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.
Table of Content
What is Mathematical Optimization?
Mathematical optimization, also known as mathematical programming, is a branch of mathematics and computer science that deals with finding the best solution from a set of feasible solutions.
Mathematical optimization involves the process of maximizing or minimizing a function, often referred to as the objective function, while satisfying a set of constraints. Optimization problems are broadly categorized as continuous or discrete based on the nature of decision variables. The utilization of objective function in an optimization problem is subject to the domain being studied.
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.
|
Time period |
Major Optimization area |
|---|---|
|
18th Century – First Industrial Revolution |
|
|
19th Century – Second Industrial Revolution |
|
|
20th Century – Third Industrial Revolution |
|
|
Present – Fourth Industrial Revolution (Present) |
|
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 in Our Daily Lives
Basic mathematical calculations are used in our day to day lives for the purpose of counting and generating statistical summaries. Mathematical optimization techniques help in minimizing future losses and ensure efficient usage of parameters (decision variables). Depending on perspective mathematical optimization can have applications spanning daily routine of an individual to large scale industrial applications.
Read More,
Conclusion
In conclusion, the real-life applications of mathematical optimization can be seen across a diverse array of industries and fields. It provides a revolutionizing way to approach complex problems and make decisions. From optimizing production processes in manufacturing to enhancing logistics and supply chain management, and from streamlining healthcare operations to maximizing financial returns while minimizing risks, mathematical optimization techniques have become very useful tools for businesses, governments, and researchers alike.
FAQs on Applications of Mathematical Optimization
Define mathematical optimization.
Mathematical optimization, also known as mathematical programming, is a branch of mathematics and computer science that deals with finding the best solution from a set of feasible solutions. It involves maximizing or minimizing a function while satisfying constraints.
What are some common optimization problems?
Common optimization problems include linear programming (LP), nonlinear programming (NLP), integer programming (IP), quadratic programming (QP), and dynamic programming. These problems arise in various fields such as operations research, engineering, finance, and data science.
What is the objective function in optimization?
The objective function is the function that needs to be optimized, either maximized or minimized. It represents the quantity to be optimized, such as profit, cost, time, or distance.
What are some optimization techniques?
Optimization techniques include linear programming, which deals with linear objective functions and constraints, nonlinear programming for nonlinear functions, integer programming for discrete decision variables, and dynamic programming for problems with overlapping subproblems.