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zChT;W)-))1cuCX*WSMZd#aL3ZAFHdYOP$=wU?4pQ*2Z-jLm)IU*kQOe0~h)#?^bUOV2CVLX34)9C7 zwrCMU__j}c(jJA0WOi@$G?v^%i^skIifBd1=Nvp?Ap!|C6rG|p1*2#^Lu4haAg#e= zGTU}yDQw^?@E-q#1V$P)+Cv%dFHk%RjPsZ+K|#EChu{~3)vDx_eN0Tu(axlI=XA}_ zXS#k`3KZjstY#9C3AUsJe>zYu=`6PNyzo20`c3JffMuYj&R|&=Vnm(B@A9}&y!$O| zZzR@LRVf>SVcxL97?g$T1ii)p;D~qrd=4(BETOq_HrC+d^!_8{_wc!M_g5Q3iyudF zEl7EHHF9DW(boVz7{V/dev/null 2>/dev/null\n", " !pip install highspy >/dev/null 2>/dev/null\n", - "\n", - " from pyomo.environ import SolverFactory\n", - " SOLVER = SolverFactory('appsi_highs')\n", - " \n", - "else:\n", - " from pyomo.environ import SolverFactory\n", - " SOLVER = SolverFactory('cbc')\n", - "\n", - "assert SOLVER.available(), f\"Solver {SOLVER} is not available.\"" + " \n", + "solver = 'appsi_highs'\n", + " \n", + "import pyomo.environ as pyo\n", + "SOLVER = pyo.SolverFactory(solver)\n", + " \n", + "assert SOLVER.available(), f\"Solver {solver} is not available.\"" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Requirement already satisfied: graphviz in /Users/jeff/opt/anaconda3/lib/python3.9/site-packages (0.20.1)\n" - ] - } - ], + "outputs": [], "source": [ - "!pip install graphviz --upgrade" + "import networkx as nx\n", + "import pandas as pd\n", + "import pyomo.environ as pyo\n", + "import numpy as np\n", + "import io" ] }, { @@ -91,8 +81,7 @@ "\n", "Needless to say, if a simple round-trip transaction like this reliably produced a net gain then there would many eager traders ready to take advantage of the situation. Trading situations offering a net gain with no risk are called arbitrage, and are the subject of intense interest by traders in the foreign exchange (forex) and crypto-currency markets around the globe.\n", "\n", - "As one might expect, arbitrage opportunities involving a simple round-trip between a pair of currencies are almost non-existent in real-world markets. When the do appear, they are easily detected and rapid and automated trading quickly exploit the situation. More complex arbitrage opportunities, however, can arise when working with three more currencies and a table of cross-currency exchange rates.\n", - "\n" + "As one might expect, arbitrage opportunities involving a simple round-trip between a pair of currencies are almost non-existent in real-world markets. When the do appear, they are easily detected and rapid and automated trading quickly exploit the situation. More complex arbitrage opportunities, however, can arise when working with three more currencies and a table of cross-currency exchange rates." ] }, { @@ -105,11 +94,11 @@ "\n", "Consider the following cross-currency matrix. \n", "\n", - "| i <- J | USD | EUR | JPY |\n", + "| i <-- j | USD | EUR | JPY |\n", "| :--- | :---: | :---: | :---: |\n", "| USD | 1.0 | 2.0 | 0.01 |\n", "| EUR | 0.5 | 1.0 | 0.0075 |\n", - "| JPY | 100.0 | 133 1/3 | 1.0 |\n", + "| JPY | 100.0 | 133.3 | 1.0 |\n", "\n", "\n", "Entry $a_{m, n}$ is the number units of currency $m$ received in exchange for one unit of currency $n$. We use the notation \n", @@ -129,7 +118,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 11, "metadata": { "colab": { "base_uri": "https://localhost:8080/", @@ -213,15 +202,13 @@ "name": "stdout", "output_type": "stream", "text": [ - "1.0\n", - "1.0\n", - "1.0\n" + "Net change factor of the transaction chain USD -> EUR -> USD is: 1.0\n", + "Net change factor of the transaction chain USD -> JPY -> USD is: 1.0\n", + "Net change factor of the transaction chain USD -> JPY -> USD is: 1.0\n" ] } ], "source": [ - "import pandas as pd\n", - "\n", "df = pd.DataFrame(\n", " [[1.0, 0.5, 100], [2.0, 1.0, 1 / 0.0075], [0.01, 0.0075, 1.0]],\n", " columns=[\"USD\", \"EUR\", \"JPY\"],\n", @@ -230,14 +217,15 @@ "\n", "display(df)\n", "\n", - "# USD -> EUR -> USD\n", - "print(df.loc[\"USD\", \"EUR\"] * df.loc[\"EUR\", \"USD\"])\n", - "\n", - "# USD -> JPY -> USD\n", - "print(df.loc[\"USD\", \"JPY\"] * df.loc[\"JPY\", \"USD\"])\n", - "\n", - "# EUR -> JPY -> EUR\n", - "print(df.loc[\"EUR\", \"JPY\"] * df.loc[\"JPY\", \"EUR\"])" + "print(\n", + " f\"Net gain factor of the currency exchange chain USD -> EUR -> USD is: {df.loc['USD', 'EUR'] * df.loc['EUR', 'USD']}\"\n", + ")\n", + "print(\n", + " f\"Net gain factor of the currency exchange chain USD -> JPY -> USD is: {df.loc['USD', 'JPY'] * df.loc['JPY', 'USD']}\"\n", + ")\n", + "print(\n", + " f\"Net gain factor of the currency exchangen USD -> JPY -> USD is: {df.loc['EUR', 'JPY'] * df.loc['JPY', 'EUR']}\"\n", + ")" ] }, { @@ -259,7 +247,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 13, "metadata": { "colab": { "base_uri": "https://localhost:8080/" @@ -283,7 +271,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "1.5\n" + "Net gain factor of the currency exchangen USD -> JPY -> EUR -> USD is: 1.5\n" ] } ], @@ -292,7 +280,9 @@ "J = \"JPY\"\n", "K = \"EUR\"\n", "\n", - "print(df.loc[I, K] * df.loc[K, J] * df.loc[J, I])" + "print(\n", + " f\"Net gain factor of the currency exchangen USD -> JPY -> EUR -> USD is: {df.loc[I, K] * df.loc[K, J] * df.loc[J, I]}\"\n", + ")" ] }, { @@ -312,11 +302,11 @@ "source": [ "## Modeling\n", "\n", - "The cross-currency table $A$ provides exchange rates among currencies. Entry $a_{i,j}$ in row $i$, column $j$ tells us how many units of currency $i$ are received in exchange for one unit of currency $j$. We'll use the notation $a_{i, j} = a_{i\\leftarrow j}$ to remind ourselves of this relationship.\n", + "The cross-currency table $A$ provides exchange rates among currencies. Entry $a_{i,j}$ in row $i$, column $j$ tells us how many units of currency $i$ are received in exchange for one unit of currency $j$. We use the notation $a_{i, j} = a_{i\\leftarrow j}$ to remind ourselves of this relationship.\n", "\n", "We start with $w_j(0)$ units of currency $j \\in N$, where $N$ is the set of all currencies in the data set. We consider a sequence of trades $t = 1, 2, \\ldots, T$ where $w_j(t)$ is the amount of currency $j$ on hand after completing trade $t$.\n", "\n", - "Each trade is executed in two phases. In the first phase an amount $x_{i\\leftarrow j}(t)$ of currency $j$ is committed for exchange to currency $i$. This allows a trade to include multiple currency transactions. After the commitment the unencumbered balance for currency $j$ must satisfy trading constraints. Each trade consists of simultaneous transactions in one or more currencies.\n", + "Each trade is executed in two phases. In the first phase an amount $x_{i\\leftarrow j}(t)$ of currency $j$ is committed for exchange to currency $i$. This allows a trade to include multiple currency transactions. After the commitment the unencumbered balance for currency $j$ must satisfy trading constraints. Each trade consists of simultaneous transactions in one or more currencies.\n", "\n", "$$w_j(t-1) - \\sum_{i\\ne j} x_{i\\leftarrow j}(t) \\geq 0$$\n", "\n", @@ -333,7 +323,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 26, "metadata": { "colab": { "base_uri": "https://localhost:8080/" @@ -357,49 +347,67 @@ "name": "stdout", "output_type": "stream", "text": [ + "Running HiGHS 1.5.3 [date: 2023-05-16, git hash: 594fa5a9d]\n", + "Copyright (c) 2023 HiGHS under MIT licence terms\n", "\n", "t = 0\n", "\n", - "w[USD,0] = 0.00 \n", - "w[EUR,0] = 100.00 \n", - "w[JPY,0] = 0.00 \n", + "w[USD,0] = 0.00000 \n", + "w[EUR,0] = 100.00000 \n", + "w[JPY,0] = 0.00000 \n", + "w[GBP,0] = 0.00000 \n", + "w[CHF,0] = 0.00000 \n", + "w[CAD,0] = 0.00000 \n", + "w[AUD,0] = 0.00000 \n", + "w[HKD,0] = 0.00000 \n", "\n", "t = 1\n", "\n", - "EUR -> USD Convert 100.0 EUR to 200.0 USD\n", + "EUR -> JPY Convert 100.00000 EUR to 13160.97000 JPY\n", "\n", - "w[USD,1] = 200.00 \n", - "w[EUR,1] = -0.00 \n", - "w[JPY,1] = 0.00 \n", + "w[USD,1] = 0.00000 \n", + "w[EUR,1] = 0.00000 \n", + "w[JPY,1] = 13160.97000 \n", + "w[GBP,1] = 0.00000 \n", + "w[CHF,1] = 0.00000 \n", + "w[CAD,1] = 0.00000 \n", + "w[AUD,1] = 0.00000 \n", + "w[HKD,1] = 0.00000 \n", "\n", "t = 2\n", "\n", - "USD -> JPY Convert 200.0 USD to 20000.0 JPY\n", + "JPY -> CAD Convert 13160.97000 JPY to 140.82238 CAD\n", "\n", - "w[USD,2] = 0.00 \n", - "w[EUR,2] = -0.00 \n", - "w[JPY,2] = 20000.00 \n", + "w[USD,2] = 0.00000 \n", + "w[EUR,2] = 0.00000 \n", + "w[JPY,2] = 0.00000 \n", + "w[GBP,2] = 0.00000 \n", + "w[CHF,2] = 0.00000 \n", + "w[CAD,2] = 140.82238 \n", + "w[AUD,2] = 0.00000 \n", + "w[HKD,2] = 0.00000 \n", "\n", "t = 3\n", "\n", - "JPY -> EUR Convert 20000.0 JPY to 150.0 EUR\n", + "CAD -> EUR Convert 140.82238 CAD to 100.44860 EUR\n", "\n", - "w[USD,3] = 0.00 \n", - "w[EUR,3] = 150.00 \n", - "w[JPY,3] = -0.00 \n", - "100.0\n", - "150.0\n" + "w[USD,3] = 0.00000 \n", + "w[EUR,3] = 100.44860 \n", + "w[JPY,3] = 0.00000 \n", + "w[GBP,3] = 0.00000 \n", + "w[CHF,3] = 0.00000 \n", + "w[CAD,3] = 0.00000 \n", + "w[AUD,3] = 0.00000 \n", + "w[HKD,3] = 0.00000 \n", + "\n", + "Initial wealth 100.00000 EUR\n", + "Final wealth 100.44860 EUR\n" ] } ], "source": [ - "import pyomo.environ as pyo\n", - "import numpy as np\n", - "from graphviz import Digraph\n", - "\n", - "\n", "def arbitrage(T, df, R=\"EUR\"):\n", - " m = pyo.ConcreteModel()\n", + " m = pyo.ConcreteModel(\"Forex Arbitrage\")\n", "\n", " # length of trading chain\n", " m.T0 = pyo.RangeSet(0, T)\n", @@ -450,19 +458,19 @@ " for i, j in m.ARCS:\n", " if m.x[i, j, t]() > 0:\n", " print(\n", - " f\"{j} -> {i} Convert {m.x[i, j, t]()} {j} to {df.loc[i,j]*m.x[i,j,t]()} {i}\"\n", + " f\"{j} -> {i} Convert {m.x[i, j, t]():11.5f} {j} to {df.loc[i,j]*m.x[i,j,t]():11.5f} {i}\"\n", " )\n", " print()\n", "\n", " for i in m.NODES:\n", - " print(f\"w[{i},{t}] = {m.w[i, t]():9.2f} \")\n", + " print(f\"w[{i},{t}] = {abs(m.w[i, t]()):11.5f} \")\n", "\n", " return m\n", "\n", "\n", "m = arbitrage(3, df, \"EUR\")\n", - "print(m.w[\"EUR\", 0]())\n", - "print(m.w[\"EUR\", 3]())" + "print(f\"\\nInitial wealth {m.w['EUR', 0]():11.5f} EUR\")\n", + "print(f\"Final wealth {m.w['EUR', 3]():11.5f} EUR\")" ] }, { @@ -476,7 +484,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 31, "metadata": {}, "outputs": [ { @@ -484,12 +492,12 @@ "output_type": "stream", "text": [ "\n", - " 100.0 EUR -> 200.0 USD -> 20000.0 JPY -> 150.0 EUR\n" + " 100.00000 USD -> 11861.00000 JPY -> 126.91270 CAD -> 100.45140 USD\n" ] }, { "data": { - "image/png": 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", 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", 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" ] @@ -499,16 +507,13 @@ } ], "source": [ - "import networkx as nx\n", - "\n", - "\n", "def display_graph(m):\n", " path = []\n", "\n", " for t in m.T0:\n", " for i in m.NODES:\n", " if m.w[i, t]() >= 1e-6:\n", - " path.append(f\"{m.w[i, t]()} {i}\")\n", + " path.append(f\"{m.w[i, t]():11.5f} {i}\")\n", " path = \" -> \".join(path)\n", " print(\"\\n\", path)\n", "\n", @@ -562,7 +567,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 32, "metadata": { "colab": { "base_uri": "https://localhost:8080/", @@ -738,16 +743,13 @@ "HKD\t7.8175\t8.6743\t0.0659\t10.2784\t8.3467\t6.1877\t5.7662\t-\n", "\"\"\"\n", "\n", - "import pandas as pd\n", - "import io\n", - "\n", "df = pd.read_csv(io.StringIO(bloomberg.replace(\"-\", \"1.0\")), sep=\"\\t\", index_col=0)\n", "display(df)" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 33, "metadata": { "colab": { "base_uri": "https://localhost:8080/", @@ -772,68 +774,73 @@ "name": "stdout", "output_type": "stream", "text": [ + "Running HiGHS 1.5.3 [date: 2023-05-16, git hash: 594fa5a9d]\n", + "Copyright (c) 2023 HiGHS under MIT licence terms\n", "\n", "t = 0\n", "\n", - "w[USD,0] = 100.00 \n", - "w[EUR,0] = 0.00 \n", - "w[JPY,0] = 0.00 \n", - "w[GBP,0] = 0.00 \n", - "w[CHF,0] = 0.00 \n", - "w[CAD,0] = 0.00 \n", - "w[AUD,0] = 0.00 \n", - "w[HKD,0] = 0.00 \n", + "w[USD,0] = 100.00000 \n", + "w[EUR,0] = 0.00000 \n", + "w[JPY,0] = 0.00000 \n", + "w[GBP,0] = 0.00000 \n", + "w[CHF,0] = 0.00000 \n", + "w[CAD,0] = 0.00000 \n", + "w[AUD,0] = 0.00000 \n", + "w[HKD,0] = 0.00000 \n", "\n", "t = 1\n", "\n", - "USD -> JPY Convert 100.0 USD to 11861.0 JPY\n", + "USD -> JPY Convert 100.00000 USD to 11861.00000 JPY\n", "\n", - "w[USD,1] = 0.00 \n", - "w[EUR,1] = 0.00 \n", - "w[JPY,1] = 11861.00 \n", - "w[GBP,1] = 0.00 \n", - "w[CHF,1] = 0.00 \n", - "w[CAD,1] = 0.00 \n", - "w[AUD,1] = 0.00 \n", - "w[HKD,1] = 0.00 \n", + "w[USD,1] = 0.00000 \n", + "w[EUR,1] = 0.00000 \n", + "w[JPY,1] = 11861.00000 \n", + "w[GBP,1] = 0.00000 \n", + "w[CHF,1] = 0.00000 \n", + "w[CAD,1] = 0.00000 \n", + "w[AUD,1] = 0.00000 \n", + "w[HKD,1] = 0.00000 \n", "\n", "t = 2\n", "\n", - "USD -> JPY Convert 1.0527111e-13 USD to 1.2486206357100001e-11 JPY\n", - "JPY -> CAD Convert 11861.0 JPY to 126.91269999999999 CAD\n", + "JPY -> CAD Convert 11861.00000 JPY to 126.91270 CAD\n", "\n", - "w[USD,2] = 0.00 \n", - "w[EUR,2] = 0.00 \n", - "w[JPY,2] = 0.00 \n", - "w[GBP,2] = -0.00 \n", - "w[CHF,2] = 0.00 \n", - "w[CAD,2] = 126.91 \n", - "w[AUD,2] = 0.00 \n", - "w[HKD,2] = 0.00 \n", + "w[USD,2] = 0.00000 \n", + "w[EUR,2] = 0.00000 \n", + "w[JPY,2] = 0.00000 \n", + "w[GBP,2] = 0.00000 \n", + "w[CHF,2] = 0.00000 \n", + "w[CAD,2] = 126.91270 \n", + "w[AUD,2] = 0.00000 \n", + "w[HKD,2] = 0.00000 \n", "\n", "t = 3\n", "\n", - "CAD -> USD Convert 126.9127 CAD to 100.45140205 USD\n", - "JPY -> EUR Convert 1.1066836e-11 JPY to 8.41079536e-14 EUR\n", + "CAD -> USD Convert 126.91270 CAD to 100.45140 USD\n", "\n", - "w[USD,3] = 100.45 \n", - "w[EUR,3] = 0.00 \n", - "w[JPY,3] = 0.00 \n", - "w[GBP,3] = 0.00 \n", - "w[CHF,3] = 0.00 \n", - "w[CAD,3] = 0.00 \n", - "w[AUD,3] = 0.00 \n", - "w[HKD,3] = 0.00 \n" + "w[USD,3] = 100.45140 \n", + "w[EUR,3] = 0.00000 \n", + "w[JPY,3] = 0.00000 \n", + "w[GBP,3] = 0.00000 \n", + "w[CHF,3] = 0.00000 \n", + "w[CAD,3] = 0.00000 \n", + "w[AUD,3] = 0.00000 \n", + "w[HKD,3] = 0.00000 \n", + "\n", + "Initial wealth: 100.00000 USD\n", + "Final wealth: 100.45140 USD\n" ] } ], "source": [ - "m = arbitrage(3, df, \"USD\")" + "m = arbitrage(3, df, \"USD\")\n", + "print(f\"\\nInitial wealth: {m.w['USD', 0]():11.5f} USD\")\n", + "print(f\"Final wealth: {m.w['USD', 3]():11.5f} USD\")" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 34, "metadata": {}, "outputs": [ { @@ -841,12 +848,12 @@ "output_type": "stream", "text": [ "\n", - " 100.0 USD -> 11861.0 JPY -> 126.9127 CAD -> 100.4514 USD\n" + " 100.00000 USD -> 11861.00000 JPY -> 126.91270 CAD -> 100.45140 USD\n" ] }, { "data": { - "image/png": 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", + "image/png": 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", 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" ] @@ -858,13 +865,6 @@ "source": [ "display_graph(m)" ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { @@ -883,7 +883,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.16" + "version": "3.10.10" } }, "nbformat": 4, diff --git a/_sources/notebooks/04/graph-coloring.ipynb b/_sources/notebooks/04/graph-coloring.ipynb index 460177f1..466afb07 100644 --- a/_sources/notebooks/04/graph-coloring.ipynb +++ b/_sources/notebooks/04/graph-coloring.ipynb @@ -17,7 +17,7 @@ "```{index} networkx\n", "```\n", "\n", - "# Scheduling as a graph coloring problem" + "# Exam room scheduling" ] }, { diff --git a/_sources/notebooks/05/markowitz_portfolio.ipynb b/_sources/notebooks/05/markowitz_portfolio.ipynb index 87f3aea6..168379b8 100644 --- a/_sources/notebooks/05/markowitz_portfolio.ipynb +++ b/_sources/notebooks/05/markowitz_portfolio.ipynb @@ -41,8 +41,7 @@ }, "outputs": [], "source": [ - "import sys\n", - "import os\n", + "import sys, os\n", "\n", "if 'google.colab' in sys.modules:\n", " !pip install idaes-pse --pre >/dev/null 2>/dev/null\n", @@ -165,7 +164,7 @@ } ], "source": [ - "# Specify the initial capital, the risk threshold, and the guaranteed return rate. \n", + "# Specify the initial capital, the risk threshold, and the guaranteed return rate.\n", "C = 1\n", "gamma = 1\n", "R = 1.01\n", @@ -179,14 +178,14 @@ "assert np.all(np.linalg.eigvals(Sigma) >= 0)\n", "\n", "# If you want to change the covariance matrix Sigma, ensure you input a semi-definite positive one.\n", - "# The easiest way to generate a random covariance matrix is first generating a random m x m matrix A \n", + "# The easiest way to generate a random covariance matrix is first generating a random m x m matrix A\n", "# and then taking the matrix A^T A (which is always semi-definite positive)\n", "# m = 3\n", "# A = np.random.rand(m, m)\n", "# Sigma = A.T @ A\n", "\n", + "\n", "def markowitz(gamma, mu, Sigma):\n", - " \n", " model = pyo.ConcreteModel(\"Markowitz portfolio optimization\")\n", "\n", " model.xtilde = pyo.Var(domain=pyo.NonNegativeReals)\n", @@ -205,13 +204,22 @@ " return sum(m.x[i] for i in range(n)) + m.xtilde == C\n", "\n", " result = pyo.SolverFactory(SOLVER).solve(model)\n", - " \n", + "\n", " return result, model\n", "\n", + "\n", "result, model = markowitz(gamma, mu, Sigma)\n", "\n", - "display(Markdown(f\"**Solver status:** *{result.solver.status}, {result.solver.termination_condition}*\"))\n", - "display(Markdown(f\"**Solution:** $\\\\tilde x = {model.xtilde.value:.3f}$, $x_1 = {model.x[0].value:.3f}$, $x_2 = {model.x[1].value:.3f}$, $x_3 = {model.x[2].value:.3f}$\"))\n", + "display(\n", + " Markdown(\n", + " f\"**Solver status:** *{result.solver.status}, {result.solver.termination_condition}*\"\n", + " )\n", + ")\n", + "display(\n", + " Markdown(\n", + " f\"**Solution:** $\\\\tilde x = {model.xtilde.value:.3f}$, $x_1 = {model.x[0].value:.3f}$, $x_2 = {model.x[1].value:.3f}$, $x_3 = {model.x[2].value:.3f}$\"\n", + " )\n", + ")\n", "display(Markdown(f\"**Maximizes objective value to:** ${model.objective():.2f}$\"))" ] }, @@ -241,17 +249,59 @@ } ], "source": [ - "gamma_values = [0.005, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1, 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.20, 0.25, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 4.75, 5, 5.25, 5.5]\n", + "gamma_values = [\n", + " 0.005,\n", + " 0.01,\n", + " 0.02,\n", + " 0.03,\n", + " 0.04,\n", + " 0.05,\n", + " 0.06,\n", + " 0.07,\n", + " 0.08,\n", + " 0.09,\n", + " 0.1,\n", + " 0.11,\n", + " 0.12,\n", + " 0.13,\n", + " 0.14,\n", + " 0.15,\n", + " 0.16,\n", + " 0.17,\n", + " 0.18,\n", + " 0.19,\n", + " 0.20,\n", + " 0.25,\n", + " 0.3,\n", + " 0.4,\n", + " 0.5,\n", + " 0.6,\n", + " 0.7,\n", + " 0.8,\n", + " 0.9,\n", + " 1,\n", + " 1.5,\n", + " 2,\n", + " 2.5,\n", + " 3,\n", + " 3.5,\n", + " 4,\n", + " 4.5,\n", + " 4.75,\n", + " 5,\n", + " 5.25,\n", + " 5.5,\n", + "]\n", "objective = []\n", "\n", - "plt.rcParams.update({'font.size': 14})\n", + "plt.rcParams.update({\"font.size\": 14})\n", "for gamma in gamma_values:\n", " _, model = markowitz(gamma, mu, Sigma)\n", - " objective.append(round(model.objective(),3))\n", + " objective.append(round(model.objective(), 3))\n", "\n", "plt.plot(gamma_values, objective, color=plt.cm.tab20c(0))\n", - "plt.xlabel(r'Risk threshold $\\gamma$')\n", - "plt.ylabel('Optimal objective value')\n", + "plt.xlabel(r\"Risk threshold $\\gamma$\")\n", + "plt.ylabel(\"Optimal objective value\")\n", "plt.tight_layout()\n", "plt.show()" ] diff --git a/_sources/notebooks/05/milk-pooling.ipynb b/_sources/notebooks/05/milk-pooling.ipynb index 895ae2f8..57dc3ac6 100644 --- a/_sources/notebooks/05/milk-pooling.ipynb +++ b/_sources/notebooks/05/milk-pooling.ipynb @@ -17,13 +17,13 @@ "```\n", "```{index} single: solver; cbc\n", "```\n", - "```{index} single: solver; couenne\n", + "```{index} single: solver; couenne, ipopt\n", "```\n", "# Milk pooling and blending\n", "\n", "Pooling and blending operations involve the \"pooling\" of various streams to create intermediate mixtures that are subsequently blended with other streams to meet final product specifications. These operations are common to the chemical processing and petroleum sectors where limited tankage may be available, or when it is necessary to transport materials by train, truck, or pipeline to remote blending terminals. Similar applications arise in agriculture, food, mining, wastewater treatment, and other industries.\n", "\n", - "This notebook considers a simple example of a wholesale milk distributor to show how **non-convexity** arises in the optimization of pooling and blending operations. Non-convexity is due to presence of **bilinear** terms that are the product of two decision variables where one is a scale-dependent **extensive** quantity measuring the amount or flow of a product, and the other is scale-independent **intensive** quantity such as product composition. The notebook then shows how to develop and solve a convex approximation of the problem, and finally demonstrates solution the use of [Couenne](https://github.com/coin-or/Couenne), a solver specifically designed to find global solutions to mixed integer nonlinear optimization (MINLO) problems." + "This notebook considers a simple example of a wholesale milk distributor to show how **non-convexity** arises in the optimization of pooling and blending operations. Non-convexity is due to presence of **bilinear** terms that are the product of two decision variables where one is a scale-dependent **extensive** quantity measuring the amount or flow of a product, and the other is scale-independent **intensive** quantity such as product composition. The notebook then shows how to develop and solve a convex approximation of the problem, and finally demonstrates solution the use of `ipotp`, a solver specifically designed to find global solutions to nonlinear optimization (NLO) problems." ] }, { @@ -35,17 +35,22 @@ }, "outputs": [], "source": [ - "# install Pyomo and solvers\n", - "import sys\n", - "import os\n", - "\n", - "SOLVER_LO = \"cbc\"\n", - "SOLVER_GNLO = \"couenne\"\n", - "\n", + "import sys, os\n", + " \n", "if 'google.colab' in sys.modules:\n", " !pip install idaes-pse --pre >/dev/null 2>/dev/null\n", " !idaes get-extensions --to ./bin \n", - " os.environ['PATH'] += ':bin'\n" + " os.environ['PATH'] += ':bin'\n", + "\n", + "import pyomo.environ as pyo\n", + "\n", + "solver_LO = 'appsi_highs'\n", + "SOLVER_LO = pyo.SolverFactory(solver_LO)\n", + "assert SOLVER_LO.available(), f\"Solver {solver_LO} is not available.\"\n", + "\n", + "solver_NLO = \"ipopt\"\n", + "SOLVER_NLO = pyo.SolverFactory(solver_NLO)\n", + "assert SOLVER_NLO.available(), f\"Solver {solver_NLO} is not available.\"" ] }, { @@ -68,19 +73,19 @@ "id": "c5123315-1824-4c68-a345-aee738d187d1", "metadata": {}, "source": [ - "## Problem: Pooling milk for wholesale blending and distribution\n", + "## Problem description: Pooling milk for wholesale blending and distribution\n", "\n", - "A bulk distributor supplies custom blends of milk to several customers. Each customer has specified a minimum fat content, a maximum price, and a maximum amount for the milk they wish to buy. The distributor sources raw milk from local farms. Each farm produces a milk with a known fat content and cost. \n", + "A bulk distributor supplies custom milk blends to several customers. Each customer has specified a minimum fat content, a maximum price, and a maximum amount of milk they wish to buy. The distributor sources raw milk from local farms. Each farm produces a milk with a known fat content and cost. \n", "\n", - "The distributor has recently identified more affordable sources raw milk from several distant farms. These distant farms produce milk grades that can be blend with milk from the local farms. However, the distributor only has one truck with a single tank available for transporting milk from the distant farms. As a result, milk from the distant farms must be combined in the tank before being transported to the blending station. This creates a \"pool\" of uniform composition which to be blended with local milk to meet customer requirements.\n", + "The distributor has recently identified more affordable sources raw milk from some remote farms. These remote farms produce milk grades that can be blended with milk from local farms. However, the distributor only has one truck with a single tank available to transport milk from the remote farms. As a result, milk from the remote farms must be mixed in the tank before being transported to the blending station. This creates a \"pool\" of uniform composition which to be blended with local milk to meet the customer's requirements.\n", "\n", - "The process is shown in the following diagram. The fat content and cost of raw milk is given for each farm. For each customer, data is given for the required milk fat content, price, and the maximum demand. The arrows indicate pooling and blending of raw milk supplies. Each arrow is labeled with the an amount of raw milk.\n", + "The process is shown in the following diagram. The fat content and cost of raw milk is given for each farm. For each customer, data is provided for the required milk fat content, price, and the maximum demand. Arrows indicate pooling and blending of raw milk supplies. Each arrow is labeled with the amount of raw milk.\n", "\n", "![](milk-pooling.png)\n", "\n", "What should the distributor do?\n", "\n", - "* Option 1. Do nothing. Continue operating the business as usual with local suppliers.\n", + "* Option 1. Do nothing and continue operating the business as usual with local suppliers.\n", "\n", "* Option 2. Buy a second truck to transport raw milk from the remote farms to the blending facility without pooling.\n", "\n", @@ -238,21 +243,25 @@ } ], "source": [ - "customers = pd.DataFrame({\n", - " \"Customer 1\": {\"min_fat\": 0.045, \"price\": 52.0, \"demand\": 6000.0},\n", - " \"Customer 2\": {\"min_fat\": 0.030, \"price\": 48.0, \"demand\": 2500.0},\n", - " \"Customer 3\": {\"min_fat\": 0.040, \"price\": 50.0, \"demand\": 4000.0},\n", - "}).T\n", - "\n", - "suppliers = pd.DataFrame({\n", - " \"Farm A\": {\"fat\": 0.045, \"cost\": 45.0, \"location\": \"local\"},\n", - " \"Farm B\": {\"fat\": 0.030, \"cost\": 42.0, \"location\": \"local\"},\n", - " \"Farm C\": {\"fat\": 0.033, \"cost\": 37.0, \"location\": \"remote\"},\n", - " \"Farm D\": {\"fat\": 0.050, \"cost\": 45.0, \"location\": \"remote\"}},\n", - " ).T\n", - "\n", - "local_suppliers = suppliers[suppliers[\"location\"]==\"local\"]\n", - "remote_suppliers = suppliers[suppliers[\"location\"]==\"remote\"]\n", + "customers = pd.DataFrame(\n", + " {\n", + " \"Customer 1\": {\"min_fat\": 0.045, \"price\": 52.0, \"demand\": 6000.0},\n", + " \"Customer 2\": {\"min_fat\": 0.030, \"price\": 48.0, \"demand\": 2500.0},\n", + " \"Customer 3\": {\"min_fat\": 0.040, \"price\": 50.0, \"demand\": 4000.0},\n", + " }\n", + ").T\n", + "\n", + "suppliers = pd.DataFrame(\n", + " {\n", + " \"Farm A\": {\"fat\": 0.045, \"cost\": 45.0, \"location\": \"local\"},\n", + " \"Farm B\": {\"fat\": 0.030, \"cost\": 42.0, \"location\": \"local\"},\n", + " \"Farm C\": {\"fat\": 0.033, \"cost\": 37.0, \"location\": \"remote\"},\n", + " \"Farm D\": {\"fat\": 0.050, \"cost\": 45.0, \"location\": \"remote\"},\n", + " },\n", + ").T\n", + "\n", + "local_suppliers = suppliers[suppliers[\"location\"] == \"local\"]\n", + "remote_suppliers = suppliers[suppliers[\"location\"] == \"remote\"]\n", "\n", "print(\"\\nCustomers\")\n", "display(customers)\n", @@ -268,7 +277,7 @@ "source": [ "## Option 1. Business as usual\n", "\n", - "The normal business of the milk distributor is to blend supplies from local farms to meet customer requirements. Let $L$ designate the set of local suppliers, and let $C$ designate the set of customers. Decision variable $z_{l, c}$ is the amount of milk from local supplier $l\\in L$ that is mixed into the blend sold to customer $c\\in C$.\n", + "The normal business of the milk distributor is to blend supplies from local farms to meet customer requirements. Let $L = \\{ A, B \\}$ designate the set of local suppliers, and let $C = \\{1,2,3\\}$ designate the set of customers. Decision variable $z_{l, c}$ is the amount of milk from local supplier $l\\in L$ that is mixed into the blend sold to customer $c\\in C$.\n", "\n", "The distributor's objectives is to maximize profit\n", "\n", @@ -288,11 +297,11 @@ "\\end{align*}\n", "$$\n", "\n", - "Let $\\text{fat}_l$ denote the fat content of the raw milke produced by farm $l$, and let $\\text{min_fat}_c$ denote the minimum fat content required by customer $c$, respectively. Assuming linear blending, the model becomes\n", + "Let $\\text{fat}_l$ denote the fat content of the raw milk produced by farm $l$, and let $\\text{fat}^{\\min}_c$ denote the minimum fat content required by customer $c$, respectively. Assuming linear blending, the model becomes\n", "\n", "$$\n", "\\begin{align*}\n", - "\\sum_{(l,c)\\ \\in\\ L \\times C} \\text{fat}_{l} z_{l,c} & \\geq \\text{min_fat}_{c} \\sum_{l\\in L} z_{l, c} & \\forall c \\in C\n", + "\\sum_{(l,c)\\ \\in\\ L \\times C} \\text{fat}_{l} \\cdot z_{l,c} & \\geq \\text{fat}^{\\min}_{c} \\sum_{l\\in L} z_{l, c} & \\forall c \\in C\n", "\\end{align*}\n", "$$\n", "\n", @@ -313,8 +322,7 @@ "text": [ "\n", "Profit = 81000.00\n", - "\n", - "Blending Plan\n" + "\n" ] }, { @@ -407,41 +415,55 @@ } ], "source": [ - "m = pyo.ConcreteModel()\n", + "m = pyo.ConcreteModel(\"Milk pooling v1\")\n", "\n", "# define sources and customers\n", - "m.L = pyo.Set(initialize=suppliers.index[suppliers[\"location\"]==\"local\"].tolist())\n", + "m.L = pyo.Set(initialize=suppliers.index[suppliers[\"location\"] == \"local\"].tolist())\n", "m.C = pyo.Set(initialize=customers.index.tolist())\n", "\n", "# define local -> customer flowrates\n", "m.z = pyo.Var(m.L * m.C, domain=pyo.NonNegativeReals)\n", "\n", + "\n", "@m.Objective(sense=pyo.maximize)\n", "def profit(m):\n", - " return sum(m.z[l, c]*(customers.loc[c, \"price\"] - suppliers.loc[l, \"cost\"]) for l, c in m.L * m.C)\n", + " return sum(\n", + " m.z[l, c] * (customers.loc[c, \"price\"] - suppliers.loc[l, \"cost\"])\n", + " for l, c in m.L * m.C\n", + " )\n", + "\n", "\n", "@m.Constraint(m.C)\n", "def demand(m, c):\n", " return sum(m.z[l, c] for l in m.L) <= customers.loc[c, \"demand\"]\n", "\n", + "\n", "@m.Constraint(m.C)\n", "def fat_content(m, c):\n", - " return sum(m.z[l, c] * suppliers.loc[l, \"fat\"] for l in m.L) >= sum(m.z[l, c] for l in m.L) * customers.loc[c, \"min_fat\"]\n", + " return (\n", + " sum(m.z[l, c] * suppliers.loc[l, \"fat\"] for l in m.L)\n", + " >= sum(m.z[l, c] for l in m.L) * customers.loc[c, \"min_fat\"]\n", + " )\n", + "\n", "\n", - "pyo.SolverFactory(SOLVER_LO).solve(m)\n", + "SOLVER_LO.solve(m)\n", "\n", - "# report results\n", "print(f\"\\nProfit = {m.profit():0.2f}\\n\")\n", "\n", - "# create dataframe of results\n", - "print(\"Blending Plan\")\n", - "Z = pd.DataFrame([[l, c, round(m.z[l, c](), 1)] for l, c in m.L * m.C], columns = [\"supplier\", \"customer\", \"\"])\n", + "Z = pd.DataFrame(\n", + " [[l, c, round(m.z[l, c](), 1)] for l, c in m.L * m.C],\n", + " columns=[\"supplier\", \"customer\", \"\"],\n", + ")\n", "Z = Z.pivot_table(index=\"customer\", columns=\"supplier\")\n", "Z[\"Total\"] = Z.sum(axis=1)\n", - "Z[\"fat content\"] = [sum(m.z[l, c]() * suppliers.loc[l, \"fat\"] for l in m.L)/sum(m.z[l, c]() for l in m.L) for c in m.C]\n", + "Z[\"fat content\"] = [\n", + " sum(m.z[l, c]() * suppliers.loc[l, \"fat\"] for l in m.L)\n", + " / sum(m.z[l, c]() for l in m.L)\n", + " for c in m.C\n", + "]\n", "Z[\"min_fat\"] = customers[\"min_fat\"]\n", "\n", - "display(Z)\n" + "display(Z)" ] }, { @@ -451,7 +473,7 @@ "source": [ "## Option 2. Buy an additional truck\n", "\n", - "The distributor can earn a profit of 81,000 using only local suppliers. Is is possible earn a higher profit by also sourcing raw milk from the remote suppliers?\n", + "As shown before, the distributor can earn a profit of 81,000 using only local suppliers. It is possible to earn a higher profit by also sourcing raw milk from the remote suppliers?\n", "\n", "Before considering pooling, the distributor may wish to know the maximum profit possible if raw milk from the remote suppliers could be blended just like local suppliers. This would require acquiring and operating a separate transport truck for each remote supplier, and is worth knowing if the additional profit would justify the additional expense.\n", "\n", @@ -575,7 +597,7 @@ } ], "source": [ - "m = pyo.ConcreteModel()\n", + "m = pyo.ConcreteModel(\"Milk pooling v2 (additional truck)\")\n", "\n", "# define sources and customers\n", "m.S = pyo.Set(initialize=suppliers.index.tolist())\n", @@ -584,28 +606,43 @@ "# define local -> customer flowrates\n", "m.z = pyo.Var(m.S * m.C, domain=pyo.NonNegativeReals)\n", "\n", + "\n", "@m.Objective(sense=pyo.maximize)\n", "def profit(m):\n", - " return sum(m.z[s, c]*(customers.loc[c, \"price\"] - suppliers.loc[s, \"cost\"]) for s, c in m.S * m.C)\n", + " return sum(\n", + " m.z[s, c] * (customers.loc[c, \"price\"] - suppliers.loc[s, \"cost\"])\n", + " for s, c in m.S * m.C\n", + " )\n", + "\n", "\n", "@m.Constraint(m.C)\n", "def demand(m, c):\n", " return sum(m.z[s, c] for s in m.S) <= customers.loc[c, \"demand\"]\n", "\n", + "\n", "@m.Constraint(m.C)\n", "def quality(m, c):\n", - " return sum(m.z[s, c] * suppliers.loc[s, \"fat\"] for s in m.S) >= sum(m.z[s, c] for s in m.S) * customers.loc[c, \"min_fat\"]\n", + " return (\n", + " sum(m.z[s, c] * suppliers.loc[s, \"fat\"] for s in m.S)\n", + " >= sum(m.z[s, c] for s in m.S) * customers.loc[c, \"min_fat\"]\n", + " )\n", + "\n", "\n", - "pyo.SolverFactory(SOLVER_LO).solve(m)\n", + "SOLVER_LO.solve(m)\n", "\n", - "# report results\n", "print(f\"\\nProfit = {m.profit():0.2f}\\n\")\n", "\n", - "# create dataframe of results\n", - "Z = pd.DataFrame([[s, c, round(m.z[s, c](), 1)] for s, c in m.S * m.C], columns = [\"supplier\", \"customer\", \"\"])\n", + "Z = pd.DataFrame(\n", + " [[s, c, round(m.z[s, c](), 1)] for s, c in m.S * m.C],\n", + " columns=[\"supplier\", \"customer\", \"\"],\n", + ")\n", "Z = Z.pivot_table(index=\"customer\", columns=\"supplier\")\n", "Z[\"Total\"] = Z.sum(axis=1)\n", - "Z[\"fat content\"] = [sum(m.z[s, c]() * suppliers.loc[s, \"fat\"] for s in m.S)/sum(m.z[s, c]() for s in m.S) for c in m.C]\n", + "Z[\"fat content\"] = [\n", + " sum(m.z[s, c]() * suppliers.loc[s, \"fat\"] for s in m.S)\n", + " / sum(m.z[s, c]() for s in m.S)\n", + " for c in m.C\n", + "]\n", "Z[\"min_fat\"] = customers[\"min_fat\"]\n", "\n", "display(Z)" @@ -632,7 +669,7 @@ "\n", "### Pooling problem\n", "\n", - "There are a several mathematical formulations of pooling problem in the academic literature. The formulation used here is called the \"p-parameterization\" where the pool composition represents a new decision variable $p$. The other additional decision variables are $x_r$ referring to the amount of raw milk purchased from remote supplier $r\\in R$, and $y_c$ which is the amount of the pooled milk included in the blend delivered to customer $c\\in C$.\n", + "There are several mathematical formulations of pooling problem in the academic literature. The formulation used here is called the **$p$-parameterization** where the pool composition represents a new decision variable $p$. The other additional decision variables are $x_r$ referring to the amount of raw milk purchased from remote supplier $r\\in R$, and $y_c$ which is the amount of the pooled milk included in the blend delivered to customer $c\\in C$.\n", "\n", "The profit objective is the difference between the income received for selling blended products and the cost of purchasing raw milk from local and remote suppliers.\n", "\n", @@ -663,7 +700,7 @@ "\n", "$$\n", "\\begin{align*}\n", - "\\sum_{r\\in R}\\text{fat}_{r}\\ x_{r} & = \\underbrace{p \\sum_{c\\in C} y_{c}}_{\\text{bilinear}}\n", + "\\sum_{r\\in R}\\text{fat}_{r}\\cdot x_{r} & = \\underbrace{p \\sum_{c\\in C} y_{c}}_{\\text{bilinear}}\n", "\\end{align*}\n", "$$\n", "\n", @@ -671,8 +708,8 @@ "\n", "$$\n", "\\begin{align*}\n", - "\\underbrace{p y_{c}}_{\\text{bilinear}} + \\sum_{(l,c)\\ \\in\\ L \\times C} \\text{fat}_{l}\\ z_{l,c}\n", - "& \\geq \\text{min_fat}_{c}\\ (\\sum_{l\\in L} z_{l, c} + y_{c})\n", + "\\underbrace{p y_{c}}_{\\text{bilinear}} + \\sum_{(l,c)\\ \\in\\ L \\times C} \\text{fat}_{l}\\cdot z_{l,c}\n", + "& \\geq \\text{fat}^{\\min}_c \\ (\\sum_{l\\in L} z_{l, c} + y_{c})\n", "& \\forall c \\in C\n", "\\end{align*}\n", "$$\n", @@ -689,17 +726,18 @@ "\n", "$$\n", "\\begin{align*}\n", - "\\max\\ \\text{Profit} = & \\sum_{(l,c)\\ \\in\\ L \\times C} (\\text{price}_c - \\text{cost}_l)\\ z_{l,c}\n", + "\\max \\quad & \\sum_{(l,c)\\ \\in\\ L \\times C} (\\text{price}_c - \\text{cost}_l)\\ z_{l,c}\n", "+ \\sum_{c\\in C} \\text{price}_c y_{c} - \\sum_{r\\in R} \\text{cost}_r x_{r} \\\\\n", - "\\text{s.t.}\\qquad & \\sum_{l\\in L} z_{l, c} + y_{c} \\leq \\text{demand}_{c} & \\forall c\\in C \\\\\n", + "\\text{s.t.}\\quad \n", + "& \\sum_{l\\in L} z_{l, c} + y_{c} \\leq \\text{demand}_{c} & \\forall c\\in C \\\\\n", "& \\sum_{r\\in R}x_{r} = \\sum_{c\\in C} y_{c} \\\\\n", - "& \\underbrace{p y_{c}}_{\\text{bilinear}} + \\sum_{(l,c)\\ \\in\\ L \\times C} \\text{fat}_{l}\\ z_{l,c} \\geq \\text{min_fat}_{c}\\ (\\sum_{l\\in L} z_{l, c} + y_{c}) & \\forall c \\in C \\\\\n", - "& \\sum_{r\\in R}\\text{fat}_{r}\\ x_{r} = \\underbrace{p \\sum_{c\\in C} y_{c}}_{\\text{bilinear}} \\\\\n", - "& p, x_r, y_c, z_{l, c} \\geq 0 & \\forall r\\in R, c\\in C, l\\in L \n", + "& \\underbrace{p y_{c}}_{\\text{bilinear}} + \\sum_{(l,c)\\ \\in\\ L \\times C} \\text{fat}_{l}\\cdot z_{l,c} \\geq \\text{fat}^{\\min}_c\\ (\\sum_{l\\in L} z_{l, c} + y_{c}) & \\forall c \\in C \\\\\n", + "& \\sum_{r\\in R}\\text{fat}_{r}\\cdot x_{r} = \\underbrace{p \\sum_{c\\in C} y_{c}}_{\\text{bilinear}} \\\\\n", + "& p, x_r, y_c, z_{l, c} \\geq 0 & \\forall r\\in R, c\\in C, l\\in L. \n", "\\end{align*}\n", "$$\n", "\n", - "Before attempting a solution to this problem, let's first consider the implications of the bilinear terms." + "Before attempting a solution to this problem, let us first consider the implications of the bilinear terms." ] }, { @@ -709,7 +747,7 @@ "source": [ "### Why are bilinear problems hard?\n", "\n", - "Bilinearity has a profound consequence on the nature of the optimization problem. To demonstrate this point, we consider a function obtained by fixing $p$ in the milk pooling problem and solving the resulting linear optimization problem for the maximum profit $f(p)$." + "Bilinearity has a profound consequence on the nature of the optimization problem. To explore this, we treat $p$ as a parameter and repeatedly solve the resulting linear problem for different values of $p$. " ] }, { @@ -721,14 +759,14 @@ }, "outputs": [], "source": [ - "# solve milk pooling problem for a fixed pool composition p\n", - "def f(p):\n", - " \n", - " m = pyo.ConcreteModel('Milk Pooling Model')\n", + "def milk_pooling_bilinear(p):\n", + " m = pyo.ConcreteModel(\"Milk pooling v3 (Bilinear formulation)\")\n", "\n", - " # define sources \n", - " m.L = pyo.Set(initialize=suppliers.index[suppliers[\"location\"]==\"local\"].tolist())\n", - " m.R = pyo.Set(initialize=suppliers.index[suppliers[\"location\"]==\"remote\"].tolist())\n", + " # define sources\n", + " m.L = pyo.Set(initialize=suppliers.index[suppliers[\"location\"] == \"local\"].tolist())\n", + " m.R = pyo.Set(\n", + " initialize=suppliers.index[suppliers[\"location\"] == \"remote\"].tolist()\n", + " )\n", "\n", " # define customers\n", " m.C = pyo.Set(initialize=customers.index.tolist())\n", @@ -737,34 +775,44 @@ " m.x = pyo.Var(m.R, domain=pyo.NonNegativeReals)\n", " m.y = pyo.Var(m.C, domain=pyo.NonNegativeReals)\n", " m.z = pyo.Var(m.L * m.C, domain=pyo.NonNegativeReals)\n", - " \n", + "\n", " m.p = pyo.Param(default=p)\n", "\n", " @m.Objective(sense=pyo.maximize)\n", " def profit(m):\n", - " return + sum(m.z[l, c]*(customers.loc[c, \"price\"] - suppliers.loc[l, \"cost\"]) for l, c in m.L * m.C) \\\n", - " + sum(m.y[c]*customers.loc[c, \"price\"] for c in m.C) \\\n", - " - sum(m.x[r]*suppliers.loc[r, \"cost\"] for r in m.R)\n", + " return (\n", + " +sum(\n", + " m.z[l, c] * (customers.loc[c, \"price\"] - suppliers.loc[l, \"cost\"])\n", + " for l, c in m.L * m.C\n", + " )\n", + " + sum(m.y[c] * customers.loc[c, \"price\"] for c in m.C)\n", + " - sum(m.x[r] * suppliers.loc[r, \"cost\"] for r in m.R)\n", + " )\n", "\n", " @m.Constraint(m.C)\n", " def customer_demand(m, c):\n", " return sum(m.z[l, c] for l in m.L) + m.y[c] <= customers.loc[c, \"demand\"]\n", - " \n", + "\n", " @m.Constraint()\n", - " def pool_balance(m,):\n", + " def pool_balance(\n", + " m,\n", + " ):\n", " return sum(m.x[r] for r in m.R) == sum(m.y[c] for c in m.C)\n", - " \n", + "\n", " @m.Constraint()\n", " def pool_quality(m):\n", - " return sum(suppliers.loc[r, \"fat\"] * m.x[r] for r in m.R) == m.p * sum(m.x[r] for r in m.R)\n", - " \n", + " return sum(suppliers.loc[r, \"fat\"] * m.x[r] for r in m.R) == m.p * sum(\n", + " m.x[r] for r in m.R\n", + " )\n", + "\n", " @m.Constraint(m.C)\n", " def customer_quality(m, c):\n", - " return m.p * m.y[c] + sum(suppliers.loc[l, \"fat\"] * m.z[l, c] for l in m.L) \\\n", - " >= customers.loc[c, \"min_fat\"] * (sum(m.z[l, c] for l in m.L) + m.y[c])\n", + " return m.p * m.y[c] + sum(\n", + " suppliers.loc[l, \"fat\"] * m.z[l, c] for l in m.L\n", + " ) >= customers.loc[c, \"min_fat\"] * (sum(m.z[l, c] for l in m.L) + m.y[c])\n", + "\n", + " SOLVER_LO.solve(m)\n", "\n", - " pyo.SolverFactory(SOLVER_LO).solve(m)\n", - " \n", " return m" ] }, @@ -778,9 +826,9 @@ "outputs": [ { "data": { - "image/png": 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\n", 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", 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" ] }, "metadata": {}, @@ -788,15 +836,16 @@ } ], "source": [ - "p_plot = np.linspace(0.025, 0.055, 200)\n", - "f_plot = [f(p).profit() for p in p_plot]\n", + "p_plot = np.linspace(0.025, 0.06, 200)\n", + "f_plot = [milk_pooling_bilinear(p).profit() for p in p_plot]\n", "\n", - "fig, ax = plt.subplots(figsize=(8, 3))\n", - "ax.plot(p_plot, f_plot)\n", - "ax.set_title(\"Milk Pooling\")\n", + "fig, ax = plt.subplots(figsize=(10, 5))\n", + "ax.plot(p_plot, f_plot, lw=2)\n", "ax.set_xlabel(\"Pool composition p\")\n", - "ax.set_ylabel(\"Profit f\")\n", + "ax.set_ylabel(\"Profit\")\n", "ax.grid(True)\n", + "plt.rcParams.update({\"font.size\": 14})\n", + "plt.tight_layout()\n", "plt.show()" ] }, @@ -823,7 +872,7 @@ "+ \\sum_{c\\in C} \\text{price}_c y_{c} - \\sum_{r\\in R} \\text{cost}_r x_{r} \\\\\n", "\\text{s.t.}\\qquad & \\sum_{l\\in L} z_{l, c} + y_{c} \\leq \\text{demand}_{c} & \\forall c\\in C \\\\\n", "& \\sum_{r\\in R}x_{r} = \\sum_{c\\in C} y_{c} \\\\\n", - "& w_c + \\sum_{(l,c)\\ \\in\\ L \\times C} \\text{fat}_{l}\\ z_{l,c} \\geq \\text{min_fat}_{c}\\ (\\sum_{l\\in L} z_{l, c} + y_{c}) & \\forall c \\in C \\\\\n", + "& w_c + \\sum_{(l,c)\\ \\in\\ L \\times C} \\text{fat}_{l}\\ z_{l,c} \\geq \\text{fat}^{\\min}_c \\ (\\sum_{l\\in L} z_{l, c} + y_{c}) & \\forall c \\in C \\\\\n", "& \\sum_{r\\in R}\\text{fat}_{r}\\ x_{r} = \\underbrace{p \\sum_{c\\in C} y_{c}}_{\\text{bilinear}} \\\\\n", "& w_c, x_r, y_c, z_{l, c} \\geq 0 & \\forall r\\in R, c\\in C, l\\in L \n", "\\end{align*}\n", @@ -880,12 +929,13 @@ "outputs": [], "source": [ "def milk_pooling_convex():\n", - " \n", - " m = pyo.ConcreteModel('Milk Pooling Model - Convex Approximation')\n", + " m = pyo.ConcreteModel(\"Milk pooling v3 (Convex approximation)\")\n", "\n", - " # define sources \n", - " m.L = pyo.Set(initialize=suppliers.index[suppliers[\"location\"]==\"local\"].tolist())\n", - " m.R = pyo.Set(initialize=suppliers.index[suppliers[\"location\"]==\"remote\"].tolist())\n", + " # define sources\n", + " m.L = pyo.Set(initialize=suppliers.index[suppliers[\"location\"] == \"local\"].tolist())\n", + " m.R = pyo.Set(\n", + " initialize=suppliers.index[suppliers[\"location\"] == \"remote\"].tolist()\n", + " )\n", "\n", " # define customers\n", " m.C = pyo.Set(initialize=customers.index.tolist())\n", @@ -894,47 +944,71 @@ " m.x = pyo.Var(m.R, domain=pyo.NonNegativeReals)\n", " m.y = pyo.Var(m.C, bounds=lambda m, c: (0, customers.loc[c, \"demand\"]))\n", " m.z = pyo.Var(m.L * m.C, domain=pyo.NonNegativeReals)\n", - " \n", + "\n", " # composition of the pool\n", - " m.p = pyo.Var(bounds=(suppliers.loc[m.R, \"fat\"].min(), suppliers.loc[m.R, \"fat\"].max()))\n", - " \n", + " m.p = pyo.Var(\n", + " bounds=(suppliers.loc[m.R, \"fat\"].min(), suppliers.loc[m.R, \"fat\"].max())\n", + " )\n", + "\n", " # w[c] to replace bilinear terms p * y[c]\n", " m.w = pyo.Var(m.C, domain=pyo.NonNegativeReals)\n", "\n", " @m.Objective(sense=pyo.maximize)\n", " def profit(m):\n", - " return + sum(m.z[l, c]*(customers.loc[c, \"price\"] - suppliers.loc[l, \"cost\"]) for l, c in m.L * m.C) \\\n", - " + sum(m.y[c]*customers.loc[c, \"price\"] for c in m.C) \\\n", - " - sum(m.x[r]*suppliers.loc[r, \"cost\"] for r in m.R)\n", - " \n", + " return (\n", + " +sum(\n", + " m.z[l, c] * (customers.loc[c, \"price\"] - suppliers.loc[l, \"cost\"])\n", + " for l, c in m.L * m.C\n", + " )\n", + " + sum(m.y[c] * customers.loc[c, \"price\"] for c in m.C)\n", + " - sum(m.x[r] * suppliers.loc[r, \"cost\"] for r in m.R)\n", + " )\n", + "\n", " # create a block of constraints for every customer\n", " @m.Block(m.C)\n", " def mccormick(b, c):\n", " m = b.model()\n", - " b.ll = pyo.Constraint(expr=m.w[c] >= m.y[c].lower * m.p + m.p.lower * m.y[c] - m.p.lower * m.y[c].lower)\n", - " b.hh = pyo.Constraint(expr=m.w[c] >= m.y[c].upper * m.p + m.p.upper * m.y[c] - m.p.upper * m.y[c].upper)\n", - " b.lh = pyo.Constraint(expr=m.w[c] <= m.y[c].upper * m.p + m.p.lower * m.y[c] - m.p.lower * m.y[c].upper)\n", - " b.hl = pyo.Constraint(expr=m.w[c] <= m.y[c].lower * m.p + m.p.upper * m.y[c] - m.p.upper * m.y[c].lower) \n", + " b.ll = pyo.Constraint(\n", + " expr=m.w[c]\n", + " >= m.y[c].lower * m.p + m.p.lower * m.y[c] - m.p.lower * m.y[c].lower\n", + " )\n", + " b.hh = pyo.Constraint(\n", + " expr=m.w[c]\n", + " >= m.y[c].upper * m.p + m.p.upper * m.y[c] - m.p.upper * m.y[c].upper\n", + " )\n", + " b.lh = pyo.Constraint(\n", + " expr=m.w[c]\n", + " <= m.y[c].upper * m.p + m.p.lower * m.y[c] - m.p.lower * m.y[c].upper\n", + " )\n", + " b.hl = pyo.Constraint(\n", + " expr=m.w[c]\n", + " <= m.y[c].lower * m.p + m.p.upper * m.y[c] - m.p.upper * m.y[c].lower\n", + " )\n", "\n", " @m.Constraint(m.C)\n", " def customer_demand(m, c):\n", " return sum(m.z[l, c] for l in m.L) + m.y[c] <= customers.loc[c, \"demand\"]\n", - " \n", + "\n", " @m.Constraint()\n", - " def pool_balance(m,):\n", + " def pool_balance(\n", + " m,\n", + " ):\n", " return sum(m.x[r] for r in m.R) == sum(m.y[c] for c in m.C)\n", - " \n", + "\n", " @m.Constraint()\n", " def pool_quality(m):\n", - " return sum(suppliers.loc[r, \"fat\"] * m.x[r] for r in m.R) == sum(m.w[c] for c in m.C)\n", - " \n", + " return sum(suppliers.loc[r, \"fat\"] * m.x[r] for r in m.R) == sum(\n", + " m.w[c] for c in m.C\n", + " )\n", + "\n", " @m.Constraint(m.C)\n", " def customer_quality(m, c):\n", - " return m.w[c] + sum(suppliers.loc[l, \"fat\"] * m.z[l, c] for l in m.L) \\\n", - " >= customers.loc[c, \"min_fat\"] * (sum(m.z[l, c] for l in m.L) + m.y[c])\n", + " return m.w[c] + sum(\n", + " suppliers.loc[l, \"fat\"] * m.z[l, c] for l in m.L\n", + " ) >= customers.loc[c, \"min_fat\"] * (sum(m.z[l, c] for l in m.L) + m.y[c])\n", + "\n", + " SOLVER_LO.solve(m)\n", "\n", - " pyo.SolverFactory(SOLVER_LO).solve(m)\n", - " \n", " return m" ] }, @@ -950,9 +1024,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "Milk Pooling Model - Convex Approximation\n", + "'Milk pooling v3 (Convex approximation)'\n", "\n", - "Pool composition = 0.04\n", + "Pool composition = 0.0400\n", "Profit = 111411.76\n", "\n", "Supplier Report\n", @@ -998,8 +1072,8 @@ " 45.0\n", " local\n", " 2500.0\n", - " 0.0000\n", - " 0.0\n", + " -0.0000\n", + " -0.0\n", " 0.0000\n", " 2500.0000\n", " 112500.0000\n", @@ -1046,7 +1120,7 @@ ], "text/plain": [ " fat cost location Customer 1 Customer 2 Customer 3 Pool \\\n", - "Farm A 0.045 45.0 local 2500.0 0.0000 0.0 0.0000 \n", + "Farm A 0.045 45.0 local 2500.0 -0.0000 -0.0 0.0000 \n", "Farm B 0.030 42.0 local 0.0 1029.4118 0.0 0.0000 \n", "Farm C 0.033 37.0 remote 0.0 0.0000 0.0 4852.9412 \n", "Farm D 0.050 45.0 remote 0.0 0.0000 0.0 4117.6471 \n", @@ -1120,7 +1194,7 @@ " 0.030\n", " 48.0\n", " 2500.0\n", - " 0.0\n", + " -0.0\n", " 1029.4118\n", " 1470.5882\n", " 2500.0\n", @@ -1132,7 +1206,7 @@ " 0.040\n", " 50.0\n", " 4000.0\n", - " 0.0\n", + " -0.0\n", " 0.0000\n", " 4000.0000\n", " 4000.0\n", @@ -1146,8 +1220,8 @@ "text/plain": [ " min_fat price demand Farm A Farm B Pool Amount \\\n", "Customer 1 0.045 52.0 6000.0 2500.0 0.0000 3500.0000 6000.0 \n", - "Customer 2 0.030 48.0 2500.0 0.0 1029.4118 1470.5882 2500.0 \n", - "Customer 3 0.040 50.0 4000.0 0.0 0.0000 4000.0000 4000.0 \n", + "Customer 2 0.030 48.0 2500.0 -0.0 1029.4118 1470.5882 2500.0 \n", + "Customer 3 0.040 50.0 4000.0 -0.0 0.0000 4000.0000 4000.0 \n", "\n", " fat delivered Income \n", "Customer 1 0.0421 312000.0 \n", @@ -1161,39 +1235,40 @@ ], "source": [ "def report_solution(m):\n", - " \n", " # Supplier report\n", " S = suppliers.copy()\n", " for l in m.L:\n", " for c in m.C:\n", - " S.loc[l, c] = m.z[l, c]() \n", + " S.loc[l, c] = m.z[l, c]()\n", " for r in m.R:\n", " S.loc[r, \"Pool\"] = m.x[r]()\n", " S = S.fillna(0)\n", " S[\"Amount\"] = S[m.C].sum(axis=1) + S[\"Pool\"]\n", - " S[\"Expense\"] = S[\"Amount\"]*S[\"cost\"]\n", + " S[\"Expense\"] = S[\"Amount\"] * S[\"cost\"]\n", "\n", - " \n", " # Customer report\n", " C = customers.copy()\n", " for c in m.C:\n", " for l in m.L:\n", " C.loc[c, l] = m.z[l, c]()\n", " for c in m.C:\n", - " C.loc[c, \"Pool\"] = m.y[c]() \n", + " C.loc[c, \"Pool\"] = m.y[c]()\n", " C = C.fillna(0)\n", " C[\"Amount\"] = C[m.L].sum(axis=1) + C[\"Pool\"]\n", - " C[\"fat delivered\"] = (sum(C[l]*S.loc[l, \"fat\"] for l in m.L) + C[\"Pool\"] * m.p())/C[\"Amount\"]\n", + " C[\"fat delivered\"] = (\n", + " sum(C[l] * S.loc[l, \"fat\"] for l in m.L) + C[\"Pool\"] * m.p()\n", + " ) / C[\"Amount\"]\n", " C[\"Income\"] = C[\"Amount\"] * C[\"price\"]\n", - " \n", + "\n", " print(m)\n", - " print(f\"\\nPool composition = {m.p()}\")\n", + " print(f\"\\nPool composition = {m.p():5.4f}\")\n", " print(f\"Profit = {m.profit():0.2f}\")\n", " print(f\"\\nSupplier Report\\n\")\n", " display(S.round(4))\n", " print(f\"\\nCustomer Report\\n\")\n", " display(C.round(4))\n", "\n", + "\n", "m_convex = milk_pooling_convex()\n", "report_solution(m_convex)" ] @@ -1216,19 +1291,9 @@ "outputs": [ { "data": { + "image/png": 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", "text/plain": [ - "Text(0.036, 106000, 'convex approximation')" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
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" ] }, "metadata": {}, @@ -1236,19 +1301,26 @@ } ], "source": [ - "fig, ax = plt.subplots(figsize=(8, 4))\n", - "ax.plot(p_plot, f_plot)\n", - "ax.set_title(\"Milk Pooling\")\n", + "fig, ax = plt.subplots(figsize=(9, 5))\n", + "ax.plot(p_plot, f_plot, lw=2)\n", "ax.set_xlabel(\"Pool composition p\")\n", "ax.set_ylabel(\"Profit\")\n", "ax.grid(True)\n", "\n", - "ax.plot(m_convex.p(), m_convex.profit(), 'ro', ms=10)\n", - "ax.axhline(m_convex.profit(), color='r', linestyle='--')\n", - "ax.axvline(m_convex.p(), color='r', linestyle='--')\n", - "ax.annotate(\"convex approximation\", xy=(m_convex.p(), m_convex.profit()),\n", - " xytext=(0.036, 106000), ha=\"right\", fontsize=14,\n", - " arrowprops=dict(shrink=0.1, width=1, headwidth=5))" + "ax.plot(m_convex.p(), m_convex.profit(), \"ro\", ms=10)\n", + "ax.axhline(m_convex.profit(), color=\"r\", linestyle=\"--\")\n", + "ax.axvline(m_convex.p(), color=\"r\", linestyle=\"--\")\n", + "ax.annotate(\n", + " \"convex approximation\",\n", + " xy=(m_convex.p(), m_convex.profit()),\n", + " xytext=(0.036, 106000),\n", + " ha=\"right\",\n", + " fontsize=14,\n", + " arrowprops=dict(shrink=0.1, width=1, headwidth=5, facecolor=\"black\"),\n", + ")\n", + "plt.rcParams.update({\"font.size\": 14})\n", + "plt.tight_layout()\n", + "plt.show()" ] }, { @@ -1274,68 +1346,14 @@ "metadata": { "tags": [] }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "m_est = f(m_convex.p())\n", - "\n", - "fig, ax = plt.subplots(figsize=(8, 4))\n", - "ax.plot(p_plot, f_plot)\n", - "ax.set_title(\"Milk Pooling\")\n", - "ax.set_xlabel(\"Pool composition p\")\n", - "ax.set_ylabel(\"Profit\")\n", - "ax.grid(True)\n", - "\n", - "ax.plot(m_convex.p(), m_convex.profit(), 'ro', ms=10)\n", - "ax.axhline(m_convex.profit(), color='r', linestyle='--')\n", - "ax.axvline(m_convex.p(), color='r', linestyle='--')\n", - "ax.annotate(\"convex approximation\", xy=(m_convex.p(), m_convex.profit()),\n", - " xytext=(0.036, 106000), ha=\"right\", fontsize=14,\n", - " arrowprops=dict(shrink=0.1, width=1, headwidth=5))\n", - "\n", - "ax.plot(m_est.p(), m_est.profit(), 'go', ms=10)\n", - "ax.axhline(m_est.profit(), color='g', linestyle='--')\n", - "ax.annotate(\"local maxima\", xy=(m_convex.p(), m_est.profit()),\n", - " xytext=(0.045, 105000), ha=\"left\", fontsize=14,\n", - " arrowprops=dict(shrink=0.1, width=1, headwidth=5))\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "8333e318-da8e-4fe8-b726-adebec04c23a", - "metadata": {}, - "source": [ - "The result shows the profit if the pooled milk transported from the remote farms has a fat content $p = 0.04$ them a profit of 100,088 is realized which is better than 81,000 earned for business as usual with just local suppliers, but falls short of the 122,441 earned if the remote milk supply could be transported without pooling.\n", - "\n", - "The following cell presents a full report of the solution." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "08283164-7c36-4788-bb74-d429af542cce", - "metadata": { - "tags": [] - }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Milk Pooling Model\n", + "'Milk pooling v3 (Bilinear formulation)'\n", "\n", - "Pool composition = 0.04\n", + "Pool composition = 0.0400\n", "Profit = 100088.24\n", "\n", "Supplier Report\n", @@ -1540,10 +1558,61 @@ }, "metadata": {}, "output_type": "display_data" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ - "report_solution(m_est)" + "m_est = milk_pooling_bilinear(m_convex.p())\n", + "report_solution(m_est)\n", + "\n", + "fig, ax = plt.subplots(figsize=(9, 5))\n", + "ax.plot(p_plot, f_plot, lw=2)\n", + "ax.set_xlabel(\"Pool composition p\")\n", + "ax.set_ylabel(\"Profit\")\n", + "ax.grid(True)\n", + "\n", + "ax.plot(m_convex.p(), m_convex.profit(), \"ro\", ms=10)\n", + "ax.axhline(m_convex.profit(), color=\"r\", linestyle=\"--\")\n", + "ax.axvline(m_convex.p(), color=\"r\", linestyle=\"--\")\n", + "ax.annotate(\n", + " \"convex approximation\",\n", + " xy=(m_convex.p(), m_convex.profit()),\n", + " xytext=(0.036, 106000),\n", + " ha=\"right\",\n", + " fontsize=14,\n", + " arrowprops=dict(shrink=0.1, width=1, headwidth=5, facecolor=\"black\"),\n", + ")\n", + "\n", + "ax.plot(m_est.p(), m_est.profit(), \"go\", ms=10)\n", + "ax.axhline(m_est.profit(), color=\"g\", linestyle=\"--\")\n", + "ax.annotate(\n", + " \"local max found\",\n", + " xy=(m_convex.p(), m_est.profit()),\n", + " xytext=(0.045, 105000),\n", + " ha=\"left\",\n", + " fontsize=14,\n", + " arrowprops=dict(shrink=0.1, width=1, headwidth=5, facecolor=\"black\"),\n", + ")\n", + "plt.rcParams.update({\"font.size\": 14})\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "8333e318-da8e-4fe8-b726-adebec04c23a", + "metadata": {}, + "source": [ + "The result shows the profit if the pooled milk transported from the remote farms has a fat content $p = 0.04$ them a profit of 100,088 is realized which is better than 81,000 earned for business as usual with just local suppliers, but falls short of the 122,441 earned if the remote milk supply could be transported without pooling." ] }, { @@ -1551,7 +1620,7 @@ "id": "8be412fa-564a-4b9a-8dda-f79fea889bab", "metadata": {}, "source": [ - "With regard to the practical impact, the results of using this particular convex approximation are mixed. The approximation successfully produced a value for the pool composition $p$ which would produce a profit of over 100,088. However, the reported value for $p$ was actually the smallest of the three local maxima for this problem. This discrepancy may have large consequences regarding the choice of suppliers." + "With regard to the practical impact, the results of using this particular convex approximation are mixed. The approximation successfully produced a value for the pool composition $p$ which would produce a profit of over $100088$. However, the reported value for $p$ was actually the smallest of the three local maxima for this problem. This discrepancy may have large consequences regarding the choice of suppliers." ] }, { @@ -1561,29 +1630,28 @@ "tags": [] }, "source": [ - "## Global Nonlinear Optimization (GNLO) solution with Couenne\n", + "## Nonlinear Optimization (NLO) solution with ipopt\n", "\n", - "The final version of this milk pooling model returns to the bilinear formulation with pool composition $p$ as a decision variable. The following Pyomo implementation needs to specify a solver capable of solving the resulting problem. This has been tested with nonlinear solvers [`ipopt`](https://github.com/coin-or/Ipopt) and [`couenne`](https://github.com/coin-or/Couenne). [Pre-compiled binaries for these solvers can be downloaded from AMPL](https://ampl.com/products/solvers/open-source/). " + "The final version of this milk pooling model returns to the bilinear formulation with pool composition $p$ as a decision variable. The following Pyomo implementation needs to specify a solver capable of solving the resulting problem, in this case we use the nonlinear solver [`ipopt`](https://github.com/coin-or/Ipopt)." ] }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 12, "id": "6472ae12-da84-430c-baaf-1310870d8050", "metadata": { "tags": [] }, "outputs": [], "source": [ - "import pyomo.environ as pyo\n", - "\n", - "def milk_pooling_bilinear():\n", - " \n", - " m = pyo.ConcreteModel('Milk Pooling Model - Bilinear')\n", + "def milk_pooling_bilinear_NLO(localmin=False):\n", + " m = pyo.ConcreteModel(\"Milk Pooling Model - Bilinear (NLO)\")\n", "\n", - " # define sources \n", - " m.L = pyo.Set(initialize=suppliers.index[suppliers[\"location\"]==\"local\"].tolist())\n", - " m.R = pyo.Set(initialize=suppliers.index[suppliers[\"location\"]==\"remote\"].tolist())\n", + " # define sources\n", + " m.L = pyo.Set(initialize=suppliers.index[suppliers[\"location\"] == \"local\"].tolist())\n", + " m.R = pyo.Set(\n", + " initialize=suppliers.index[suppliers[\"location\"] == \"remote\"].tolist()\n", + " )\n", "\n", " # define customers\n", " m.C = pyo.Set(initialize=customers.index.tolist())\n", @@ -1592,40 +1660,55 @@ " m.x = pyo.Var(m.R, domain=pyo.NonNegativeReals)\n", " m.y = pyo.Var(m.C, bounds=lambda m, c: (0, customers.loc[c, \"demand\"]))\n", " m.z = pyo.Var(m.L * m.C, domain=pyo.NonNegativeReals)\n", - " \n", " m.p = pyo.Var(bounds=(remote_suppliers[\"fat\"].min(), remote_suppliers[\"fat\"].max()))\n", "\n", " @m.Objective(sense=pyo.maximize)\n", " def profit(m):\n", - " return + sum(m.z[l, c]*(customers.loc[c, \"price\"] - suppliers.loc[l, \"cost\"]) for l, c in m.L * m.C) \\\n", - " + sum(m.y[c]*customers.loc[c, \"price\"] for c in m.C) \\\n", - " - sum(m.x[r]*suppliers.loc[r, \"cost\"] for r in m.R)\n", + " return (\n", + " +sum(\n", + " m.z[l, c] * (customers.loc[c, \"price\"] - suppliers.loc[l, \"cost\"])\n", + " for l, c in m.L * m.C\n", + " )\n", + " + sum(m.y[c] * customers.loc[c, \"price\"] for c in m.C)\n", + " - sum(m.x[r] * suppliers.loc[r, \"cost\"] for r in m.R)\n", + " )\n", "\n", " @m.Constraint(m.C)\n", " def customer_demand(m, c):\n", " return sum(m.z[l, c] for l in m.L) + m.y[c] <= customers.loc[c, \"demand\"]\n", - " \n", + "\n", " @m.Constraint()\n", - " def pool_balance(m,):\n", + " def pool_balance(\n", + " m,\n", + " ):\n", " return sum(m.x[r] for r in m.R) == sum(m.y[c] for c in m.C)\n", - " \n", + "\n", " @m.Constraint()\n", " def pool_quality(m):\n", - " return sum(suppliers.loc[r, \"fat\"] * m.x[r] for r in m.R) == m.p * sum(m.x[r] for r in m.R)\n", - " \n", + " return sum(suppliers.loc[r, \"fat\"] * m.x[r] for r in m.R) == m.p * sum(\n", + " m.x[r] for r in m.R\n", + " )\n", + "\n", " @m.Constraint(m.C)\n", " def customer_quality(m, c):\n", - " return m.p * m.y[c] + sum(suppliers.loc[l, \"fat\"] * m.z[l, c] for l in m.L) \\\n", - " >= customers.loc[c, \"min_fat\"] * (sum(m.z[l, c] for l in m.L) + m.y[c])\n", + " return m.p * m.y[c] + sum(\n", + " suppliers.loc[l, \"fat\"] * m.z[l, c] for l in m.L\n", + " ) >= customers.loc[c, \"min_fat\"] * (sum(m.z[l, c] for l in m.L) + m.y[c])\n", + "\n", + " # change ipopt options to find local minima instead of the global one\n", + " if localmin:\n", + " SOLVER_NLO.options[\"bound_frac\"] = 0.5\n", + " else:\n", + " SOLVER_NLO.options[\"bound_frac\"] = 0.01\n", + "\n", + " SOLVER_NLO.solve(m)\n", "\n", - " pyo.SolverFactory(SOLVER_GNLO).solve(m)\n", - " \n", - " return m\n" + " return m" ] }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 13, "id": "653ba91b-8c7d-4aaa-9478-0160db734594", "metadata": { "tags": [] @@ -1635,9 +1718,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "Milk Pooling Model - Bilinear\n", + "'Milk Pooling Model - Bilinear (NLO)'\n", "\n", - "Pool composition = 0.033\n", + "Pool composition = 0.0330\n", "Profit = 102833.33\n", "\n", "Supplier Report\n", @@ -1682,19 +1765,19 @@ " 0.045\n", " 45.0\n", " local\n", - " 6000.0\n", - " 0.0\n", - " 2333.3333\n", + " 6000.0001\n", + " -0.0\n", + " 2333.3334\n", " 0.0000\n", - " 8333.3333\n", - " 375000.0000\n", + " 8333.3334\n", + " 375000.0037\n", " \n", " \n", " Farm B\n", " 0.030\n", " 42.0\n", " local\n", - " 0.0\n", + " -0.0000\n", " 0.0\n", " -0.0000\n", " 0.0000\n", @@ -1706,19 +1789,19 @@ " 0.033\n", " 37.0\n", " remote\n", - " 0.0\n", + " 0.0000\n", " 0.0\n", " 0.0000\n", " 4166.6667\n", " 4166.6667\n", - " 154166.6667\n", + " 154166.6683\n", " \n", " \n", " Farm D\n", " 0.050\n", " 45.0\n", " remote\n", - " 0.0\n", + " 0.0000\n", " 0.0\n", " 0.0000\n", " -0.0000\n", @@ -1731,15 +1814,15 @@ ], "text/plain": [ " fat cost location Customer 1 Customer 2 Customer 3 Pool \\\n", - "Farm A 0.045 45.0 local 6000.0 0.0 2333.3333 0.0000 \n", - "Farm B 0.030 42.0 local 0.0 0.0 -0.0000 0.0000 \n", - "Farm C 0.033 37.0 remote 0.0 0.0 0.0000 4166.6667 \n", - "Farm D 0.050 45.0 remote 0.0 0.0 0.0000 -0.0000 \n", + "Farm A 0.045 45.0 local 6000.0001 -0.0 2333.3334 0.0000 \n", + "Farm B 0.030 42.0 local -0.0000 0.0 -0.0000 0.0000 \n", + "Farm C 0.033 37.0 remote 0.0000 0.0 0.0000 4166.6667 \n", + "Farm D 0.050 45.0 remote 0.0000 0.0 0.0000 -0.0000 \n", "\n", " Amount Expense \n", - "Farm A 8333.3333 375000.0000 \n", + "Farm A 8333.3334 375000.0037 \n", "Farm B -0.0000 -0.0000 \n", - "Farm C 4166.6667 154166.6667 \n", + "Farm C 4166.6667 154166.6683 \n", "Farm D -0.0000 -0.0000 " ] }, @@ -1793,51 +1876,51 @@ " 0.045\n", " 52.0\n", " 6000.0\n", - " 6000.0000\n", - " 0.0\n", + " 6000.0001\n", + " -0.0\n", " 0.0000\n", - " 6000.0\n", + " 6000.0001\n", " 0.045\n", - " 312000.0\n", + " 312000.0031\n", " \n", " \n", " Customer 2\n", " 0.030\n", " 48.0\n", " 2500.0\n", - " 0.0000\n", + " -0.0000\n", " 0.0\n", " 2500.0000\n", - " 2500.0\n", + " 2500.0000\n", " 0.033\n", - " 120000.0\n", + " 120000.0012\n", " \n", " \n", " Customer 3\n", " 0.040\n", " 50.0\n", " 4000.0\n", - " 2333.3333\n", + " 2333.3334\n", " -0.0\n", " 1666.6667\n", - " 4000.0\n", + " 4000.0000\n", " 0.040\n", - " 200000.0\n", + " 200000.0020\n", " \n", " \n", "\n", "" ], "text/plain": [ - " min_fat price demand Farm A Farm B Pool Amount \\\n", - "Customer 1 0.045 52.0 6000.0 6000.0000 0.0 0.0000 6000.0 \n", - "Customer 2 0.030 48.0 2500.0 0.0000 0.0 2500.0000 2500.0 \n", - "Customer 3 0.040 50.0 4000.0 2333.3333 -0.0 1666.6667 4000.0 \n", + " min_fat price demand Farm A Farm B Pool Amount \\\n", + "Customer 1 0.045 52.0 6000.0 6000.0001 -0.0 0.0000 6000.0001 \n", + "Customer 2 0.030 48.0 2500.0 -0.0000 0.0 2500.0000 2500.0000 \n", + "Customer 3 0.040 50.0 4000.0 2333.3334 -0.0 1666.6667 4000.0000 \n", "\n", - " fat delivered Income \n", - "Customer 1 0.045 312000.0 \n", - "Customer 2 0.033 120000.0 \n", - "Customer 3 0.040 200000.0 " + " fat delivered Income \n", + "Customer 1 0.045 312000.0031 \n", + "Customer 2 0.033 120000.0012 \n", + "Customer 3 0.040 200000.0020 " ] }, "metadata": {}, @@ -1845,9 +1928,9 @@ }, { "data": { - "image/png": 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\n", 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" ] }, "metadata": {}, @@ -1855,70 +1938,314 @@ } ], "source": [ - "m_global = milk_pooling_bilinear()\n", + "m_global = milk_pooling_bilinear_NLO()\n", + "report_solution(m_global)\n", "\n", - "fig, ax = plt.subplots(figsize=(8, 4))\n", - "ax.plot(p_plot, f_plot)\n", - "ax.set_title(\"Milk Pooling\")\n", + "fig, ax = plt.subplots(figsize=(9, 5))\n", + "ax.plot(p_plot, f_plot, lw=2)\n", "ax.set_xlabel(\"Pool composition p\")\n", "ax.set_ylabel(\"Profit\")\n", "ax.grid(True)\n", - "\n", - "ax.plot(m_convex.p(), m_convex.profit(), 'ro', ms=10)\n", - "ax.axhline(m_convex.profit(), color='r', linestyle='--')\n", - "ax.axvline(m_convex.p(), color='r', linestyle='--')\n", - "ax.annotate(\"convex approximation\", xy=(m_convex.p(), m_convex.profit()),\n", - " xytext=(0.036, 106000), ha=\"right\", fontsize=14,\n", - " arrowprops=dict(shrink=0.1, width=1, headwidth=5))\n", - "\n", - "ax.plot(m_est.p(), m_est.profit(), 'go', ms=10)\n", - "ax.axhline(m_est.profit(), color='g', linestyle='--')\n", - "ax.annotate(\"local maxima\", xy=(m_convex.p(), m_est.profit()),\n", - " xytext=(0.045, 105000), ha=\"left\", fontsize=14,\n", - " arrowprops=dict(shrink=0.1, width=1, headwidth=5))\n", - "\n", - "ax.plot(m_global.p(), m_global.profit(), 'bo', ms=10)\n", - "ax.axhline(m_global.profit(), color='b', linestyle='--')\n", - "ax.annotate(\"global maxima\", xy=(m_global.p(), m_global.profit()),\n", - " xytext=(0.025, 95000), ha=\"left\", fontsize=14,\n", - " arrowprops=dict(shrink=0.1, width=1, headwidth=5))\n", - "\n", - "report_solution(m_global)" + "ax.plot(m_global.p(), m_global.profit(), \"go\", ms=10)\n", + "ax.axhline(m_global.profit(), color=\"g\", linestyle=\"--\")\n", + "ax.annotate(\n", + " \"global max found\",\n", + " xy=(m_global.p(), m_global.profit()),\n", + " xytext=(0.035, 87000),\n", + " ha=\"left\",\n", + " fontsize=14,\n", + " arrowprops=dict(shrink=0.1, width=1, headwidth=5, facecolor=\"black\"),\n", + ")\n", + "plt.rcParams.update({\"font.size\": 14})\n", + "plt.tight_layout()\n", + "plt.show()" ] }, { "cell_type": "markdown", - "id": "7e32fe3b-7b1e-4714-a64d-b29da624a10b", + "id": "fadba4ca", "metadata": {}, "source": [ - "## Concluding Remarks\n", + "In this case, the convergence to the global optimum was pure luck. The way general non-linear optimization solvers work is that they begin from an initial solution and improve from then on, stopping when a set of conditions, known as the **KKT conditions**, is met. If we change the `ipopt` settings for how to pick the initial point, we can end up in one of the suboptimal local minima. \n", "\n", - "The solution for the bilinear pooling model reveals several features of the problem. \n", - "\n", - "* For the given parameters, pooling raw materials for shipment from remote suppliers yields the most profitable solution, but that solution is only possible because there are local suppliers to augment the pool blend to meet individual customer requirements. \n", + "Setting the `localmin` optional argument to `True`, we can trigger this behavior and obtain a solution that is not the global optimum." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "01a5f695", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "'Milk Pooling Model - Bilinear (NLO)'\n", + "\n", + "Pool composition = 0.0450\n", + "Profit = 101392.16\n", + "\n", + "Supplier Report\n", + "\n" + ] + }, + { + "data": { + "text/html": [ + "
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Customer 10.04552.06000.00.0-0.00006000.00016000.00010.045312000.0031
Customer 20.03048.02500.0-0.02500.0000-0.00002500.00000.030120000.0012
Customer 30.04050.04000.0-0.01333.33332666.66674000.00000.040200000.0020
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" + ], + "text/plain": [ + " min_fat price demand Farm A Farm B Pool Amount \\\n", + "Customer 1 0.045 52.0 6000.0 0.0 -0.0000 6000.0001 6000.0001 \n", + "Customer 2 0.030 48.0 2500.0 -0.0 2500.0000 -0.0000 2500.0000 \n", + "Customer 3 0.040 50.0 4000.0 -0.0 1333.3333 2666.6667 4000.0000 \n", + "\n", + " fat delivered Income \n", + "Customer 1 0.045 312000.0031 \n", + "Customer 2 0.030 120000.0012 \n", + "Customer 3 0.040 200000.0020 " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "m_global2 = milk_pooling_bilinear_NLO(localmin=True)\n", + "report_solution(m_global2)\n", "\n", - "* Customer 2 receives a blend that is 3.3% exceeding the requirement of 3%. This results in some \"give away\" of product quality in return for the economic benefits of pooling." + "fig, ax = plt.subplots(figsize=(9, 5))\n", + "ax.plot(p_plot, f_plot, lw=2)\n", + "ax.set_xlabel(\"Pool composition p\")\n", + "ax.set_ylabel(\"Profit\")\n", + "ax.grid(True)\n", + "ax.plot(m_global.p(), m_global.profit(), \"bo\", ms=10)\n", + "ax.axhline(m_global.profit(), color=\"b\", linestyle=\"--\")\n", + "ax.annotate(\n", + " \"global max\",\n", + " xy=(m_global.p(), m_global.profit()),\n", + " xytext=(0.0245, 96000),\n", + " ha=\"left\",\n", + " fontsize=14,\n", + " arrowprops=dict(shrink=0.1, width=1, headwidth=5, facecolor=\"black\"),\n", + ")\n", + "ax.plot(m_global2.p(), m_global2.profit(), \"go\", ms=10)\n", + "ax.axhline(m_global2.profit(), color=\"g\", linestyle=\"--\")\n", + "ax.annotate(\n", + " \"local max found\",\n", + " xy=(m_global2.p(), m_global2.profit()),\n", + " xytext=(0.0495, 93000),\n", + " ha=\"left\",\n", + " fontsize=14,\n", + " arrowprops=dict(shrink=0.1, width=1, headwidth=5, facecolor=\"black\"),\n", + ")\n", + "plt.rcParams.update({\"font.size\": 14})\n", + "plt.tight_layout()\n", + "plt.show()" ] }, { "cell_type": "markdown", - "id": "1ff20541-70e9-4ba9-a6e1-8c072a8964f1", - "metadata": { - "jp-MarkdownHeadingCollapsed": true, - "tags": [] - }, + "id": "7e32fe3b-7b1e-4714-a64d-b29da624a10b", + "metadata": {}, "source": [ - "## Suggested Exercises\n", - "\n", - "This simple model demonstrates practical issues that arise in modeling the non-convex problems. Take time explore the behavior of the model to parameter changes and the nature of the solution. \n", - "\n", - "1. Examine the model data and explain why the enhanced profits are observed only for a particular range of values in $p$.\n", + "## Concluding Remarks\n", "\n", - "2. Think carefully about the non-convex behavior observed in the plot of profit versus parameter $p$. Why are the local maxima located where they are, and how are they related to problem data? Test your hypothesis by changing the problem data. What happens when the product specification for Customer A is set equal to 0.045? What happens when it is set to 0.04?\n", + "The solution for the bilinear pooling model reveals several features of the problem. \n", "\n", - "3. Revise the Pyomo model using 'cbc', 'gurobi_direct', 'ipopt', and 'bonmin' to find a solution. Did you find a solver that could solve this nonlinear problem?\n", + "* For the given parameters, pooling raw materials for shipment from remote suppliers yields the most profitable solution, but that solution is only possible because there are local suppliers to augment the pool blend to meet individual customer requirements. \n", "\n", - "4. The above analysis assumed unlimited transport. If the truck turns out to have a limit of 4,000 units of milk, write the mathematical constraint necessary to introduce that limit into the model. Add that constraint to the Pyomo model and discuss the impact on profit." + "* Customer 2 receives a blend that is 3.3% exceeding the requirement of 3%. This results in some \"give away\" of product quality in return for the economic benefits of pooling." ] }, { @@ -1951,14 +2278,6 @@ "\n", "Applications for pooling and blending are probably underappreciated. In particular, what role might pooling and blending problems have in projects like the World Food Programme (WFP)?" ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1c8b31c5-f529-4dda-8b88-9a3100d39b0d", - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { @@ -1977,7 +2296,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.16" + "version": "3.10.10" } }, "nbformat": 4, diff --git a/genindex.html b/genindex.html index dca859ac..e97b2340 100644 --- a/genindex.html +++ b/genindex.html @@ -211,13 +211,13 @@
  • Minimum-Cost Flow Problem
  • Gasoline distribution
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  • Scheduling as a graph coloring problem
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  • Exam room scheduling
  • Cryptocurrency arbitrage search
  • Extra material: Energy dispatch problem
  • -
  • Forex Arbitrage
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  • Extra material: Forex Arbitrage
  • 5. Convex Optimization