Introduction to Linear Programming: Meaning, Importance, and Limitations

A generic linear programming problem is defined as follows:

Step 1 : Determining the decision variables.

Step 2 : Defining the objective function and deciding whether the function should be minimized or maximized.

Step 3 : Explaining the constraints.

Step 4 : Ensuring each decision variable is greater than or equal to 0 (Non-negative restraint).

Step 5 : Using either the simplex or graphical methods to solve the linear programming problem.

A linear programming problem must have linear functions for the decision variables, objective functions, and constraints. The linear program is defined as one that satisfies all three conditions.

Importance of Linear Programming

Some of the advantages of linear programming problems are,

1. A linear program can provide insight into a business problem and helps solve multidimensional problems.
2. Linear programming techniques provide practical solutions for problems having operating constraints.
3. A linear programming technique improves the quality of decisions by calculating the cost and profit of different things. The user’s approach to decision-making becomes more objective with this technique.
4. It helps in maximizing the use of productive resources through linear programming.
5. This technique is most useful for highlighting bottlenecks in production processes.
6. As conditions change, linear programming also helps re-evaluate a basic plan.

Applications of Linear Programming

Linear Programming is widely used in all fields, including agriculture, engineering, manufacturing, energy, logistical, and supply chain activities.

• Engineering – Using linear programming, engineers optimize resources in the manufacturing and production industries to maximize profits.
• Logistics – Transportation and logistics companies use linear programming to calculate the shortest routes, travel times, and pricing strategies.
• Agriculture – Engineering can use linear programming in agriculture to determine what crops to grow and how much to grow to increase revenue.

• Food Industry – To keep away from noncommunicable diseases, linear programming can help health managers and nutritionists plan dietary needs.
• Energy Sector – This technique is also applied in the energy sector to optimize the electric load, the shortest distribution lines, and the electrical power grid design.
• Programming and Data Science – Data Scientists encounter linear programming problems regularly. Data science developers can benefit from linear programming.
• Linear Programming in Python – Any linear programming problems can be solved by using PuLP, one of the libraries in python ecosystems, to optimize any problems.

Limitations of Linear Programming

• It is important to have an objective that is clearly defined and quantifiable. In real life, however, such objectives are not achievable, such as maximizing sales, profit, or minimizing costs
• Time and uncertainty are not taken into account in linear programming models
• Often, in real-life situations, parameters that appear in the model are neither known nor constant
• An organization cannot take into account factors such as human behavior, weather conditions, and the stress of employees, which can adversely affect its performance
• In real life, problems arise with multiple objectives rather than one single objective.

By using this technique, we can reduce or maximize a linear function subject to multiple constraints. In addition to several business planning applications, this technique can direct quantitative judgments in industrial engineering and, to a lesser extent, in social and physical sciences.

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