What is Linear Programming in Data Science: Overview

Author: Skill Slash

With its rapid expansion, "Data Science" has emerged as a truly multidisciplinary field that draws upon many other disciplines besides computer science, mathematics, data analysis, statistics, etc. The innovations it has brought about have allowed businesses all across the world to make better, more data-driven decisions. Therefore, modern businesses understand the value of their accumulated data.

With the help of cutting-edge software, data scientists evaluate real-world business scenarios by drawing conclusions from existing data, discovering hidden correlations, and spotting meaningful trends. Descriptive analytics is the term for this approach. In addition, data scientists engage in a field of study called Predictive Analytics, in which they investigate causal relationships between several variables.

Predictive analytics is useful for foreseeing potential outcomes since it establishes links between variables. Despite appearances, this is not a simple matter. The existing state of knowledge, limitations, and other factors all add complexity to any organization.

If you want to make a good prediction, you have to factor in all of these factors and find the best possible answer. To solve this problem, we turn to Linear Programming. Data scientists rely heavily on the mathematical technique of linear programming to help them find the best possible answers to a wide range of challenges. Linear Programming takes into account all relevant parameters, equality, and inequality conditions, and arrives at an accurate prediction.

In this section, we'll define Linear Programming and explore the various Linear Programming techniques.

Linear Programming: An Introduction

Before diving into the specifics, it's important to clarify that "programming" in the context of Linear Programming does not relate to coding for a computer or a piece of software. Linear Programming, on the other hand, is an optimization method (Linear Optimization) that can be used to great effect when searching for optimal results in mathematical models. Knowledge of these foundational concepts in Linear Programming is necessary for formulating a linear program:

  • Decision Variables: This is shorthand for the variables we haven't been able to pin down yet, the ones we need to find out.
  • Objective Function: This is shorthand for the linear function that represents the quantities that must be minimized or maximized.
  • Constraints: All the constraints on our decision variable are represented by this set of inequalities or equality constraints.
  • Non-negative restrictions: This refers to an important point of constraint in which the values of decision variables cannot be negative.

Now that we have a shared understanding of the fundamental concepts, we can examine the various methods available for resolving a Linear Programming problem.

Linear Programming Methods

To solve a Linear Programming problem successfully, we must adopt:

  • The process of determining the decision variables
  • Establishing the role of the objective function
  • Establishing the parameters of the constraints
  • Noting the constraints on non-negative outcomes

However, in this section, we will examine the many different ways in which you can tackle a problem involving linear programming. To choose from, you have four basic options:

  • Graphical Method: When faced with a Linear Programming problem with two variables, the graphical technique is the first port of call. It is typically employed when there are just two potential outcomes. To use the graphical technique, you must first construct a series of linear inequalities, and then solve them under the appropriate conditions or constraints. Finally, the viable region is found by graphing all linear equations on the X-Y plane and identifying the region where they intersect. This region represents a model's values and yields the best possible answer.
  • Simplex Method: This is an effective strategy for resolving issues with linear programming, and to find the answer that is best for the problem, it employs an iterative process. In this method, the essential variables are changed one at a time until the maximum or minimum value (depending on the requirements) for the primary target function is reached.
  • Northwest Corner and Least Cost Method: These are certain types of procedures that are utilized for figuring out the most effective way to convey items or things, and they are employed for transportation challenges. As a consequence of this, the approach of optimization shown here is practical for solving supply-demand problems. The use of this strategy is predicated on the idea that there is just a single product. On the other hand, there are a variety of origins for the demand for this product, and these origins contribute individually and together to the total supply. As a result, the objective of this strategy is to reduce the cost of transportation as much as possible.
  • Solving using R: When it comes to statistics and data analysis, R is among the most popular programs available. Using the IpSolve package, optimizing a problem is a breeze in R, requiring only a few lines of code.
Final Words

We reach the final part of the article, understanding in-depth linear programming in data science. If you wish to enter this domain, Skillslash can help you through its best Data Science Course In Noida, Skillslash provides a comprehensive Full-Stack Developer Course In Noida with a placement guarantee. Get in touch with the support team to know more.