Linear programming + hands-on of pulp

Overview of linear programming

• Linear programming (LP; linear programming) is a mathematical programming method that maximizes a linear expression among the values of variables that satisfy several linear inequalities and linear programming. This is a method of finding the value to be minimized. The optimization problem that is the target of linear programming is called the linear programming problem. Source: [Wikipedia]

• How to find the largest (smallest) objective variable by setting constraints with multiple linear inequalities and linear equations for the target variable

Hands-on

problem

example1

• How can I maximize profits based on the following constraints?
• Process 1 is up to 7 hours a day
• Process 2 is up to 14 hours a day

Source code

• Use pulp to solve the profit maximization problem
• pulp is a library for solving optimization problems

Library import

from pulp import *

Problem-solving source code

#Generate problem object
prob = LpProblem(name='Integer programming exapmle1',sense=LpMaximize)

#Variable setting
x1 = LpVariable('x1',lowBound=0)
x2 = LpVariable('x2',lowBound=0)

#Setting the objective variable
prob += 4*x1 + 5*x2
#Constraint setting
prob += 2*x1 + 2*x2 <= 7,'ineq1'
prob += 3*x1 + 5*x2 <= 14,'ineq2'

#Problem output
print('-------Problem information output-------')
print(prob)

#Find a solution
prob.solve()

#How was it solved
print('-------Solution information-------')
print(LpStatus[prob.status])

#Optimal value output
print('-------Optimal value output-------')
print('Optimal Value ={}'.format(value(prob.objective)))
#Optimal solution output
print('-------Optimal solution output-------')
for val in prob.variables():
    print('{}={}'.format(val.name,value(val)))

result

-------Problem information output-------
Integer programming exapmle1:
MAXIMIZE
4*x1 + 5*x2 + 0
SUBJECT TO
ineq1: 2 x1 + 2 x2 <= 7

ineq2: 3 x1 + 5 x2 <= 14

VARIABLES
x1 Continuous
x2 Continuous

-------Solution information-------
Optimal
-------Optimal value output-------
Optimal Value =15.75
-------Optimal solution output-------
x1=1.75
x2=1.75

Summary

• I somehow found a simple example.
• It seems difficult to formulate for social issues.
• I also want to do mixed integer linear programming.

reference

Python in optimization