Everything You Need To Know About Linear Programming

Everything You Need To Know About Linear Programming

In this world of detailed organization and the implementation of complex operations, it is important to constantly find ways to enhance those processes being implemented and find ways to optimize solutions in order to solve problems and to become more efficient every day.

There are many ways to do this and a large amount of tools and solutions available to managers so they can plan, organize, project and execute according to the mission and always with the success of the operation in mind.

Today in David Kiger’s Blog, we want to talk about a concept called linear programming and how it can be used in logistics in order to organize, plan and implement the carrying out of operations while considering variables that affect outcomes.

The purpose of optimization is to use all available resources and the technology within reach, in the best possible way. When this is done at the planning stage, results are much better since higher costs can be avoided and the best possible outcome for the operation can be chosen beforehand. Today with computers and the use of linear programming as a tool, this can be easily accomplished for most problems dealing with transportation solutions.

What is linear programming?

First of all, what is linear programming? Linear programming is a mathematical method for solving constrained maximization and minimization issues when there are a number of constraints, and both the objective function to be optimized as well as the constrained encountered are linear, meaning they can be represented by lines. Linear programming was postulated by L. V. Kantorovich in 1939 and further developed by G. B. Dantzig in 1947. The fact that we have powerful computers today able to do the complex operations involved in linear programming is what has made this method so popular and so useful in today’s logistics planning. Linear programming is a powerful technique that is regularly used by corporations, government agencies and not-for-profit organizations, to analyze complex financial, commercial, production, and many other activities that are part of their daily operation.

The principle rests on the fact that companies face many constraints in achieving their goals and finding ways to maximize their profit. In an ideal world where only one single constraint existed, these problems could be easily solved by other traditional methods, but that is simply not the reality these organizations must face every day. 

Examples of this are for instance the fact that a company may not be able to get more than a set amount of a raw material, or a firm may not be able to hire more labor with some type of specialized skill, purchase some type of advanced equipment, be bound for contractual agreements, local regulations.

As we mentioned before, assuming that the objective function the company seeks to optimize (Minimize or maximize, that depends on the particular case) can be represented in a graphic by using lines, just like the constraints set in place by things like the factors we previously mentioned, then we can safely say that linear programming can be used to find solutions to these problems.

Image courtesy of Frans de Wit at Flickr.com

What are some of its applications?

Linear programming can be applied to different areas such as:

Optimal selection of processes

The majority of products are manufactured by implementing a series of processes; each of those processes requires different technologies and a combination of inputs. By having the input prices and the quantities the company wants to produce of said products, linear programming can be used to determine the best combination of processes needed to produced the level of output the company desires at the lowest possible cost by considering the constraints the company has, things like capital, cost of labor, regulations and time available.

Best product mix

Companies usually produce more than one type of product, so they have to find the best way to use their plants, labor, and other resources to produce a combination of products that ensure the maximization of their total profit while considering their constraints. For example, a company may produce a product that while gives them the best possible return in profit for their operation; it doesn’t use all the resources available. This means the company may use resources to produce other products but by keeping in mind that such branching should not affect overall profits. Linear programming allows for the company to make such planning by keeping the continuation or maximization of profit margins to be set as a constant in the form of a constraint.

Meeting the minimum requirements

Sometimes in production, you are faced with a situation that asks for minimum requirements to be met. In the food business, for example, you may have to prepare meals with very specific minimum requirements in minerals, vitamins, protein and other aspects at a minimal cost. Linear programming allows you to find the best combinations in order to find food products that contain higher concentrations at a lower cost of the specific components you need.

* Featured Image courtesy of Unsplash at Pexels.com

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