Operations Research

MATH 333, Spring Semester, 2017

 

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Instructor:    Dr. Shieu-Hong Lin   LinEmail

Class time:      MW     10:30-11:45pm at Grove 4B

Office Hours: M~Th  8:30-10:30 am

 

Syllabus: compact version

 

Books and references

·       Prajit K. Dutta. Strategies and Games: Theory and Practice. MIT Press, 1999. (Required textbook)

·       Robert Fourer, David M. Gay, and Brian W. Kernighan. AMPL: A Modeling Language for Mathematical Programming (online)

·       Online service for mathematical programming using AMPL 

·       R. Vanderbei. Linear Programming: Foundations and Extensions, 2nd ed.  Springer 2001.

 

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About the reading reports:

·     Effort (2 points): How much time have you spent in the reading? What percentage of the contents in the reading do you think you understand? Have you come to the class this week?  Assessment: The student is expected to (i) have attended the class this week at least once (0.5 point), and(ii) have either gained a good understanding of 80% or more of the contents or have spent at least three hours in the reading (1.5 points).

·     Reflection on the reading (2 points): Put down 1~2 paragraphs of your thoughts such as notes of new insight you gained, interesting things encountered, questions of things you don’t understand,  and so forth.  Assessment: the student is expected to show substantial evidence of understanding or effort of trying to understand the contents in the reading.

 

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Week 1: Introduction to Mathematical Programming and AMPL: Production Models

 

Showcase 1: Optimization Problems for Vehicle Refueling Planning

Showcase 2: Mechanism of a Bidding Game: Design and Analysis

 

Enter your report online under Canvas according to this format.

 

 

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Week 2: More on Linear Programming Using AMPL: Diet Models

 

 

·       Explore the continuous knapsack problem and see an example in 1 about how we can solve the problem efficiently. As discussed 02/06 in the class, the optimization problem in the production domain depicted in Chapter 1 of the AMPL book can be viewed and efficiently solved as the continuous knapsack problem without using linear programming. Please reflect on how this and describe how this can be done in your report.

·       Show in your report how you can apply your understanding of the continuous knapsack problem above to solve the production domain case depicted in the AMPL sample code on P.5 of Chapter 1 without using linear programming.

 

 

 

 

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Week 3: More on Linear Programming Using AMPL: Transportation and Assignment Models

 

 

 

 

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Week 4: Transportation/Assignment Model + Dominant Strategies in Strategic Form Games

 

 

·       Homework #3 Due: Wednesday March 8

 

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Week 5: Dominant Strategies in Strategic Form Games

 

 

 

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Week 6: Dominance Solvability in Strategic Form Games

 

 

 

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Week 7: Dominance Solvability in Strategic Form Games and Nash Equilibria

 

 

 

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Week 8: Nash Equilibrium

 

 

 

 

 

Note: Be very careful about the following definitions of terms in the textbook:

                        i.         A strategy s is a dominant strategy for player i if and only if s weakly dominates all other strategies for player i.

                      ii.         A strategy s is a dominated strategy for player i if and only if s is weakly dominated by one or more strategies for player i.

 

 

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Weeks 9-10: Application of Nash Equilibrium: Cournot Duopoly | Spring Break

 

 

 

 

Test #1 (in-class open-book test) on Chapters 3-5 of Strategies and Games: Theory and Practice: Wednesday April 12

1)     Carefully review Homework #4A and Homework #4B. What would happen if we adopt a similar "Third Price" sealed bid auction mechanism where the winner pays the third highest price among all bids?  Carefully review Homework #5. What would happen if we adopt the variant mentioned in the end of Homework #5. It is recommended that you print out the rules of all the games involved in them and bring them with you for your reference during the test. We may ask you questions related to these games or their related variants.

2)     Carefully review (i) the voting game on pages 10, 53, and 54, (ii) the hawk-and-dove game on page 37 and the spider-fight variant in Section 5.3, and (iii) the odd-couple example on Pages 52, 53, and 67.

 

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Week 11: Mixed Strategies

 

 

 

 

 

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Power point class notes available under Files in our Canvas class site.

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TA:  William Tan.  TA hours in MATH lab: Monday/Wednesday 2:00~3:00pm

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