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Practice notebook with PuLP package
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‎PuLP_practice.ipynb

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"from pulp import *"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Small cat food problem"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Create the 'prob' variable to contain the problem data\n",
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"prob = LpProblem(\"The Whiskas Problem\",LpMinimize)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"x1=LpVariable(\"ChickenPercent\",0,100,LpInteger)\n",
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"x2=LpVariable(\"BeefPercent\",0,100)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [],
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"source": [
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"# The objective function is added to 'prob' first\n",
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"prob += 0.013*x1 + 0.008*x2, \"Total Cost of Ingredients per can\""
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [],
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"source": [
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"prob += x1 + x2 == 100, \"PercentagesSum\"\n",
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"prob += 0.100*x1 + 0.200*x2 >= 8.0, \"ProteinRequirement\"\n",
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"prob += 0.080*x1 + 0.100*x2 >= 6.0, \"FatRequirement\"\n",
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"prob += 0.001*x1 + 0.005*x2 <= 2.0, \"FibreRequirement\"\n",
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"prob += 0.002*x1 + 0.005*x2 <= 0.4, \"SaltRequirement\""
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [],
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"source": [
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"# The problem data is written to an .lp file\n",
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"prob.writeLP(\"WhiskasModel.lp\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"1"
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]
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},
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"execution_count": 9,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# The problem is solved using PuLP's choice of Solver\n",
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"prob.solve()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Status: Optimal\n"
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]
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}
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],
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"source": [
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"# The status of the solution is printed to the screen\n",
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"print(\"Status:\", LpStatus[prob.status])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"BeefPercent = 66.0\n",
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"ChickenPercent = 34.0\n"
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]
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}
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],
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"source": [
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"# Each of the variables is printed with it's resolved optimum value\n",
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"for v in prob.variables():\n",
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" print(v.name, \"=\", v.varValue)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Total Cost of Ingredients per can = 0.97\n"
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]
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}
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],
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"source": [
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"# The optimised objective function value is printed to the screen\n",
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"print(\"Total Cost of Ingredients per can = \", value(prob.objective))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Large cat food problem"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Creates a list of the Ingredients\n",
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"Ingredients = ['CHICKEN', 'BEEF', 'MUTTON', 'RICE', 'WHEAT', 'GEL']\n",
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"\n",
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"# A dictionary of the costs of each of the Ingredients is created\n",
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"costs = {'CHICKEN': 0.013, \n",
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" 'BEEF': 0.008, \n",
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" 'MUTTON': 0.010, \n",
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" 'RICE': 0.002, \n",
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" 'WHEAT': 0.005, \n",
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" 'GEL': 0.001}\n",
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"\n",
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"# A dictionary of the protein percent in each of the Ingredients is created\n",
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"proteinPercent = {'CHICKEN': 0.100, \n",
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" 'BEEF': 0.200, \n",
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" 'MUTTON': 0.150, \n",
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" 'RICE': 0.000, \n",
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" 'WHEAT': 0.040, \n",
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" 'GEL': 0.000}\n",
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"\n",
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"# A dictionary of the fat percent in each of the Ingredients is created\n",
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"fatPercent = {'CHICKEN': 0.080, \n",
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" 'BEEF': 0.100, \n",
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" 'MUTTON': 0.110, \n",
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" 'RICE': 0.010, \n",
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" 'WHEAT': 0.010, \n",
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" 'GEL': 0.000}\n",
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"\n",
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"# A dictionary of the fibre percent in each of the Ingredients is created\n",
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"fibrePercent = {'CHICKEN': 0.001, \n",
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" 'BEEF': 0.005, \n",
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" 'MUTTON': 0.003, \n",
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" 'RICE': 0.100, \n",
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" 'WHEAT': 0.150, \n",
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" 'GEL': 0.000}\n",
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"\n",
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"# A dictionary of the salt percent in each of the Ingredients is created\n",
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"saltPercent = {'CHICKEN': 0.002, \n",
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" 'BEEF': 0.005, \n",
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" 'MUTTON': 0.007, \n",
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" 'RICE': 0.002, \n",
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" 'WHEAT': 0.008, \n",
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" 'GEL': 0.000}"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Create the 'prob' variable to contain the problem data\n",
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"prob = LpProblem(\"The Whiskas Problem\", LpMinimize)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"metadata": {},
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"outputs": [],
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"source": [
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"# A dictionary called 'ingredient_vars' is created to contain the referenced Variables\n",
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"ingredient_vars = LpVariable.dicts(\"Ingr\",Ingredients,0)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"{'BEEF': Ingr_BEEF,\n",
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" 'CHICKEN': Ingr_CHICKEN,\n",
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" 'GEL': Ingr_GEL,\n",
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" 'MUTTON': Ingr_MUTTON,\n",
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" 'RICE': Ingr_RICE,\n",
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" 'WHEAT': Ingr_WHEAT}"
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]
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},
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"execution_count": 16,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"ingredient_vars"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"metadata": {},
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"outputs": [],
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"source": [
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"# The objective function is added to 'prob' first\n",
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"prob += lpSum([costs[i]*ingredient_vars[i] for i in Ingredients]), \"Total Cost of Ingredients per can\""
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]
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"metadata": {},
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"outputs": [],
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"source": [
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"# The five constraints are added to 'prob'\n",
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"prob += lpSum([ingredient_vars[i] for i in Ingredients]) == 100, \"PercentagesSum\"\n",
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"prob += lpSum([proteinPercent[i] * ingredient_vars[i] for i in Ingredients]) >= 8.0, \"ProteinRequirement\"\n",
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"prob += lpSum([fatPercent[i] * ingredient_vars[i] for i in Ingredients]) >= 6.0, \"FatRequirement\"\n",
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"prob += lpSum([fibrePercent[i] * ingredient_vars[i] for i in Ingredients]) <= 2.0, \"FibreRequirement\"\n",
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"prob += lpSum([saltPercent[i] * ingredient_vars[i] for i in Ingredients]) <= 0.4, \"SaltRequirement\""
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]
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},
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{
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"cell_type": "code",
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"execution_count": 19,
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"metadata": {},
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"outputs": [],
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"source": [
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"# The problem data is written to an .lp file\n",
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"prob.writeLP(\"WhiskasModelBig.lp\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 20,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"1"
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]
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},
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"execution_count": 20,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# The problem is solved using PuLP's choice of Solver\n",
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"prob.solve()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Ingr_BEEF = 60.0\n",
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"Ingr_CHICKEN = 0.0\n",
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"Ingr_GEL = 40.0\n",
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"Ingr_MUTTON = 0.0\n",
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"Ingr_RICE = 0.0\n",
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"Ingr_WHEAT = 0.0\n"
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]
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}
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],
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"source": [
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"# Each of the variables is printed with it's resolved optimum value\n",
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"for v in prob.variables():\n",
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" print(v.name, \"=\", v.varValue)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 22,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Total Cost of Ingredients per can = 0.52\n"
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]
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}
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],
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"source": [
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"# The optimised objective function value is printed to the screen\n",
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"print(\"Total Cost of Ingredients per can = \", value(prob.objective))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"LaTeX_envs_menu_present": true,
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"autoclose": false,
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"autocomplete": true,
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"bibliofile": "biblio.bib",
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"cite_by": "apalike",
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