Results obtained using Gurobi for solving a nonlinear Facility Location Problem (FLP), using the models described in Mathematical Optimization: Solving Problems using Python and Gurobi.
Parameters used: number of facilities is 10% of the number of customers.
CPU time limited to 300 seconds. (Click on values for selecting data to display.)Instance family | Type | Description |
Num.Int=2 | random | Number of linear segments in the approximation: 2 |
Num.Int=5 | random | Number of linear segments in the approximation: 5 |
Num.Int=10 | random | Number of linear segments in the approximation: 10 |
Num.Int=20 | random | Number of linear segments in the approximation: 20 |
Num.Int=50 | random | Number of linear segments in the approximation: 50 |
Num.Int=100 | random | Number of linear segments in the approximation: 100 |
Num.Int=200 | random | Number of linear segments in the approximation: 200 |
Num.Int=500 | random | Number of linear segments in the approximation: 500 |
Num.Int=1000 | random | Number of linear segments in the approximation: 1000 |
Label | Description |
mselect | multiple selection model |
cc_dis | disaggregated convex combination model |
cc_dis_log | disaggregated convex combination model with a logarithmic number of variables |
cc_agg | (aggregated) convex combination model |
cc_agg_log | (aggregated) convex combination model with a logarithmic number of variables |
sos | model using sos constraints of type 2 |
size | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
20 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
50 | 0.01 | 0.01 | 0.01 | 0.02 | 0.01 | 0.01 |
100 | 0.02 | 0.03 | 0.04 | 0.03 | 0.03 | 0.02 |
200 | 0.10 | 0.14 | 0.17 | 0.16 | 0.15 | 0.07 |
500 | 0.87 | 1.65 | 2.03 | 1.90 | 1.67 | 0.96 |
1000 | 9.78 | 15.32 | 16.34 | 17.29 | 15.10 | 13.14 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.01 | 0.00 | 0.00 | 0.00 | 0.01 | 0.01 |
1 | 0.00 | 0.01 | 0.00 | 0.00 | 0.01 | 0.00 |
2 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 |
3 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
4 | 0.00 | 0.01 | 0.01 | 0.01 | 0.00 | 0.00 |
5 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 |
6 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 0.01 |
7 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 |
8 | 0.00 | 0.01 | 0.01 | 0.00 | 0.01 | 0.00 |
9 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.01 | 0.00 | 0.01 | 0.00 | 0.01 | 0.01 |
1 | 0.01 | 0.00 | 0.01 | 0.00 | 0.01 | 0.01 |
2 | 0.00 | 0.01 | 0.00 | 0.01 | 0.00 | 0.00 |
3 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 |
4 | 0.01 | 0.00 | 0.01 | 0.00 | 0.00 | 0.01 |
5 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 |
6 | 0.01 | 0.00 | 0.01 | 0.00 | 0.01 | 0.00 |
7 | 0.01 | 0.01 | 0.00 | 0.00 | 0.01 | 0.00 |
8 | 0.01 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 |
9 | 0.01 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.02 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 |
1 | 0.00 | 0.00 | 0.00 | 0.01 | 0.01 | 0.01 |
2 | 0.02 | 0.01 | 0.01 | 0.02 | 0.02 | 0.02 |
3 | 0.01 | 0.00 | 0.01 | 0.02 | 0.01 | 0.01 |
4 | 0.02 | 0.02 | 0.02 | 0.02 | 0.01 | 0.00 |
5 | 0.01 | 0.01 | 0.01 | 0.02 | 0.00 | 0.00 |
6 | 0.01 | 0.01 | 0.01 | 0.01 | 0.02 | 0.01 |
7 | 0.01 | 0.01 | 0.02 | 0.03 | 0.01 | 0.00 |
8 | 0.01 | 0.01 | 0.01 | 0.00 | 0.00 | 0.00 |
9 | 0.01 | 0.01 | 0.02 | 0.01 | 0.00 | 0.01 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.01 | 0.01 | 0.01 | 0.02 | 0.01 | 0.01 |
1 | 0.02 | 0.04 | 0.04 | 0.03 | 0.03 | 0.03 |
2 | 0.01 | 0.03 | 0.04 | 0.03 | 0.04 | 0.02 |
3 | 0.03 | 0.04 | 0.05 | 0.03 | 0.04 | 0.02 |
4 | 0.02 | 0.05 | 0.06 | 0.04 | 0.04 | 0.03 |
5 | 0.05 | 0.04 | 0.05 | 0.04 | 0.03 | 0.01 |
6 | 0.02 | 0.02 | 0.01 | 0.02 | 0.02 | 0.03 |
7 | 0.02 | 0.04 | 0.03 | 0.02 | 0.03 | 0.01 |
8 | 0.02 | 0.04 | 0.05 | 0.04 | 0.04 | 0.03 |
9 | 0.02 | 0.02 | 0.03 | 0.04 | 0.05 | 0.01 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.14 | 0.12 | 0.20 | 0.19 | 0.21 | 0.07 |
1 | 0.08 | 0.12 | 0.13 | 0.12 | 0.10 | 0.04 |
2 | 0.12 | 0.18 | 0.18 | 0.19 | 0.15 | 0.07 |
3 | 0.12 | 0.17 | 0.23 | 0.18 | 0.17 | 0.08 |
4 | 0.11 | 0.16 | 0.16 | 0.15 | 0.15 | 0.08 |
5 | 0.09 | 0.12 | 0.13 | 0.13 | 0.15 | 0.04 |
6 | 0.11 | 0.22 | 0.20 | 0.23 | 0.24 | 0.08 |
7 | 0.08 | 0.11 | 0.13 | 0.11 | 0.11 | 0.06 |
8 | 0.05 | 0.10 | 0.11 | 0.11 | 0.10 | 0.06 |
9 | 0.13 | 0.13 | 0.21 | 0.18 | 0.12 | 0.07 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.93 | 1.43 | 2.24 | 2.14 | 2.20 | 1.47 |
1 | 0.91 | 1.58 | 2.12 | 2.05 | 1.55 | 1.19 |
2 | 0.93 | 2.10 | 2.68 | 2.11 | 2.19 | 1.18 |
3 | 0.78 | 1.91 | 1.97 | 1.83 | 2.15 | 0.92 |
4 | 0.85 | 2.21 | 3.24 | 3.04 | 1.98 | 0.96 |
5 | 0.57 | 0.56 | 0.88 | 0.77 | 0.58 | 0.43 |
6 | 0.75 | 1.64 | 1.88 | 1.42 | 1.90 | 0.93 |
7 | 1.62 | 2.14 | 2.62 | 2.70 | 1.98 | 1.28 |
8 | 0.72 | 1.72 | 1.64 | 1.85 | 1.27 | 0.71 |
9 | 0.59 | 1.18 | 1.03 | 1.07 | 0.92 | 0.51 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 11.51 | 23.09 | 26.04 | 21.58 | 20.66 | 19.58 |
1 | 8.53 | 14.77 | 21.40 | 17.18 | 12.38 | 10.72 |
2 | 10.13 | 16.88 | 16.73 | 16.05 | 16.55 | 12.69 |
3 | 9.14 | 18.61 | 19.98 | 36.55 | 15.17 | 23.34 |
4 | 7.02 | 7.06 | 6.27 | 11.19 | 11.17 | 6.81 |
5 | 12.80 | 21.37 | 13.49 | 20.55 | 22.44 | 10.91 |
6 | 10.08 | 16.17 | 16.75 | 12.29 | 18.07 | 15.57 |
7 | 8.91 | 15.09 | 16.20 | 12.87 | 14.01 | 14.01 |
8 | 14.87 | 15.34 | 20.11 | 20.19 | 15.92 | 14.53 |
9 | 4.79 | 4.84 | 6.45 | 4.42 | 4.62 | 3.26 |