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LINEAR PROGRAMING Mathematical optimization
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# LINEAR PROGRAMING Mathematical optimization"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import numpy as np\n",
"import scipy as sp\n",
"from pandas import DataFrame\n",
"import matplotlib as plt\n",
"import matplotlib.pyplot as plt\n",
"from matplotlib import pyplot\n",
"import seaborn\n",
"import warnings\n",
"import seaborn as sns\n",
"warnings.filterwarnings('ignore')\n",
"from sklearn.preprocessing import scale\n",
"import plotly.plotly as py\n",
"import plotly.graph_objs as go\n",
"from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot\n",
"from plotly.graph_objs import *\n",
"% matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# PL Introduction: representation and PuLP"
]
},
{
"attachments": {
"imagen.png": {
"image/png": "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"
}
},
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll plot the feasible region of this function and we'll evaluate this objective function in its vertices to compute the MAXIMA and MINIMA\n",
"\n",
"\n",
"![imagen.png](attachment:imagen.png)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### FEASIBLE REGION & Maxima/Minima vertices in a 2D PLOT"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x2b8ef79add8>"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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fz6xsA2cv22600rhWUJHHdOfr6WxyLZ1LrqdzyfV0nvyu5VGVku+9NHzsrSmhiES5Sb6F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\nSUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x2b8e9dafc88>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Construct lines\n",
"# x1 >= 0\n",
"x1 = np.linspace(0, 20, 2000)\n",
"\n",
"#Constraints\n",
"y0 =0\n",
"# 3x1 -x2 >=6\n",
"y1 = (3*x1 -6)\n",
"# x1 + x2 <=12\n",
"y2= (-x1+12)\n",
"# x1 -2x2 <=6\n",
"y3=(6-x1)/(-2)\n",
"\n",
"#Minima line\n",
"y7=(-44 + 5*x1) / 3\n",
"\n",
"#Maxima\n",
"y8=7.5\n",
"# Plot\n",
"\n",
"#MAXIMA \n",
"\n",
"VX=np.array([[10,4.5]])\n",
"VY=np.array([[2,7.5]])\n",
"\n",
"plt.subplots(figsize=(12, 12), facecolor='lightblue') \n",
"plt.plot(x1, y1, linewidth=5, label=r'$ 3(x1) - x2 \\geq 6 $')\n",
"plt.plot(x1, y2, linewidth=5, label=r'$ x1 + x2 \\leq 12 $')\n",
"plt.plot(x1, y3, linewidth=5, label=r'$ x1 -(2)x2 \\leq 6 $')\n",
"plt.plot(x1, y7, linewidth=2, label=r'MINIMA (10, 2 -> Z= -44)',color='cyan',linestyle='dashed')\n",
"plt.axhline(y=7.5,linewidth=2,label=r'MAXIMA (4.5, 7.5 -> Z= 0)',color='red',linestyle='dashed')\n",
"plt.axhline(y=0,linewidth=5, label=r'$ x1 \\geq 0 $', color='coral')\n",
"plt.axvline(x=0,linewidth=5, label=r'$ x2 \\geq 0 $', color='coral')\n",
"plt.plot(VX,VY,marker='X',markersize=15, color='red')\n",
"\n",
"plt.xlim((0, 20)) ; plt.ylim((0, 15)) ; plt.xlabel(r'$X1$', size=20) ; plt.ylabel(r'$X2$', size=20)\n",
"\n",
"# Fill feasible region\n",
"y5 = np.minimum(y1, y2)\n",
"y6 = np.maximum(y0, y3)\n",
"\n",
"plt.fill_between(x1, y5, y6, where=y5>y6, color='gold', alpha=0.4, hatch='flower')\n",
"plt.legend(bbox_to_anchor=(0.7, 0.9), loc=7, borderaxespad=0.)\n",
"\n",
"bbox_props = dict(boxstyle=\"larrow\", fc=\"gold\", ec=\"b\", lw=2, alpha=0.4)\n",
"t = plt.text(10, 5, \"Feasible Region\", ha=\"center\", va=\"center\", rotation=380,\n",
" size=15, bbox=bbox_props)\n",
"\n",
"bbox_props = dict(boxstyle=\"larrow\", fc=\"cyan\", ec=\"b\", lw=2, alpha=0.4)\n",
"t = plt.text(11.5, 2, \"Minima\", ha=\"center\", va=\"center\", rotation=365,\n",
" size=12, bbox=bbox_props)\n",
"\n",
"bbox_props = dict(boxstyle=\"larrow\", fc=\"red\", ec=\"b\", lw=2, alpha=0.4)\n",
"t = plt.text(6, 8, \"Maxima\", ha=\"center\", va=\"center\", rotation=380,\n",
" size=12, bbox=bbox_props)\n",
"\n",
"plt.rc('xtick', labelsize=18) ; plt.rc('ytick', labelsize=24) \n",
"plt.title('FEASIBLE REGION',size=20) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Both the MAXIMA and the MINIMA have to be contained inside the yellow feasible region in the graph above. We also know that in linear programming problems both, the MAXIMA and the MINIMA, have to lie at the the vertices of the feasible region.\n",
"\n",
"In our case example, there are only 4 vertices to our feasible region, so we have to find the solutions for each corner at our objective function to find our MAXIMA & MINIMA\n",
"\n",
"** OBJECTIVE FUNCION F(x1,x2)= -5x1+ 3x2**\n",
"\n",
"The four corners are between the lines:\n",
"\n",
"\n",
" - 1 Vertex: $ \\Rightarrow\\ $*x1=2, x2=0 $ \\Rightarrow\\ $ Z= -10* \n",
" \n",
"\n",
" - 2 Vertex: $ \\Rightarrow\\ $*x1=6, x2=0 $ \\Rightarrow\\ $ Z= -30*\n",
" \n",
" \n",
" - 3 Vertex: $ \\Rightarrow\\ $*x1=10, x2=2 $ \\Rightarrow\\ $ Z= -44* **<span style=\"color:red\">*MIN*</span>**\n",
" \n",
"\n",
" - 4 Vertex: $ \\Rightarrow\\ $*x1=4.5,x2=7.5 $ \\Rightarrow\\ $ Z= 0* **<span style=\"color:red\">*MAX*</span>** "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Optimization with the PuLP pyhton extension "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from pulp import * "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can instantiate a problem class, we’ll name it **“My LP problem”** and we’ll search our optimal MAXIMA & MINIMA\n",
"\n",
"** Decision variables definition & bounding :**\n",
"We model our decision variables using the LpVariable class. In our example, X1 & X2 have both a lower bound of 0. Upper bounds can be assigned using the upBound parameter."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"my_lp_problem = pulp.LpProblem(\"My LP Problem\", pulp.LpMaximize)\n",
"x1 = pulp.LpVariable('x1', lowBound=0, cat='Continuous')\n",
"x2 = pulp.LpVariable('x2', lowBound=0, cat='Continuous')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Objective function & constraints definition**\n",
"\n",
"The objective function and constraints are added using the += operator to our model.\n",
"\n",
"First we add the objective function and then the individual constraints."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Objective function\n",
"my_lp_problem += -5 * x1 + 3 * x2, \"Z\"\n",
"\n",
"# Constraints\n",
"my_lp_problem += 3 * x1 - x2 >= 6\n",
"my_lp_problem += x1 + x2 <= 12\n",
"my_lp_problem += x1 - 2 * x2 <= 6"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**We check our LP problem : **"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"My LP Problem:\n",
"MAXIMIZE\n",
"-5*x1 + 3*x2 + 0\n",
"SUBJECT TO\n",
"_C1: 3 x1 - x2 >= 6\n",
"\n",
"_C2: x1 + x2 <= 12\n",
"\n",
"_C3: x1 - 2 x2 <= 6\n",
"\n",
"VARIABLES\n",
"x1 Continuous\n",
"x2 Continuous"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"my_lp_problem"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**We check if the algorithm finds an Optimal solution : **"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'Optimal'"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"my_lp_problem.solve()\n",
"pulp.LpStatus[my_lp_problem.status]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The algorithm has 5 status references :\n",
"\n",
"\n",
" **Not Solved:** Status prior to solving the problem.\n",
" \n",
" **Optimal:** An optimal solution has been found.\n",
" \n",
" \n",
" **Infeasible:** There are no feasible solutions (e.g. if you set the constraints x1 <= 5 and x2 >=8).\n",
" \n",
" **Unbounded:** The constraints are not bounded, maximising the solution will tend towards infinity (e.g. if the only constraint was x >= 3).\n",
" \n",
" **Undefined:** The optimal solution may exist but may not have been found."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now view our maximal variable values and the maximum value of Z. We can use the varValue method to retrieve the values of our variables X1 and X2, and the pulp.value function to view the maximum value of the objective function."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Optimal Result:\n",
"x1 = 4.5\n",
"x2 = 7.5\n",
"Total Maxima:\n",
"0.0\n"
]
}
],
"source": [
"print (\"Optimal Result:\")\n",
"for variable in my_lp_problem.variables():\n",
" print (variable.name, \"=\", variable.varValue)\n",
"print (\"Total Maxima:\")\n",
"print (value(my_lp_problem.objective))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Minima \n",
"We' ll follow the same steps to compute the minima (just need to introduce pulp.LpMinimize)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"my_lp_problem = pulp.LpProblem(\"My LP Problem\", pulp.LpMinimize)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Objective function\n",
"my_lp_problem += -5 * x1 + 3 * x2, \"Z\"\n",
"\n",
"# Constraints\n",
"my_lp_problem += 3 * x1 - x2 >= 6\n",
"my_lp_problem += x1 + x2 <= 12\n",
"my_lp_problem += x1 - 2 * x2 <= 6"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"My LP Problem:\n",
"MINIMIZE\n",
"-5*x1 + 3*x2 + 0\n",
"SUBJECT TO\n",
"_C1: 3 x1 - x2 >= 6\n",
"\n",
"_C2: x1 + x2 <= 12\n",
"\n",
"_C3: x1 - 2 x2 <= 6\n",
"\n",
"VARIABLES\n",
"x1 Continuous\n",
"x2 Continuous"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"my_lp_problem"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'Optimal'"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"my_lp_problem.solve()\n",
"pulp.LpStatus[my_lp_problem.status]"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Optimal Result:\n",
"x1 = 10.0\n",
"x2 = 2.0\n",
"Total Minima:\n",
"-44.0\n"
]
}
],
"source": [
"print (\"Optimal Result:\")\n",
"for variable in my_lp_problem.variables():\n",
" print (variable.name, \"=\", variable.varValue)\n",
"print (\"Total Minima:\")\n",
"print (value(my_lp_problem.objective))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Optimization with Scipy"
]
},
{
"attachments": {
"imagen.png": {
"image/png": "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"
}
},
"cell_type": "markdown",
"metadata": {},
"source": [
"![imagen.png](attachment:imagen.png)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With the scipy.optimize.linprog command we can minimize a linear objective function subject to linear equality and inequality constraints.\n",
"\n",
"**Minimize: c^T * x **\n",
"\n",
"**Subject to: A_ub * x <= b_ub\n",
" A_eq * x == b_eq **"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from scipy.optimize import linprog"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Optimization terminated successfully.\n",
" Current function value: -44.000000 \n",
" Iterations: 3\n"
]
}
],
"source": [
"c = [-5, 3] #Our objective function\n",
"A = [[-3, 1], [1, 1],[1,-2]] # Constrains coefficients\n",
"b = [-6, 12,6] # Independent terms of the cnstraint equations \n",
"x0_bounds = (0, None)\n",
"x1_bounds = (0, None)\n",
"res = linprog(c, A_ub=A, b_ub=b, bounds=(x0_bounds, x1_bounds),options={\"disp\": True})"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" fun: -44.0\n",
" message: 'Optimization terminated successfully.'\n",
" nit: 3\n",
" slack: array([ 22., 0., 0.])\n",
" status: 0\n",
" success: True\n",
" x: array([ 10., 2.])\n"
]
}
],
"source": [
"print(res)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Maximize \n",
"\n",
"We know that in order to find our MAXIMA we just have to apply a **-** (to our objective function coefficients):"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Optimization terminated successfully.\n",
" Current function value: -0.000000 \n",
" Iterations: 2\n"
]
}
],
"source": [
"c = [5, -3] #Our objective function with (-)\n",
"A = [[-3, 1], [1, 1],[1,-2]] #constrains coefficients\n",
"b = [-6, 12,6] #independent terms\n",
"x0_bounds = (0, None)\n",
"x1_bounds = (0, None)\n",
"res = linprog(c, A_ub=A, b_ub=b, bounds=(x0_bounds, x1_bounds),options={\"disp\": True})"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" fun: -1.7763568394002505e-15\n",
" message: 'Optimization terminated successfully.'\n",
" nit: 2\n",
" slack: array([ 0. , 16.5, 0. ])\n",
" status: 0\n",
" success: True\n",
" x: array([ 4.5, 7.5])\n"
]
}
],
"source": [
"print(res)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Optimize Sales of 2 products (X1/X2 = sales in Kg)\n",
"\n",
"We have to maximize the profit of 2 products \n",
"\n",
"- X1= Product 1 \n",
"- X2= Product 2 \n",
"\n",
"Our production chain uses two main components (C1 / C2). \n",
"\n",
"- Each Kg of X1 requires 1 Kg of C1 and 0.5 of C2.\n",
"\n",
"- Each Kg of X2 requires 1 Kg of C1 and 0.25 of C2.\n",
"\n",
"- Each Kg sold of X1 generates a profit of 0.5€\n",
"\n",
"- Each Kg sold of X2 generates a profit of 0.4€ \n",
"\n",
"Our daily availability is 175Kg for C1 & 60Kg for C2.\n",
"\n",
"Our labour productivuty & capital capacity restricts our production limit to a daily maximum of 140Kg of X1 & 135Kg of X2.\n",
"\n",
"| Product | Requirement of C1 | Requirement of C2 | Profit | Production limit | \n",
"|:- | :- | :- | :- | :- | \n",
"|X1| 1Kg | 0.5Kg | 0.5€KG | 140Kg |\n",
"|X2| 1Kg | 0.25Kg | 0.4€KG | 135Kg |\n",
"\n",
"\n",
"** Objective function : **\n",
"\n",
"**5 * x1 + 4 * x2, \"Z\" **\n",
"\n",
"Constraints :\n",
"\n",
"- x1 + x2 <= 175\n",
"- 0.5x1 + 0.25x2 <= 60\n",
"- x1<=140 \n",
"- x2 <=135 \n",
"- X1>=0 \n",
"- X2>=0"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Maximize the profits :"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"my_lp_problem = pulp.LpProblem(\"My LP Problem\", pulp.LpMaximize)\n",
"x1 = pulp.LpVariable('x1', lowBound=0, upBound=140, cat='Continuous')\n",
"x2 = pulp.LpVariable('x2', lowBound=0, upBound=135, cat='Continuous')\n",
"\n",
"# Objective function\n",
"my_lp_problem += 5 * x1 + 4 * x2, \"Z\"\n",
"\n",
"# Constraints\n",
"my_lp_problem += x1 + x2 <= 175\n",
"my_lp_problem += 0.5*x1 + 0.25*x2 <= 60"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"My LP Problem:\n",
"MAXIMIZE\n",
"5*x1 + 4*x2 + 0\n",
"SUBJECT TO\n",
"_C1: x1 + x2 <= 175\n",
"\n",
"_C2: 0.5 x1 + 0.25 x2 <= 60\n",
"\n",
"VARIABLES\n",
"x1 <= 140 Continuous\n",
"x2 <= 135 Continuous"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"my_lp_problem"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'Optimal'"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"my_lp_problem.solve()\n",
"pulp.LpStatus[my_lp_problem.status]"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Optimal Result:\n",
"x1 = 65.0\n",
"x2 = 110.0\n",
"Total Maximum production:\n",
"765.0\n"
]
}
],
"source": [
"print (\"Optimal Result:\")\n",
"for variable in my_lp_problem.variables():\n",
" print (variable.name, \"=\", variable.varValue)\n",
"print (\"Total Maximum production:\")\n",
"print (value(my_lp_problem.objective))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**We can conclude that with the given constraints our profits will be maximized when we produce 65KG of the product 1 & 110KG of the product 2**"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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CyC/tL9jD/oI9Ee/3y0AKh1/iByIvf1Rdpmly0e338MI9v2XhjE858exhtO9xfFn74Zb4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kxLC2fpwmQ0Tcdud2yLfuzjC9m4bjp+viYOF1bz4j+PDY8hSY5x5mXHEhMViKbrdPdY6Ogc8Mgc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\nrOE+mNmVAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x2b8f030e438>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Construct lines\n",
"# x1 >= 0\n",
"x1 = np.linspace(0, 300, 1050)\n",
"\n",
"y0=140 + x1*0\n",
"y1=135 + x1*0\n",
"y2 =(175- x1) \n",
"y3= (240 -2*x1)\n",
"\n",
"# Make plot \n",
"plt.subplots(figsize=(10, 10),facecolor='lightblue')\n",
"plt.plot(x1, y2, linewidth=5,color='darkcyan')\n",
"plt.plot(x1, y3, linewidth=5, color='lightblue')\n",
"plt.plot(x1, y1, linewidth=5, color='orange')\n",
"plt.plot(y0,x1, linewidth=5, color='green') \n",
"\n",
"VX=65\n",
"VY=110\n",
"plt.plot(VX,VY, marker='X',markersize=15, color='magenta')\n",
"\n",
"plt.xlim((0, 250)); plt.ylim((0, 250)); plt.xlabel(r'$X1$', size=20) ;plt.ylabel(r'$X2$', size=20)\n",
"plt.rc('xtick', labelsize=18) ;plt.rc('ytick', labelsize=20)\n",
"plt.title('FEASIBLE REGION',size=20) \n",
"\n",
"bbox_props = dict(boxstyle=\"larrow\", fc=\"cyan\", ec=\"b\", lw=2, alpha=0.8)\n",
"t = plt.text(105, 135, \"Minima {x1=65 , x2=110}\", ha=\"center\", va=\"center\", rotation=390,\n",
" size=14, bbox=bbox_props)\n",
"\n",
"bbox_props = dict(boxstyle=\"round\", fc=\"gold\", ec=\"b\", lw=2, alpha=0.4)\n",
"t = plt.text(50, 65, \"Feasible Region\", ha=\"center\", va=\"center\", rotation=300,\n",
" size=36, bbox=bbox_props)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Warehouse logistics management : 3 cities & 2 warehouses "
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"City = [{'Cost_€_City1':350, 'Cost_€_City2':292, 'Cost_€_City3':415},\n",
" {'Cost_€_City1':265, 'Cost_€_City2':400, 'Cost_€_City3':330}]\n",
"i=['Warehouse 1','Warehouse 2']\n",
"df = pd.DataFrame(City, index=i)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Transport costs per truck from these 3 cities to our warehouses :"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style>\n",
" .dataframe thead tr:only-child th {\n",
" text-align: right;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: left;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Cost_€_City1</th>\n",
" <th>Cost_€_City2</th>\n",
" <th>Cost_€_City3</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>Warehouse 1</th>\n",
" <td>350</td>\n",
" <td>292</td>\n",
" <td>415</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Warehouse 2</th>\n",
" <td>265</td>\n",
" <td>400</td>\n",
" <td>330</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Cost_€_City1 Cost_€_City2 Cost_€_City3\n",
"Warehouse 1 350 292 415\n",
"Warehouse 2 265 400 330"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This objective function will allow us to minimze the total cost of the transport \n",
"\n",
"**O.F. Min (X1A,X1B,X2A,X2B,X3A,X3B) = 350X1A + 265X1B +295X2A + 400X2B + 415X3A+330X3B**\n",
"\n",
"*Restrictions of minimum transport needs for each city:*\n",
"\n",
"- R1 : X1A + X1B >=15\n",
"- R2: X2A+ X2B >=15 \n",
"- R3: X3A + X3B >=12\n",
"\n",
"*Restrictions of maximum capacity of our warehouses :*\n",
"\n",
"- R4: X1A + X2A + X3A <= 25\n",
"- R5: X1B + X2B + X3B <= 20\n",
"\n",
"- R6: X1A,X1B,X2A,X2B,X3A,X3B >=0"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Our model\n",
"\n",
"my_lp_problem = pulp.LpProblem(\"My LP Problem\", pulp.LpMinimize)\n",
"x1a = pulp.LpVariable('x1a', lowBound=0, cat='Continuous')\n",
"x1b = pulp.LpVariable('x1b', lowBound=0, cat='Continuous')\n",
"x2a = pulp.LpVariable('x2a', lowBound=0, cat='Continuous')\n",
"x2b = pulp.LpVariable('x2b', lowBound=0, cat='Continuous')\n",
"x3a = pulp.LpVariable('x3a', lowBound=0, cat='Continuous')\n",
"x3b = pulp.LpVariable('x3b', lowBound=0, cat='Continuous')\n",
"\n",
"# Objective function\n",
"my_lp_problem += 350*x1a + 265*x1b +295*x2a + 400*x2b + 415*x3a +330*x3b, \"Z\"\n",
"\n",
"# Constraints\n",
"my_lp_problem += x1a + x1b >=15\n",
"my_lp_problem += x2a + x2b >= 15\n",
"my_lp_problem += x3a + x3b >=12\n",
"my_lp_problem += x1a + x2a + x3a <=25\n",
"my_lp_problem += x1b + x2b + x3b <=20"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"My LP Problem:\n",
"MINIMIZE\n",
"350*x1a + 265*x1b + 295*x2a + 400*x2b + 415*x3a + 330*x3b + 0\n",
"SUBJECT TO\n",
"_C1: x1a + x1b >= 15\n",
"\n",
"_C2: x2a + x2b >= 15\n",
"\n",
"_C3: x3a + x3b >= 12\n",
"\n",
"_C4: x1a + x2a + x3a <= 25\n",
"\n",
"_C5: x1b + x2b + x3b <= 20\n",
"\n",
"VARIABLES\n",
"x1a Continuous\n",
"x1b Continuous\n",
"x2a Continuous\n",
"x2b Continuous\n",
"x3a Continuous\n",
"x3b Continuous"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"my_lp_problem"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'Optimal'"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"my_lp_problem.solve()\n",
"pulp.LpStatus[my_lp_problem.status]"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Optimal Result:\n",
"x1a = 7.0\n",
"x1b = 8.0\n",
"x2a = 15.0\n",
"x2b = 0.0\n",
"x3a = 0.0\n",
"x3b = 12.0\n",
"Total min:\n",
"12955.0\n"
]
}
],
"source": [
"print (\"Optimal Result:\")\n",
"for variable in my_lp_problem.variables():\n",
" print (variable.name, \"=\", variable.varValue)\n",
"print (\"Total min:\")\n",
"print (value(my_lp_problem.objective))"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"### MINImization LP "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Min Z = 4X1 + 5X2\n",
"- X1 + 2X2 >= 9\n",
"- 7X1 + 30X2 >=80\n",
"- 5X1 + X2 >= 10\n",
"- X1>=0, X2 >= 0 \n"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"my_lp_problem = pulp.LpProblem(\"My LP Problem\", pulp.LpMinimize)\n",
"x1 = pulp.LpVariable('x1', lowBound=0, cat='Continuous')\n",
"x2 = pulp.LpVariable('x2', lowBound=0, cat='Continuous')\n",
"\n",
"# Objective function\n",
"my_lp_problem += 4 * x1 + 5 * x2, \"Z\"\n",
"\n",
"\n",
"# Constraints\n",
"my_lp_problem += x1 + 2 * x2 >= 9\n",
"my_lp_problem += 7 * x1 + 30 * x2 >= 80\n",
"my_lp_problem += 5 * x1 + x2 >= 10"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"My LP Problem:\n",
"MINIMIZE\n",
"4*x1 + 5*x2 + 0\n",
"SUBJECT TO\n",
"_C1: x1 + 2 x2 >= 9\n",
"\n",
"_C2: 7 x1 + 30 x2 >= 80\n",
"\n",
"_C3: 5 x1 + x2 >= 10\n",
"\n",
"VARIABLES\n",
"x1 Continuous\n",
"x2 Continuous"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"my_lp_problem"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'Optimal'"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"my_lp_problem.solve()\n",
"pulp.LpStatus[my_lp_problem.status]"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Optimal Result:\n",
"x1 = 1.2222222\n",
"x2 = 3.8888889\n",
"Total Minima\n",
"24.3333333\n"
]
}
],
"source": [
"print (\"Optimal Result:\")\n",
"for variable in my_lp_problem.variables():\n",
" print (variable.name, \"=\", variable.varValue)\n",
"print (\"Total Minima\")\n",
"print (value(my_lp_problem.objective))"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"data": {
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iWAqCIiIiIgalICgiIiJiUAqCIiIiIgalICgiIiJiUAqCIiIiIgalICgiIiJiUAqCIiIi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V3EgtSOGVI75hJOXPMMPFMsvFMtrDdcGNniRgutj1xYH7ngWmgaFiSxV4bkhDTJXdIQGoizKQMh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\nXFFRVdbqk9EAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x2b8f08d57f0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Construct lines\n",
"# x1 >= 0\n",
"x1 = np.linspace(0, 20, 2000)\n",
"\n",
"y1=(4.5-x1/2)\n",
"y2= ((80- 7*x1)/30) \n",
"y3 =(10-5*x1) \n",
"y4=((36-4*x1)/8)\n",
"y5=((24.33 -4*x1)/5)\n",
"\n",
"# Make plot\n",
"plt.subplots(figsize=(10, 10),facecolor='lightblue') \n",
"\n",
"plt.plot(x1, y1, linewidth=5, color='magenta')\n",
"plt.plot(x1, y2, linewidth=5, color='magenta')\n",
"plt.plot(x1, y3, linewidth=5, color='magenta')\n",
"plt.axhline(y=0,linewidth=5, color='coral')\n",
"plt.axvline(x=0,linewidth=5, color='coral')\n",
"\n",
"plt.rc('xtick', labelsize=18) \n",
"plt.rc('ytick', labelsize=20) \n",
"\n",
"plt.title('FEASIBLE REGION',size=20) \n",
"\n",
"VX = 1.2\n",
"VY = 3.8\n",
"plt.plot(VX,VY, marker='D',markersize=15, color='blue')\n",
"\n",
"plt.xlim((0, 20))\n",
"plt.ylim((0, 15))\n",
"plt.xlabel(r'$X1$', size=20)\n",
"plt.ylabel(r'$X2$', size=20)\n",
"\n",
"\n",
"bbox_props = dict(boxstyle=\"larrow\", fc=\"cyan\", ec=\"b\", lw=2, alpha=0.8)\n",
"t = plt.text(2.5, 4, \"Minima\", ha=\"center\", va=\"center\", rotation=360,\n",
" size=10, bbox=bbox_props)\n",
"\n",
"plt.legend(bbox_to_anchor=(1.0, 0.9), loc=7, borderaxespad=0.,prop={'size': 22})\n",
"\n",
"bbox_props = dict(boxstyle=\"rarrow\", fc=\"coral\", ec=\"b\", lw=2, alpha=0.7)\n",
"t = plt.text(7, 6, \"Feasible Region\", ha=\"center\", va=\"center\", rotation=380,\n",
" size=32, bbox=bbox_props)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chenei Electric company dedicated to the manufacture of medium voltage transformers."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The company currently sells transformers of three different sizes with the following benefit margin : \n",
"\n",
"* A $ \\Rightarrow\\ $ net benefit of 42€ $ \\Rightarrow\\ $ dimension 2 $ m^2$ \n",
"* B $ \\Rightarrow\\ $ net benefit of 36€ $ \\Rightarrow\\ $ dimension 1.5 $ m^2$ \n",
"* C $ \\Rightarrow\\ $ net benefit of 30€ $ \\Rightarrow\\ $ dimension 1.2 $ m^2$ \n",
"\n",
"\n",
"- The company has 3 production plants, 1, 2 and 3 with a capacity for manpower and equipment to produce 75, 90 and 45 units per day of this product, respectively, regardless of the size or combination of sizes concerned.\n",
"\n",
"\n",
"- The amount of space available to store material in process also imposes limitations on the production rates of the new product. Plants 1, 2 and 3 have 100, 130 and 70 square meters of respective space, for material in the process of daily production. \n",
"\n",
"\n",
"- Each type of transformer A, B and C that is produced requires 2, 1.5 and 1.2 square meters, respectively. \n",
"\n",
"\n",
"- The sales forecasts indicate that if they are available, they can not be sold more than 90, 120 and 75 units per day of the respective models A, B and C.\n",
"\n",
"\n",
"- It should be taken into account that they need to produce at least 10 units of model C for to meet a pending order. \n",
"\n",
"\n",
"- In addition, the management has decided that the three plants must use the same percentage of their capacity of manpower to manufacture transformers. \n",
"\n",
"\n",
"#### Transformer restrictions \n",
"\n",
"|Restriction| Transformer A | Transformer B | Transformer C |\n",
"|:- | :- | :- | :- | \n",
"|Net Benefit | 42€ | 36€ | 30€ | \n",
"|Dimension square metre| 2 | 1.5 |1.2 |\n",
"|Production capacity| 90 | 120 |75 |\n",
"|Minim production required by management | - | - |10 |\n",
"\n",
"\n",
"#### Plants restrictions \n",
"\n",
"|Restriction| Production plant 1 | Production plant 2 | Production plant 3 |\n",
"|:- | :- | :- | :- | \n",
"|Manpower limits | 75 | 90 | 45 | \n",
"|Space s/metres available per plant | 100 | 130 | 70 |"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##### We have to maximize the net profit computing how many units of each transformer have to be produced in each plant "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### LP model "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- *Transformers index \tA,B,C*\n",
"- *Plants index \t\t1,2,3*\n",
"\n",
" \n",
" \n",
"\n",
" **<span style=\"color:red\"> MAX Z = 42XA1 + 42XA2 + 42XA3 + 36XB1 + 36XB2 + 36XB3 + 30XC1 + 30XC2 + 30XC1 </span>**\n",
"\n",
"**Restrictions production capacity (labor force) of each plant:**\n",
"\n",
"- XA1 + XB1 + XC1 <= 75\n",
"- XA2 + XB2 + XC2 <= 90\n",
"- XA3 + XB3 + XC3 <= 45\n",
"\n",
"**Restriction available floor space:** \n",
"\n",
"- 2XA1 + 1.5XB1 + 1.2XC1 <= 100\n",
"- 2XA2 + 1.5XB2 + 1.2XC2 <= 130\n",
"- 2XA3 + 1.5XB3 + 1.2XC3 <= 70\n",
"\n",
"\n",
"**Limit of daily sales:**\n",
"\n",
"- XA1 + XA2 + XA3 <=90\n",
"- XB1 +XB2 + XB2 <=120\n",
"- XC1 + XC2 + XC3 <= 75\n",
"\n",
"**Minimum production transformer C**\n",
"- XC1 + XC2 + XC3 >= 10\n",
"\n",
"** Restriction same percentatge of labour used in each plant **\n",
"\n",
"- (XA1 + XB1 + XC1)/75 = (XA2 + XB2 + XC2)/90 = (XA3 + XB3 + XC3)/45\n",
"\n",
"Computing :\n",
"- 90XA1 + 90XB1 + 90XC1 − 75XA2 − 75XB2 − 75XC2 = 0\n",
"- 45XA2 + 45XB2 + 45XC2 − 90XA3 − 90XB3 − 90XC3 = 0"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [],
"source": [
"my_lp_problem = pulp.LpProblem(\"My LP Problem\", pulp.LpMaximize)\n",
"XA1 = pulp.LpVariable('XA1', lowBound=0, cat='Continuous')\n",
"XA2 = pulp.LpVariable('XA2', lowBound=0, cat='Continuous')\n",
"XA3 = pulp.LpVariable('XA3', lowBound=0, cat='Continuous')\n",
"XB1 = pulp.LpVariable('XB1', lowBound=0, cat='Continuous')\n",
"XB2 = pulp.LpVariable('XB2', lowBound=0, cat='Continuous')\n",
"XB3 = pulp.LpVariable('XB3', lowBound=0, cat='Continuous')\n",
"XC1 = pulp.LpVariable('XC1', lowBound=0, cat='Continuous')\n",
"XC2 = pulp.LpVariable('XC2', lowBound=0, cat='Continuous')\n",
"XC3 = pulp.LpVariable('XC3', lowBound=0, cat='Continuous')\n",
"\n",
"# Objective function\n",
"my_lp_problem += 42*XA1 + 42*XA2 + 42*XA3 + 36*XB1 + 36*XB2 + 36*XB3 + 30*XC1 + 30*XC2 + 30*XC1 , \"Z\"\n",
"\n",
"# Constraints\n",
"my_lp_problem += XA1 + XB1 + XC1 <= 75\n",
"my_lp_problem += XA2 + XB2 + XC2 <= 90\n",
"my_lp_problem += XA2 + XB2 + XC2 <= 45\n",
"my_lp_problem += 2*XA1 + 1.5*XB1 + 1.2*XC1 <= 100\n",
"my_lp_problem += 2*XA2 + 1.5*XB2 + 1.2*XC2 <= 130\n",
"my_lp_problem += 2*XA3 + 1.5*XB3 + 1.2*XC3 <= 70\n",
"my_lp_problem += XA1 + XA2 + XA3 <=90\n",
"my_lp_problem += XB1 +XB2 + XB2 <=120\n",
"my_lp_problem += XC1 + XC2 + XC3 <= 75\n",
"my_lp_problem += XC1 + XC2 + XC3 >= 10\n",
"\n",
"my_lp_problem += 90*XA1 + 90*XB1 + 90*XC1 - 75*XA2 - 75*XB2 - 75*XC2 == 0\n",
"my_lp_problem += 45*XA2 + 45*XB2 + 45*XC2 - 90*XA3 - 90*XB3 - 90*XC3 == 0\n"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"My LP Problem:\n",
"MAXIMIZE\n",
"42*XA1 + 42*XA2 + 42*XA3 + 36*XB1 + 36*XB2 + 36*XB3 + 60*XC1 + 30*XC2 + 0\n",
"SUBJECT TO\n",
"_C1: XA1 + XB1 + XC1 <= 75\n",
"\n",
"_C2: XA2 + XB2 + XC2 <= 90\n",
"\n",
"_C3: XA2 + XB2 + XC2 <= 45\n",
"\n",
"_C4: 2 XA1 + 1.5 XB1 + 1.2 XC1 <= 100\n",
"\n",
"_C5: 2 XA2 + 1.5 XB2 + 1.2 XC2 <= 130\n",
"\n",
"_C6: 2 XA3 + 1.5 XB3 + 1.2 XC3 <= 70\n",
"\n",
"_C7: XA1 + XA2 + XA3 <= 90\n",
"\n",
"_C8: XB1 + 2 XB2 <= 120\n",
"\n",
"_C9: XC1 + XC2 + XC3 <= 75\n",
"\n",
"_C10: XC1 + XC2 + XC3 >= 10\n",
"\n",
"_C11: 90 XA1 - 75 XA2 + 90 XB1 - 75 XB2 + 90 XC1 - 75 XC2 = 0\n",
"\n",
"_C12: 45 XA2 - 90 XA3 + 45 XB2 - 90 XB3 + 45 XC2 - 90 XC3 = 0\n",
"\n",
"VARIABLES\n",
"XA1 Continuous\n",
"XA2 Continuous\n",
"XA3 Continuous\n",
"XB1 Continuous\n",
"XB2 Continuous\n",
"XB3 Continuous\n",
"XC1 Continuous\n",
"XC2 Continuous\n",
"XC3 Continuous"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"my_lp_problem"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'Optimal'"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"my_lp_problem.solve()\n",
"pulp.LpStatus[my_lp_problem.status]"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Optimal Result:\n",
"XA1 = 0.0\n",
"XA2 = 45.0\n",
"XA3 = 22.5\n",
"XB1 = 0.0\n",
"XB2 = 0.0\n",
"XB3 = 0.0\n",
"XC1 = 37.5\n",
"XC2 = 0.0\n",
"XC3 = 0.0\n",
"Total Maxima\n",
"5085.0\n"
]
}
],
"source": [
"print (\"Optimal Result:\")\n",
"for variable in my_lp_problem.variables():\n",
" print (variable.name, \"=\", variable.varValue)\n",
"print (\"Total Maxima\")\n",
"print (value(my_lp_problem.objective))"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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