Linear Programming and its Uses

7 Min Read. |

Optimization is the new need of the hour. Everything in this world revolves around the concept of optimization.  It finds its use in normal production time to supply chain issues.  To solve these problems, we need optimization concepts. In the curriculum of a data science course, optimization is one such tool that works everywhere. You can perform optimization in various ways. In the data science course, the optimization topic is the most important. It gives insights about the ways of optimization. A problem can be simple and complex. In both cases, optimization works very effectively. There are various ways to do optimization. But linear programming is the most simple and easy one. 

It does not take your lot of time and optimize problems easily. Linear programming finds its use in every sphere of life, including personal as well as professional. It has applications everywhere. 

When going home, you take the shortest route to save time. You are using linear ways of programming to reach home early. This kind of programming has various uses in school and college projects also. 

What is Linear Programming? 

Linear programming is the simplest method to do optimization. The optimization process ranges from simple problems to complex problems. But with this, you can solve all problems in less time with simplicity. It helps you to solve all complex problems through its simplified assumptions.  If you are a data analyst from a data science course, then you are bound to solve problems through this. 

The linear technique is used across applications and websites to solve any supply chain and complex problems. However, it doesn’t get that much attention as other forms in the data science course.  It does not mean that linear programming is not worthy of it. It is the most worthy process of optimization; you will ever come across. 

In linear ways of programming, the problems of complex relationships are solved through the use of linear functions.  It is done to find the optimum points to solve the problem.  Here, complex problems are depicted. The actual problem may be more complex. Yet, by the use of this type of programming, you can solve it.  

In most cases, it is seen that such forms of programming are used for obtaining suitable optimal solutions for the problem.

It is done by considering constraints for solving problems. You must be wondering how real-life problems can get solved by this. The question is normal to come. But the answer is we can solve real-life problems from linear programming by using a mathematical model.

The model comprises objective functions and linear inequalities that are subject to the provided constraints. 

How does Linear Programming work? 

In the data science course, all such programming mechanisms are covered for a better understanding of matter.  As a data analyst, you must be doing a lot of this form of programming that leads you to easy and optimal solutions. Certain steps are followed for working on such programming models and problems. 

  1. The first step deals with the identification of the problem. There are a variety of uses of linear programming surrounding our world. You only need a keen eye to observe it.  Read thoroughly about the problem before heading on your programming journey. Take the problem into consideration and mark all the linear functions used in the linear programming process. 
  2. After the perfect analysis of the complex problem, you need to write all the decision variables and objective functions. Decision variables are the type of variables that decides your problem outcome. The variables represent your optimal solution at the last of this programming process.  

An objective function is termed as the functions for problem objectives that are to be considered. The objective functions help make the process of this programming conclusive.  

Take account of all the variables and functions for obtaining the optimal solutions for problems. 

  1. Note all constraints of the depicted mathematical model in your programming process. The constraints are defined as the limitations on the decision variables that are considered for programming. For all such programs, the decision variables should be non-negative. It cannot take negative values.  It means they should be greater than or equal to zero. 
  2. Now, after noting all the variables, constraints, and functions, you can head towards the solving process. In this type of  programming, you can solve the problems in various ways : 
  • Through graphical methods 
  • Through R – the open-source tool popular among data science analysts 
  • Through open solver- other open-source linear programmer and optimizer
  • Through the simplex method – the powerful and popular methods for linear programming

You can solve your complex problem through any of these mentioned ways. A good data science course mentions all the methods of solving complex problems. Pick one method out of your preferences, and solve the programming problems. 

Some famous methods to do Linear Programming 

Linear programming is indeed the simplest form of programming done in the data science field. Some famous methods prevail in the field that is followed for executing the process. 

 Let us look into those famous methods in the following section of the article: 

1) Simplex Method 

As the name depicts itself, it is the simplest method to do programming.  The simplex method is a powerful method that involves iterative procedures for programming.  

After the whole procedure, you will get a feasible result as an outcome.  The method involves the transformation of values of basic variables to get optimized value for the objective function. 

Following are the steps involved in the simplex method procedure: 

  • Step 1: Identify all decision variables first like any other linear programming procedure. List all variables of your problem that will be required to solve your problem using LP. 
  • Step 2:  Determine the objective of the company involved in this method. In this method, the main objective of the company is to maximize the audience. All objectives should be defined by the executioner in the simplex method. 
  • Step 3:  the next step is to list down the constraints of the problem. These constraints are the values at which most of the basic variables depend. The constraints limit the values of the basic variables. 
  • Step 4:  make the equation out of this and solve it accordingly. The equation formed is of linear nature that revolves around the basic linear mathematical process. 

The simplex method is very easy to follow, as it does not involve any complex mathematical tool.  Many data scientists make use of this method for solving linear equation problems. 

2) Northwest corner method 

This is one of the special types of linear programming methods that are famous among data scientists.  Here the transportation of problems is done into linear programming equations to generate a feasible outcome. 

All values accommodate from the top-left corner of the equation table. 

This is one of the specialities of the northwest corner method. This method finds its application in the commodities transportation industry.  

The method includes the following components: 

  • Level of supply and demand of each commodity. It should be known to the programmer before executing programming. 
  •  The unit of transportation is used for transporting the commodity from source to destiny.  This factor also determines the execution of the linear programming process. 

This method runs in the hypothetical theory that the total demand is equal to the total supply. It means that the model or equation is balanced in every way.   

However, the demand for the supply may come from multiple sources in the industry. 

3) Least count method 

This is one of the best methods to solve programming procedures. It generates more feasible and accurate results than the northwest corner method.  

It is also used in the transportation industry in manufacturing units.  

The procedure of the least count method is the same as any other method of linear programming. Yet, the method generates more accurate results than any other method listed above. 

Applications of Linear Programming 

Uses of linear programming have many practical applications. They are used for optimizing complex problems. Many industries are implementing linear programming tools for obtaining optimal solutions. The manufacturing and servicing industries are using this programming method regularly.  

Linear programming finds its applications in various industries that use it for the supply chain process.  As a data analyst in these industries, you know about the uses of this programming very well. 

The following are the industries and areas where this type of programming finds its uses: 

1) Food and agriculture industry 

All farmers apply such programming techniques to farming to know what crops can be grown in the land. Farmers know the uses of linear programming, so they use it for better farming practices. With a linear technique, they can generate more revenues for their land for making profits. 

2) Transportation optimization 

The transportation industry works on such programming techniques for cost and time efficiency. All buses and train routes are optimized through linear programming methods.  In the data science course also, transportation optimization is taught as a distinct subject. 

3) Manufacturing units 

The manufacturing industry uses this type of programming as the principal optimization tool.  The industry works on this technique to generate more profit for the company. All uses of linear programming are well used in the industry. 

In Conclusion 

You can find other uses of linear programming in the data science course.  

Linear programming techniques are crucial for the industries mentioned above. Most of the optimization works happen on linear programming for solving complex problems. To learn and master linear programming, enrol yourself in a data science course now.

In case of any doubts about linear programming, feel free to ask us in the comment section.

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