**Typically offered during both the fall and spring semesters.**

Survey of methods of stochastic operations research including reliability, Markov processes, queuing theory, and decision theory. Computer used for modeling and solving problems.

STA 301/401/501 or concurrent registration or STA 368.

- Review of probability (1)
- Markov chain models (3)
- stochastic processes, Markov chains
- classification of states of a Markov chain
- steady-state probabilities and first passage times
- absorbing states

- Decision analysis (2)
- decision making under uncertainty
- decision making under risk: with and without experimentation
- decision trees and Baye's rule

- Queuing models (5)
- pure birth, pure death and birth-death processes
- queuing models based on birth-death processes
- models involving non-exponential distributions

- Optional topics (3.5)
- reliability
- introduction to game theory: two-person zero-sum games
- introduction to inventory models: basic EOQ model, single-period decision models, news vendor problems
- introduction to forecasting: moving average, simple exponential smoothing, Holt's method (trend)
- introduction to simulation
- utility theory

- Exams/Review (1)

- To be able to apply previous knowledge of probability theory to construct stochastic models of random systems
- The student can use probability distributions to represent random components of a system
- The student can use the probability theory to compute event probabilities, expected values, and variances in random environments
- The student can use the theoretical distributions Binomial, Poisson, Normal, and Exponential to represent random components of a system

- To be able to model time dependent random phenomena as a Markov chain
- The student can explain the fundamental assumptions and terminologies of a Markov chain
- The student can recognize and compute state probabilities and expected passage times for ergodic Markov chains
- The student can recognize and compute absorption probabilities and expected time until absorption for absorbing Markov chains

- To be able to model birth-death queuing systems in steady state
- The student can explain the fundamental assumptions and terminologies of birth-death queuing systems
- The student can recognize and compute state probabilities, expected utilizations, expected time in the system, and expected number in the system for birth-death queuing systems with various numbers of servers, various amounts of queuing space, and various size populations
- The student can recognize and perform similar computations to those listed in (3b) for a simple non birth-death queuing systems
- The student can recognize and perform similar computations to those listed in (3b) for a birth-death queuing networks with and without feedback

- To be able to model decisions with uncertain outcomes
- The student can represent a decision problem with uncertain outcomes as a decision tree and determine the action with the best expected performance
- The student can compute the expected performance improvement by obtaining additional information and perfect information
- The student can apply Bayes' rule to compute posterior probabilities based on the value of the additional information
- The student can model a decision maker's behavior using utility functions

- To be able to deal effectively with stochastic elements in a wide variety of systems
- The student can apply the fundamentals developed in Objectives 1-4 to a wide variety of application areas
- The student understands how to use data to model stochastic elements of a system

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