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, 368, or 401, or concurrent registration in STA 401

- 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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