Transcript Slide 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)
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.
BACKGROUND SCIENCE


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.
ACTIVITY No. 1
•
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?
1-CENTER LOCATION ON TREE NETWORK
A
C
5
J
6
E
1
4
5
2
I
L
B
3
7
K
8
F
G
1
D
4
H
1-CENTER LOCATION ON TREE NETWORK
STEPS
A
C
5
J
6
E
1
1
4
5
2
I
L
B
3
7
K
8
G
F
D
4
H
1-CENTER LOCATION ON TREE NETWORK
STEPS
A
C
5
J
6
E
1
1
4
5
2
I
L
B
3
7
K
8
G
F
D
4
H
1-CENTER LOCATION ON TREE NETWORK
STEPS
A
C
5
J
6
E
1
1
4
5
2
I
L
B
3
7
K
8
G
F
D
4
H
1-CENTER LOCATION ON TREE NETWORK
STEPS
A
8
14
C
8
16
5
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6
E
K
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1
L
4
5
11
2
I
14
B
3
G
F
D
4
H
5
1-CENTER LOCATION ON TREE NETWORK
STEPS
A
8
14
C
8
16
5
J
7
6
E
K
1
1
L
4
5
11
2
I
14
B
3
G
F
D
4
H
5
1-CENTER LOCATION ON TREE NETWORK
STEPS
A
C
8
16
5
J
7
6
E
1
1
L
4
5
2
I
K
B
3
G
F
D
4
H
1-CENTER LOCATION ON TREE NETWORK
STEPS
A
C
8
16
5
J
7
6
E
1
1
L
4
5
2
I
K
B
3
G
F
D
4
H
1-CENTER LOCATION ON TREE NETWORK
24
STEPS
A
18
C
8
16
5
J
7
6
E
K
1
1
L
4
5
21
2
I
12
B
3
F
D
4
G
H
16
19
1-CENTER LOCATION ON TREE NETWORK
24
STEPS
A
18
C
8
16
5
J
7
6
E
K
1
1
L
4
5
21
2
I
12
B
3
F
D
4
G
H
16
19
1-CENTER LOCATION ON TREE NETWORK
24
STEPS
A
C
8
16
5
J
7
6
E
1
1
L
4
5
2
I
K
B
3
G
F
D
4
H
1-CENTER LOCATION ON TREE NETWORK
24
RESULT
A
C
5
J
E
6
I
1
4
5
2
D
1-center
1
L
B
3
7
K
8
G
F
4
H
The Physical Analogy Model
1-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.
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” ?
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.
DIAGRAM:
C
D=3 km
v=30km/h
B
t= 5 min
D
D=5km
v=60km/h
t= 5 min
E
D=3.5km
v=30km/h
D=1.5km
v=30km/h
t= 7 min
F
D=3.5km
v=30km/h
D=2km
v=30km/h
D=4km
v=60km/h
t= 4 min
D= 5km
v=60km/h
t= 3 min
D=2.75km
v=55km/h
t=3 min
t= 4 min
A
t= 4 min
t= 6 min
D=3.75km
v=45km/h
D=4 km
v=60 km/h
t= 7 min
G
t= 5 min
Dijkstra’s Algorithm:
STEPS:
1.
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.
STEPS:
∞
∞
6
4
B
C
7
0
A
3
5
5
∞
D
3
F
4
5
7
G
E
∞
4
∞
∞
STEPS:
∞
∞ 4A
6
4
B
C
7
0
A
3
5
5
∞
D
3
F
4
5
7
G
E
∞
4
∞
∞ 5A
STEPS:
∞ 10B
4A
6
4
B
C
7
0
A
3
5
5
∞
D
3
F
4
5
7
G
E
∞
4
∞
∞ 5A
STEPS:
10B 12F
4A
6
4
B
C
7
0
A
3
5
5
∞ 8F
D
3
F
4
5
7
G
E
∞
4
∞ 12F
5A
STEPS:
10B 13D
4A
6
4
B
C
7
0
A
3
5
5
8F
D
3
F
4
5
7
G
E
∞ 13D
4
12F 12D
5A
STEPS:
10B
4A
6
4
B
C
7
0
A
3
5
5
8F
D
3
F
4
5
7
G
E
∞ 13D
4
12F 12D
5A
STEPS:
10B
4A
6
4
B
C
7
0
A
3
5
5
8F
D
3
F
4
5
7
G
E
∞ 13D
4
12D,F
5A
STEPS:
10B
4A
6
4
B
C
7
0
A
3
5
5
8F
D
3
F
4
5
7
G
E
13D 16G
4
12D,F
5A
STEPS:
10B
4A
6
4
B
C
7
0
A
3
5
5
8F
D
3
F
4
5
7
G
E
13D
4
12D,F
5A
RESULT:
10B
4A
6
4
B
C
7
0
A
3
5
5
8F
D
3
F
4
5
7
G
E
13D
4
12D,F
5A
Dijkstra’s Algorithm
Circled Node
Adjacent Nodes
(uncircled)
1st A
Path (from A)
B
AB
F
AF
2nd B
F
C
ABF
ABC
3rd F
D
AFD
G
C
4th D
____________
____________
____________
5th C
NONE
6th _____
________
7th _____
NONE
AFG
AFC
Total Time
4
5
7
10
8
12
12
____________ ____________
____________ ____________
____________ ____________
_________
____________
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.
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.
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

Burcu B. Keskin (Ph.D. candidate)


Research Laboratory, Department of Industrial and Systems Engineering,
Texas A & M University, College Station, TX.
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)
REFERENCES
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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?i
d=040402133024
http://www.sciencejoywagon.com/physicszone/lessonch/o1
motion/linear/velocity/avg.htm
http://www.teachengineering.com