Applications of Mathematical Optimization

Mathematical optimization plays a crucial role in various aspects of our daily lives, impacting industries, services, and decision-making processes. It is extensively used in fields like transportation, logistics, finance, healthcare, and more. Optimization models aim to maximize or minimize objectives under specific constraints, ensuring efficient resource allocation and decision-making.

Examples include minimizing costs in production systems, optimizing wait times in hospitals, maximizing profits in marketing, and designing optimal routes for humanitarian operations. Mathematical optimization is a powerful tool that helps in achieving the best outcomes given the circumstances, making it a fundamental aspect of real-world problem-solving

Major applications of mathematical optimization through industrial revolution are explained in the table below.

Healthcare Systems

In this domain IBM CPLEX solver is used to perform high performance mathematical programming operations for linear programming problems. Mathematical modelling performs modeling and simulation of clinical trials. IBM CPLEX is a decision optimization application that helps in easy building and deployment of optimization models. Mathematical optimization approach to oncology research was developed in mid 20th century and since been implemented for research and development in medical sciences.

Energy Systems

In the domain of energy systems the energy consumed by a system is the objective function. The goal of energy system is to reduce energy consumption hence, the objective function is minimized. Energy and efficiency of energy management system is dependent on the forecasting algorithm and energy management scheme(EMS) used. The energy management systems in conventional electricity grids involve the implementation of Fuzzy-logic, game theory and reinforcement learning to name a few. Fuzzy logic based EMS is efficient in optimizing operational cost whereas Game theory based EMS is efficient in reducing total electricity used and reduced emission cost of the energy system.

Mathematical Optimization is one of the many branches in mathematics which help us optimize any objective function by systematically analyzing decision variables and constraints to find the most efficient or effective solution. In this article, we will discuss all the relevant application of Mathematical Optimization.