Objective Function

What is Objective Function?

Definition: The objective function is a mathematical term that describes how different variables contribute to a certain value that is being sought to be optimized.

What does Objective Function mean?

Say, a company is trying to maximize the profits that it makes in a certain project. Or it may be trying to minimize the costs associated with the project. The function that is being sought to be optimized, which in this case is the profit or the cost, is referred to as the objective function.

It’s important to understand that the objective function will be associated with a number of variables. These are referred to as linear inequalities. These could be the labor requirements or material requirements of the project.

The project could have many different outcomes. This depends on the inputs that are used. The objective function shows us how each of these inputs or variables contributes to the value that is being optimized.

Example of Objective Function

The objective function has many practical applications. These include:

  • Allocating machinery and labor between different products so that profit is maximized or costs are minimized.
  • Managing the inventory of raw materials and spare parts in a factory. Maintaining a large inventory of raw materials and spare parts has certain advantages (easy availability, low lead time, no stoppage of work) and certain costs (storage costs, capital getting blocked, insurance.) Manufacturing companies can benefit by maintaining an optimum level of inventory. By doing this, they will minimize costs and also allow the production process to continue without any interruption.
  • Selecting the vendors for large manufacturing companies that have multiple factories. This can help to cut down supplier costs and maximize efficiencies.
  • Managing truck fleets and determining the most profitable routes.
  • Managing blending problems in processes where different inputs are used to produce products like animal feed, petroleum products, and other chemical products.

In fact, the objective function can be used across a wide range of applications.


The objective function is a mathematical expression used in linear programming. It can be used to solve resource allocation problems in industrial production systems and in other business situations.