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 | 0.04 | 0.05 | 0.13 | 0.18 | 0.09 | 0.01 |
20 | 0.08 | 0.11 | 0.27 | 0.50 | 0.25 | 0.02 |
50 | 0.61 | 2.97 | 1.01 | 1.57 | 0.42 | 0.05 |
100 | 8.07 | 51.13 | 1.79 | 2.78 | 1.15 | 0.13 |
200 | - | - | 5.20 | 4.76 | 2.57 | 0.30 |
500 | - | - | 26.27 | 29.08 | 11.69 | 2.15 |
1000 | - | - | - | - | 85.19 | 18.63 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.04 | 0.05 | 0.12 | 0.15 | 0.12 | 0.02 |
1 | 0.04 | 0.04 | 0.23 | 0.19 | 0.05 | 0.01 |
2 | 0.04 | 0.05 | 0.11 | 0.18 | 0.13 | 0.01 |
3 | 0.05 | 0.05 | 0.11 | 0.18 | 0.05 | 0.01 |
4 | 0.04 | 0.06 | 0.12 | 0.15 | 0.08 | 0.01 |
5 | 0.05 | 0.06 | 0.09 | 0.17 | 0.14 | 0.01 |
6 | 0.04 | 0.06 | 0.06 | 0.23 | 0.12 | 0.02 |
7 | 0.04 | 0.07 | 0.09 | 0.24 | 0.05 | 0.01 |
8 | 0.04 | 0.05 | 0.10 | 0.17 | 0.09 | 0.01 |
9 | 0.04 | 0.05 | 0.24 | 0.16 | 0.04 | 0.02 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.08 | 0.10 | 0.29 | 0.45 | 0.30 | 0.02 |
1 | 0.07 | 0.11 | 0.21 | 0.53 | 0.23 | 0.02 |
2 | 0.08 | 0.11 | 0.23 | 0.55 | 0.37 | 0.01 |
3 | 0.07 | 0.10 | 0.31 | 0.50 | 0.18 | 0.02 |
4 | 0.09 | 0.11 | 0.25 | 0.45 | 0.38 | 0.01 |
5 | 0.09 | 0.11 | 0.25 | 0.52 | 0.16 | 0.02 |
6 | 0.09 | 0.13 | 0.43 | 0.51 | 0.25 | 0.03 |
7 | 0.08 | 0.09 | 0.23 | 0.52 | 0.22 | 0.01 |
8 | 0.08 | 0.10 | 0.26 | 0.47 | 0.22 | 0.01 |
9 | 0.08 | 0.10 | 0.25 | 0.48 | 0.20 | 0.02 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.32 | 0.24 | 0.21 | 0.45 | 0.07 | 0.02 |
1 | 0.42 | 2.27 | 0.78 | 1.74 | 0.53 | 0.05 |
2 | 0.96 | 9.58 | 0.91 | 1.37 | 0.38 | 0.05 |
3 | 0.38 | 2.49 | 1.55 | 1.96 | 0.32 | 0.04 |
4 | 1.84 | 1.40 | 1.01 | 1.31 | 0.40 | 0.05 |
5 | 0.40 | 1.01 | 1.08 | 1.50 | 0.73 | 0.05 |
6 | 0.38 | 0.70 | 1.14 | 1.74 | 0.44 | 0.04 |
7 | 0.58 | 7.47 | 1.21 | 1.41 | 0.27 | 0.05 |
8 | 0.38 | 3.30 | 1.23 | 2.03 | 0.47 | 0.04 |
9 | 0.46 | 1.28 | 0.94 | 2.19 | 0.63 | 0.06 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.48 | 0.31 | 0.32 | 0.69 | 0.15 | 0.04 |
1 | 5.15 | 38.45 | 2.19 | 3.50 | 1.24 | 0.12 |
2 | 7.93 | 18.63 | 0.73 | 3.35 | 1.08 | 0.12 |
3 | 1.80 | 32.49 | 2.34 | 3.13 | 1.37 | 0.13 |
4 | 6.77 | 12.63 | 1.63 | 1.90 | 1.25 | 0.11 |
5 | 19.96 | 36.79 | 1.92 | 2.98 | 1.20 | 0.14 |
6 | 0.58 | 9.30 | 1.51 | 3.12 | 1.00 | 0.10 |
7 | 7.37 | 165.28 | 2.47 | 3.54 | 1.42 | 0.29 |
8 | 0.81 | 13.44 | 1.82 | 2.09 | 1.16 | 0.14 |
9 | 29.86 | 183.95 | 2.97 | 3.46 | 1.66 | 0.13 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 273.75 | 282.39 | 4.75 | 3.47 | 2.51 | 0.30 |
1 | - | - | 4.64 | 6.19 | 2.32 | 0.26 |
2 | - | - | 5.81 | 5.58 | 3.32 | 0.31 |
3 | - | - | 4.77 | 4.81 | 3.09 | 0.37 |
4 | - | - | 4.55 | 4.02 | 3.02 | 0.35 |
5 | - | - | 3.19 | 4.90 | 2.07 | 0.27 |
6 | - | - | 3.59 | 5.37 | 2.39 | 0.29 |
7 | - | - | 8.77 | 5.41 | 2.99 | 0.29 |
8 | - | - | 6.81 | 4.93 | 1.85 | 0.32 |
9 | - | - | 5.08 | 2.95 | 2.15 | 0.24 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | - | - | 24.00 | 12.01 | 8.70 | 1.77 |
1 | - | - | 28.19 | 20.75 | 12.17 | 1.72 |
2 | - | - | 21.30 | 58.28 | 19.37 | 2.27 |
3 | - | - | 17.53 | 30.46 | 10.13 | 1.96 |
4 | - | - | 42.79 | 12.91 | 15.31 | 1.83 |
5 | - | - | 5.16 | 9.82 | 2.51 | 0.95 |
6 | - | - | 26.01 | 10.64 | 11.17 | 1.66 |
7 | - | - | 46.19 | 18.81 | 13.99 | 3.19 |
8 | - | - | 34.49 | 110.37 | 14.21 | 4.86 |
9 | - | - | 17.00 | 6.79 | 9.33 | 1.27 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | - | - | 273.28 | 277.95 | 110.12 | 25.31 |
1 | - | - | 161.26 | - | 62.46 | 10.93 |
2 | - | - | 263.95 | - | 116.91 | 17.74 |
3 | - | - | 251.88 | - | 133.77 | 37.38 |
4 | - | - | 196.46 | - | 63.38 | 10.75 |
5 | - | - | 276.46 | - | 147.59 | 33.79 |
6 | - | - | - | - | 63.90 | 14.37 |
7 | - | - | - | - | 60.42 | 13.10 |
8 | - | - | - | - | 79.68 | 18.41 |
9 | - | - | - | - | 13.63 | 4.53 |