The p-Median Problem - Location Science - page 37

Fig. 2.4 Histogram of the
frequency of county selection
out of 325 possible cases

Percent of Possible Occurences

50%

40%

30%

20%

10%

0%

Candidate Site Number

Fig. 2.5 Percent error due to
limiting the candidate
node set

Percent Error Due to Using a Subset of the Candidate
Facility Sites

4.5%

4.0%

3.5%

3.0%

2.5%

2.0%

1.5%

1.0%

0.5%

0.0%

0 5 10 15 20 25 30

Number of Medians

% Error using 100 nodes % Error using 200 nodes

% Error using 300 nodes % Error using 400 nodes

With 1-25 medians being selected, there conceivably could be 325 unique nodes
chosen as medians. This was not the case. Only 55 unique nodes were selected and
these were biased toward the larger demand nodes. With the dataset sorted from
the most populous to the least populous county, Fig. 2.4 plots the distribution of
the number of times nodes in different groupings were selected. Nearly half of the
counties selected were among the top 50 most populous counties. Over 75 % of the
selected counties were in the top 150 most populous counties.
Figure 2.5 plots the percent error due to limiting the candidate solution set to
the most populous 100, 200, 300 and 400 counties, compared to allowing all 500
counties to be in the solution. The errors are generally less than 1 % as long as at
least 200 nodes are in the candidate set. Even when the candidate set is limited to
only 100 nodes, the maximum error in the 25 runs was under 4 %, though the error
seems to be growing with the number of medians in this case.