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Learning Outcomes

This course will cover important topics in Applied Probability, Operations Research and Stochastic Optimization. It will focus on methodology, modeling techniques and mathematical insights. The aim is to train students to a level of technical competency to appreciate and understand current literatures. This is a core module for PhD students in the Decision Science department.

Prerequisites

TopProbability Theory.

Teaching Modes

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The course is primarily lecture based. Each lecture per week is roughly 3 hours and tutorial questions will be given at the end of the lecture. Students are expected to COMPLETE the assignment questions before the next lecture. They may be asked to present their solutions in class as part of their assessment.

Syllabus

TopLecture 1: Preliminaries
Lecture 2: Definition, Properties, and Limit Behaviors of Renewal Processes;
Lecture 3: Wald's Equation; Elementary Renewal Theorem; Key Limit Theorem; and Delay, Stationary and Alternative Renewal Processes;
Lecture 4: Renewal Reward Process, and Application in Inventory Models, Queueing Models and Reliability Theory;
Lecture 5: Finite Horizon Markov Decision Processes;
Lecture 6: Discounted Dynamic Programming;
Lecture 7: Minimizing Costs--Negative Dynamic Programming;
Lecture 8: Maximizing Rewards--Positive Dynamic Programming;
Lecture 9: Average Reward Criterion;
Lecture 10: Applications in Inventory Models, Scheduling Problems, and Equipment Maintenance Problems;
Lecture 11: Stochastic Orders;
Lecture 12: Applications in Inventory Models, Queueing Models and Reliability Theory

Assessment

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Midterm exam: 30%

Final exam: 30%

Class Participation and Assignments: 40%

Preclusions

TopNIL

Workload

Top3-0-0-4-3

Workload Components : A-B-C-D-E
A: no. of lecture hours per week
B: no. of tutorial hours per week
C: no. of lab hours per week
D: no. of hours for projects, assignments, fieldwork etc per week
E: no. of hours for preparatory work by a student per week