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L ESSON ON N ETWORKS: Finding the Shortest Route and 1-Center Location

L ESSON ON N ETWORKS: Finding the Shortest Route and 1-Center Location. ELENA I. PASCUAL Eisenhower 9th Grade Center Aldine ISD Houston, Texas. Mentors: Dr. HALIT USTER Director of logistics and Networked Systems Research Laboratory Department of Industrial Engineering

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L ESSON ON N ETWORKS: Finding the Shortest Route and 1-Center Location

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  1. LESSON ON NETWORKS: Finding the Shortest Route and 1-Center Location ELENA I. PASCUAL Eisenhower 9th Grade Center Aldine ISD Houston, Texas Mentors: Dr. HALIT USTER Director of logistics and Networked Systems Research Laboratory Department of Industrial Engineering Texas A & M, College Station BURCU B. KESKIN (Ph. D. expected 2006)

  2. OBJECTIVES:In this lesson, the students will: 1. become familiar with basic elements of a network; 2. integrate physics concepts and skills to solve engineering problems; 3. find the shortest route and 1-center location using algorithms. 4. design a network system to solve real life situation problems.

  3. BACKGROUNDSCIENCE • Before presenting this lesson, the students should have mastered their skills on physics concepts of speed, distance, displacement, velocity, and acceleration. • The students have demonstrated mastery on problem solving and critical thinking.

  4. Mayor White of Houston wants to improve the service efficiency of the Harris County Fire Department. As such, he proposed that the location of the Harris County Fire Department Headquarter must be relocated in such a way that the Fire Fighters must be able to reach any of their assigned service areas, the easiest and the shortest time possible. In order to solve the problem, and at the same time to please the mayor, Maj. Browne, the newly assigned Head of the Fire Department , consulted Industrial Engr. Spencer to decide where is the best location for them to move the Headquarter. Looking at the different service areas covered by Harris County, as shown in the diagram, where should be the right location that Engr. Spencer would recommend to Maj. Browne so as to solve the problem? ACTIVITY No. 1

  5. 1-CENTER LOCATION ON TREE NETWORK A C 8 5 J 3 B 7 5 E 6 2 D I F 4 1 1 G H K 4 L

  6. 1-CENTER LOCATION ON TREE NETWORKSTEPS A C 8 5 J 3 B 7 5 E 6 2 D I F 4 1 1 G H K 4 L

  7. 1-CENTER LOCATION ON TREE NETWORKSTEPS A C 8 5 J 3 B 7 5 E 6 2 D I F 4 1 1 G H K 4 L

  8. 1-CENTER LOCATION ON TREE NETWORKSTEPS A C 8 5 J 3 B 7 5 E 6 2 D I F 4 1 1 G H K 4 L

  9. 1-CENTER LOCATION ON TREE NETWORKSTEPS A 8 14 C 8 16 5 J 3 B 7 5 E 11 6 2 D I F 4 1 14 1 G H K 4 L 5

  10. 1-CENTER LOCATION ON TREE NETWORKSTEPS A 8 14 C 8 16 5 J 3 B 7 5 E 11 6 2 D I F 4 1 14 1 G H K 4 L 5

  11. 1-CENTER LOCATION ON TREE NETWORKSTEPS A C 8 16 5 J 3 B 7 5 E 6 2 D I F 4 1 1 G H K 4 L

  12. 1-CENTER LOCATION ON TREE NETWORKSTEPS A C 8 16 5 J 3 B 7 5 E 6 2 D I F 4 1 1 G H K 4 L

  13. 1-CENTER LOCATION ON TREE NETWORKSTEPS 24 A 18 C 8 16 5 J 3 B 7 5 E 21 6 2 D I F 4 1 12 1 G H K 4 L 16 19

  14. 1-CENTER LOCATION ON TREE NETWORKSTEPS 24 A 18 C 8 16 5 J 3 B 7 5 E 21 6 2 D I F 4 1 12 1 G H K 4 L 16 19

  15. 1-CENTER LOCATION ON TREE NETWORKSTEPS 24 A C 8 16 5 J 3 B 7 5 E 6 2 D I F 4 1 1 G H K 4 L

  16. 1-CENTER LOCATION ON TREE NETWORKRESULT 24 A C 8 5 J 3 B 7 5 E 6 2 D 1-center I F 4 1 1 G H K 4 L

  17. The Physical Analogy Model1-Center Algorithm: 1. Pick a tip node, call it v. 2. Find the tip node farthest away from v, call it v’. 3. Find the tip node farthest away from v’, call it v”. 4. Find the midpoint of the path v’-v”. This is the optimum 1-center location.

  18. Activity NO.2 Speedy Delivery: Finding the Shortest Route • Mr. Pete Zahat, the driver of a Pizza delivery in the Greater Houston area , wants to find the quickest route from the pizzeria (A) to the largest customer (E) before the pizza becomes cold. What route from A to E do you think requires the least time for him to take in order to satisfy his customers by delivering them really “Hot Pizzas” ?

  19. Activity No. 2 Speedy Delivery: Finding the Shortest Route Hint: • First, find the time it takes for him to travel between each given distances denoted by the line segments, using the given speed for each specific location. Use the formula v=d/t or t=d/v • Label the time between each node in the graph, and then use Dijktra’s Algorithm to find the shortest route. Fill up Table B as you do the Algorithm.

  20. DIAGRAM: D=4 km v=60 km/h D=3 km v=30km/h B C A t= 4 min t= 6 min D=3.5km v=30km/h D=3.75km v=45km/h D=1.5km v=30km/h D= 5km v=60km/h t= 7 min t= 5 min t= 3 min t= 5 min D F D=2.75km v=55km/h t=3 min D=5km v=60km/h D=3.5km v=30km/h D=2km v=30km/h t= 5 min t= 7 min t= 4 min G E D=4km v=60km/h t= 4 min

  21. Dijkstra’s Algorithm: STEPS: • Circle the starting node(vertex). Examine all arcs (edges) that have that node as an endpoint. 2. Examine all uncircled nodes that are adjacent to the circled nodes in the graph. 3. Using only circled nodes, find lengths of each path from starting point to those nodes in step 2. Choose the node and arc that yield the shortest path. Circle this node. Ties are broken arbitrarily ( if two or more paths have the same total length, then you can choose either of them). 4. Repeat steps 2 and 3 until all nodes are circled. Using the labels and distances next to each node, you can back trace the shortest path from each node to your starting point.

  22. STEPS: ∞ 0 ∞ 6 4 B C A 7 3 5 5 ∞ 3 D F ∞ 4 5 7 G E 4 ∞ ∞

  23. STEPS: ∞ 4A 0 ∞ 6 4 B C A 7 3 5 5 ∞ 3 D F ∞ 5A 4 5 7 G E 4 ∞ ∞

  24. STEPS: ∞ 10B 4A 0 6 4 B C A 7 3 5 5 ∞ 3 D F ∞ 5A 4 5 7 G E 4 ∞ ∞

  25. STEPS: 10B 12F 4A 0 6 4 B C A 7 3 5 5 ∞ 8F 3 D F 5A 4 5 7 G E 4 ∞ 12F ∞

  26. STEPS: 10B 13D 4A 0 6 4 B C A 7 3 5 5 8F 3 D F 5A 4 5 7 G E 4 12F 12D ∞ 13D

  27. STEPS: 10B 4A 0 6 4 B C A 7 3 5 5 8F 3 D F 5A 4 5 7 G E 4 12F 12D ∞ 13D

  28. STEPS: 10B 4A 0 6 4 B C A 7 3 5 5 8F 3 D F 5A 4 5 7 G E 4 12D,F ∞ 13D

  29. STEPS: 10B 4A 0 6 4 B C A 7 3 5 5 8F 3 D F 5A 4 5 7 G E 4 12D,F 13D 16G

  30. STEPS: 10B 4A 0 6 4 B C A 7 3 5 5 8F 3 D F 5A 4 5 7 G E 4 12D,F 13D

  31. RESULT: 10B 4A 0 6 4 B C A A 7 3 5 5 8F 3 D D F F 5A 4 5 7 G E E 4 12D,F 13D

  32. Dijkstra’s Algorithm B AB F AF D AFD

  33. RESEARCH PROJECT Situation: It has been an observation that many residents in different neighborhoods in the Houston area are victims of theft and burglary. Most of these victims have a burglar alarm system installed in their houses. However, most of the time when the alarm goes off, when intruders or robbers breaks in, before the police could even arrive, the robbers are long gone with all the most expensive and valuable belongings they could get.

  34. RESEARCH PROJECT cont… Problem: • Design a network system in your area wherein you could set the best possible location of a police station such that when their services are needed, they could reach the residents the fastest and the earliest possible time. • Draw a model of your network system and explain your procedure on how to solve the problem.

  35. ACKNOWLEDGEMENT • E3 Organizing Committee led by Dr. Jan Rinehart at Texas A & M University, College Station, Tx • Dr. Bruce Herbert, Facilitator E3 Summer Institute for Secondary Science and Math Teachers, 2006 • Dr. Halit Uster, Director of the Logistics and Networked Systems Research Laboratory, Department of Industrial and Systems Engineering, Texas A & M University, College Station, TX. • Burcu B. Keskin (Ph.D. candidate) • Other Members of the Logistics and Networked Systems Research Laboratory Gopal Easwaran (Ph.D. candidate) Panitan Kewcharoenwong (Ph.D. student) Hui Lin (Ph. D. student) Richard A. Ivey (USRG, Summer 2006) • Annette Coronado (Team member, E3 Summer Institute 2006)

  36. REFERENCES • Krajewski, Lee., Ritzman, Larry P. “Operations Management Strategy and Analysis”,6th edition, 2002 • Jay Heiser, Barry Render, “Operations Management”, 8TH edition, 2006 • http://ie.tamu.edu/ • http://hsor.org/modules.cfm?name=Speedy_Delivery • http://www.nasaexplores.com/show_912_teacher_st.php?id=040402133024 • http://www.sciencejoywagon.com/physicszone/lessonch/o1motion/linear/velocity/avg.htm • http://www.teachengineering.com

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