Data for Continuous Location Problems
The following files contain a list of randomly generated demand points in a unit square. The number of demand points is indicated by the name of the file. Each file contains a list of 4 values for each demand point: the serial number, the weight (all weights are equal to 1) x-coordinate and y-coordinate. The coordinates were generated by the following single precision FORTRAN program (that can be easily translated to other languages with the same results) and are given to eight decimal places.
real function rand(ist)
rand = (2 * (ist / 256) + 1) / 16777216.0
The following short code generates the problems
do 1 i=1,n
Note that the file containing 10,000 demand points actually contains all other files. The first n lines in this file generate the problems with n demand points given in the other files.
The solutions to minimizing the variance of the distances to all demand points are given below. The relative accuracy of the solutions is 10-10 which means that the minimal value of the objective function is correct to about 12 digits after the decimal point. These solutions were obtained by the method in the paper
Drezner Tammy and Drezner Zvi "Equity Models in Planar Location," Computational Management Science, forthcoming.
n=10 n=20 n=50 n=100 n=200 n=500 n=1000 n=2000 n=5000 n=10000
n x y Variance
10 0.573433 0.470696 0.0112030165
20 0.574664 0.517689 0.0142405692
50 0.586012 0.507993 0.0148886611
100 0.523409 0.494597 0.0176998509
200 0.490274 0.471602 0.0189152542
500 0.498967 0.478063 0.0190569059
1000 0.488398 0.501897 0.0205675105
2000 0.496767 0.489679 0.0204669774
5000 0.500107 0.496037 0.0203239336
10000 0.497735 0.500865 0.0205132773