IE 373LR – Optimization in Deterministic Systems: Techniques, Methods, and Applications
Introduction
- Definition of optimization in deterministic systems
- Importance of optimization in deterministic systems
- Overview of IE 373LR course
Optimization Techniques in Deterministic Systems
Linear Programming
- Introduction to linear programming
- Formulation of linear programming problems
- Simplex method and its variants
- Duality theory
- Sensitivity analysis
Nonlinear Programming
- Introduction to nonlinear programming
- Unconstrained optimization
- Constrained optimization
- Gradient-based methods
- Penalty and barrier methods
- Karush-Kuhn-Tucker (KKT) conditions
Integer Programming
- Introduction to integer programming
- Formulation of integer programming problems
- Branch and bound method
- Cutting plane method
- Branch and cut method
- Mixed-integer programming
Dynamic Programming
- Introduction to dynamic programming
- Bellman’s principle of optimality
- Applications of dynamic programming
- Finite horizon problems
- Infinite horizon problems
- Approximate dynamic programming
Convex Optimization
- Introduction to convex optimization
- Convex sets and functions
- Convex optimization problems
- Duality in convex optimization
- Applications of convex optimization
Applications of Optimization in Deterministic Systems
Supply Chain Management
- Inventory control
- Production planning
- Distribution network design
- Transportation planning
- Facility location
Operations Management
- Process design and control
- Capacity planning
- Quality control
- Project management
- Scheduling
Finance
- Portfolio optimization
- Option pricing
- Risk management
- Credit scoring
- Algorithmic trading
Engineering
- Design optimization
- Control system design
- Signal processing
- Robotics
- Aerospace engineering
Conclusion
- Recap of IE 373LR course
- Importance of optimization in deterministic systems
- Future research directions
FAQs
- What is optimization in deterministic systems?
- Optimization in deterministic systems is the process of finding the best solution to a problem subject to a set of constraints and a given objective function.
- What are the most common optimization techniques used in deterministic systems?
- The most common optimization techniques used in deterministic systems are linear programming, nonlinear programming, integer programming, dynamic programming, and convex optimization.
- What are some real-world applications of optimization in deterministic systems?
- Some real-world applications of optimization in deterministic systems are supply chain management, operations management, finance, and engineering.
- How does optimization help in supply chain management?
- Optimization helps in supply chain management by optimizing inventory control, production planning, distribution network design, transportation planning, and facility location.
- What are some future research directions in optimization in deterministic systems?
- Some future research directions in optimization in deterministic systems are multi-objective optimization, robust optimization, stochastic optimization, and machine learning-based optimization.