COURSE OUTLINE: MH4702

Intended Learning Outcomes

Upon successfully completing this course, you should be able to:

1. Recognise a queueing system and determine its expected queue length and average waiting time.
2. Evaluate a stochastic system, e.g. queueing system using the simulation method
3. Model an operational problem under an uncertain circumstance in a mathematical form
4. Solve the optimization problem under uncertainties
5. Formulate a Markov decision model to solve for a sequential decision making under uncertainty
6. Use one of the algorithms discussed in the lecture to determine the optimal policy for a Markov decision process.

Course Content

General Introduction to Operations Research: Revision of Basic Probability Theory

Basic Queueing System, Birth-death Process, Little’s Formula, The M/M/s, M/M/s/K models, Queue Length and Waiting Time,

Sampling continuous and discrete distribution, Monto Carlo methods, Variance Reduction Techniques

Sensitivity Analysis in a Linear Program, Sample Average Approximation Method, Robust Optimization with Box Uncertainty Set

Formulating Markov Decision Model, Linear Programming Approach, Policy Improvement Algorithm

Assessment

Formative Feedback

Midterm Test: Feedback on common mistakes and the level of difficulty of the problems will be given.

Assignments: Students will receive individual written and/or verbal feedback about their assignments, as the lecturer will return each assignment individually.

Learning and Teaching Approach

Reading and References

1. Introduction to Operations Research. Hillier & Lieberman, 10th Ed, McGraw Hill (ISBN 10: 0073376299 ISBN 13: 978-0072535105)
2. Introduction to Probability Models, by Sheldon M. Ross. 10th Edition. (ISBN: 9780128143469)
3. Stochastic Models in Operations Research by D. Heyman and M. Sobel (2 volumes) (ISBN 10: 0486432602 ISBN 13: 9780486432601)

Course Policies and Student Responsibilities

(1) General

You are expected to complete all assignments and take the midterm test. You are expected to take responsibility to follow up with course notes, assignments and course related announcements if they are absent.

(2) Absenteeism

Absence from test and examination without a valid reason will affect your overall course grade. Valid reasons include falling sick supported by a medical certificate and participation in NTU’s approved activities supported by an excuse letter from the relevant bodies.

(3) Absence Due to Medical or Other Reasons

If you are sick and not able to attend the midterm, you have to submit the original Medical Certificate (or another relevant document) to the administration to obtain official leave. In this case, the missed assessment component will not be counted towards the final grade. There are no make-up midterm.

Academic Integrity

Good academic work depends on honesty and ethical behaviour. The quality of your work as a student relies on adhering to the principles of academic integrity and to the NTU Honour Code, a set of values shared by the whole university community. Truth, Trust and Justice are at the core of NTU’s shared values.

As a student, it is important that you recognize your responsibilities in understanding and applying the principles of academic integrity in all the work you do at NTU. Not knowing what is involved in maintaining academic integrity does not excuse academic dishonesty. You need to actively equip yourself with strategies to avoid all forms of academic dishonesty, including plagiarism, academic fraud, collusion and cheating. If you are uncertain of the definitions of any of these terms, you should go to the Academic Integrity website for more information. Consult your instructor(s) if you need any clarification about the requirements of academic integrity in the course.

Course Instructors

Planned Weekly Schedule