Education and Training (updating for more notes)
Part 1: Probability & Statistics
OPIM 701, Probability and Statistics, Instructor: Prof. Rowan Wang.
Combinatorial Analysis, Axioms of Probability
Conditional Probability
Random Variable, Joint Distribution, Expectation
Limit Theorem & Law of large numbers, Simulation
Descriptive Statistics & Sampling
Confidence Interval, Hypothesis Test, Regression
Part 2: Linear & Convex Optimization
OPIM 700, Linear Optimization, Instructor: Prof. Sarah Yini Gao.
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Introduction to Linear Models, Geometry of Linear Programming
The Simplex Method, Duality Theory and Sensitivity Analysis
Introduction to Large-scale Optimization and Stochastic Programming
Network Flow Problems
Discrete Optimization
OPIM 705, Topics in Advanced Optimisation Techniques, Instructor: Prof. ZHENG Zhichao Daniel.
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Introduction to Convex Optimization, Convex Sets
Convex Functions I
Convex Functions II
Convex Optimization Problems
Duality
Applications of Convex Optimization in Statistical Estimation
Paper reading session on Robust Optimization, Distributionally Robust Optimization and their applications.
Part 3: Inventory Management & Dynamic Programming
OPIM 702, Foundations of Operations Management, Instructor: Prof. Buket AVCI.
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Deterministic Inventory Models: EOQ Model and Variations
Stochastic Inventory Models I: Single Period Newsvendor Set-up and Solution
Newsvendor Generalizations: Distribution Free Newsvendor Problem, Simultaneous Quantity & Effort Decisions, Price-Setting Newsvendor
Dealing with uncertainty in Inventory Optimization: Risk pooling & Transshipment & Partial Variety Postponement
Supply Chain Contracting: Wholesale price, Buyback, Revenue sharing, Quantity flexibility, Sales rebate, Quantity discount contracts
Stochastic Inventory Models II: Multiple Periods Inventory Problem, Base Stock Policies, (s,S) Policies, (r,Q) Policies.
Queue I: Waiting Line Management, Little’s Law. PASTA property, Birth &Death Processes
Queue II: Waiting Times in M/M/1 and M/M/c Queues, Simple Markovian Queueing Models
OPIM 703, Dynamic Programming, Instructor: Prof. FENG Guiyun.
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Principle of optimality
Inventory applications: convexity and K-convexity, Basestock policies, (s,S) policies
Optimal stopping problems: parking problem, secretary problem
Monotonic policy and submodularity/supermodularity
Discounted infinite-horizon problems
Value Iteration, Policy Iteration, linear programming approach
Stochastic shortest path problem and Undiscounted infinite-horizon problem with average cost
Paper reading session on approximate policy iteration and other approximation methods for ADP
Part 4: Game Theory
OPIM 706, Topics in Game Theory and its Application, Instructor: Prof. FANG Xin.
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Normal Form, Dominance, Nash Equilibrium, Mixed Strategies
Dynamic Games, Backwards Induction, Repeated Games
Price and Quantity Competition, Quality and Spatial Competition
Incomplete Information, Bayesian Nash, Perfect Bayesian
Signaling
Principal Agent and Contracting
Bargaining and Negotiation
Cooperative Game Theory
Part 5: Stochastic Model
OPIM 704, Stochastic Models, Instructor: Prof. Sharafali MOOSA.
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Exponential distribution and Poisson process
Renewal theory
Discrete time Markov chains
Continuous time Markov Chains
Stochastic orders