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 | 0.01 | 0.03 | 0.01 | 0.02 | 0.01 |
50 | 0.06 | 0.07 | 0.09 | 0.10 | 0.05 | 0.01 |
100 | 0.22 | 0.22 | 0.12 | 0.22 | 0.08 | 0.03 |
200 | 1.69 | 1.53 | 0.46 | 0.62 | 0.31 | 0.12 |
500 | 19.51 | 25.15 | 3.64 | 4.17 | 2.59 | 1.47 |
1000 | - | - | 40.93 | 67.33 | 25.87 | 14.87 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.00 | 0.00 | 0.00 | 0.01 | 0.01 | 0.00 |
1 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 |
2 | 0.01 | 0.00 | 0.01 | 0.01 | 0.00 | 0.02 |
3 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 |
4 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
5 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
6 | 0.01 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 |
7 | 0.00 | 0.01 | 0.01 | 0.00 | 0.00 | 0.00 |
8 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | 0.01 |
9 | 0.00 | 0.00 | 0.00 | 0.01 | 0.01 | 0.00 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.01 | 0.01 | 0.04 | 0.01 | 0.00 | 0.01 |
1 | 0.00 | 0.02 | 0.02 | 0.01 | 0.01 | 0.01 |
2 | 0.01 | 0.01 | 0.03 | 0.00 | 0.02 | 0.00 |
3 | 0.01 | 0.00 | 0.03 | 0.01 | 0.01 | 0.02 |
4 | 0.02 | 0.01 | 0.03 | 0.01 | 0.02 | 0.00 |
5 | 0.01 | 0.00 | 0.03 | 0.00 | 0.02 | 0.00 |
6 | 0.01 | 0.02 | 0.03 | 0.01 | 0.04 | 0.01 |
7 | 0.01 | 0.00 | 0.05 | 0.00 | 0.01 | 0.01 |
8 | 0.00 | 0.01 | 0.01 | 0.01 | 0.01 | 0.00 |
9 | 0.01 | 0.01 | 0.02 | 0.02 | 0.03 | 0.00 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.02 | 0.02 | 0.02 | 0.03 | 0.02 | 0.00 |
1 | 0.03 | 0.09 | 0.08 | 0.09 | 0.05 | 0.00 |
2 | 0.11 | 0.08 | 0.11 | 0.10 | 0.10 | 0.03 |
3 | 0.05 | 0.06 | 0.08 | 0.13 | 0.06 | 0.02 |
4 | 0.06 | 0.07 | 0.17 | 0.10 | 0.08 | 0.02 |
5 | 0.03 | 0.07 | 0.10 | 0.11 | 0.05 | 0.01 |
6 | 0.04 | 0.06 | 0.09 | 0.09 | 0.03 | 0.02 |
7 | 0.10 | 0.09 | 0.08 | 0.11 | 0.03 | 0.01 |
8 | 0.04 | 0.06 | 0.10 | 0.10 | 0.04 | 0.02 |
9 | 0.11 | 0.06 | 0.10 | 0.12 | 0.05 | 0.01 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.08 | 0.04 | 0.03 | 0.06 | 0.02 | 0.01 |
1 | 0.21 | 0.24 | 0.15 | 0.27 | 0.07 | 0.02 |
2 | 0.46 | 0.19 | 0.17 | 0.18 | 0.10 | 0.02 |
3 | 0.18 | 0.29 | 0.12 | 0.27 | 0.07 | 0.04 |
4 | 0.28 | 0.32 | 0.09 | 0.19 | 0.08 | 0.02 |
5 | 0.26 | 0.26 | 0.11 | 0.25 | 0.06 | 0.02 |
6 | 0.08 | 0.24 | 0.12 | 0.17 | 0.09 | 0.02 |
7 | 0.31 | 0.32 | 0.12 | 0.30 | 0.14 | 0.03 |
8 | 0.11 | 0.16 | 0.14 | 0.19 | 0.08 | 0.03 |
9 | 0.23 | 0.17 | 0.19 | 0.33 | 0.08 | 0.04 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 4.55 | 3.75 | 0.56 | 0.50 | 0.44 | 0.12 |
1 | 1.00 | 1.08 | 0.58 | 0.66 | 0.27 | 0.11 |
2 | 5.14 | 4.58 | 0.36 | 0.65 | 0.35 | 0.11 |
3 | 1.67 | 1.43 | 0.50 | 0.61 | 0.32 | 0.14 |
4 | 1.10 | 1.15 | 0.59 | 0.58 | 0.39 | 0.14 |
5 | 0.54 | 0.54 | 0.41 | 0.41 | 0.24 | 0.10 |
6 | 0.96 | 0.94 | 0.49 | 0.46 | 0.33 | 0.13 |
7 | 0.68 | 0.55 | 0.39 | 0.50 | 0.29 | 0.09 |
8 | 0.40 | 0.47 | 0.28 | 1.47 | 0.20 | 0.10 |
9 | 0.84 | 0.79 | 0.47 | 0.41 | 0.28 | 0.15 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 14.80 | 19.03 | 2.39 | 7.08 | 2.19 | 1.85 |
1 | 7.09 | 28.02 | 5.73 | 3.62 | 2.82 | 1.74 |
2 | 7.33 | 9.25 | 2.76 | 2.46 | 2.47 | 1.74 |
3 | 5.55 | 5.16 | 1.98 | 3.05 | 2.63 | 1.26 |
4 | 29.03 | 34.16 | 5.25 | 4.43 | 4.02 | 1.26 |
5 | 2.33 | 1.38 | 1.05 | 1.22 | 0.67 | 0.67 |
6 | 3.67 | 18.47 | 2.76 | 4.26 | 2.60 | 1.20 |
7 | 95.60 | 81.72 | 6.59 | 5.22 | 3.92 | 2.39 |
8 | 27.81 | 44.31 | 6.24 | 5.22 | 3.03 | 1.82 |
9 | 1.87 | 9.99 | 1.62 | 5.14 | 1.51 | 0.81 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 254.62 | 281.03 | 55.58 | 153.91 | 36.45 | 27.84 |
1 | 68.49 | - | 59.22 | 70.34 | 29.83 | 8.35 |
2 | 277.73 | - | 87.98 | 98.77 | 52.50 | 13.08 |
3 | - | - | 34.60 | 104.48 | 19.54 | 17.04 |
4 | - | - | 16.60 | 23.51 | 11.72 | 6.72 |
5 | - | - | 45.76 | 68.12 | 27.31 | 18.52 |
6 | - | - | 50.81 | 23.60 | 29.96 | 16.47 |
7 | - | - | 20.19 | 86.38 | 24.70 | 12.44 |
8 | - | - | 31.90 | 36.69 | 22.22 | 22.81 |
9 | - | - | 6.68 | 7.55 | 4.50 | 5.45 |