Jordan Hauer
9/9/04
ENGRI 115 Lab Section: Monday
Homework #1
1.
(See attached)
2.
I would convert this problem into an input in the traveling salesman mold by
making each dropoff a city and make my home the starting and ending city. The
information about avenues taking three times as long to cross would also need to
be inputted. The last required input is the time or cost it takes to travel from city
to city, or dropoff to dropoff. Each path would have a certain time T(s,d) where
s is the starting city and d is the destination city. The time is calculated by finding
the time it takes to get from the starting city to the pickup point and then to the
dropoff point. In this problem, calculating the time is a twostep process instead
of a onestep process.
s: (x
s
, y
s
)
pickup (p): (x
p
, y
p
)
d: (x
d
, y
d
)
T(s,d) = T(s,p) + T(p,d) = 3x
s
– x
p
 + y
s
– y
p
 + 3x
p
– x
d
 + y
p
– y
d

3.
The input in question 2 is not symmetric because of the fact that you need to
travel to an intermediate point before you travel to your destination, and the
pickup point is different for all the destinations. For example, if you travel from
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 Fall '05
 TROTTER
 Operations Research, Travelling salesman problem, NPcomplete, Function problem, dropoff

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