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 | 0.02 | 0.01 | 0.01 | 0.01 |
20 | 0.01 | 0.01 | 0.07 | 0.03 | 0.03 | 0.01 |
50 | 0.12 | 0.21 | 0.15 | 0.20 | 0.08 | 0.01 |
100 | 0.57 | 0.72 | 0.24 | 0.43 | 0.14 | 0.03 |
200 | 5.30 | 8.87 | 1.09 | 1.14 | 0.53 | 0.16 |
500 | - | - | 6.49 | 5.73 | 4.28 | 1.83 |
1000 | - | - | 70.49 | 90.27 | 36.64 | 19.88 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.00 | 0.00 | 0.02 | 0.02 | 0.00 | 0.01 |
1 | 0.01 | 0.01 | 0.03 | 0.01 | 0.01 | 0.00 |
2 | 0.01 | 0.01 | 0.02 | 0.00 | 0.00 | 0.02 |
3 | 0.01 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 |
4 | 0.00 | 0.02 | 0.02 | 0.00 | 0.01 | 0.00 |
5 | 0.01 | 0.00 | 0.02 | 0.01 | 0.00 | 0.00 |
6 | 0.00 | 0.02 | 0.02 | 0.01 | 0.01 | 0.01 |
7 | 0.01 | 0.02 | 0.01 | 0.01 | 0.02 | 0.01 |
8 | 0.00 | 0.02 | 0.01 | 0.01 | 0.01 | 0.01 |
9 | 0.01 | 0.01 | 0.01 | 0.00 | 0.00 | 0.01 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.01 | 0.01 | 0.07 | 0.03 | 0.04 | 0.01 |
1 | 0.01 | 0.00 | 0.05 | 0.06 | 0.01 | 0.00 |
2 | 0.01 | 0.02 | 0.07 | 0.02 | 0.02 | 0.01 |
3 | 0.01 | 0.01 | 0.05 | 0.03 | 0.03 | 0.01 |
4 | 0.01 | 0.01 | 0.08 | 0.03 | 0.05 | 0.02 |
5 | 0.01 | 0.01 | 0.07 | 0.04 | 0.02 | 0.00 |
6 | 0.02 | 0.03 | 0.11 | 0.04 | 0.02 | 0.01 |
7 | 0.01 | 0.01 | 0.08 | 0.04 | 0.03 | 0.01 |
8 | 0.01 | 0.01 | 0.04 | 0.02 | 0.02 | 0.00 |
9 | 0.01 | 0.01 | 0.04 | 0.02 | 0.01 | 0.00 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.06 | 0.06 | 0.02 | 0.09 | 0.02 | 0.00 |
1 | 0.10 | 0.25 | 0.11 | 0.19 | 0.08 | 0.02 |
2 | 0.21 | 0.24 | 0.16 | 0.22 | 0.09 | 0.01 |
3 | 0.09 | 0.15 | 0.11 | 0.23 | 0.07 | 0.01 |
4 | 0.12 | 0.16 | 0.18 | 0.16 | 0.08 | 0.02 |
5 | 0.09 | 0.20 | 0.19 | 0.21 | 0.09 | 0.01 |
6 | 0.09 | 0.24 | 0.16 | 0.20 | 0.03 | 0.01 |
7 | 0.22 | 0.44 | 0.17 | 0.22 | 0.13 | 0.01 |
8 | 0.09 | 0.14 | 0.12 | 0.23 | 0.09 | 0.02 |
9 | 0.17 | 0.21 | 0.26 | 0.22 | 0.07 | 0.02 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.15 | 0.11 | 0.04 | 0.14 | 0.03 | 0.02 |
1 | 0.46 | 0.79 | 0.27 | 0.46 | 0.14 | 0.03 |
2 | 1.15 | 0.62 | 0.28 | 0.44 | 0.18 | 0.03 |
3 | 0.31 | 0.86 | 0.17 | 0.53 | 0.15 | 0.03 |
4 | 0.59 | 1.03 | 0.16 | 0.37 | 0.14 | 0.03 |
5 | 0.79 | 0.95 | 0.23 | 0.52 | 0.14 | 0.04 |
6 | 0.18 | 0.64 | 0.25 | 0.30 | 0.13 | 0.03 |
7 | 1.16 | 1.26 | 0.43 | 0.50 | 0.14 | 0.04 |
8 | 0.28 | 0.37 | 0.28 | 0.47 | 0.13 | 0.04 |
9 | 0.60 | 0.61 | 0.33 | 0.58 | 0.17 | 0.05 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 10.15 | 32.91 | 1.32 | 0.93 | 0.66 | 0.16 |
1 | 2.39 | 4.21 | 0.78 | 1.41 | 0.61 | 0.16 |
2 | 18.95 | 19.85 | 1.41 | 1.15 | 0.64 | 0.15 |
3 | 7.99 | 9.83 | 1.19 | 0.99 | 0.47 | 0.22 |
4 | 3.60 | 3.34 | 1.20 | 1.04 | 0.71 | 0.21 |
5 | 0.83 | 1.93 | 0.96 | 1.12 | 0.30 | 0.13 |
6 | 1.60 | 2.90 | 0.92 | 1.36 | 0.54 | 0.13 |
7 | 3.96 | 3.76 | 1.59 | 0.74 | 0.45 | 0.14 |
8 | 1.42 | 3.07 | 0.45 | 1.83 | 0.30 | 0.13 |
9 | 2.10 | 6.85 | 1.09 | 0.86 | 0.67 | 0.19 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 30.64 | 22.82 | 5.55 | 5.06 | 3.97 | 1.91 |
1 | 34.53 | 59.70 | 4.48 | 4.04 | 3.09 | 2.06 |
2 | 12.44 | 37.85 | 6.89 | 2.71 | 3.71 | 1.93 |
3 | 8.92 | 8.64 | 4.96 | 4.85 | 3.69 | 1.40 |
4 | 137.85 | 119.42 | 7.49 | 4.54 | 3.54 | 1.83 |
5 | 2.99 | 1.44 | 1.21 | 1.52 | 0.91 | 0.67 |
6 | 20.64 | 10.81 | 7.14 | 5.28 | 4.34 | 1.38 |
7 | 290.00 | 286.96 | 15.59 | 7.93 | 8.13 | 2.95 |
8 | - | - | 9.78 | 17.35 | 9.62 | 3.41 |
9 | - | - | 1.77 | 4.03 | 1.79 | 0.72 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | - | - | 110.06 | 114.80 | 39.01 | 37.80 |
1 | - | - | 74.03 | 37.07 | 50.51 | 13.49 |
2 | - | - | 130.16 | 57.42 | 77.79 | 17.44 |
3 | - | - | 41.75 | 196.99 | 53.01 | 30.40 |
4 | - | - | 15.55 | 20.21 | 13.68 | 8.44 |
5 | - | - | 72.69 | 259.21 | 30.61 | 31.16 |
6 | - | - | 85.35 | 30.46 | 32.05 | 16.58 |
7 | - | - | 39.62 | 146.92 | 35.83 | 14.23 |
8 | - | - | 125.29 | 31.67 | 27.03 | 25.49 |
9 | - | - | 10.38 | 7.96 | 6.90 | 3.76 |