operations research: inquiring minds want to know! evan glazer [email protected] thomas jefferson...
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Operations Research: Inquiring Minds Want to Know!
Evan [email protected]
Thomas Jefferson High School for Science and Technology
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The origins of my interest in mathematics
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Operations Research Scientific approach
to analyzing problems and making decisions
Develop algorithms from theory and simulation to make sense out of a system
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Connecting OR to Math Curricula
Local contributors include:
Lisa BredienbachEllen ChienIlana HandHazel OrthHelen Snyder
http://www.hsor.org/
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http://academics.tjhsst.edu/mathcs/courses.htm
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OR student assignments/projects Optimizing ant colony heuristic to a
dynamic traveling salesman problem
Identifying transformations to improve a driving simulator
Optimizing flow movement in and out of school
Developing an algorithm to improve calculation of speed of planes as they approach an airport
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TJHSST homecoming
Raggedy Ann and Andy
Hotdog and ketchup
Teenage Mutant Nija Turtles
We’re inseparable
dy = x + ydx
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Operations Research Encourages… a systematic
approach to solving non-routine problems
a systematic approach to evaluation
simulation to understand the unknown
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Encourages a Systematic Approach to Solving Problems
Knownalgorithm
Linear Programming
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Navigating across Romania
Try navigating Fairfax County
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Dijkstra's shorters path algorithm1. Create a distance list, a previous vertex list, a visited list,
and a current vertex. 2. All the values in the distance list are set to infinity except
the starting vertex which is set to zero. 3. All values in visited list are set to false. 4. All values in the previous list are set to a special value
signifying that they are undefined, such as null. 5. Current vertex is set as the starting vertex. 6. Mark the current vertex as visited. 7. Update distance and previous lists based on those
vertices which can be immediately reached from the current vertex.
8. Update the current vertex to the unvisited vertex that can be reached by the shortest path from the starting vertex.
9. Repeat (from step 6) until all nodes are visited. Source: http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
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Develop an algorithm
http://academics.tjhsst.edu/compsci/CSweb/Unit3/Lab15/Applet15.html
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Develop an algorithm In a game of Nim, you start with 17
pennies The goal to win is to leave your
opponent with the last penny on the table
You can select 1, 2, or 3 pennies when it is your turn
Keep taking turns until there is only one penny remaining
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Unknownalgorithm
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Encourages a Systematic Approach to Evaluation
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Google PageTMRank
http://en.wikipedia.org/wiki/PageRank
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NCAA Quarterback Rating
+ + +
NFL Quarterback Rating
http://en.wikipedia.org/wiki/Passer_rating
Guess this ranking formula
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Appropriation of Seats to Congress
The Constitution provides that each state will have a minimum of one member in the House of Representatives, and the current size of the House (435 seats) has not changed since the apportionment following the 1910 census. Thus, the apportionment calculation for Census 2000 will divide 385 seats among the 50 states. Congress decides the method used to calculate the apportionment….Adopted by congress in 1941 and used through the 1990 census, the method of equal proportions also results in a listing of the states according to a priority value--calculated by dividing the population of each state by the geometric mean of its current and next seats….
http://www.census.gov/population/www/censusdata/apportionment/history.htmlhttp://www.census.gov/population/www/censusdata/apportionment/calculated.html
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Which factors influence the 2008 vote?
Discuss issues that affect someone’s vote
Identify corresponding weight
Develop method for prediction
18% voters undecided (as of Sep 24, according to Yahoo polls)
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Encourages Simulation to Understand the Unknown
http://quantio.cz/demo/simul/
Note normal distribution, random selection
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Queuing Theory L = a/(h – a) W = L/a
L = average length of lineW = total waiting and service time
a = average arrival rateh = average help/service rate
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How should you divide portables for equitable access?
Think about: Service time for
men and women Proportional
usage by men and women
L = a/(h – a)W = L/a
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http://www.arcytech.org/java/population/index.html
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Math applications Inquiry Hypotheses Discovery
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Operations Research: Inquiring Minds Want to Know!
Evan [email protected]
Thomas Jefferson High School for Science and Technology