Operations Research 2

Description:

Concept and solution approaches of advanced optimization models and their application to engineering. Goal programming, dynamic programming, decision theory, game theory, Markov models, and queuing theory.

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Topics:

1. Goal Programming: Multi-Objective LP Problem
a. Concept and Formulation
b. Graphical Solution

2. Dynamic Programming (DP)
a. Concept, Properties, Principle of Optimality
b. Formulation of Deterministic and Probabilistic DP
i. Backward and Forward Recursive Equations
c. Backward and Forward Solution Approaches

3. Decision Theory
a. Concept and Decision-Making Scenarios
b. Certainty and Uncertainty Scenarious
i. Perfect Information
ii. Decision-Making Criteria Under Uncertainty
c. Decision-Making Under Risk

i . Risk Bayes' Rule
ii. Posterior Analysis
iii. Decision Trees
iv. Utility Theory

4. Game Theory: Decision-Making under Conflict
a. Concept and Structure of Games
b. Solution to Two-Person, Zero-Sum Games
c. Non-Zero Sum Games

5. Queuing Theory
a. Definition, Basic Elements, and Properties
b. Queuing Models with Poisson Input and Output:
i. Self-Service
ii. Single and Multiple Servers

6. Markov Theory
a. Definition, Characteristics, and Assumptions
b. Components of a Markov Chain
c. Classification of States
d. Markov Decision Processes


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