Fig. 2.8 Sample tradeoff
between average distance and
PERCENT COVERAGE VS. AVERAGE DISTANCE
Demand-Weighted Average Distance
this approach seems to also be a weighting approach since we are assigning a large
weight to any distance greater than or equal to the most recently found maximum
distance, it is really the constraint method (Cohon 1978 ) since we are precluding the
assignment of demand nodes to facilities that are too far away. This approach will
find all non-dominated solutions.
We close this section by illustrating these two multi-objective problems. Fig-
ure 2.8 plots the tradeoff between the average distance and the percent of the demand
covered within 200 miles using ten facilities with demand represented by the 500
most populous counties of the contiguous United States. The maximum covering
solution results in nearly an 18 % increase in the average distance from 137.32 to
161.93 miles, while increasing the percent covered by approximately 4 %. Obtaining
the 12 solutions shown in the figure took under 10 min of solution time.
Figure 2.9 is a sample center-median tradeoff curve using the 250 most populous
counties in the contiguous US. While this is under 10 % of the counties, it still
encompasses over 61 % of the total population in the contiguous US. The algorithm
above found 22 solutions (shown with squares and a solid line), only nine of which
(shown with circles and a dashed line) could be found using a weighting method.
The average distance ranges from about 125 miles to 152 miles, while the maximum
distance ranges from a low of 349 miles to a high of 553 miles. Several good
compromise solutions are clearly shown at the bend in the curve. Figure 2.10 is
an example of one such compromise solution. Obtaining the 22 solutions shown in
the figure took nearly 16 h of computing time.