The Bicycle Problem
# OR 389 Student Seminar

# "On the Bicycle Problem"

## V.
Chvátal, * Disc. Appl. Math.*
** 5** (1983): 165-173

Given one single-seat bicycle, *n* people with known walking and
biking speeds, and a track of length *d* miles, devise a
schedule that minimizes the arrival time of the last person at the finish
line. Note that an optimal schedule might require biking backwards.

The following four animations illustrate some possible schedules for
*n* = 3 and *d* = 10, where the first two people have walking
speed 2 miles/hour and biking speed 12 miles/hour, and the third person
has walking speed 4 miles/hour and biking speed 16 miles/hour.

For the two ε-optimal schedules, we must add the time
necessary to get from the starting line to the initial positions and
from the final positions to the finish line. The point is that, with
enough stages, we can make this additional time less than any given
ε > 0.

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