Dr. Julie Ivy
Industrial and Systems Engineering
ISE 560 Stochastic Models in Industrial Engineering
3 Credit Hours
This course will introduce mathematical modeling, analysis, and solution procedures applicable to uncertain (stochastic) production and service systems. Methodologies covered include probability theory and stochastic processes including discrete and continuous Markov processes. Applications relate to design and analysis of problems, capacity planning, inventory control, waiting lines, and system reliability and maintainability. This course will be taught at the Masters’ level.
A previous course in probability and statistics.
This course has three components:
- Probability Tools: characterizing uncertainty using probabilities and random variables.
- Decision Modeling under Uncertainty: models for decision making under uncertainty: decision tress, utility theory, value of information, Bayes rule.
- Stochastic Modeling: characterizing uncertainty over time and space using:
- Discrete Time Markov Chains: Markov decision processes
- Probabilistic Inventory Models and
- Queuing Theory: Poisson Processes and Continuous Time Markov Chains
Upon the completion of this course, students will be able to use the tools of probability and stochastic processes to develop models to improve decision-making in an uncertain environment. Specifically:
Probability Objectives: Students will be able to:
- Identify and Apply probability distributions appropriately to various applications
- Understand probability distributions (unconditional and conditional) for single and multivariate random variables
Decision Modeling Objectives: Students will be able to:
- Formulate/Structure decision problems using tables and decision trees
- Use various criteria to evaluate decision problems
- Estimate the value of perfect and sample information
- Demonstrate understanding of utility theory and calculate a utility
- Formulate dynamic decision problems using a Markov decision process
Stochastic Modeling Objectives: Students will be able to:
- Define and characterize a stochastic process
- Identify, Define and Apply stochastic models particularly, Markov chains (discrete and continuous), queueing models and inventory models
- Develop Stochastic Models for various real world applications
- Apply stochastic modeling theory to a real world problem.
The course will require regular homework assignments, exams, and a project –the weights for each will be determined.
Required – Online Reserve:
Introduction to Probability Theory, Hoel, Port, and Stone, 1971. Chapters: 1 – 7, 9.
Publisher: Boston: Houghton Mifflin.
Introduction to Operations Research, Ninth Edition, Hillier and Lieberman, 2010.
Chapters: 15, 16, 17, 19. Publisher: McGraw-Hill.
Markov Chains: From Theory to Implementation and Experimentation, Gagniuc, 2017.