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 | 0.01 | 0.01 | 0.03 | 0.05 | 0.02 | 0.01 |
20 | 0.02 | 0.03 | 0.12 | 0.25 | 0.06 | 0.01 |
50 | 0.20 | 0.72 | 0.38 | 0.52 | 0.16 | 0.02 |
100 | 1.34 | 3.56 | 0.58 | 0.82 | 0.27 | 0.05 |
200 | 37.58 | - | 2.08 | 1.85 | 0.90 | 0.18 |
500 | - | - | 10.65 | 10.26 | 4.68 | 1.43 |
1000 | - | - | 93.39 | - | 57.40 | 17.88 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.01 | 0.00 | 0.02 | 0.04 | 0.02 | 0.00 |
1 | 0.00 | 0.02 | 0.04 | 0.05 | 0.03 | 0.01 |
2 | 0.01 | 0.02 | 0.04 | 0.05 | 0.01 | 0.01 |
3 | 0.01 | 0.01 | 0.01 | 0.05 | 0.03 | 0.00 |
4 | 0.02 | 0.02 | 0.02 | 0.04 | 0.03 | 0.01 |
5 | 0.01 | 0.01 | 0.02 | 0.05 | 0.03 | 0.00 |
6 | 0.01 | 0.01 | 0.03 | 0.05 | 0.02 | 0.01 |
7 | 0.00 | 0.02 | 0.04 | 0.05 | 0.01 | 0.01 |
8 | 0.02 | 0.02 | 0.04 | 0.06 | 0.01 | 0.01 |
9 | 0.01 | 0.01 | 0.02 | 0.05 | 0.02 | 0.00 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.02 | 0.04 | 0.17 | 0.26 | 0.08 | 0.01 |
1 | 0.02 | 0.02 | 0.06 | 0.31 | 0.03 | 0.02 |
2 | 0.02 | 0.03 | 0.15 | 0.15 | 0.05 | 0.01 |
3 | 0.02 | 0.03 | 0.10 | 0.21 | 0.10 | 0.01 |
4 | 0.02 | 0.03 | 0.09 | 0.35 | 0.05 | 0.01 |
5 | 0.02 | 0.01 | 0.10 | 0.17 | 0.04 | 0.01 |
6 | 0.01 | 0.03 | 0.17 | 0.50 | 0.09 | 0.01 |
7 | 0.03 | 0.04 | 0.15 | 0.23 | 0.08 | 0.01 |
8 | 0.02 | 0.02 | 0.06 | 0.14 | 0.04 | 0.01 |
9 | 0.02 | 0.03 | 0.17 | 0.17 | 0.08 | 0.02 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.21 | 0.16 | 0.05 | 0.18 | 0.02 | 0.01 |
1 | 0.25 | 0.79 | 0.52 | 0.50 | 0.23 | 0.01 |
2 | 0.41 | 0.90 | 0.32 | 0.57 | 0.14 | 0.02 |
3 | 0.16 | 0.42 | 0.50 | 0.59 | 0.25 | 0.03 |
4 | 0.18 | 0.66 | 0.49 | 0.50 | 0.21 | 0.01 |
5 | 0.15 | 0.35 | 0.38 | 0.59 | 0.13 | 0.01 |
6 | 0.16 | 0.39 | 0.36 | 0.49 | 0.14 | 0.02 |
7 | 0.17 | 2.41 | 0.50 | 0.43 | 0.14 | 0.02 |
8 | 0.16 | 0.74 | 0.35 | 0.64 | 0.24 | 0.01 |
9 | 0.17 | 0.39 | 0.35 | 0.67 | 0.13 | 0.02 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.26 | 0.21 | 0.10 | 0.29 | 0.04 | 0.02 |
1 | 1.58 | 5.12 | 0.64 | 0.92 | 0.29 | 0.06 |
2 | 1.20 | 3.58 | 0.73 | 1.06 | 0.28 | 0.05 |
3 | 0.59 | 3.44 | 0.36 | 0.87 | 0.29 | 0.05 |
4 | 1.22 | 3.87 | 0.78 | 0.66 | 0.37 | 0.05 |
5 | 2.70 | 4.88 | 0.71 | 1.02 | 0.30 | 0.05 |
6 | 0.33 | 0.52 | 0.41 | 0.74 | 0.20 | 0.04 |
7 | 2.92 | 7.41 | 0.49 | 0.87 | 0.28 | 0.06 |
8 | 0.59 | 1.04 | 0.64 | 0.65 | 0.29 | 0.05 |
9 | 2.00 | 5.52 | 0.92 | 1.12 | 0.34 | 0.06 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 65.31 | 288.33 | 2.30 | 1.43 | 0.93 | 0.17 |
1 | 8.88 | - | 1.95 | 2.33 | 0.84 | 0.18 |
2 | 194.94 | - | 2.32 | 1.94 | 1.05 | 0.17 |
3 | 41.42 | - | 2.73 | 2.04 | 0.67 | 0.26 |
4 | 19.26 | - | 1.83 | 1.60 | 0.93 | 0.21 |
5 | 1.79 | - | 1.82 | 1.74 | 1.01 | 0.16 |
6 | 5.59 | - | 1.46 | 1.95 | 0.75 | 0.18 |
7 | 15.01 | - | 2.65 | 1.94 | 1.13 | 0.16 |
8 | 13.52 | - | 1.85 | 2.32 | 0.82 | 0.19 |
9 | 10.06 | - | 1.93 | 1.18 | 0.89 | 0.13 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 39.76 | - | 8.73 | 7.81 | 3.18 | 1.19 |
1 | 197.97 | - | 11.90 | 7.33 | 7.97 | 1.18 |
2 | 44.35 | - | 11.72 | 5.41 | 5.06 | 1.54 |
3 | 35.38 | - | 8.00 | 5.23 | 4.02 | 1.21 |
4 | 287.05 | - | 11.86 | 5.30 | 4.56 | 1.13 |
5 | - | - | 2.16 | 2.70 | 1.21 | 0.63 |
6 | - | - | 8.86 | 5.65 | 2.63 | 1.08 |
7 | - | - | 22.83 | 21.22 | 9.93 | 2.41 |
8 | - | - | 17.67 | 38.61 | 6.67 | 3.23 |
9 | - | - | 2.81 | 3.38 | 1.60 | 0.67 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | - | - | 85.74 | 229.52 | 119.27 | 24.38 |
1 | - | - | 57.87 | 37.89 | 81.29 | 9.17 |
2 | - | - | 150.26 | 145.34 | 96.55 | 13.43 |
3 | - | - | 49.60 | 285.44 | 55.50 | 27.62 |
4 | - | - | 76.46 | - | 42.25 | 8.85 |
5 | - | - | 140.01 | - | 37.27 | 39.11 |
6 | - | - | 36.22 | - | 37.96 | 16.99 |
7 | - | - | 144.09 | - | 60.98 | 11.95 |
8 | - | - | 175.81 | - | 33.24 | 22.44 |
9 | - | - | 17.81 | - | 9.65 | 4.88 |