The role and function of linear programming in business

Linear Programming

Linear Programming is a mathematical method for maximizing profits using linear equations and inequalities. In business to efficiently allocate resources, such as labor, raw materials, or production time.

Linier Programming -  mahasiswa STIE Indocakti

Basic concept of Linear Programming

1. Decision variable: A variable whose value can be changed and will affect the value of the objective. For example, the number of products produced, the amount of raw materials used.
2. Objective function: Describes the goal to be achieved, such as maximizing profits.
3. Constraints: An equation or linear inequality that limits the value of the decision variable, such as limited resources.

A simple example

A company produces two types of products, A and B. Each product requires different raw materials and production time. The company wants to maximize profits by considering the limited raw materials and production time. So the analysis.

1. Decision variables: The number of products A and B produced.
2. Objective function: Maximize total profit
3. Constraints: Raw material availability, production capacity, and market demand.

Benefits of Linear Programming

1. Helps allocate resources efficiently.
2. Helps make rational decisions.
3. Helps optimal production
4. Manage inventory efficiently
5. Designing the most efficient route for shipping goods

Linear Programming Solution Methods

1. Graph method: Excellent for two decision variables.
2. Simplex method: A more general method for problems with many variables.
3. Optimization software: Software like Excel Solver, LINGO for solving more complex problems.

Types of Linear Programming Models

1. Standard Model

The standard model is a form of equation with an excess or deficiency variable, added to turn the inequality into an equation. This model assumes all variables are non-negative.

2. Dual Model

The Dual Model is a concept in optimization theory that deals with any linear programming problem, called a primal problem.

From each of these primal problems, another problem can be formed called a dual problem.

3. Integer Model

In this model, all decision variables are constrained to take integer values. Used in the case of decisions that cannot be broken down into small parts, such as the number of goods produced.

4. Transportation Model

This model is to minimize the cost of shipping goods from several sources to several destinations, taking into account the source capacity and destination demand. This model is widely used in logistics.

5. Assignment Model

This model is to optimally assign jobs, workers, or machines, with the aim of minimizing costs.

6. Mixed Model

This model is a combination of ordinary and integer Linear Programming models, some decision variables must be integers and others can be fractional. This model is used for more complex problems, where integer and linear decisions are interrelated.

7. Multi-Objective Model

Multi-objective models address problems by finding solutions that satisfy the balance between multiple objectives.