Advanced Operations Research
Teaching · IE 5301 · UT Arlington · 2023–
A survey of quantitative methods for modeling and decision-making, deterministic and stochastic, for graduate students.
Topics
- Linear, integer and convex programming: simplex, interior point, branch-and-bound
- Network analysis, facility location, and transportation and assignment problems
- Nonlinear and multi-objective programming, and game theory
- Decision trees and Monte Carlo simulation
- Markov chains and queuing theory
How it is taught and assessed
- Exams on deterministic and stochastic operations research, and a final (60%)
- A team project that applies the course to a dataset, with a report and presentation (25%)
- Homework, mostly computer assignments done in groups (10%)
- Quizzes and short assignments (5%)
Tools. Optimization modeling in Python (GurobiPy) and Excel; stochastic modeling, simulation, visualization and reports in Python and Jupyter notebooks.
Textbook
Operations Research: An Introduction, 10th edition, Hamdy Taha available through the UTA library
Key concepts
- Problem classes
- LP, MILP (some integer variables), NLP (nonlinear), QP (quadratic objective) and MINLP: the class decides which solver can be trusted to find the optimum.
- KKT conditions
- The conditions a solution of a smooth constrained problem must satisfy; for convex problems they are also enough to prove it optimal.
- Decomposition
- Splitting a large problem into a master problem and subproblems that pass information back and forth, as in Benders decomposition and column generation.
- Stochastic program
- An optimization model whose data are uncertain, with some decisions made now and others after the uncertainty is revealed.
- Value of the stochastic solution (VSS)
- How much better the stochastic solution does than planning on the average scenario; the expected-value approach assumes the future will equal the historical average.
- Markov chain
- A system that moves between states with probabilities that depend only on the current state.
- Queue utilization
- ρ = λ/μ, the arrival rate over the service rate; as it approaches 1, waiting times grow without bound.
Interactive models
- Accurate, and Still Wrong: a Gaussian-process surrogate linking two optimization models
Code examples
- Quadratic programming examples and algorithms
- Basics of Markov chains
- The basics of simulation
- Benders decomposition explained
- Decomposition algorithms broken down and explained
Free tools and readings
Learn
- Sequential Decision Analytics and Modeling (Warren Powell)
- Stochastic Programming Society
- KKT conditions, APMonitor
- Column generation, explained
- Queueing simulation with SimPy