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Operations Research: Inquiring Minds Want to Know!

Operations Research: Inquiring Minds Want to Know!. Evan Glazer Evan.Glazer@fcps.edu Thomas Jefferson High School for Science and Technology. The origins of my interest in mathematics. Operations Research. Scientific approach to analyzing problems and making decisions

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Operations Research: Inquiring Minds Want to Know!

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  1. Operations Research: Inquiring Minds Want to Know! Evan GlazerEvan.Glazer@fcps.edu Thomas Jefferson High School for Science and Technology

  2. The origins of my interest in mathematics

  3. Operations Research • Scientific approach to analyzing problems and making decisions • Develop algorithms from theory and simulation to make sense out of a system

  4. Connecting OR to Math Curricula • Local contributors include:Lisa BredienbachEllen ChienIlana HandHazel OrthHelen Snyder http://www.hsor.org/

  5. http://academics.tjhsst.edu/mathcs/courses.htm

  6. 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

  7. dy = x + ydx We’re inseparable TJHSST homecoming • Raggedy Ann and Andy • Hotdog and ketchup • Teenage Mutant Nija Turtles

  8. Operations Research Encourages… • a systematic approach to solving non-routine problems • a systematic approach to evaluation • simulation to understand the unknown

  9. Encourages a Systematic Approach to Solving Problems KnownalgorithmLinear Programming

  10. Navigating across Romania Try navigating Fairfax County

  11. Dijkstra's shorters path algorithm • Create a distance list, a previous vertex list, a visited list, and a current vertex. • All the values in the distance list are set to infinity except the starting vertex which is set to zero. • All values in visited list are set to false. • All values in the previous list are set to a special value signifying that they are undefined, such as null. • Current vertex is set as the starting vertex. • Mark the current vertex as visited. • Update distance and previous lists based on those vertices which can be immediately reached from the current vertex. • Update the current vertex to the unvisited vertex that can be reached by the shortest path from the starting vertex. • Repeat (from step 6) until all nodes are visited. Source: http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm

  12. Develop an algorithm http://academics.tjhsst.edu/compsci/CSweb/Unit3/Lab15/Applet15.html

  13. 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

  14. Unknownalgorithm

  15. Encourages a Systematic Approach to Evaluation

  16. Google PageTMRank http://en.wikipedia.org/wiki/PageRank

  17. NFL Quarterback Rating http://en.wikipedia.org/wiki/Passer_rating NCAA Quarterback Rating + + + Guess this ranking formula

  18. 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/calculated.html http://www.census.gov/population/www/censusdata/apportionment/history.html

  19. 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)

  20. Encourages Simulation to Understand the Unknown http://quantio.cz/demo/simul/ Note normal distribution, random selection

  21. Queuing Theory • L = a/(h – a) • W = L/a L = average length of line W = total waiting and service time a = average arrival rate h = average help/service rate

  22. 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

  23. http://www.arcytech.org/java/population/index.html

  24. Math applications • Inquiry • Hypotheses • Discovery

  25. Operations Research: Inquiring Minds Want to Know! Evan GlazerEvan.Glazer@fcps.edu Thomas Jefferson High School for Science and Technology

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