Geoscience Reference

In-Depth Information

Fig. 2.8
Sample tradeoff

between average distance and

percent covered

PERCENT COVERAGE VS. AVERAGE DISTANCE

82

81

80

79

78

77

135

140

145

150

155

160

165

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.