Typically offered during both the fall and spring semesters.

Catalog description:

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

Prerequisites:

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

Required topics (approximate weeks allocated):

• 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)

Course Outcomes

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
2. 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
3. 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
4. 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
5. 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