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 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
50 | 0.01 | 0.01 | 0.02 | 0.01 | 0.01 | 0.01 |
100 | 0.05 | 0.04 | 0.04 | 0.04 | 0.03 | 0.02 |
200 | 0.21 | 0.20 | 0.21 | 0.18 | 0.16 | 0.07 |
500 | 1.66 | 2.40 | 1.85 | 3.39 | 2.36 | 1.15 |
1000 | 11.05 | 27.67 | 18.26 | 29.86 | 20.81 | 14.65 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
1 | 0.00 | 0.01 | 0.00 | 0.01 | 0.00 | 0.00 |
2 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
3 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 |
4 | 0.01 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 |
5 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
6 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
7 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 |
8 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 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 | 0.00 | 0.01 | 0.00 | 0.00 |
1 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 |
2 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 |
3 | 0.00 | 0.01 | 0.01 | 0.00 | 0.00 | 0.01 |
4 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 |
5 | 0.00 | 0.01 | 0.00 | 0.00 | 0.01 | 0.00 |
6 | 0.00 | 0.00 | 0.01 | 0.01 | 0.00 | 0.00 |
7 | 0.01 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 |
8 | 0.00 | 0.01 | 0.00 | 0.01 | 0.00 | 0.00 |
9 | 0.00 | 0.01 | 0.02 | 0.01 | 0.00 | 0.01 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.00 | 0.01 | 0.00 | 0.01 | 0.01 | 0.00 |
1 | 0.02 | 0.02 | 0.01 | 0.00 | 0.01 | 0.01 |
2 | 0.03 | 0.02 | 0.02 | 0.02 | 0.01 | 0.02 |
3 | 0.01 | 0.01 | 0.00 | 0.01 | 0.02 | 0.00 |
4 | 0.02 | 0.02 | 0.03 | 0.03 | 0.02 | 0.01 |
5 | 0.01 | 0.01 | 0.02 | 0.02 | 0.01 | 0.00 |
6 | 0.01 | 0.01 | 0.02 | 0.01 | 0.00 | 0.02 |
7 | 0.01 | 0.01 | 0.04 | 0.02 | 0.02 | 0.01 |
8 | 0.01 | 0.02 | 0.01 | 0.02 | 0.01 | 0.01 |
9 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.00 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 |
1 | 0.06 | 0.05 | 0.05 | 0.05 | 0.03 | 0.02 |
2 | 0.05 | 0.05 | 0.04 | 0.03 | 0.04 | 0.01 |
3 | 0.06 | 0.05 | 0.04 | 0.04 | 0.03 | 0.03 |
4 | 0.04 | 0.07 | 0.08 | 0.05 | 0.07 | 0.01 |
5 | 0.11 | 0.06 | 0.06 | 0.07 | 0.05 | 0.03 |
6 | 0.03 | 0.02 | 0.02 | 0.05 | 0.01 | 0.02 |
7 | 0.05 | 0.06 | 0.05 | 0.04 | 0.04 | 0.02 |
8 | 0.04 | 0.03 | 0.06 | 0.05 | 0.03 | 0.02 |
9 | 0.04 | 0.04 | 0.04 | 0.04 | 0.04 | 0.01 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.22 | 0.24 | 0.34 | 0.20 | 0.26 | 0.08 |
1 | 0.17 | 0.14 | 0.15 | 0.13 | 0.10 | 0.07 |
2 | 0.29 | 0.30 | 0.22 | 0.28 | 0.14 | 0.07 |
3 | 0.25 | 0.27 | 0.24 | 0.20 | 0.20 | 0.07 |
4 | 0.29 | 0.25 | 0.24 | 0.22 | 0.19 | 0.10 |
5 | 0.17 | 0.16 | 0.12 | 0.18 | 0.11 | 0.05 |
6 | 0.23 | 0.19 | 0.24 | 0.23 | 0.18 | 0.09 |
7 | 0.16 | 0.13 | 0.19 | 0.11 | 0.15 | 0.07 |
8 | 0.10 | 0.12 | 0.13 | 0.12 | 0.11 | 0.07 |
9 | 0.24 | 0.19 | 0.21 | 0.17 | 0.19 | 0.06 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 1.39 | 2.06 | 1.77 | 1.68 | 2.63 | 1.33 |
1 | 1.56 | 2.35 | 1.81 | 2.83 | 2.57 | 1.43 |
2 | 1.45 | 1.88 | 1.81 | 3.02 | 2.84 | 1.25 |
3 | 1.11 | 2.12 | 1.89 | 1.87 | 2.02 | 0.94 |
4 | 1.46 | 2.91 | 2.53 | 4.01 | 2.92 | 1.15 |
5 | 0.74 | 0.65 | 0.66 | 1.03 | 0.88 | 0.45 |
6 | 0.95 | 2.93 | 1.31 | 4.08 | 2.01 | 0.99 |
7 | 5.28 | 5.28 | 3.93 | 9.12 | 4.11 | 2.36 |
8 | 1.84 | 2.81 | 1.96 | 4.96 | 2.50 | 1.05 |
9 | 0.81 | 0.98 | 0.84 | 1.31 | 1.12 | 0.58 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 24.92 | 82.41 | 28.45 | 48.49 | 32.14 | 22.41 |
1 | 9.62 | 26.21 | 10.23 | 17.34 | 19.29 | 8.70 |
2 | 12.48 | 25.74 | 19.04 | 33.06 | 22.70 | 13.01 |
3 | 10.72 | 30.34 | 24.82 | 34.38 | 19.41 | 30.36 |
4 | 5.92 | 14.30 | 11.94 | 12.94 | 8.29 | 12.27 |
5 | 10.11 | 38.96 | 28.04 | 85.85 | 32.90 | 15.72 |
6 | 8.05 | 18.80 | 18.01 | 16.86 | 21.84 | 12.00 |
7 | 6.47 | 18.39 | 16.34 | 18.88 | 21.55 | 11.02 |
8 | 17.70 | 17.25 | 20.63 | 24.48 | 23.61 | 17.65 |
9 | 4.50 | 4.32 | 5.10 | 6.37 | 6.35 | 3.39 |