Application of Linear Programming (LP) and the usefulness of LP

Linear Programming is basically a planning tool to find out the best solutions under constraints or limiting factors. The main objective of a linear programming problem is to maximize or to minimize some numerical value.

However, Linear Programming is the statistical tool for finding the most optimum solutions to real world problems which have a set of variables linearly related to each other and are guided by a set of constraints. In simple terms, a business scenario can involve many parameters for production or minimizing loss/error for maximizing profit. These can be solved using a Linear Programming model using the simplex method by identifying the decision variables and constraints involved.

Historical purview:

George Bernard Dantzig, while working with US Air Force during World War II, developed this technique, primarily for solving military logistics problems. But now, it is being used extensively in all functional areas of management, hospitals, airlines, agriculture, military operations, oil refining, education, energy planning, pollution control, transportation planning and scheduling, research and development, etc.

I believe there are different areas where Linear Programming can be applied. Below I have enlisted the top 5 areas with examples supporting my understanding.

Day to Day Life

1. Monthly Financial Budgeting where one tries to achieve the maximum saving from the fixed monthly income without compromising on the basic necessities of groceries and vegetables.
2. Weekly Haat/ Mandi for vegetable shopping where one optimizes the different vegetables, they can buy with the fixed money they carry.

Banking Domain:

1. In Branches to optimize the profit and general necessities of the public via Banking, Banks set minimum target in Advances, CASA, Government Scheme, Bank Assurance via Portfolio Management and Product Management,
2. Internal on day to day basis, Bank needs to carry out optimization of number of currency notes for each denomination to suffice the general public needs via Cash Management i.e. Currency notes management

Supply Chain Management:

1. Route Optimization for Shortest time is one of the best use cases for Linear Programming. Google Maps uses the same when identifying the shortest route. Even, Supply Chain management companies when transporting goods from one place to another use route optimization.
2. Warehouse level Inventory Management is another use case where the optimal number of stocks per products needs to be calculated to meet the demand and have minimal to no stock leftovers.

Event Management:

1. Ticket Price Optimization is finding the optimal amount chargeable for a event ticket using the cost incurred, Minimum amount of people assumed and maximizing profit

Telecom:

1. Capacity Management is determining the minimum number of CMTS (Nodes) that would be required to meet the demands by the customers. It has to not only cater to peak hour demands but also provide quality service to all the customers in that region.
2. Call Routing Optimization is finding the optimal route between the caller and receiver by using minimum number of jumps btw transmitting towers.

Machine Learning and Linear Programming:

Linear programming is also used in machine learning applications where a neural network is trained to fit model of a function in order to label input data and predict unknown future values.

Conclusion:

Linear Programming has came a long way from wars to industrial usage to modern e-commerce industries supply chain problems to basic agricultural solutions. But India being an Agri economy its application are not completely utilized by a farmer. Use cases have increased but application on sector base should also increase and help balance out the profitability of country’s economic growth as Optimization is crucial for investigating complex issues, identifying and solving problems, and data-driven decision-making.