MttH165dNX36dL3xxht69dVX5XA4tHnzZnXt2lXNmjXTzp079cILL+i5555TZmamatWqpaioKOf3vyr6eFq1aqXt27crPj5e06dPV05OjkJDQ3XPPfc4r6Zdz3H4+vqqXbt2+p//+R8dOnRIly9fVkREhKZOnapnnnnG2a+o81gWx1zUttu3b1+i2opSrVo11a5dWzExMXr44YcLLL906ZIOHDjgDIwAgOLZjDGmoosAAACVw4IFCzRjxgylp6crOjq6wPLTp0+rQYMGOnHihGrXrl0BFQKAZ+EKGwAAuC4XLlzQ7t27lZaWphkzZmjOnDmFhjXpP0/oHD58uCIiIhQdHa3t27ff4GoBwLNwhQ0AAFyXdevWqX///goNDdW4ceMUHx9f0SUBQKVBYAMAAAAAi+IfZwMAAACARRHYAAAAAMCiCGwAAAAAYFFuPyXyn//8p+bPn68dO3bo+PHjeu+999SvX78Sr+9wOHTs2DEFBATIZrO5u3sAAAAA8HjGGOXk5CgsLEzVqhV9Hc3twJabm6tWrVppzJgxGjhwoNuFHTt2TOHh4W6vBwAAAACVzZEjR9SwYcMil7sd2Hr16qVevXqVuqCAgABnYYGBgaXeDgAAAAB4quzsbIWHhzvzUVHK/R9n5+XlKS8vzzmfk5MjSQoMDCSwAQAAAKjSrvU1sXIPbImJiZo1a1Z57wYAgErh5mkbi1x2aG6fG1gJPF1xY0liPME9vDdVnHJ/SuT06dOVlZXlnI4cOVLeuwQAAACASqHcr7DZ7XbZ7fby3g0AAAAAVDr8HzYAAAAAsCi3r7CdP39eP/zwg3P+4MGDSk9PV506dRQREVGmxQEAAABAVeZ2YPv666/VrVs353xcXJwkafTo0UpKSiqzwgAAAACgqnM7sHXt2lXGmPKoBQAAAADwK3yHDQAAAAAsisAGAAAAABZFYAMAAAAAiyKwAQAAAIBFEdgAAAAAwKIIbAAAAABgUQQ2AAAAALAoAhsAAAAAWBSBDQAAAAAsisAGAAAAABZFYAMAAAAAiyKwAQAAAIBFEdgAAAAAwKIIbAAAAABgUQQ2AAAAALAoAhsAAAAAWBSBDQAAAAAsisAGAAAAABZFYAMAAAAAiyKwAQAAAIBFEdgAAAAAwKIIbAAAAABgUQQ2AAAAALAoAhsAAAAAWBSBDQAAAAAsisAGAAAAABZFYAMAAAAAiyKwAQAAAIBFEdgAAAAAwKIIbAAAAABgUQQ2AAAAALAoAhsAAAAAWBSBDQAAAAAsisAGAAAAABZFYAMAAAAAiyKwAQAAAIBFEdgAAAAAwKIIbAAAAABgUQQ2AAAAALAoAhsAAAAAWBSBDQAAAAAsisAGAAAAABZFYAMAAAAAiyKwAQAAAIBFEdgAAAAAwKIIbAAAAABgUQQ2AAAAALAoAhsAAAAAWBSBDQAAAAAsisAGAAAAABZFYAMAAAAAiyKwAQAAAIBFEdgAAAAAwKJKFdiWL1+uyMhI+fr6qk2bNvriiy/Kui4AAAAAqPLcDmxr167V5MmTNWPGDO3atUudOnVSr169dPjw4fKoDwAAAACqLLcD26JFi/TII4/o0UcfVXR0tBYvXqzw8HCtWLGiPOoDAAAAgCrL253Oly5d0o4dOzRt2jSX9p49e2rr1q2FrpOXl6e8vDznfFZWliQpOzvb3VoBAKj0HHkXilzG7064o7ixJDGe4B7em8re1fNmjCm2n1uB7dSpU7py5YpCQkJc2kNCQpSRkVHoOomJiZo1a1aB9vDwcHd2DQBAlRe0uKIrQGXCeEJZYSxdn5ycHAUFBRW53K3AdpXNZnOZN8YUaLtq+vTpiouLc847HA6dOXNGwcHBRa4DeKLs7GyFh4fryJEjCgwMrOhygDLHGEdlxxhHZcb4th5jjHJychQWFlZsP7cCW926deXl5VXgalpmZmaBq25X2e122e12l7ZatWq5s1vAowQGBvJGiEqNMY7KjjGOyozxbS3FXVm7yq2Hjvj4+KhNmzZKSUlxaU9JSVGHDh3cqw4AAAAAUCy3b4mMi4vTyJEjFRMTo/bt22vVqlU6fPiwxo0bVx71AQAAAECV5XZ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" ] }, "metadata": {}, @@ -248,7 +216,7 @@ ], "source": [ "def maintenance_planning(c, M, P):\n", - " m = pyo.ConcreteModel()\n", + " m = pyo.ConcreteModel(\"Maintenance planning\")\n", "\n", " T = len(c)\n", " m.T = pyo.RangeSet(1, T)\n", @@ -277,28 +245,48 @@ "\n", " pyo.TransformationFactory(\"gdp.hull\").apply_to(m)\n", "\n", + " SOLVER.solve(m)\n", + "\n", " return m\n", "\n", "\n", "def plot_schedule(m):\n", - " fig, ax = plt.subplots(3, 1, figsize=(9, 4))\n", + " tab20 = plt.get_cmap(\"tab20\", 20)\n", + " colors = [tab20(i) for i in [0, 2, 4, 6]]\n", + "\n", + " fig, ax = plt.subplots(3, 1, figsize=(12, 6))\n", "\n", - " ax[0].bar(m.T, [m.c[t] for t in m.T])\n", - " ax[0].set_title(\"daily profit $c_t$\")\n", + " ax[0].bar(m.T, [m.c[t] for t in m.T], color=colors[0])\n", + " ax[0].set_title(\"Daily profit $c_t$\")\n", "\n", - " ax[1].bar(m.T, [m.x[t]() for t in m.T], label=\"normal operation\")\n", - " ax[1].set_title(\"unit operating schedule $x_t$\")\n", + " ax[1].bar(m.T, [m.x[t]() for t in m.T], color=colors[2])\n", + " ax[1].set_title(\"Optimal operating schedule $x_t$\")\n", + " ax[1].set_ylabel(\"Capacity used\")\n", + "\n", + " ax[2].bar(m.Y, [m.y[t]() for t in m.Y], color=colors[3])\n", + " ax[2].set_title(\"Optimal maintenance starting moments $y_t$\")\n", + " ax[2].yaxis.set_ticks([])\n", + " ax[2].yaxis.set_ticklabels([])\n", "\n", - " ax[2].bar(m.Y, [m.y[t]() for t in m.Y])\n", - " ax[2].set_title(str(P) + \" maintenance starts $y_t$\")\n", " for a in ax:\n", " a.set_xlim(0.1, len(m.T) + 0.9)\n", + " a.set_xlabel(\"Days\")\n", "\n", " plt.tight_layout()\n", "\n", "\n", - "model = maintenance_planning(c, 4, 3)\n", - "SOLVER.solve(model)\n", + "# setting problem parameters\n", + "T = 90 # planning horizon\n", + "M = 3 # length of maintenance period\n", + "P = 4 # number of maintenance periods\n", + "\n", + "# create a random number generator\n", + "rng = np.random.default_rng(2023)\n", + "\n", + "# use the random number generator to generate random daily profits\n", + "c = {k: rng.uniform() for k in range(1, T + 1)}\n", + "\n", + "model = maintenance_planning(c, M, P)\n", "plot_schedule(model)" ] }, @@ -311,17 +299,17 @@ "source": [ "## Ramping constraints\n", "\n", - "Prior to maintenance shutdown, a large processing unit may take some time to safely ramp down from full production. And then require more time to safely ramp back up to full production following maintenance. To provide for ramp-down and ramp-up periods, we modify the problem formation in the following ways.\n", + "Prior to maintenance shutdown, a large processing unit may take some time to safely ramp down from full production. Furthermore, it also requires more time to safely ramp back up to full production after maintenance. To account for ramp-down and ramp-up periods, we modify the problem formation in the following ways.\n", "\n", "* The variable denoting unit operation, $x_t$ is changed from a binary variable to a continuous variable $0 \\leq x_t \\leq 1$ denoting the fraction of total capacity at which the unit is operating on day $t$.\n", "\n", "* Two new variable sequences, $0 \\leq u_t^+ \\leq u_t^{+,\\max}$ and $0\\leq u_t^- \\leq u_t^{-,\\max}$, are introduced which denote the fraction increase or decrease in unit capacity to completed on day $t$.\n", "\n", - "* An additional sequence of equality constraints is introduced relating $x_t$ to $u_t^+$ and $u_t^-$.\n", + "* An additional sequence of equality constraints is introduced relating $x_t$ to $u_t^+$ and $u_t^-$:\n", "\n", "$$\n", "\\begin{align*}\n", - "x_{t} & = x_{t-1} + u^+_t - u^-_t\n", + "x_{t} & = x_{t-1} + u^+_t - u^-_t \\quad \\forall \\, t = 1, 2, \\ldots, T-1.\n", "\\end{align*}\n", "$$\n", "\n", @@ -330,21 +318,7 @@ }, { "cell_type": "code", - "execution_count": 5, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "9fRtZc5nCInh" - }, - "outputs": [], - "source": [ - "upos_max = 0.3334\n", - "uneg_max = 0.5000" - ] - }, - { - "cell_type": "code", - "execution_count": 6, + "execution_count": 4, "metadata": { "colab": { "base_uri": "https://localhost:8080/", @@ -368,9 +342,9 @@ "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "
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" ] }, "metadata": {}, @@ -378,8 +352,13 @@ } ], "source": [ + "# Parameters for ramping constraints\n", + "upos_max = 0.3334\n", + "uneg_max = 0.5000\n", + "\n", + "\n", "def maintenance_planning_ramp(c, M, P):\n", - " m = pyo.ConcreteModel()\n", + " m = pyo.ConcreteModel(\"Maintenance planning with ramping constraints\")\n", "\n", " T = len(c)\n", " m.T = pyo.RangeSet(1, T)\n", @@ -417,11 +396,12 @@ "\n", " pyo.TransformationFactory(\"gdp.hull\").apply_to(m)\n", "\n", + " SOLVER.solve(m)\n", + "\n", " return m\n", "\n", "\n", "m = maintenance_planning_ramp(c, M, P)\n", - "SOLVER.solve(m)\n", "plot_schedule(m)" ] }, @@ -459,20 +439,7 @@ }, { "cell_type": "code", - "execution_count": 7, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "fEOMGHPvUJzJ" - }, - "outputs": [], - "source": [ - "N = 10 # minimum number of operational days between maintenance periods" - ] - }, - { - "cell_type": "code", - "execution_count": 8, + "execution_count": 5, "metadata": { "colab": { "base_uri": "https://localhost:8080/", @@ -496,9 +463,9 @@ "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "
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" ] }, "metadata": {}, @@ -506,8 +473,14 @@ } ], "source": [ + "# Set the minimum number of operational days between maintenance periods\n", + "N = 10\n", + "\n", + "\n", "def maintenance_planning_ramp_operational(c, T, M, P, N):\n", - " m = pyo.ConcreteModel()\n", + " m = pyo.ConcreteModel(\n", + " \"Maintenance planning with ramping constraints and minimum operational days\"\n", + " )\n", "\n", " m.T = pyo.RangeSet(1, T)\n", " m.Y = pyo.RangeSet(1, T - M + 1)\n", @@ -543,22 +516,24 @@ "\n", " # Choose one or the other the following methods. Comment out the method not used.\n", "\n", + " # Disjunctive constraint\n", " # @m.Disjunction(m.Y)\n", " # def disj(m, t):\n", " # return [m.y[t] == 0,\n", " # sum(m.x[t+s] for s in m.W if t + s <= T) == 0]\n", " # pyo.TransformationFactory('gdp.bigm').apply_to(m)\n", "\n", - " # disjunctive constraints, big-M method.\n", + " # big-M method\n", " @m.Constraint(m.Y)\n", " def bigm(m, t):\n", " return sum(m.x[t + s] for s in m.S) <= (M + N) * (1 - m.y[t])\n", "\n", + " SOLVER.solve(m)\n", + "\n", " return m\n", "\n", "\n", "m = maintenance_planning_ramp_operational(c, T, M, P, N)\n", - "SOLVER.solve(m)\n", "plot_schedule(m)" ] }, @@ -593,7 +568,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.16" + "version": "3.10.10" } }, "nbformat": 4, diff --git a/notebooks/03/strip-packing.ipynb b/notebooks/03/strip-packing.ipynb index 4126562c..d82fc92a 100644 --- a/notebooks/03/strip-packing.ipynb +++ b/notebooks/03/strip-packing.ipynb @@ -13,7 +13,7 @@ "\n", "# Extra material: Strip packing\n", "\n", - "*Strip packing* (SP) refers to the problem of packing rectangles onto a two dimensional strip of fixed width. \n", + "*Strip packing* (SP) refers to the problem of packing rectangles onto a 2-dimensional strip of fixed width. \n", "\n", "Many variants of this problem have been studied, the most basic is the pack a set of rectangles onto the shortest possible strip without rotation. Other variants allow rotation of the rectangles, require a packing that allows cutting the rectangles out of the strip with edge-to-edge cuts (guillotine packing), extends the strip to three dimensions, or extends the packing to non-rectangular shapes.\n", "\n", @@ -28,7 +28,7 @@ "\n", "Finding optimal solutions to strip packing problems is combinatorially difficult. Strip packing belongs to a class of problems called \"NP-hard\" for which known solution algorithms require effort that grows exponentially with problem size. For that reason much research on strip packing has been directed towards practical heuristic algorithms for finding good, though not optimal, for industrial applications.\n", "\n", - "Here we consider we develop Pyomo models to find optimal solutions to smaller but economically relevant problems. We use the problem of packing boxes onto shortest possible shelf of fixed width." + "In this notebook, we illustrate Pyomo models to find optimal solutions to smaller but economically relevant problems. We use the problem of packing boxes onto the shortest possible shelf of fixed depth." ] }, { @@ -81,7 +81,7 @@ "source": [ "## Problem Statment\n", "\n", - "Imagine a collection of $N$ boxes that are to placed on shelf. The shelf depth is $D$, and the dimensions of the boxes are $(w_i, d_i)$ for $i=0, \\ldots, N-1$. The boxes can be rotated, if needed, to fit on the shelf. How wide of a shelf is needed?\n", + "Assume you are given a collection of $N$ boxes, whose dimensions are $(w_i, d_i)$ for $i=0, \\ldots, N-1$. These boxes are to placed on shelf of depth $D$. The boxes can be rotated, if needed, to fit on the shelf. How wide of a shelf is needed?\n", "\n", "We will start by creating a function to generate a table of $N$ boxes. For concreteness, we assume the dimensions are in millimeters." ] @@ -119,43 +119,43 @@ " \n", " \n", " 0\n", - " 82\n", - " 103\n", + " 138\n", + " 71\n", " \n", " \n", " 1\n", - " 73\n", - " 48\n", + " 154\n", + " 117\n", " \n", " \n", " 2\n", - " 171\n", - " 53\n", + " 139\n", + " 176\n", " \n", " \n", " 3\n", - " 73\n", - " 99\n", + " 121\n", + " 175\n", " \n", " \n", " 4\n", - " 167\n", - " 85\n", + " 196\n", + " 117\n", " \n", " \n", " 5\n", - " 151\n", - " 172\n", + " 186\n", + " 85\n", " \n", " \n", " 6\n", - " 54\n", - " 130\n", + " 126\n", + " 99\n", " \n", " \n", " 7\n", - " 126\n", - " 94\n", + " 65\n", + " 85\n", " \n", " \n", "\n", @@ -163,14 +163,14 @@ ], "text/plain": [ " w d\n", - "0 82 103\n", - "1 73 48\n", - "2 171 53\n", - "3 73 99\n", - "4 167 85\n", - "5 151 172\n", - "6 54 130\n", - "7 126 94" + "0 138 71\n", + "1 154 117\n", + "2 139 176\n", + "3 121 175\n", + "4 196 117\n", + "5 186 85\n", + "6 126 99\n", + "7 65 85" ] }, "metadata": {}, @@ -180,7 +180,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Shelf Depth = 344\n" + "Shelf Depth = 352\n" ] } ], @@ -189,21 +189,21 @@ "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from matplotlib.patches import Rectangle\n", - "\n", - "# random seed\n", - "random.seed(1842)\n", + "import pyomo.environ as pyo\n", + "import pyomo.gdp as gdp\n", "\n", "\n", - "# generate boxes\n", "def generate_boxes(N, max_width=200, max_depth=200):\n", + " rng = random.Random(2023)\n", " boxes = pd.DataFrame()\n", - " boxes[\"w\"] = [random.randint(0.2 * max_width, max_width) for i in range(N)]\n", - " boxes[\"d\"] = [random.randint(0.2 * max_depth, max_depth) for i in range(N)]\n", + " boxes[\"w\"] = [rng.randint(0.2 * max_width, max_width) for i in range(N)]\n", + " boxes[\"d\"] = [rng.randint(0.2 * max_depth, max_depth) for i in range(N)]\n", " return boxes\n", "\n", "\n", + "# set the number N of boxes and generate their dimensions at random\n", "N = 8\n", - "boxes = generate_boxes(8)\n", + "boxes = generate_boxes(N)\n", "display(boxes)\n", "\n", "# set shelf width as a multiple of the deepest box\n", @@ -217,20 +217,24 @@ "source": [ "## A lower and upper bounds on shelf width\n", "\n", - "A lower bound on the shelf width is established by from the area required to place all boxes on the shelf.\n", + "A lower bound on the shelf width can be obtained by dividing the total area required to place all boxes on the shelf by the shelf depth. The area of box $i$ is $w_i d_i$, therefore the lower bound is given by\n", + "\n", + "$$W_{lb} = \\frac{1}{D}\\sum_{i=0}^{N-1} w_i d_i.$$\n", "\n", - "$$W_{lb} = \\frac{1}{D}\\sum_{i=0}^{N-1} w_i d_i$$\n", + "An upper bound on the shelf width $W_{ub}$ can be obtained aligning the boxes along the front of the shelf without rotation. To set the stage for later calculations, the position of box $i$ on the shelf is defined by the coordinates $(x_{i,1}, y_{i,1})$ and $(x_{i,2}, y_{i,2})$, corresponding to the lower left corner and the upper right corner, respectively. \n", "\n", - "An upper bound is established by aligning the boxes along the front of the shelf without rotation. To set the stage for later calculations, the position of the rectangle on the shelf is defined by bounding box $(x_{i,1}, y_{i,1})$ and $(x_{i,2}, y_{i,2})$ extending from the lower left corner to the upper right corner. \n", + "The two set of coordinates of box $i$ are linked to the width $w_i$ and depth $d_i$ by the following equations:\n", "\n", "$$\n", "\\begin{align*}\n", "x_{i,2} & = x_{i,1} + w_i \\\\\n", - "y_{i,2} & = y_{i,1} + d_i \\\\\n", + "y_{i,2} & = y_{i,1} + d_i\n", "\\end{align*}\n", "$$\n", "\n", - "An additional binary variable $r_i$ designates whether the rectangle has been rotated. The following cell performs these calculations to create and display a data frame showing the bounding boxes." + "An additional binary variable $r_i$ designates whether the rectangle has been rotated, with $r_i=0$ denoting no rotation and $r_i=1$ denoting a 90 degree rotation (all other rotations yield one of these two configurations). \n", + "\n", + "The following cell create and display a data frame showing the bounding boxes and performs calculations to obtain the trivial box arrangement, as well as the lower and upper bounds." ] }, { @@ -271,82 +275,82 @@ " \n", " \n", " 0\n", - " 82\n", - " 103\n", + " 138\n", + " 71\n", " 0\n", - " 82\n", + " 138\n", " 0\n", - " 103\n", + " 71\n", " 0\n", " \n", " \n", " 1\n", - " 73\n", - " 48\n", - " 82\n", - " 155\n", + " 154\n", + " 117\n", + " 138\n", + " 292\n", " 0\n", - " 48\n", + " 117\n", " 0\n", " \n", " \n", " 2\n", - " 171\n", - " 53\n", - " 155\n", - " 326\n", + " 139\n", + " 176\n", + " 292\n", + " 431\n", " 0\n", - " 53\n", + " 176\n", " 0\n", " \n", " \n", " 3\n", - " 73\n", - " 99\n", - " 326\n", - " 399\n", + " 121\n", + " 175\n", + " 431\n", + " 552\n", " 0\n", - " 99\n", + " 175\n", " 0\n", " \n", " \n", " 4\n", - " 167\n", - " 85\n", - " 399\n", - " 566\n", + " 196\n", + " 117\n", + " 552\n", + " 748\n", " 0\n", - " 85\n", + " 117\n", " 0\n", " \n", " \n", " 5\n", - " 151\n", - " 172\n", - " 566\n", - " 717\n", + " 186\n", + " 85\n", + " 748\n", + " 934\n", " 0\n", - " 172\n", + " 85\n", " 0\n", " \n", " \n", " 6\n", - " 54\n", - " 130\n", - " 717\n", - " 771\n", + " 126\n", + " 99\n", + " 934\n", + " 1060\n", " 0\n", - " 130\n", + " 99\n", " 0\n", " \n", " \n", " 7\n", - " 126\n", - " 94\n", - " 771\n", - " 897\n", + " 65\n", + " 85\n", + " 1060\n", + " 1125\n", " 0\n", - " 94\n", + " 85\n", " 0\n", " \n", " \n", @@ -354,23 +358,31 @@ "" ], "text/plain": [ - " w d x1 x2 y1 y2 r\n", - "0 82 103 0 82 0 103 0\n", - "1 73 48 82 155 0 48 0\n", - "2 171 53 155 326 0 53 0\n", - "3 73 99 326 399 0 99 0\n", - "4 167 85 399 566 0 85 0\n", - "5 151 172 566 717 0 172 0\n", - "6 54 130 717 771 0 130 0\n", - "7 126 94 771 897 0 94 0" + " w d x1 x2 y1 y2 r\n", + "0 138 71 0 138 0 71 0\n", + "1 154 117 138 292 0 117 0\n", + "2 139 176 292 431 0 176 0\n", + "3 121 175 431 552 0 175 0\n", + "4 196 117 552 748 0 117 0\n", + "5 186 85 748 934 0 85 0\n", + "6 126 99 934 1060 0 99 0\n", + "7 65 85 1060 1125 0 85 0" ] }, "metadata": {}, "output_type": "display_data" }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lower bound on shelf width = 370\n", + "Upper bound on shelf width = 1125\n" + ] + }, { "data": { - "image/png": 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"text/plain": [ "
" ] @@ -387,11 +399,14 @@ " soln[\"y1\"] = 0\n", " soln[\"y2\"] = soln[\"d\"]\n", " soln[\"r\"] = 0\n", + "\n", " return soln\n", "\n", "\n", - "def show_boxes(soln, D):\n", - " \"\"\"Show bounding boxes on a diagram of the shelf.\"\"\"\n", + "def show_boxes(soln, D, W_ub=None):\n", + " tab20 = plt.get_cmap(\"tab20\", 20)\n", + " colors = [tab20(i) for i in [0, 2, 4, 6, 8]]\n", + "\n", " fig, ax = plt.subplots(1, 1, figsize=(14, 4))\n", " for i, x, y, w, h, r in zip(\n", " soln.index, soln[\"x1\"], soln[\"y1\"], soln[\"w\"], soln[\"d\"], soln[\"r\"]\n", @@ -400,7 +415,9 @@ " if r:\n", " h, w = w, h\n", " c = \"r\"\n", - " ax.add_patch(Rectangle((x, y), w, h, edgecolor=\"k\", facecolor=c, alpha=0.6))\n", + " ax.add_patch(\n", + " Rectangle((x, y), w, h, edgecolor=\"k\", facecolor=colors[2], alpha=0.6)\n", + " )\n", " xc = x + w / 2\n", " yc = y + h / 2\n", " ax.annotate(\n", @@ -408,18 +425,35 @@ " )\n", "\n", " W_lb = (soln[\"w\"] * soln[\"d\"]).sum() / D\n", + " W = soln[\"x2\"].max()\n", + "\n", + " print(f\"Lower bound on shelf width = {W_lb:.0f}\")\n", + " if W_ub is None:\n", + " print(f\"Upper bound on shelf width = {W:.0f}\")\n", + " else:\n", + " print(f\"Upper bound on shelf width = {W_ub:.0f}\")\n", + " print(f\"Optimal shelf width = {W:.0f}\")\n", + "\n", " ax.set_xlim(0, 1.1 * soln[\"w\"].sum())\n", " ax.set_ylim(0, D * 1.1)\n", - " ax.axhline(D, label=\"shelf depth $D$\", lw=0.8)\n", - " ax.axvline(W_lb, label=\"lower bound $W_{lb}$\", color=\"g\", lw=0.8)\n", - " ax.axvline(soln[\"x2\"].max(), label=\"shelf width $W$\", color=\"r\", lw=0.8)\n", - " ax.fill_between([0, ax.get_xlim()[1]], [D, D], color=\"b\", alpha=0.1)\n", - " ax.set_title(f\"shelf width $W$ = {soln['x2'].max():.0f}\")\n", + " ax.axhline(D, label=\"shelf depth $D$\", color=colors[0], lw=1.5)\n", + " ax.axvline(W_lb, label=\"lower bound $W_{lb}$\", color=colors[1], lw=1.5, ls=\"--\")\n", + " if W_ub is None:\n", + " ax.axvline(W, label=\"upper bound $W_{ub}$\", color=colors[3], lw=1.5, ls=\"--\")\n", + " else:\n", + " ax.axvline(\n", + " W_ub + 2, label=\"upper bound $W_{ub}$\", color=colors[3], lw=1.5, ls=\"--\"\n", + " )\n", + " ax.axvline(W, label=\"optimal solution $W$\", color=colors[4], lw=1.5, ls=\"-\")\n", + " ax.fill_between([0, ax.get_xlim()[1]], [D, D], color=colors[0], alpha=0.2)\n", " ax.set_xlabel(\"width\")\n", " ax.set_ylabel(\"depth\")\n", " ax.set_aspect(\"equal\")\n", " ax.legend(loc=\"upper right\")\n", "\n", + " plt.tight_layout()\n", + " plt.show()\n", + "\n", "\n", "soln = pack_boxes_V0(boxes)\n", "display(soln)\n", @@ -432,11 +466,11 @@ "source": [ "## Modeling Strategy\n", "\n", - "At this point the reader may have some ideas on how to efficiently pack boxes on the shelf. For example, one might start by placing the larger boxes to left edge of the shelf, then rotating and placing the smaller boxes with a goal of minimized the occupied with of the shelf. \n", + "At this point, one may have some ideas on how to efficiently pack boxes on the shelf. For example, one might start by placing the larger boxes to left edge of the shelf, then rotating and placing the smaller boxes with a goal of minimized the occupied with of the shelf. \n", "\n", - "Modeling for optimization takes a different approach. The strategy is to describe constraints that must be satisfied for any solution to the problem, then let the solver find the a choice for the decision variables that minimizes width. The constraints include:\n", + "Optimization takes a different, less algorithmic approach. The strategy is to describe constraints that must be satisfied for any solution to the problem, then let the solver find the values of the decision variables that minimizes the shelf width. The constraints include:\n", "\n", - "* The bounding boxes must fit within the boundaries of the shelf, and to the left of vertical line drawn at $x = W$.\n", + "* The bounding boxes must fit within the boundaries of the shelf, and to the left of vertical line drawn at $x = W$, where the shelf width $W$ is a decision variable.\n", "* The boxes can be rotated 90 degrees.\n", "* The boxes must not overlap in either the $x$ or $y$ dimensions." ] @@ -451,14 +485,11 @@ "\n", "$$\n", "\\begin{align*}\n", - "& \\min W \\\\\n", - "\\text{subject to:}\\qquad\\qquad \\\\\n", - "x_{i, 2} & = x_{i, 1} + w_i & \\forall i\\\\\n", - "x_{i, 2} & \\leq W & \\forall i\\\\\n", - "x_{i, 1}, x_{i, 2} & \\geq 0 & \\forall i \\\\\n", - "\\\\\n", - "[x_{i, 2} \\leq x_{j,1}] & \\veebar [ x_{j, 2} \\leq x_{i, 1}] & \\forall i < j \\\\\n", - "\\\\\n", + "\\min \\quad & W \\\\\n", + "\\text{s.t.} \\quad & x_{i, 2} = x_{i, 1} + w_i & \\forall \\, i\\\\\n", + "& x_{i, 2} \\leq W & \\forall \\, i\\\\\n", + "& x_{i, 1}, x_{i, 2} \\geq 0 & \\forall \\, i \\\\\n", + "& [x_{i, 2} \\leq x_{j,1}] \\veebar [ x_{j, 2} \\leq x_{i, 1}] & \\forall \\, i < j\n", "\\end{align*}\n", "$$\n", "\n", @@ -507,82 +538,82 @@ " \n", " \n", " 0\n", - " 82\n", - " 103\n", - " 815.0\n", - " 897.0\n", + " 138\n", + " 71\n", + " 987.0\n", + " 1125.0\n", " 0\n", - " 103\n", + " 71\n", " 0\n", " \n", " \n", " 1\n", - " 73\n", - " 48\n", - " 742.0\n", - " 815.0\n", + " 154\n", + " 117\n", + " 833.0\n", + " 987.0\n", " 0\n", - " 48\n", + " 117\n", " 0\n", " \n", " \n", " 2\n", - " 171\n", - " 53\n", - " 571.0\n", - " 742.0\n", + " 139\n", + " 176\n", + " 694.0\n", + " 833.0\n", " 0\n", - " 53\n", + " 176\n", " 0\n", " \n", " \n", " 3\n", - " 73\n", - " 99\n", - " 498.0\n", - " 571.0\n", + " 121\n", + " 175\n", + " 573.0\n", + " 694.0\n", " 0\n", - " 99\n", + " 175\n", " 0\n", " \n", " \n", " 4\n", - " 167\n", - " 85\n", - " 331.0\n", - " 498.0\n", + " 196\n", + " 117\n", + " 377.0\n", + " 573.0\n", " 0\n", - " 85\n", + " 117\n", " 0\n", " \n", " \n", " 5\n", - " 151\n", - " 172\n", - " 180.0\n", - " 331.0\n", + " 186\n", + " 85\n", + " 191.0\n", + " 377.0\n", " 0\n", - " 172\n", + " 85\n", " 0\n", " \n", " \n", " 6\n", - " 54\n", - " 130\n", - " 126.0\n", - " 180.0\n", + " 126\n", + " 99\n", + " 65.0\n", + " 191.0\n", " 0\n", - " 130\n", + " 99\n", " 0\n", " \n", " \n", " 7\n", - " 126\n", - " 94\n", + " 65\n", + " 85\n", " 0.0\n", - " 126.0\n", + " 65.0\n", " 0\n", - " 94\n", + " 85\n", " 0\n", " \n", " \n", @@ -590,23 +621,32 @@ "" ], "text/plain": [ - " w d x1 x2 y1 y2 r\n", - "0 82 103 815.0 897.0 0 103 0\n", - "1 73 48 742.0 815.0 0 48 0\n", - "2 171 53 571.0 742.0 0 53 0\n", - "3 73 99 498.0 571.0 0 99 0\n", - "4 167 85 331.0 498.0 0 85 0\n", - "5 151 172 180.0 331.0 0 172 0\n", - "6 54 130 126.0 180.0 0 130 0\n", - "7 126 94 0.0 126.0 0 94 0" + " w d x1 x2 y1 y2 r\n", + "0 138 71 987.0 1125.0 0 71 0\n", + "1 154 117 833.0 987.0 0 117 0\n", + "2 139 176 694.0 833.0 0 176 0\n", + "3 121 175 573.0 694.0 0 175 0\n", + "4 196 117 377.0 573.0 0 117 0\n", + "5 186 85 191.0 377.0 0 85 0\n", + "6 126 99 65.0 191.0 0 99 0\n", + "7 65 85 0.0 65.0 0 85 0" ] }, "metadata": {}, "output_type": "display_data" }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lower bound on shelf width = 370\n", + "Upper bound on shelf width = 1125\n", + "Optimal shelf width = 1125\n" + ] + }, { "data": { - "image/png": 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", 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tt92msWPHKiMjQ0888YQGDBjAyBYAAAAAAOAXTC2+ZGZmqm/fvkpPT5fD4VDTpk313Xff6aqrrtLevXv1ww8/aPz48crLy1NSUpJ69+6tJ554wvN+m82mmTNn6r777lNqaqoiIiLUr18/jR492sSzAgAAAAAA+JOpxZd33nnnpNuSkpKUlpZ22n0kJyfrm2++Kc9YAAAAAAAA5cbv5nwBAAAAAAAIJBRfACCAlYbGqDQ0xuwYAAAAfq/7VZ019OHBZsc4rVPlNGw2yWar4ETezpfPsaJRfAGAAGUEh2vTrWu06dY1MoLDzY4DAAAAX6tdV0adepLVYnaSk7rz9r66+e83erWlzZuniJBgjR75lFf7K+PGqXZykoqLiysyok9QfAEAAAAAwM8EQsHhRKId0cpx5ni1vTr+FYWEhMiZ82d7aWmppkyepPv+NUB2u72iY5Y7ii8AAAAAAByjqKhIQwY9pOTqiYqJqqQuV1yulSuWe7Z/+7//KTEuVi6XS5K0du0aRYQE68nHH/P0+de99+jO2/tKktxut14c+4Ia16+nKo5ItWl1iT7/7L9ex+x+VWcNfvABDX14sGokJuj6a64+aT5XaakGP/iAqlWtohoXJej5cc/IMIwy529Uv65ee3WC1z7btm6pZ5/+88nB3a/qrCGDHtLjwx9V9YQ41apR3Wu7JOXl5emuO29XXEy0aicnacIrr5z2s3VER3sVWbZs3qwf5/ygW2/r61WU+ey/n+rwoUPqf/c9p93n+YDiCwAEKEtpoWrN/IdqzfyHLKWFZscBAAA4bzw+/FF98cXnevPtd7Vw6TLVrlNH11/TU4cPH5YktbvsMh05ckRr16yWJC2YP1+xsbH6af6fT+xdMP8ndex4uSTppbEv6N8ffqgJr03SitVrNfCBB9X/9n76af58r+N+9OEHstvt+mFumiZMnHTSfB99+IFsQUFKW7BIY196WVPenqQPZ0yTft0ry949evzRU+cvq48+/EARERGa99NCPfPcGI159hnN+eGHPz+nR4dpwU8/6eNPP9NX//tGP81P05rVq0+5T4cjWs4cp2d94oTx6v33v6tho0Ze7a+9OkG39e2nmJjAmL/Q1EdNAwB8yHCrUsYSzzIAAIBpivNOvs1qk4JCy9bXYpWCw07f1x5xZvmOkZeXp7fffENvvP2OunXvLkmaNPkNNZpTV9Pee0+DHn5YDodDTZs10/y0+bqkZSv9NH++Bj7woJ575mnl5ubKmZOj7du36bIOHVVUVKQXX3heM7+dpTZtUyVJtWrX1uJFC/XO22+pQ8eOnmPXqVtXz455/rQZq1dP0tiXxslisah+/QZavXS13nzndf3rms7Ky8/T22+dOn9ZNUlJ0WNPPClJqluvnt6Y/Lrmzf1Rnbt0UW5urqZNfU/vTJ2mK668UpL05jvvqn7tmqfcZ3S0Q87fR7gcPHhQM/49XXN/WqC1a9Z42hcuWKDVq1bpvWkfeN4386uvNG/eXHXpcpW+/26WXp7wapnPwx9QfAEAAAAA+FT4SzVOus1V5yoV3TTDsx42oaEsJfkn7lujvYpu/erPvpNayFJw6Lh++Y8d31ZWO3ZsV0lJiVJT23nagoOD1apVa23ZssnTdlmHjvppfpoeHDRIixYu0Kinn9F/P/1EixYuVFbWYVVLTFTdevW0ceMG5efn69qre3gdp7i4WM2aN/dqa3HJJWXK2LrNpbJY/pxUt9Ull2rK26/J5XJpx969ZcpfFk2apHitJyRU08GDmZKOfk7FxcVq3fpSz/aYmBjVq1//lPt0REcr5/fbjt6cMlmp7dorJaWpdu7Y4WmfOGG8rrn2OtWpW9fzvvXr1yklJUXr1q9T02bNzug8/AHFFwAAAAAAzlDHjpfrg2lT9fPPaxUUHKwGDRuqQ8fL9dP8NGVnZemyDkdHtOTl5kqS/vvFV0pMTPTaR0hIiNd6ePjZj9g5E1aL1WuOGEkqLSk9rl9QcLDXusVikdt9biOqHY5olZSUKCsrS2+9+YbefneqJCkyMkrOHKd2bN+u/838WrN/nOv1vvXr1umqrl316oQJSkxMVPu2l6qwoFDTP/6PGjRseE6ZKgLFFwAAAACAT+UP2XPyjVab12rBg5tP3tfiPW1pwYBTzy9yNmrXriO73a7FixepRnKyJKmkpEQrV67QgIEPePr9Me/La69OUIffCy0dO16ucS+NVXZWth546CFJUsNGjRUSEqK9e/d43WJ0LlYsW+61vnL1ctWuWUc2m021k5JOmz+2aqwyMjI873c6ndq1a+cZZahdu46Cg4O1fPkyJdU4OrIpKytL27Zu9RSeTiQ62iFJmvL6JMXHx6vLVVdJkhyOKDmdOZo08VW1at1abY8ZuSNJmzZuVOOLm2jDunW69NJLtXDJMr379luaMP5lvT7lzTPKbgaKLwAAAAAA3zqTOVh81beMIiIidNc9/6fHhz+qypVjlFQjSa+Me0kF+fnqd8cdnn6VK1dWk5QUffzvf+vl8UefHNS+Qwfd1ucWlZSUeAoQkZGRenDQYD06dIjcbrfatWuvHGeOlixapMioKN16W98zzrh37x4NGzpE/e+6W2tWr9Y7097UqMefOZo/PFx33X3q/Jd3ukIffvC+ru55jRzRDj0zapRsNtupDnmcSpUqqd/td+jx4Y8qJqaKqsZV1agRI2S1nvq5Pg5HtKSjE+qOHfeypz0yMkrZ2dn68IP3NeWtt73eU1BQIEmyWq3Kz8/XfQMGSpKaNmum72bNOqPcZqH4AgAAAADAMZ5+9jkZbrfuvvN2HTlyRJe0bKkvZ/5PlStX9up3WYeO+nntWnX4/alGMTExatiokTIzM1W/QQNPvxEjRyk2Nlbjxo7VwJ075IiOVvPmLTR02KNnle+ffW5VYUGBLr+snWw2m+6+417d9s87pNxfj+Z/5lkZxsnzD3lkmHbv2qUb/3a9ohwOPfnUyDMe+SJJzz7/gnLzcvX3XjeoUmSkHnhwkGfS3JNxREdLksIjIvSPm272tEc5HHK5XIqNrarrrr/B6z0bN6xXo8aNtWnTRjVo2NBT4FmzerWapHjPS+OvLMZfb/S6ADmdTjkcDv24dqdiYyqf/g0AcB6wlOSr8UctJEkb+6yWERxuciIAABDojNJiGUcyVSM5WSGhoad/A86dIeVmHJ2guFLePlkMQ0adepLVcpo3nj+mvfeu0tPTVT0pSS+98IKWr16jrKws9br+Wn3+1UxVrVrVp8cvKizUnt27ZYmMkyXI7rXtt8NZurJZLeXk5CgqKuqk+2DkCwAEKCM4XBtu32J2DAAAAFSUOvVkBE7NxWPdunXq1OkKLVjwk7pffbU6tGsrl8ul58e+5PPCS3mh+AIAAAAAAPzWSy+/Ikm65rrrTE5y9k49Ew4AAAAAAADOCcUXAAhQltJCJX93u5K/u12W0kKz4wAAAMDX9v8qy75fJaZ29TvcdgQAgcpwK2rvj55lAAAABDZLXp4kQzIkBeDcL+czRr4AAAAAAAD4EMUXAAAAAAAAH6L4AgAAAAAA4EMUXwAAAAAAAHyI4gsAAAAAAIAPUXwBAAAAAADwIR41DQAByggO17q79pgdAwAAABXEqNeAR0z7KUa+AAAAAAAA+BDFFwAAAAAAzkPdr+qsoUMGmx3jhLpf1VlDH/bPbGag+AIAAcpSWqgac+5VjTn3ylJaaHYcAAAA+Fr6fln275MMw+wkZXLn7X11899v9GpLmzdPESHBGj3yKa/2V8aNU+3kJBUXF1dkxHJD8QUAApXhlmPnN3Ls/EYy3GanAQAAwFk4k2KDJfeIlHtEOj9qL4p2RCvHmePV9ur4VxQSEiJnzp/tpaWlmjJ5ku771wDZ7faKjlkuKL4AAAAAAC54jerX1WuvTvBqa9u6pZ59erSko7fRDH7wAQ1+8AFVq1pFNRITNHrkUzKOGWVSlj5ut1svjn1BjevXUxVHpNq0ukSff/bf4/Yx9OHBqpGYoOuvufqUuV2lpRo+YojqpiQpqcNlGjVxoud4RUVFGjLoISVXT1RMVCV1ueJyrVyx/IzO+49MQwY9pMeHP6rqCXGqVaO61/a8vDzddeftiouJVu3kJE145ZVTZv6DIzraq8iyZfNm/TjnB916W1+vosxn//1Uhw8dUv+77ynTfv0RxRcAAAAAgE+58/NP+jKKisrc111YWKa+vvLRhx/IFhSktAWLNHbcy5o4YbymvvvOGfV5aewL+veHH2rCa5O0YvVaDXzgQfW/vZ9+mj/fax92u10/zE3ThImTTp/JFqRZX/yoF4c9qokffKCp770rSXp8+KP64ovP9ebb72rh0mWqXaeOrr+mpw4fPnxW5x4REaF5Py3UM8+N0Zhnn9GcH344epxHh2nBTz/p408/01f/+0Y/zU/TmtWrT7tPhyNazhynZ33ihPHq/fe/q2GjRl7tr706Qbf17aeYmJgzzu0vTH3U9OTJkzV58mTt2rVLknTxxRdrxIgR6tGjhySpsLBQDz/8sGbMmKGioiJ169ZNr7/+uuLj4z372LNnj+677z7NnTtXlSpVUr9+/TRmzBgFBfEUbQAAAADwB3vbtjnptrAOHRQ36XXP+q+dOskoLDhh35BWrZTw7nue9X09usudlXVcv+Sf151D2pOrXj1JY18aJ4vFovoNGmjD+vV67dVXdUf/u8rUp6ioSC++8LxmfjtLbdqmSpJq1a6txYsW6p2331KHjh0lSXXq1tWzY54vc6anR4yRxWJRi7hQbdj6i16bOEH/uOUWvf3mG3rj7XfUrXt3SdKkyW+o0Zy6mvbeexr08MNndO5NUlL02BNPSpLq1qunNya/rnlzf1Sbtm01bep7emfqNF1x5ZWSpDffeVf1a9c87T6jox1y/j7C5eDBg5rx7+ma+9MCrV2zxtO+cMECrV61Su9N++C0+5v1zTf6/rtZennCq2d0bhXB1JEv1atX1/PPP6+VK1dqxYoVuvLKK3X99ddrw4YNkqRBgwbp66+/1ieffKK0tDTt379fvXr18rzf5XKpZ8+eKi4u1qJFizRt2jRNnTpVI0aMMOuUAAAAAAABqnWbS2WxWDzrbdq01bZtW+VyucrUZ/v2bcrPz9e1V/dQXEy05zX9ww+1c8d2z3taXHJJ2TNd6n28S5s107Zt27R9+zaVlJQoNbWdZ1twcLBatWqtLVs2nfG5N2mS4rWekFBNBw9maseO7SouLlbr1pd6tsXExKhe/fqn3acjOlo5v9929OaUyUpt114pKU0VFRXlaZ84YbyuufY61alb97T7W7d+nZo2a3Ymp1VhTB0ecu2113qtP/vss5o8ebKWLFmi6tWr65133tH06dN15e/Vs/fee0+NGjXSkiVL1LZtW33//ffauHGjfvjhB8XHx6t58+Z6+umnNWzYMI0cOfK8nYgHAAAAAAJJ0pKlJ91msdm81qvPm3fyHVm9xw9c9O2sc4nlvWuL1WtuFkkqLSktt/1LUl5uriTpv198pcTERK9tISEhnuXw8IhyPe6plPW8g4KDvdYtFovc7nN7qIPDEa2SkhJlZWXprTff0NvvTpUkRUZGyZnj1I7t2/W/mV9r9o9zPe9p16a1/jfre1WuXFlLFi/S66+9pvc/mi5JWr9unRITE9W+7aUqLCjU9I//owYNG55TxvLiN3O+uFwuzZgxQ3l5eUpNTdXKlStVUlKiLl26ePo0bNhQNWrU0OLFiyVJixcvVkpKitdtSN26dZPT6fSMngEAAAAAmMsaHn7Sl+WYosPp+lpDQ8vU92zEVo1VRkaGZ93pdGrXrp1efVYs856sdtmypapbt55sxxSQTtWnYaPGCgkJ0d69e1Snbl2vV/WkpLPKvWK59/GW//yz6tatqzp16sput2vx4kWebSUlJVq5coUaNmx8Rud9KrVr11FwcLCWL1/macvKytK2rVtP+97oaIckacrrkxQfH68uV10lSXI4ouR05mjSxFfVqnVrtf199E5paamcOU5VrlxZkrRh/Xpd3KSJZ38b1q1T9erVtXDJMg24/35NGP9ymc/D10yfGGXdunVKTU1VYWGhKlWqpM8//1yNGzfWmjVrZLfbFR0d7dU/Pj7ec2FkZGR4FV7+2P7HtpMpKipS0TGTOjmdzpP2BYDzlREUpvX9NnuWAQAAcHKXd7pCH37wvq7ueY0c0Q49M2qUV1FFkvbu3aNhQ4eo/113a82a1Zry+iSNeWFsmftERkbqwUGD9ejQIXK73WrXrr1ynDlasmiRIqOidOttfc849969ezTi6cfU95936Je9GzV5xgyNeWGsIiIidNc9/6fHhz+qypVjlFQjSa+Me0kF+fnqd8cdZ3Tep1KpUiX1u/0OPT78UcXEVFHVuKoaNWKErNbTj/VwOKIlHZ1Qd+y4PwslkZFRys7O1ocfvK8pb73tad+69Rev2482btigTlccvVOmqKhI+fn5um/AQElS02bN9N2s8hsZda5ML740aNBAa9asUU5Ojj799FP169dPaWlpPj3mmDFjNGrUKJ8eAwBMZ7HICD67f/kBAAC40Ax5ZJh279qlG/92vaIcDj351MjjRoD8s8+tKiwo0OWXtZPNZtO/Bt6vO++6+4z6jBg5SrGxsRo3dqwG7twhR3S0mjdvoaHDHj2r3P/sc6sKcwvU/YYrFRTkfbynn31Ohtutu++8XUeOHNElLVvqy5n/84wcKet5n86zz7+g3Lxc/b3XDaoUGakHHhzkmTD3VBy/D7YIj4jQP2662dMe5XDI5XIpNraqrrv+Bk/7xg0b1Pjiiz3rq1at1ID7H5Akbdq0UQ0aNvQUfdasXq0mKd7z1JjJYvz15i6TdenSRXXq1NFNN92kzp07Kysry2v0S3Jysh566CENGjRII0aM0FdffaU1a9Z4tu/cuVO1a9fWqlWr1KJFixMe40QjX5KSkvTj2p2Kjal8wvcAAAAAAE7NKC2WcSRTNZKTFfKXW4TOd92v6qyUps304riT38pSlj7lzpByM44+XrtSQrhkOU3/89jbb76hQ4cOadjwx7R40UL97bprlX7wkCwWiz784H299MILWr56jbKystTr+mv1+VczVbVq1XM+blFhofbs3i1LZJwsQd5zy/52OEtXNqulnJwcRUVFnXQfpo98+Su3262ioiK1bNlSwcHBmjNnjnr37i1J2rJli/bs2aPU1KOP5EpNTdWzzz6rzMxMxcXFSZJmz56tqKgoNW7c+KTHCAkJ8ZrMCAACkcVVpIsWDJck7btsjAwbv/cAAAAC2oEMWWTIiE+QLIFXhenarbv+cWMvbd36i2rUSFaDhg09T3pav26dul99tTq0ayuXy6Xnx75ULoWX8mJq8WX48OHq0aOHatSooSNHjmj69OmaN2+evvvuOzkcDvXv31+DBw9WTEyMoqKidP/99ys1NVVt27aVJHXt2lWNGzfWbbfdprFjxyojI0NPPPGEBgwYQHEFANwuVd76qSRpX7tnpLLfugsAAIDzkMWZI8mQ4hICcgRMjeRkLVm+0rM+YuSf04k8P/ZFMyKVmanFl8zMTPXt21fp6elyOBxq2rSpvvvuO131+wzHr7zyiqxWq3r37q2ioiJ169ZNr7/+uuf9NptNM2fO1H333afU1FRFRESoX79+Gj16tFmnBAAAAAAIQLNmzymXPrgwmVp8eeedd065PTQ0VJMmTdKkSZNO2ic5OVnffPNNeUcDAAAAAAAoF6d/9hMAAAAAAADOGsUXAAAAAAAAH6L4AgAAAAAA4EMUXwAAAAAAAHzI1Al3AQC+YwSFaWOf1Z5lAAAABDajdt2jj5i2BuBzps9zFF8AIFBZLHKFVTE7BQAAACqKzXa0+AK/w21HAAAAAAAAPsTIFwAIUBZXkaoteVqSlN72SRm2EJMTAQAAwKcyD8hikYyqcZKFITD+hJEvABCo3C5V2fS+qmx6X3K7zE4DAAAAH7PkZEvZWZJhdhL8FcUXAAAAAAB8pPtVnTX04cE+P87fbuqpoS8877P9l9d5VNTn4W8ovgAAAAAAUA5OVFiY/vEnGjFylEmJzGXm53Hn7X11899v9GpLmzdPESHBGj3yKa/2V8aNU+3kJBUXF/ssD3O+AAAAAADgIzExMWZH8CsV9XlEO6KVnp7u1fbq+FcUEhIiZ06Op620tFRTJk/Sff8aILvd7rM8jHwBAAAAAFzwioqKNGTQQ0qunqiYqErqcsXlWrliuWd796s6a/CDD2jwgw+oWtUqqpGYoNEjn5JhHJ1g5Z677tRP8+fr9dcmKiIkWBEhwdq9a9dxoz+6X9VZDz/0oIY+PFgXxVdVzaSL9N47bysvL0//d3d/xVeprJRGDfXdrFle+b7/7jt1ueJyJcbFKqlavHrfcL12bN9e5vP7/LP/qvUlzVXFEamkavHq2b2b8vLyynz+f9Wofl299uoEr7a2rVvq2adHn9HnUZbjdr+qs4YMekiPD39U1RPiVKtGdc9xTsYRHe1VZNmyebN+nPODbr2tr3Kcf7Z/9t9PdfjQIfW/+55T7u9cUXwBAAAAAPiEYRgqKXKZ8vqjKFJWjw9/VF988bnefPtdLVy6TLXr1NH11/TU4cOHPX0++vAD2YKClLZgkcaOe1kTJ4zX1HffkSS9OO4VtWnbVnfc2V/bd+/V9t17VT0p6YTH+ujDDxQbG6u0BYt0378G6MH7B+rWW25W27apWrhkmTp36aK777xd+fn5nvfk5+fp/gcf0k+LlmjmrO9ktVp18z9ulNvtPu25paen6/bbblXffrdr1dp1+nb2D7r+hhu8PqOynP+ZKOvnUdbjfvThB4qIiNC8nxbqmefGaMyzz2jODz+c9PgOR7ScOU7P+sQJ49X7739Xw0aNvNpfe3WCbuvbz+cjcrjtCAAAAADgE6XFbn04dKEpx771xfYKDrGVqW9eXp7efvMNvfH2O+rWvbskadLkN9RoTl1Ne+89DXr4YUlS9epJGvvSOFksFtVv0EAb1q/Xa6++qjv63yWHwyG73a6w8HAlJCSc8ngpTZtq2PDHJElDHhmmcS+OVZXYKrqj/12SpEcff0JvvfmG1q/7WZe2aStJuuFvvbz2MfnNt5R8UTVt2rRRyVVqn/J4GRnpKi0t1fU3/E01kpMlSU2apJzx+Z+JsnweZ3LcJikpeuyJJyVJdevV0xuTX9e8uT+qc5cuJ9x3dLRDzt9HuBw8eFAz/j1dc39aoLVr1njaFy5YoNWrVum9aR+c8fmdKUa+AECAMoJCtfmmhdp800IZQaFmxwEAAPBbO3ZsV0lJiVJT23nagoOD1apVa23ZssnT1rrNpbJYLJ71Nm3aatu2rXK5XGd0vGMLHzabTTFVqujii/9si4+PlyQdzDzoadu2dav63XarLm5QXwmxMWpcv64kae/evZ4+RpRDRq060jEZJalp02bqdMWVurRlC916y8167523lZWVdcbnX97O5LjHfmaSlJBQTQcPZp50347oaOX8ftvRm1MmK7Vde6WkNFVUVJSnfeKE8brm2utUp27d8jqlk2LkCwAEKotVJZEnHuoKAABQEYLsVt36YnvTju2vgoKDvdYtFouCg4O81iV53VL0915/U1KNGnpt8hRVq1ZNbsOt1i2aq+TYJ/RYrdJf9i0dLfDM/HaWlixepDk//KDJr0/SyKdGKO2nhapZq9ZZnYPVYj3u1q7SktKz2ldZnOgzO9UtVw5HtEpKSpSVlaW33nxDb787VZIUGRklZ45TO7Zv1/9mfq3ZP871WeZj+e/VCAAAAAA4r1ksFgWH2Ex5Wf4y+uNUateuI7vdrsWLF3naSkpKtHLlCjVs2NjTtmKZ90Swy5YtVd269WSzHb29KTjYLvcZjoIpi0OHDumXX7Zo2PDHdMWVV6pho0bKPmbkSllYLBaltmuvJ0Y8pcXLVshut+urL7+QVPbzP1Zs1VhlZGR41p1Op3bt2unV53Sfx9kct6yiox2SpCmvT1J8fLy6XHWVJMnhiJLTmaNJE19Vq9a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"text/plain": [ "
" ] @@ -616,15 +656,11 @@ } ], "source": [ - "import pyomo.environ as pyo\n", - "import pyomo.gdp as gdp\n", - "\n", - "\n", "def pack_boxes_V1(boxes):\n", - " # a simple upper bound on shelf width\n", + " # derive the upper bound on shelf width\n", " W_ub = boxes[\"w\"].sum()\n", "\n", - " m = pyo.ConcreteModel()\n", + " m = pyo.ConcreteModel(\"Packing boxes problem\")\n", "\n", " m.BOXES = pyo.Set(initialize=boxes.index)\n", " m.PAIRS = pyo.Set(initialize=m.BOXES * m.BOXES, filter=lambda m, i, j: i < j)\n", @@ -658,12 +694,20 @@ " soln[\"y1\"] = [0 for i in boxes.index]\n", " soln[\"y2\"] = soln[\"y1\"] + soln[\"d\"]\n", " soln[\"r\"] = [0 for i in boxes.index]\n", - " return soln\n", + "\n", + " return m, soln, W_ub\n", "\n", "\n", - "soln = pack_boxes_V1(boxes)\n", + "m, soln, W_ub = pack_boxes_V1(boxes)\n", "display(soln)\n", - "show_boxes(soln, D)" + "show_boxes(soln, D, W_ub)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The solution that we found is not better than the upper bound. This is not surprising, since we did not consider rotation of the boxes." ] }, { @@ -672,32 +716,31 @@ "source": [ "## Version 2: Rotating boxes\n", "\n", - "Rotating the boxes is an option for packing the boxes more tightly on the shelf. The boxes can be placed either in their original orientation or in a rotated orientation. This introduces a second exclusive or disjunction to the model that determines the orientation of the bounding box. A boolean indicator variable $r_i$ tracks which boxes were rotated which is used in the `show_boxes` function to show which boxes have been rotated.\n", + "Rotating the boxes is an option for packing the boxes more tightly on the shelf. The boxes can be placed either in their original orientation or in a rotated orientation. This introduces a second exclusive OR disjunction to the model that determines the orientation of the bounding box. A binary indicator variable $r_i$ tracks which boxes were rotated which is used in the `show_boxes` function to show which boxes have been rotated.\n", "\n", "$$\n", "\\begin{align*}\n", - "& \\min W \\\\\n", - "\\text{subject to:}\\qquad\\qquad \\\\\n", - "x_{i, 2} & \\leq W & \\forall i\\\\\n", - "x_{i, 1}, x_{i, 2} & \\geq 0 & \\forall i \\\\\n", - "y_{i, 1} & = 0 & \\forall i \\\\\n", - "\\\\\n", - "[x_{i, 2} \\leq x_{j,1}] & \\veebar [ x_{j, 2} \\leq x_{i, 1}] & \\forall i < j \\\\\n", - "\\\\\n", - "\\begin{bmatrix}\n", - "\\neg r_i \\\\\n", + "\\min \\quad & W \\\\\n", + "\\text{s.t} \\quad\n", + "& x_{i, 2} \\leq W & \\forall \\, i\\\\\n", + "& x_{i, 1}, x_{i, 2} \\geq 0 & \\forall \\, i \\\\\n", + "& y_{i, 1} = 0 & \\forall \\, i \\\\\n", + "& [x_{i, 2} \\leq x_{j,1}] \\veebar [ x_{j, 2} \\leq x_{i, 1}] & \\forall \\, i < j \\\\\n", + "\n", + "& \\begin{bmatrix}\n", + "r_i = 0 \\\\\n", "x_{i,2} = x_{i,1} + w_i\\\\\n", "y_{i,2} = y_{i,1} + d_i\\\\\n", - "\\end{bmatrix} & \\veebar \n", + "\\end{bmatrix} \\veebar \n", "\\begin{bmatrix}\n", - "r_i \\\\\n", + "r_i = 1 \\\\\n", "x_{i,2} = x_{i,1} + d_i\\\\\n", "y_{i,2} = y_{i,1} + w_i\\\\\n", - "\\end{bmatrix} & \\forall i < j\n", + "\\end{bmatrix} & \\forall \\, i < j\n", "\\end{align*}\n", "$$\n", "\n", - "For this version of the model the boxes will be lined up against the edge of the shelf with $y_{i,1} = 0$. Decision variables are now included in the model for rotation $r$ to the $y$ dimension of the bounding boxes." + "In this version of the model, the boxes will be lined up against the edge of the shelf with $y_{i,1} = 0$. Decision variables are now included in the model for rotation $r$ to the $y$ dimension of the bounding boxes." ] }, { @@ -738,83 +781,83 @@ " \n", " \n", " 0\n", - " 82\n", - " 103\n", - " 558.0\n", - " 640.0\n", + " 138\n", + " 71\n", + " 743.0\n", + " 814.0\n", " 0.0\n", - " 103.0\n", - " 0\n", + " 138.0\n", + " 1\n", " \n", " \n", " 1\n", - " 73\n", - " 48\n", - " 510.0\n", - " 558.0\n", + " 154\n", + " 117\n", + " 626.0\n", + " 743.0\n", " 0.0\n", - " 73.0\n", + " 154.0\n", " 1\n", " \n", " \n", " 2\n", - " 171\n", - " 53\n", - " 457.0\n", - " 510.0\n", + " 139\n", + " 176\n", + " 487.0\n", + " 626.0\n", " 0.0\n", - " 171.0\n", - " 1\n", + " 176.0\n", + " 0\n", " \n", " \n", " 3\n", - " 73\n", - " 99\n", - " 384.0\n", - " 457.0\n", + " 121\n", + " 175\n", + " 366.0\n", + " 487.0\n", " 0.0\n", - " 99.0\n", + " 175.0\n", " 0\n", " \n", " \n", " 4\n", - " 167\n", - " 85\n", - " 299.0\n", - " 384.0\n", + " 196\n", + " 117\n", + " 249.0\n", + " 366.0\n", " 0.0\n", - " 167.0\n", + " 196.0\n", " 1\n", " \n", " \n", " 5\n", - " 151\n", - " 172\n", - " 148.0\n", - " 299.0\n", + " 186\n", + " 85\n", + " 164.0\n", + " 249.0\n", " 0.0\n", - " 172.0\n", - " 0\n", + " 186.0\n", + " 1\n", " \n", " \n", " 6\n", - " 54\n", - " 130\n", - " 94.0\n", - " 148.0\n", + " 126\n", + " 99\n", + " 65.0\n", + " 164.0\n", " 0.0\n", - " 130.0\n", - " 0\n", + " 126.0\n", + " 1\n", " \n", " \n", " 7\n", - " 126\n", - " 94\n", + " 65\n", + " 85\n", " 0.0\n", - " 94.0\n", + " 65.0\n", " 0.0\n", - " 126.0\n", - " 1\n", + " 85.0\n", + " 0\n", " \n", " \n", "\n", @@ -822,22 +865,31 @@ ], "text/plain": [ " w d x1 x2 y1 y2 r\n", - "0 82 103 558.0 640.0 0.0 103.0 0\n", - "1 73 48 510.0 558.0 0.0 73.0 1\n", - "2 171 53 457.0 510.0 0.0 171.0 1\n", - "3 73 99 384.0 457.0 0.0 99.0 0\n", - "4 167 85 299.0 384.0 0.0 167.0 1\n", - "5 151 172 148.0 299.0 0.0 172.0 0\n", - "6 54 130 94.0 148.0 0.0 130.0 0\n", - "7 126 94 0.0 94.0 0.0 126.0 1" + "0 138 71 743.0 814.0 0.0 138.0 1\n", + "1 154 117 626.0 743.0 0.0 154.0 1\n", + "2 139 176 487.0 626.0 0.0 176.0 0\n", + "3 121 175 366.0 487.0 0.0 175.0 0\n", + "4 196 117 249.0 366.0 0.0 196.0 1\n", + "5 186 85 164.0 249.0 0.0 186.0 1\n", + "6 126 99 65.0 164.0 0.0 126.0 1\n", + "7 65 85 0.0 65.0 0.0 85.0 0" ] }, "metadata": {}, "output_type": "display_data" }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lower bound on shelf width = 370\n", + "Upper bound on shelf width = 1125\n", + "Optimal shelf width = 814\n" + ] + }, { "data": { - "image/png": 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"text/plain": [ "
" ] @@ -847,14 +899,10 @@ } ], "source": [ - "import pyomo.environ as pyo\n", - "import pyomo.gdp as gdp\n", - "\n", - "\n", "def pack_boxes_V2(boxes):\n", " W_ub = boxes[\"w\"].sum()\n", "\n", - " m = pyo.ConcreteModel()\n", + " m = pyo.ConcreteModel(\"Packing boxes problem with rotation\")\n", "\n", " m.BOXES = pyo.Set(initialize=boxes.index)\n", " m.PAIRS = pyo.Set(initialize=m.BOXES * m.BOXES, filter=lambda m, i, j: i < j)\n", @@ -864,7 +912,7 @@ " m.x2 = pyo.Var(m.BOXES, bounds=(0, W_ub))\n", " m.y1 = pyo.Var(m.BOXES, bounds=(0, W_ub))\n", " m.y2 = pyo.Var(m.BOXES, bounds=(0, W_ub))\n", - " m.r = pyo.Var(m.BOXES, domain=pyo.Boolean)\n", + " m.r = pyo.Var(m.BOXES, domain=pyo.Binary)\n", "\n", " @m.Objective()\n", " def minimize_width(m):\n", @@ -882,12 +930,12 @@ " def rotate(m, i):\n", " return [\n", " [\n", - " m.r[i] == False,\n", + " m.r[i] == 0,\n", " m.x2[i] == m.x1[i] + boxes.loc[i, \"w\"],\n", " m.y2[i] == m.y1[i] + boxes.loc[i, \"d\"],\n", " ],\n", " [\n", - " m.r[i] == True,\n", + " m.r[i] == 1,\n", " m.x2[i] == m.x1[i] + boxes.loc[i, \"d\"],\n", " m.y2[i] == m.y1[i] + boxes.loc[i, \"w\"],\n", " ],\n", @@ -905,14 +953,14 @@ " soln[\"x2\"] = [m.x2[i]() for i in boxes.index]\n", " soln[\"y1\"] = [m.y1[i]() for i in boxes.index]\n", " soln[\"y2\"] = [m.y2[i]() for i in boxes.index]\n", - " soln[\"r\"] = [round(m.r[i]()) for i in boxes.index]\n", + " soln[\"r\"] = [int(m.r[i]()) for i in boxes.index]\n", "\n", - " return soln\n", + " return m, soln, W_ub\n", "\n", "\n", - "soln = pack_boxes_V2(boxes)\n", + "m, soln, W_ub = pack_boxes_V2(boxes)\n", "display(soln)\n", - "show_boxes(soln, D)" + "show_boxes(soln, D, W_ub)" ] }, { @@ -927,21 +975,20 @@ "\n", "$$\n", "\\begin{align*}\n", - "& \\min W \\\\\n", - "\\text{subject to:}\\qquad\\qquad \\\\\n", - "x_{i, 2} & \\leq W & \\forall i\\\\\n", - "y_{i, 2} & \\leq D & \\forall i\\\\\n", - "x_{i, 1}, x_{i, 2} & \\geq 0 & \\forall i \\\\\n", - "y_{i, 1}, y_{i, 2} & \\geq 0 & \\forall i \\\\\n", - "\\\\\n", - "\\begin{bmatrix}\n", + "\\min \\quad & W \\\\\n", + "\\text{s.t.} \\quad\n", + "& x_{i, 2} \\leq W & \\forall i\\\\\n", + "& y_{i, 2} \\leq D & \\forall i\\\\\n", + "& x_{i, 1}, x_{i, 2} \\geq 0 & \\forall i \\\\\n", + "& y_{i, 1}, y_{i, 2} \\geq 0 & \\forall i \\\\\n", + "& \\begin{bmatrix}\n", "x_{i, 2} \\leq x_{j,1} \\\\\n", "\\end{bmatrix}\n", "\\veebar\n", "\\begin{bmatrix}\n", "x_{j, 2} \\leq x_{i, 1} \\\\\n", "\\end{bmatrix}\n", - "& \\veebar \n", + " \\veebar \n", "\\begin{bmatrix}\n", "y_{i, 2} \\leq y_{j, 1} \\\\\n", "\\end{bmatrix}\n", @@ -950,14 +997,13 @@ "y_{j, 2} \\leq y_{i, 1} \\\\\n", "\\end{bmatrix}\n", "& \\forall i < j \\\\\n", - "\\\\\n", - "\\begin{bmatrix}\n", - "\\neg r_i \\\\\n", + "& \\begin{bmatrix}\n", + "r_i = 0 \\\\\n", "x_{i,2} = x_{i,1} + w_i\\\\\n", "y_{i,2} = y_{i,1} + d_i\\\\\n", - "\\end{bmatrix} & \\veebar \n", + "\\end{bmatrix} \\veebar \n", "\\begin{bmatrix}\n", - "r_i \\\\\n", + "r_i = 1 \\\\\n", "x_{i,2} = x_{i,1} + d_i\\\\\n", "y_{i,2} = y_{i,1} + w_i\\\\\n", "\\end{bmatrix} & \\forall i < j\n", @@ -1003,83 +1049,83 @@ " \n", " \n", " 0\n", - " 82\n", - " 103\n", - " 178.0\n", - " 260.0\n", - " 0.0\n", - " 103.0\n", + " 138\n", + " 71\n", + " 121.0\n", + " 259.0\n", + " 85.0\n", + " 156.0\n", " 0\n", " \n", " \n", " 1\n", - " 73\n", - " 48\n", - " 0.0\n", - " 48.0\n", - " 53.0\n", - " 126.0\n", + " 154\n", + " 117\n", + " 259.0\n", + " 376.0\n", + " 85.0\n", + " 239.0\n", " 1\n", " \n", " \n", " 2\n", - " 171\n", - " 53\n", - " 0.0\n", - " 171.0\n", + " 139\n", + " 176\n", " 0.0\n", - " 53.0\n", + " 139.0\n", + " 175.0\n", + " 351.0\n", " 0\n", " \n", " \n", " 3\n", - " 73\n", - " 99\n", + " 121\n", + " 175\n", " 0.0\n", - " 99.0\n", - " 258.0\n", - " 331.0\n", - " 1\n", + " 121.0\n", + " 0.0\n", + " 175.0\n", + " 0\n", " \n", " \n", " 4\n", - " 167\n", - " 85\n", - " 99.0\n", - " 266.0\n", - " 258.0\n", - " 343.0\n", - " 0\n", + " 196\n", + " 117\n", + " 139.0\n", + " 256.0\n", + " 156.0\n", + " 352.0\n", + " 1\n", " \n", " \n", " 5\n", - " 151\n", - " 172\n", - " 94.0\n", - " 266.0\n", - " 107.0\n", - " 258.0\n", - " 1\n", + " 186\n", + " 85\n", + " 121.0\n", + " 307.0\n", + " 0.0\n", + " 85.0\n", + " 0\n", " \n", " \n", " 6\n", - " 54\n", - " 130\n", - " 48.0\n", - " 178.0\n", - " 53.0\n", - " 107.0\n", - " 1\n", + " 126\n", + " 99\n", + " 256.0\n", + " 382.0\n", + " 239.0\n", + " 338.0\n", + " 0\n", " \n", " \n", " 7\n", - " 126\n", - " 94\n", + " 65\n", + " 85\n", + " 307.0\n", + " 372.0\n", " 0.0\n", - " 94.0\n", - " 126.0\n", - " 252.0\n", - " 1\n", + " 85.0\n", + " 0\n", " \n", " \n", "\n", @@ -1087,22 +1133,31 @@ ], "text/plain": [ " w d x1 x2 y1 y2 r\n", - "0 82 103 178.0 260.0 0.0 103.0 0\n", - "1 73 48 0.0 48.0 53.0 126.0 1\n", - "2 171 53 0.0 171.0 0.0 53.0 0\n", - "3 73 99 0.0 99.0 258.0 331.0 1\n", - "4 167 85 99.0 266.0 258.0 343.0 0\n", - "5 151 172 94.0 266.0 107.0 258.0 1\n", - "6 54 130 48.0 178.0 53.0 107.0 1\n", - "7 126 94 0.0 94.0 126.0 252.0 1" + "0 138 71 121.0 259.0 85.0 156.0 0\n", + "1 154 117 259.0 376.0 85.0 239.0 1\n", + "2 139 176 0.0 139.0 175.0 351.0 0\n", + "3 121 175 0.0 121.0 0.0 175.0 0\n", + "4 196 117 139.0 256.0 156.0 352.0 1\n", + "5 186 85 121.0 307.0 0.0 85.0 0\n", + "6 126 99 256.0 382.0 239.0 338.0 0\n", + "7 65 85 307.0 372.0 0.0 85.0 0" ] }, "metadata": {}, "output_type": "display_data" }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lower bound on shelf width = 370\n", + "Upper bound on shelf width = 1125\n", + "Optimal shelf width = 382\n" + ] + }, { "data": { - "image/png": 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"text/plain": [ "
" ] @@ -1112,14 +1167,10 @@ } ], "source": [ - "import pyomo.environ as pyo\n", - "import pyomo.gdp as gdp\n", - "\n", - "\n", "def pack_boxes_V3(boxes, D):\n", " W_ub = boxes[\"w\"].sum()\n", "\n", - " m = pyo.ConcreteModel()\n", + " m = pyo.ConcreteModel(\"Packing boxes problem with rotation and shelf depth\")\n", "\n", " m.D = pyo.Param(mutable=True, initialize=D)\n", "\n", @@ -1131,7 +1182,7 @@ " m.x2 = pyo.Var(m.BOXES, bounds=(0, W_ub))\n", " m.y1 = pyo.Var(m.BOXES, bounds=(0, W_ub))\n", " m.y2 = pyo.Var(m.BOXES, bounds=(0, W_ub))\n", - " m.r = pyo.Var(m.BOXES, domain=pyo.Boolean)\n", + " m.r = pyo.Var(m.BOXES, domain=pyo.Binary)\n", "\n", " @m.Objective()\n", " def minimize_width(m):\n", @@ -1149,12 +1200,12 @@ " def rotate(m, i):\n", " return [\n", " [\n", - " m.r[i] == False,\n", + " m.r[i] == 0,\n", " m.x2[i] == m.x1[i] + boxes.loc[i, \"w\"],\n", " m.y2[i] == m.y1[i] + boxes.loc[i, \"d\"],\n", " ],\n", " [\n", - " m.r[i] == True,\n", + " m.r[i] == 1,\n", " m.x2[i] == m.x1[i] + boxes.loc[i, \"d\"],\n", " m.y2[i] == m.y1[i] + boxes.loc[i, \"w\"],\n", " ],\n", @@ -1177,13 +1228,14 @@ " soln[\"x2\"] = [m.x2[i]() for i in boxes.index]\n", " soln[\"y1\"] = [m.y1[i]() for i in boxes.index]\n", " soln[\"y2\"] = [m.y2[i]() for i in boxes.index]\n", - " soln[\"r\"] = [round(m.r[i]()) for i in boxes.index]\n", - " return soln\n", + " soln[\"r\"] = [int(m.r[i]()) for i in boxes.index]\n", + "\n", + " return m, soln, W_ub\n", "\n", "\n", - "soln = pack_boxes_V3(boxes, D)\n", + "m, soln, W_ub = pack_boxes_V3(boxes, D)\n", "display(soln)\n", - "show_boxes(soln, D)" + "show_boxes(soln, D, W_ub)" ] }, { @@ -1192,11 +1244,9 @@ "source": [ "## Advanced Topic: Symmetry Breaking\n", "\n", - "One of the issues in combinatorial problem is the challenge of symmetries. A symmetry is a situation where a change in solution configuration leaves the objective unchanged. Strip packing problems are especially susceptible to symmetries.\n", - "\n", - "Symmetries can significantly increase the effort needed to find and and verify an optimal solution. Trespalacios and Grossmann recently presented modification to the strip packing problem to reduce the number of symmetries. This is described in the following paper and implemented in the accompanying Pyomo model.\n", + "One of the issues in combinatorial problem is the challenge of symmetries. A symmetry is a situation where a change in solution configuration leaves the objective unchanged. Strip packing problems are especially susceptible to symmetries. Symmetries can significantly increase the effort needed to find and verify an optimal solution. In [1], Trespalacios and Grossmann introduced a modification to the strip packing problem to reduce the number of symmetries. We implement this new model formulation in Pyomo in the following cell.\n", "\n", - "Trespalacios, F., & Grossmann, I. E. (2017). Symmetry breaking for generalized disjunctive programming formulation of the strip packing problem. Annals of Operations Research, 258(2), 747-759.\n" + "[1] _Trespalacios, F., & Grossmann, I. E. (2017). Symmetry breaking for generalized disjunctive programming formulation of the strip packing problem. Annals of Operations Research, 258(2), 747-759. DOI [10.1007/s10479-016-2112-9](https://doi.org/10.1007/s10479-016-2112-9)_" ] }, { @@ -1237,83 +1287,83 @@ " \n", " \n", " 0\n", - " 82\n", - " 103\n", - " 0.0\n", - " 82.0\n", - " 73.0\n", - " 176.0\n", + " 138\n", + " 71\n", + " 123.0\n", + " 261.0\n", + " 196.0\n", + " 267.0\n", " 0\n", " \n", " \n", " 1\n", - " 73\n", - " 48\n", - " 218.0\n", - " 266.0\n", - " 138.0\n", - " 211.0\n", + " 154\n", + " 117\n", + " 0.0\n", + " 117.0\n", + " 99.0\n", + " 253.0\n", " 1\n", " \n", " \n", " 2\n", - " 171\n", - " 53\n", - " 95.0\n", - " 266.0\n", - " 85.0\n", - " 138.0\n", + " 139\n", + " 176\n", + " 243.0\n", + " 382.0\n", + " 0.0\n", + " 176.0\n", " 0\n", " \n", " \n", " 3\n", - " 73\n", - " 99\n", - " 0.0\n", - " 99.0\n", - " 0.0\n", - " 73.0\n", - " 1\n", + " 121\n", + " 175\n", + " 261.0\n", + " 382.0\n", + " 176.0\n", + " 351.0\n", + " 0\n", " \n", " \n", " 4\n", - " 167\n", - " 85\n", - " 99.0\n", - " 266.0\n", + " 196\n", + " 117\n", + " 126.0\n", + " 243.0\n", " 0.0\n", - " 85.0\n", - " 0\n", + " 196.0\n", + " 1\n", " \n", " \n", " 5\n", - " 151\n", - " 172\n", + " 186\n", + " 85\n", " 0.0\n", - " 172.0\n", - " 193.0\n", - " 344.0\n", - " 1\n", + " 186.0\n", + " 267.0\n", + " 352.0\n", + " 0\n", " \n", " \n", " 6\n", - " 54\n", - " 130\n", - " 88.0\n", - " 218.0\n", - " 139.0\n", - " 193.0\n", - " 1\n", + " 126\n", + " 99\n", + " 0.0\n", + " 126.0\n", + " 0.0\n", + " 99.0\n", + " 0\n", " \n", " \n", " 7\n", - " 126\n", - " 94\n", - " 172.0\n", - " 266.0\n", - " 211.0\n", - " 337.0\n", - " 1\n", + " 65\n", + " 85\n", + " 196.0\n", + " 261.0\n", + " 267.0\n", + " 352.0\n", + " 0\n", " \n", " \n", "\n", @@ -1321,22 +1371,31 @@ ], "text/plain": [ " w d x1 x2 y1 y2 r\n", - "0 82 103 0.0 82.0 73.0 176.0 0\n", - "1 73 48 218.0 266.0 138.0 211.0 1\n", - "2 171 53 95.0 266.0 85.0 138.0 0\n", - "3 73 99 0.0 99.0 0.0 73.0 1\n", - "4 167 85 99.0 266.0 0.0 85.0 0\n", - "5 151 172 0.0 172.0 193.0 344.0 1\n", - "6 54 130 88.0 218.0 139.0 193.0 1\n", - "7 126 94 172.0 266.0 211.0 337.0 1" + "0 138 71 123.0 261.0 196.0 267.0 0\n", + "1 154 117 0.0 117.0 99.0 253.0 1\n", + "2 139 176 243.0 382.0 0.0 176.0 0\n", + "3 121 175 261.0 382.0 176.0 351.0 0\n", + "4 196 117 126.0 243.0 0.0 196.0 1\n", + "5 186 85 0.0 186.0 267.0 352.0 0\n", + "6 126 99 0.0 126.0 0.0 99.0 0\n", + "7 65 85 196.0 261.0 267.0 352.0 0" ] }, "metadata": {}, "output_type": "display_data" }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lower bound on shelf width = 370\n", + "Upper bound on shelf width = 1125\n", + "Optimal shelf width = 382\n" + ] + }, { "data": { - "image/png": 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"text/plain": [ "
" ] @@ -1346,14 +1405,12 @@ } ], "source": [ - "import pyomo.environ as pyo\n", - "import pyomo.gdp as gdp\n", - "\n", - "\n", "def pack_boxes_V4(boxes, D):\n", " W_ub = boxes[\"w\"].sum()\n", "\n", - " m = pyo.ConcreteModel()\n", + " m = pyo.ConcreteModel(\n", + " \"Packing boxes problem with rotation and shelf depth (symmetry breaking model)\"\n", + " )\n", "\n", " m.D = pyo.Param(mutable=True, initialize=D)\n", "\n", @@ -1365,7 +1422,7 @@ " m.x2 = pyo.Var(m.BOXES, bounds=(0, W_ub))\n", " m.y1 = pyo.Var(m.BOXES, bounds=(0, W_ub))\n", " m.y2 = pyo.Var(m.BOXES, bounds=(0, W_ub))\n", - " m.r = pyo.Var(m.BOXES, domain=pyo.Boolean)\n", + " m.r = pyo.Var(m.BOXES, domain=pyo.Binary)\n", "\n", " @m.Objective()\n", " def minimize_width(m):\n", @@ -1383,12 +1440,12 @@ " def rotate(m, i):\n", " return [\n", " [\n", - " m.r[i] == False,\n", + " m.r[i] == 0,\n", " m.x2[i] == m.x1[i] + boxes.loc[i, \"w\"],\n", " m.y2[i] == m.y1[i] + boxes.loc[i, \"d\"],\n", " ],\n", " [\n", - " m.r[i] == True,\n", + " m.r[i] == 1,\n", " m.x2[i] == m.x1[i] + boxes.loc[i, \"d\"],\n", " m.y2[i] == m.y1[i] + boxes.loc[i, \"w\"],\n", " ],\n", @@ -1407,25 +1464,19 @@ " SOLVER.solve(m)\n", "\n", " soln = boxes.copy()\n", - " soln[\"x1\"] = [m.x1[i]() for i in boxes.index]\n", - " soln[\"x2\"] = [m.x2[i]() for i in boxes.index]\n", - " soln[\"y1\"] = [m.y1[i]() for i in boxes.index]\n", - " soln[\"y2\"] = [m.y2[i]() for i in boxes.index]\n", - " soln[\"r\"] = [round(m.r[i]()) for i in boxes.index]\n", - " return soln\n", + " soln[\"x1\"] = [m.x1[i]() for i in m.BOXES]\n", + " soln[\"x2\"] = [m.x2[i]() for i in m.BOXES]\n", + " soln[\"y1\"] = [m.y1[i]() for i in m.BOXES]\n", + " soln[\"y2\"] = [m.y2[i]() for i in m.BOXES]\n", + " soln[\"r\"] = [int(m.r[i]()) for i in m.BOXES]\n", + "\n", + " return m, soln, W_ub\n", "\n", "\n", - "soln = pack_boxes_V4(boxes, D)\n", + "m, soln, W_ub = pack_boxes_V4(boxes, D)\n", "display(soln)\n", - "show_boxes(soln, D)" + "show_boxes(soln, D, W_ub)" ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { @@ -1444,7 +1495,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.16" + "version": "3.10.10" } }, "nbformat": 4, diff --git a/notebooks/08/bim-robust-optimization.ipynb b/notebooks/08/bim-robust-optimization.ipynb index ccec4221..cdff2254 100644 --- a/notebooks/08/bim-robust-optimization.ipynb +++ b/notebooks/08/bim-robust-optimization.ipynb @@ -64,8 +64,12 @@ "\n", "# Check that all solvers have been installed correctly and are available\n", "assert pyo.SolverFactory(SOLVER).available(), f\"Solver {SOLVER} is not available.\"\n", - "assert pyo.SolverFactory(SOLVER_NLO).available(), f\"Solver NLO {SOLVER_NLO} is not available.\"\n", - "assert pyo.SolverFactory(SOLVER_MINLO).available(), f\"Solver NLO {SOLVER_MINLO} is not available.\"" + "assert pyo.SolverFactory(\n", + " SOLVER_NLO\n", + ").available(), f\"Solver NLO {SOLVER_NLO} is not available.\"\n", + "assert pyo.SolverFactory(\n", + " SOLVER_MINLO\n", + ").available(), f\"Solver NLO {SOLVER_MINLO} is not available.\"" ] }, { @@ -76,7 +80,7 @@ "source": [ "## Original BIM production planning model\n", "\n", - "The full description of the BIM production problem, can be found here [here](../02/bim.ipynb). The resulting optimization problem was the following LP:\n", + "The full description of the BIM production problem, can be found [here](../02/bim.ipynb). The resulting linear optimization problem was formulated as follows:\n", "\n", "$$\n", "\\begin{array}{rrcrcl}\n", @@ -155,9 +159,13 @@ "source": [ "def ShowDuals(model):\n", " import fractions\n", + "\n", " print(\"The dual variable corresponding to:\")\n", " for c in model.component_objects(pyo.Constraint, active=True):\n", - " print(f\"- the constraint on {c} is equal to {str(fractions.Fraction(model.dual[c]))}\")\n", + " print(\n", + " f\"- the constraint on {c} is equal to {str(fractions.Fraction(model.dual[c]))}\"\n", + " )\n", + "\n", "\n", "m.dual = pyo.Suffix(direction=pyo.Suffix.IMPORT)\n", "pyo.SolverFactory(SOLVER).solve(m)\n", @@ -313,7 +321,7 @@ "\\end{array}\n", "$$\n", "\n", - "The above model has an infinite number of constraints, one for every realization of the uncertain coefficients $z$. However, using linear duality, we can deal with this and obtain a robustified LP that we can solve. " + "The above model has an infinite number of constraints, one for every realization of the uncertain coefficients $z$. However, using linear duality, we can deal with this and obtain a robustified linear optimization problem that we can solve. " ] }, { @@ -398,8 +406,7 @@ " m.w = pyo.Var(m.chips, domain=pyo.NonNegativeReals)\n", "\n", " m.robustcopper = pyo.Constraint(\n", - " expr=sum([upper[c] * m.y[c] - lower[c] * m.w[c] for c in m.chips])\n", - " <= 4800\n", + " expr=sum([upper[c] * m.y[c] - lower[c] * m.w[c] for c in m.chips]) <= 4800\n", " )\n", "\n", " @m.Constraint(m.chips)\n", @@ -957,17 +964,12 @@ "\n", " m.silicon = pyo.Constraint(expr=m.x[\"logic\"] <= 1000)\n", " m.gemanium = pyo.Constraint(expr=m.x[\"memory\"] <= 1500)\n", - " m.plastic = pyo.Constraint(\n", - " expr=pyo.quicksum([m.x[c] for c in m.chips]) <= 1750\n", - " )\n", + " m.plastic = pyo.Constraint(expr=pyo.quicksum([m.x[c] for c in m.chips]) <= 1750)\n", "\n", " @m.Constraint(m.scenarios)\n", " def balance(m, i):\n", " z = Z[i]\n", - " return (\n", - " pyo.quicksum(copper[c] * m.x[c] * (1 + z[c]) for c in m.chips)\n", - " <= 4800\n", - " )\n", + " return pyo.quicksum(copper[c] * m.x[c] * (1 + z[c]) for c in m.chips) <= 4800\n", "\n", " pyo.SolverFactory(SOLVER).solve(m)\n", "\n", @@ -1023,9 +1025,7 @@ " )\n", " m.violation = pyo.Objective(\n", " expr=-4800\n", - " + pyo.quicksum(\n", - " [copper[c] * x[c] * (1 + delta * m.z[c]) for c in m.chips]\n", - " ),\n", + " + pyo.quicksum([copper[c] * x[c] * (1 + delta * m.z[c]) for c in m.chips]),\n", " sense=pyo.maximize,\n", " )\n", " pyo.SolverFactory(SOLVER).solve(m)\n", @@ -1167,6 +1167,7 @@ "source": [ "import pyomo.kernel as pyk\n", "\n", + "\n", "def BIMWithBallUncertainty(radius, domain_type=pyk.RealSet):\n", " idxChips = range(len(chips))\n", "\n", @@ -1263,7 +1264,7 @@ " \"and yields a profit of\",\n", " round(pyk.value(m.profit), 3),\n", " \"\\n\",\n", - ")\n" + ")" ] }, { @@ -1323,7 +1324,7 @@ " \"and yields a profit of\",\n", " round(pyk.value(m.profit), 3),\n", " \"\\n\",\n", - ")\n" + ")" ] }, { @@ -1345,9 +1346,7 @@ }, "outputs": [], "source": [ - "def BIMWithBallUncertaintyAsSquaredSecondOrderCone(\n", - " r, domain=pyo.NonNegativeReals\n", - "):\n", + "def BIMWithBallUncertaintyAsSquaredSecondOrderCone(r, domain=pyo.NonNegativeReals):\n", " m = pyo.ConcreteModel(\"BIM with Ball Uncertainty as SOC\")\n", "\n", " m.chips = pyo.Set(initialize=chips)\n", @@ -1366,9 +1365,7 @@ " m.copper = pyo.Constraint(\n", " expr=m.y == 4800 - sum(copper[c] * m.x[c] for c in m.chips)\n", " )\n", - " m.robust = pyo.Constraint(\n", - " expr=sum((r * m.x[c]) ** 2 for c in m.chips) <= m.y**2\n", - " )\n", + " m.robust = pyo.Constraint(expr=sum((r * m.x[c]) ** 2 for c in m.chips) <= m.y**2)\n", "\n", " return m" ] @@ -1400,7 +1397,7 @@ ")\n", "print(\n", " f\"The optimal solution is x={[round(pyo.value(m.x[c]),3) for c in m.chips]} and yields a profit of {pyo.value(m.profit):.2f}\\n\"\n", - ")\n" + ")" ] }, { @@ -1449,7 +1446,7 @@ ")\n", "print(\n", " f\"The optimal solution is x={[round(pyo.value(m.x[c]),3) for c in m.chips]} and yields a profit of {pyo.value(m.profit):.2f}\\n\"\n", - ")\n" + ")" ] } ], diff --git a/notebooks/09/seafood.ipynb b/notebooks/09/seafood.ipynb index 4373c887..ffb83d4c 100644 --- a/notebooks/09/seafood.ipynb +++ b/notebooks/09/seafood.ipynb @@ -57,8 +57,8 @@ " !pip install pyomo >/dev/null 2>/dev/null\n", " !pip install highspy >/dev/null 2>/dev/null\n", "\n", - " from pyomo.contrib import appsi\n", - " SOLVER = appsi.solvers.Highs(only_child_vars=False)\n", + " from pyomo.environ import SolverFactory\n", + " SOLVER = SolverFactory('appsi_highs')\n", " \n", "else:\n", " from pyomo.environ import SolverFactory\n", @@ -225,9 +225,7 @@ "ax.legend()\n", "fig.tight_layout()\n", "\n", - "print(\n", - " f\"The quantile of interest given the parameters is equal to q = {q:.4f}.\\n\"\n", - ")\n", + "print(f\"The quantile of interest given the parameters is equal to q = {q:.4f}.\\n\")\n", "\n", "for name, distribution in distributions.items():\n", " x_opt = distribution.ppf(q)\n", @@ -242,7 +240,7 @@ "source": [ "## Deterministic solution for average demand\n", "\n", - "We now find the optimal solution of the *deterministic LP model* obtained by assuming the demand is constant and equal to the average demand, i.e., $z = \\bar{z} = \\mathbb E z = 100$." + "We now find the optimal solution of the *deterministic linear problem model* obtained by assuming the demand is constant and equal to the average demand, i.e., $z = \\bar{z} = \\mathbb E z = 100$." ] }, { @@ -338,7 +336,7 @@ "\n", "We now assess how well we perform by taking the average demand as input for each of the three demand distributions above.\n", "\n", - "For a fixed decision variable $x=100$, approximate the expected net profit of the seafood distribution center for each of the three distributions above using the Sample Average Approximation method with $N=2500$ points. More specifically, generate $N=2500$ samples from the considered distribution and solve the extensive form of the stochastic LP resulting from those $N=2500$ scenarios." + "For a fixed decision variable $x=100$, approximate the expected net profit of the seafood distribution center for each of the three distributions above using the Sample Average Approximation method with $N=2500$ points. More specifically, generate $N=2500$ samples from the considered distribution and solve the extensive form of the stochastic linear problem resulting from those $N=2500$ scenarios." ] }, { @@ -370,7 +368,7 @@ } ], "source": [ - "# SAA of the two-stage stochastic LP to calculate the expected profit when buying the average\n", + "# SAA of the two-stage stochastic linear problem to calculate the expected profit when buying the average\n", "\n", "\n", "def NaiveSeafoodStockSAA(N, sample, distributiontype):\n", @@ -402,18 +400,14 @@ " model.fishdonotdisappear.add(expr=model.y[i] + model.z[i] == model.x)\n", "\n", " def second_stage_profit(model):\n", - " return sum(\n", - " [p * model.y[i] - h * model.z[i] for i in model.indices]\n", - " ) / float(N)\n", + " return sum([p * model.y[i] - h * model.z[i] for i in model.indices]) / float(N)\n", "\n", " model.second_stage_profit = pyo.Expression(rule=second_stage_profit)\n", "\n", " def total_profit(model):\n", " return model.first_stage_profit + model.second_stage_profit\n", "\n", - " model.total_expected_profit = pyo.Objective(\n", - " rule=total_profit, sense=pyo.maximize\n", - " )\n", + " model.total_expected_profit = pyo.Objective(rule=total_profit, sense=pyo.maximize)\n", "\n", " result = pyo.SolverFactory(SOLVER).solve(model)\n", "\n", @@ -452,7 +446,7 @@ "source": [ "## Approximating the solution using Sample Average Approximation method\n", "\n", - "We now approximate the optimal solution of stock optimization problem for each of the three distributions above using the Sample Average Approximation method. More specifically, generate $N=5000$ samples from each of the three distributions and thhen solve the extensive form of the stochastic LP resulting from those $N=5000$ scenarios. For each of the three distribution, we compare the optimal expected profit with that obtained before and calculate the value of the stochastic solution (VSS)." + "We now approximate the optimal solution of stock optimization problem for each of the three distributions above using the Sample Average Approximation method. More specifically, generate $N=5000$ samples from each of the three distributions and then solve the extensive form of the stochastic linear problem resulting from those $N=5000$ scenarios. For each of the three distribution, we compare the optimal expected profit with that obtained before and calculate the value of the stochastic solution (VSS)." ] }, { @@ -494,7 +488,7 @@ } ], "source": [ - "# Two-stage stochastic LP using SAA\n", + "# Two-stage stochastic linear problem using SAA\n", "\n", "\n", "def SeafoodStockSAA(N, sample, distributiontype, printflag=True):\n", @@ -528,18 +522,14 @@ " model.fishdonotdisappear.add(expr=model.y[i] + model.z[i] == model.x)\n", "\n", " def second_stage_profit(model):\n", - " return sum(\n", - " [p * model.y[i] - h * model.z[i] for i in model.indices]\n", - " ) / float(N)\n", + " return sum([p * model.y[i] - h * model.z[i] for i in model.indices]) / float(N)\n", "\n", " model.second_stage_profit = pyo.Expression(rule=second_stage_profit)\n", "\n", " def total_profit(model):\n", " return model.first_stage_profit + model.second_stage_profit\n", "\n", - " model.total_expected_profit = pyo.Objective(\n", - " rule=total_profit, sense=pyo.maximize\n", - " )\n", + " model.total_expected_profit = pyo.Objective(rule=total_profit, sense=pyo.maximize)\n", "\n", " result = pyo.SolverFactory(SOLVER).solve(model)\n", "\n", diff --git a/python/helper.py b/python/helper.py deleted file mode 100644 index 978ccea4..00000000 --- a/python/helper.py +++ /dev/null @@ -1,242 +0,0 @@ -import shutil -import sys -import os.path -import os -import subprocess - -def _check_available(executable_name): - """Return True if the executable_name is found in the search path.""" - return (shutil.which(executable_name) is not None) or os.path.isfile(executable_name) - -def package_available(package_name): - """Return True if package_name is installed.""" - return _check_available("glpsol") if package_name == "glpk" else _check_available(package_name) - -def package_found(package_name): - """Print message confirming that package was found, then return True or False.""" - is_available = package_available(package_name) - if is_available: - print(f"{package_name} was previously installed") - return is_available - -def package_confirm(package_name): - """Confirm package is available after installation.""" - if package_available(package_name): - print("installation successful") - return True - else: - print("installation failed") - return False - -def on_colab(): - """Return True if running on Google Colab.""" - return "google.colab" in sys.modules - -def install_pyomo(): - """Install pyomo from idaes_pse to include enhanced LA solvers.""" - if package_found("pyomo"): - return True - print("Installing pyomo from idaes_pse via pip ... ", end="") - os.system("pip install -q idaes_pse") - return package_confirm("pyomo") - -def install_idaes(): - if package_found("idaes"): - return - print("Installing idaes from idaes_pse via pip ... ", end="") - os.system("pip install -q idaes_pse") - return package_confirm("idaes") - -def install_ipopt(): - if package_found("ipopt"): - return True - - # try idaes version of ipopt with HSL solvers - if on_colab(): - # Install idaes solvers - print("Installing ipopt and k_aug on Google Colab via idaes get-extensions ... ", end="") - os.system("idaes get-extensions") - - # Add symbolic link for idaes solvers - os.system("ln -s /root/.idaes/bin/ipopt ipopt") - os.system("ln -s /root/.idaes/bin/k_aug k_aug") - - # check again - if package_confirm("ipopt"): - return True - - # try coin-OR version of ipopt with mumps solvers - if on_colab(): - print("Installing ipopt on Google Colab via zip file ... ", end="") - os.system('wget -N -q "https://ampl.com/dl/open/ipopt/ipopt-linux64.zip"') - os.system('!unzip -o -q ipopt-linux64') - else: - print("Installing Ipopt via conda ... ", end="") - os.system('conda install -c conda-forge ipopt') - return package_confirm("ipopt") - -def install_glpk(): - if package_found("glpk"): - return True - if on_colab(): - print("Installing glpk on Google Colab via apt-get ... ", end="") - os.system('apt-get install -y -qq glpk-utils') - else: - print("Installing glpk via conda ... ", end="") - os.system('conda install -c conda-forge glpk') - return package_confirm("glpk") - -def install_cbc(): - if package_found("cbc"): - return True - if on_colab(): - print("Installing cbc on Google Colab via zip file ... ", end="") - os.system('wget -N -q "https://ampl.com/dl/open/cbc/cbc-linux64.zip"') - os.system('unzip -o -q cbc-linux64') - else: - print("Installing cbc via apt-get ... ", end="") - os.system('apt-get install -y -qq coinor-cbc') - return package_confirm("cbc") - -def install_bonmin(): - if package_found("bonmin"): - return True - if on_colab(): - print("Installing bonmin on Google Colab via zip file ... ", end="") - os.system('wget -N -q "https://ampl.com/dl/open/bonmin/bonmin-linux64.zip"') - os.system('unzip -o -q bonmin-linux64') - else: - print("No procedure implemented to install bonmin ... ", end="") - return package_confirm("bonmin") - -def install_couenne(): - if package_found("couenne"): - return - if on_colab(): - print("Installing couenne on Google Colab via via zip file ... ", end="") - os.system('wget -N -q "https://ampl.com/dl/open/couenne/couenne-linux64.zip"') - os.system('unzip -o -q couenne-linux64') - else: - print("No procedure implemented to install couenne ... ", end="") - return package_confirm("couenne") - -def install_gecode(): - if package_found("gecode"): - return - if on_colab(): - print("Installing gecode on Google Colab via via zip file ... ", end="") - os.system('wget -N -q "https://ampl.com/dl/open/gecode/gecode-linux64.zip"') - os.system('unzip -o -q gecode-linux64') - else: - print("No procedure implemented to install gecode ... ", end="") - return package_confirm("gecode") - -def install_scip(): - if package_found("scip"): - return - - if on_colab(): - print("Installing scip on Google Colab via conda ... ", end="") - try: - import condacolab - except: - os.system("pip install -q condacolab") - import condacolab - condacolab.install() - os.system("conda install -y pyscipopt") - - return package_confirm("scip") - -def install_gurobi(): - try: - import gurobipy - except ImportError: - pass - else: - print("gurobi was previously installed") - return - - if on_colab(): - print("Installing gurobi on Google Colab via pip ... ", end="") - os.system("pip install gurobipy") - else: - print("Consult gurobi.com for installation procedures ... ", end="") - - try: - import gurobipy - print("installation successful") - return True - except ImportError: - print("installation failed") - return False - -def install_cplex(): - try: - import cplex - except ImportError: - pass - else: - print("cplex was previously installed") - return - - if on_colab(): - print("Installing cplex on Google Colab via pip ... ", end="") - os.system("pip install cplex") - else: - print("Consult ibm.com for installation procedures ... ", end="") - - try: - import cplex - print("installation successful") - return True - except ImportError: - print("installation failed") - return False - -def install_mosek(): - try: - import mosek.fusion - except ImportError: - pass - else: - print("mosek was previously installed") - return - - if on_colab(): - print("Installing mosek on Google Colab via pip ... ", end="") - os.system("pip install mosek") - else: - print("Consult docs.mosek.com for installation procedures ... ", end="") - - try: - import mosek.fusion - print("installation successful") - return True - except ImportError: - print("installation failed.") - return False - -def install_xpress(): - try: - import xpress - except ImportError: - pass - else: - print("Xpress was previously installed") - return - - if on_colab(): - print("Installing xpress on Google Colab via pip ... ", end="") - os.system("pip install xpress") - else: - print("Installing xpress via conda ... ", end="") - os.system("conda install -c fico-xpress xpress") - - try: - import xpress - print("installation successful") - return True - except ImportError: - print("installation failed") - return False -