OPTIMIZATION MODEL

Do you know that you can apply an optimization model to real-life situations? This is my main learning takeaway from a recent class on the topic. I would like to share just a bit about it in this post.

WHAT IS AN OPTIMISATION MODEL?

An optimization model is a form of mathematics that attempts to determine the optimal maximum or minimum value of a complex equation. It is a translation of the key characteristics of the business problem you are trying to solve into a mathematical equation.

Meanwhile, the resources of an organization are usually scarce and limited in supply. In order to achieve the objectives of the organization, a manager must be able to manage these limited resources. In other words, the manager will need a technique to optimize the resources.

A mathematical optimization model consists of an objective function and a set of constraints in the form of a system of equations or inequalities.

The basic goal of the optimization process is to find values of the variables that minimize or maximize the objective function while satisfying the constraints.

Basically, an optimization model is the use of mathematical techniques to solve problems based on certain characteristics by applying some techniques.

We have a few of such techniques:

• Linear programming (LP)
• Mixed integer programming (MIP)
• Nonlinear programming (NLP)
• Constraint programming (CP)

However, in this post, we are going to be looking at the use of the Linear programming technique to optimize resources.

WHAT IS LINEAR PROGRAMMING?

Linear programming is a mathematical technique for allocating limited resources in an optimal manner.

Thus, we use linear programming for selecting the best possible strategies from a number of alternatives.

Therefore, Linear programming is to maximise our objectives given certain constraints.

Applications of linear programming are everywhere around us. We can use linear programming for personal and professional decisions.

You are using linear programming when you are driving from home to work and want to take the shortest route. Or when you have a project delivery you make strategies to make your team work efficiently for on-time delivery.

Also, you can use linear programming when you have more than one investment opportunity with limited funds.

CHARACTERISTICS OF LINEAR PROGRAMMING

All linear programming problems must have the following five characteristics:

(1) Objective function:

There must be a clearly defined objective which can be stated in a quantitative way. The objective is generally profit maximization or cost minimization.

(2) Constraints:

Also. all constraints (limitations) regarding resources should be fully spelt out in a mathematical form.

(3) Non-negativity:

The value of variables must be zero or positive and not negative. For example, in the case of production, the number of any particular product should be positive or minimum of zero, not negative.

(4) Linearity:

The relationships between variables must be linear. Linear means a proportional relationship between two or more variables. It should be a maximum of one.

(5) Finiteness:

The number of inputs and outputs needs to be finite.

ASSUMPTIONS OF LINEAR PROGRAMMING

The following assumptions are applicable in Linear programming:

• Resources are limited.
• There is only one objective.
• Data are available to specify the problem.
• There are a number of constraints or restrictions- expressible in quantitative terms.
• The relationship between objective function and constraints is linear.
• The objective function is to be optimized i.e., profit maximization or cost minimization.
• There are non-negativity constraints.

In summary, an optimization model will save the day for any manager or individual in deciding how to use limited resources. Either for profit maximization or cost minimization.

Thanks for reading.