Operations Research: Math, Engineering, Physics, Finance
Readers will gain the knowledge and skills they need to solve complex problems in a variety of fields.
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Thank you to our Editors, Igor Tarasenko, Lalin Laudis, Eye Of Unity, The Angineer, Varun Tyagi, Optimization team!
About ORB Editors
Varun Tyagi is a seasoned pro in LLM, ML, mathematics, innovative pricing strategies, and data engineering with a knack for leadership. Passionate about leveraging futuristic tech to tackle business challenges. Simplifying Logistics with Python: A Practical Guide to Bundling Moves
Optimization team, Dr. Alireza Soroudi, writer of the book “Power system optimization in GAMS”. My passion is solving challenging real world problems using optimization tools such as Pyomo, GAMS and Google OR-Tools. A Pyomo Approach to Deal with Graph Related Optimization Problems
Igor Tarasenko, experienced iOS developer skilled in ML integration. Values health, family, and adventure. Committed to community and helping others. Mastering AI Problem-Solving
Lalin Laudis, I am a futurist. I think of future technologies. I’m working on evolving ‘Predictive Science’ through which I agog to predict Various Diseases. Predictive Science: The Science of Future
My name is Michael David Kemble also known as Eye Of Unity. My blog covers everything from cryptocurrency and NFTs to technology and science with expert insight and thought-provoking content. How AI Is Transforming Decision-Making Processes
I am The Angineer, an aspiring engineer with an inquisitive mind and passion for engineering physics. My articles particularly ponder on renewable energy and informing readers about sustainability. Pumped Hydro — The Veteran in need of support
Operations Research
- Mathematical Methods
- Engineering Applications
- Physics Applications
- Finance Applications
Knowledge and Skills
- Understand the basic concepts and principles of OR
- Formulate and solve OR models
- Use OR software to solve real-world problems
- Communicate the results of OR analyses effectively
Topics
- Introduction to OR
- Linear programming
- Integer programming
- Dynamic programming
- Network optimization
- Queueing theory
- Simulation
- Decision analysis
The will cover a variety of OR topics, including:
- Linear programming
- Integer programming
- Network flows
- Dynamic programming
- Simulation
- Decision analysis
Additional Resources OR
- The Operations Research Society of America (INFORMS)
- The International Federation of Operational Research Societies (IFORS)
The prerequisites for this are designed to provide students with the necessary mathematical foundation to succeed in the course. Real Analysis I and II cover the fundamental concepts of calculus, including limits, derivatives, integrals, and infinite series. Measure and Integration Theory provides a rigorous treatment of the concept of measure and the Lebesgue integral. Introduction to Functional Analysis introduces students to the basic concepts of functional analysis, such as vector spaces, linear operators, and Hilbert spaces. Applied Mathematics I and II cover a variety of mathematical topics that are useful for solving real-world problems, such as linear algebra, differential equations, and numerical analysis. General Topology introduces students to the basic concepts of topology, such as sets, open sets, closed sets, and continuity.
All of these prerequisites are essential for understanding and applying the concepts and techniques of OR. For example, linear programming is a fundamental OR technique that is used to solve a wide variety of problems. Linear programming problems are often formulated using real-valued variables and linear constraints. The Lebesgue integral is a powerful tool that can be used to solve a variety of OR problems, such as those involving queuing theory and inventory management. Functional analysis is useful for understanding and analyzing OR problems that involve uncertainty and risk. Applied mathematics is essential for solving OR problems using numerical methods. And general topology is useful for understanding the topological structure of OR models.
Mathematical Methods
This is a challenging but rewarding experience for readers who are serious about their mathematical studies. Readers who complete this, will be well-prepared for careers in a variety of fields, including engineering, science, finance, and academia.
Must start with a strong foundation in calculus, linear algebra, and probability and statistics
- Calculus
- Real analysis
- Complex analysis
- Abstract mathematics
- Algebra: groups, rings, fields, modules, vector spaces, linear algebra
- Analysis: real analysis, complex analysis, functional analysis
- Geometry: differential geometry, algebraic geometry, topology
- Topology: point-set topology, algebraic topology
The prerequisites are designed to provide students with the necessary mathematical foundation to succeed in the course.
- Real Analysis I and II: These courses cover the fundamental concepts of calculus, which are essential for understanding and applying the concepts and techniques of OR. For example, linear programming is a fundamental OR technique that is used to solve a wide variety of problems. Linear programming problems are often formulated using real-valued variables and linear constraints.
- Measure and Integration Theory: This course provides a rigorous treatment of the concept of measure and the Lebesgue integral. The Lebesgue integral is a powerful tool that can be used to solve a variety of OR problems, such as those involving queuing theory and inventory management.
- Introduction to Functional Analysis: This course introduces students to the basic concepts of functional analysis, such as vector spaces, linear operators, and Hilbert spaces. Functional analysis is useful for understanding and analyzing OR problems that involve uncertainty and risk.
- Applied Mathematics I and II: These courses cover a variety of mathematical topics that are useful for solving real-world problems, such as linear algebra, differential equations, and numerical analysis. Applied mathematics is essential for solving OR problems using numerical methods.
- General Topology: This course introduces students to the basic concepts of topology, such as sets, open sets, closed sets, and continuity. General topology is useful for understanding the topological structure of OR models.
Additional Resources Math
- American Mathematical Society (AMS)
- Mathematical Association of America (MAA)
- Society for Industrial and Applied Mathematics (SIAM)
- [Textbook] Advanced Mathematics for Engineering and Science by W.E. Boyce and R.C. DiPrima
- [Textbook] Advanced Mathematics: A Comprehensive Approach by William H. Ruckle
Engineering Applications
Readers should have a strong foundation in calculus, linear algebra, and probability and statistics.
Upon completion, readers will be able to:
- Understand the basic concepts and techniques of OR.
- Formulate mathematical models of engineering problems.
- Solve OR models using a variety of methods.
- Interpret the results of OR models and apply them to real-world engineering problems.
Math Topics
- Introduction to OR
- Linear programming
- Integer programming
- Dynamic programming
- Network optimization
- Queueing theory
- Simulation
- Decision analysis
Application Topics
- Production planning
- Inventory management
- Supply chain management
- Scheduling
- Project management
- Quality control
- Transportation planning
Career opportunities for readers who complete:
- Operations research analyst
- Industrial engineer
- Manufacturing engineer
- Supply chain manager
- Transportation engineer
- Project manager
- Quality control engineer
Additional Resources Engineering
- Operations Research: An Introduction, 10th Edition by Hamdy A. Taha
Physics Applications
Readers should have a strong foundation in calculus, linear algebra, and probability and statistics. They should also have some familiarity with basic physics concepts.
Upon completion, readers will be able to:
- Understand the basic concepts and techniques of OR.
- Formulate mathematical models of real-world physics problems.
- Solve OR models using a variety of methods.
- Interpret the results of OR models and apply them to real-world physics problems.
applications in physics, such as:
- Analysis of complex data sets: OR can be used to analyze complex data sets, such as experimental data from physics experiments and observational data from astronomical surveys.
- Development of new physical theories: OR can be used to develop new physical theories by providing insights into the behavior of complex systems.
- Experiment design: OR can be used to design experiments that are efficient and informative.
- Data analysis: OR can be used to analyze experimental data and extract meaningful insights.
- Model development: OR can be used to develop mathematical models of physical systems.
- Simulation: OR can be used to simulate physical systems to test hypotheses and predict behavior.
- Optimization: OR can be used to optimize physical systems for performance or efficiency.
Topics
- Introduction to OR
- Linear programming
- Integer programming
- Dynamic programming
- Network optimization
- Queueing theory
- Simulation
- Decision analysis
- OR applications in physics
Finance Applications
- Understand the basic concepts and techniques of OR.
- Formulate mathematical models of real-world financial problems.
- Solve OR models using a variety of methods.
- Interpret the results of OR models and apply them to real-world financial problems.
Specific OR applications in finance that may be covered include:
- Portfolio management: OR can be used to develop and optimize investment portfolios under various risk and return constraints.
- Risk management: OR can be used to identify and assess risks in financial markets, and to develop strategies to mitigate those risks.
- Pricing and hedging of financial instruments: OR can be used to price and hedge financial instruments, such as options and derivatives.
- Algorithmic trading: OR techniques can be used to develop and implement algorithmic trading strategies.
- Risk management in high-frequency trading: OR techniques can be used to manage risks in high-frequency trading, such as market microstructure risk and operational risk.
- Credit scoring for emerging markets: OR techniques can be used to develop credit scoring models for emerging markets, where data is often scarce and unreliable.
- Fraud detection in online banking: OR techniques can be used to develop and implement systems to detect and prevent fraud in online banking.
This will cover the following topics:
- Introduction to OR
- Linear programming
- Integer programming
- Dynamic programming
- Network optimization
- Queueing theory
- Simulation
- Decision analysis
- OR applications in finance
Additional Resources Finance
- The Financial Management Association International (FMA)
- The Chartered Institute for Securities & Investment (CISI)
