Operations Research: Inquiring Minds Want to Know!

Evan GlazerEvan.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

Develop algorithms from theory and simulation to make sense out of a system

Connecting OR to Math Curricula

Local contributors include:

Lisa BredienbachEllen ChienIlana HandHazel OrthHelen Snyder

http://www.hsor.org/

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

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

TJHSST homecoming

Raggedy Ann and Andy

Hotdog and ketchup

Teenage Mutant Nija Turtles

We’re inseparable

dy = x + ydx

Operations Research Encourages… a systematic

approach to solving non-routine problems

a systematic approach to evaluation

simulation to understand the unknown

Encourages a Systematic Approach to Solving Problems

Knownalgorithm

Linear Programming

Navigating across Romania

Try navigating Fairfax County

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

Develop an algorithm

http://academics.tjhsst.edu/compsci/CSweb/Unit3/Lab15/Applet15.html

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

Unknownalgorithm

Encourages a Systematic Approach to Evaluation

Google PageTMRank

http://en.wikipedia.org/wiki/PageRank

NCAA Quarterback Rating

+ + +

NFL Quarterback Rating

http://en.wikipedia.org/wiki/Passer_rating

Guess this ranking formula

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

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)

Encourages Simulation to Understand the Unknown

http://quantio.cz/demo/simul/

Note normal distribution, random selection

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

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

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

Math applications Inquiry Hypotheses Discovery

Operations Research: Inquiring Minds Want to Know!

Evan GlazerEvan.Glazer@fcps.edu

Thomas Jefferson High School for Science and Technology