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 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
50 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 |
100 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 |
200 | 0.06 | 0.11 | 0.10 | 0.12 | 0.11 | 0.13 |
500 | 0.72 | 1.67 | 1.74 | 1.59 | 1.59 | 1.79 |
1000 | 6.14 | 9.00 | 11.32 | 11.78 | 12.15 | 12.99 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 |
1 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
2 | 0.00 | 0.01 | 0.01 | 0.00 | 0.00 | 0.00 |
3 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
4 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 |
5 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
6 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 |
7 | 0.01 | 0.00 | 0.01 | 0.00 | 0.00 | 0.01 |
8 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
9 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 |
1 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
2 | 0.01 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 |
3 | 0.01 | 0.01 | 0.01 | 0.00 | 0.00 | 0.00 |
4 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 |
5 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 |
6 | 0.01 | 0.00 | 0.01 | 0.00 | 0.00 | 0.01 |
7 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
8 | 0.01 | 0.00 | 0.01 | 0.00 | 0.01 | 0.00 |
9 | 0.00 | 0.01 | 0.00 | 0.00 | 0.01 | 0.01 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.00 | 0.01 | 0.00 | 0.00 | 0.01 | 0.01 |
1 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 |
2 | 0.00 | 0.01 | 0.01 | 0.01 | 0.01 | 0.00 |
3 | 0.02 | 0.01 | 0.01 | 0.00 | 0.01 | 0.01 |
4 | 0.01 | 0.00 | 0.02 | 0.02 | 0.01 | 0.00 |
5 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 |
6 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 |
7 | 0.01 | 0.00 | 0.00 | 0.00 | 0.01 | 0.01 |
8 | 0.00 | 0.01 | 0.00 | 0.02 | 0.01 | 0.00 |
9 | 0.01 | 0.01 | 0.01 | 0.00 | 0.01 | 0.01 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.01 | 0.00 | 0.00 | 0.01 | 0.00 | 0.01 |
1 | 0.02 | 0.02 | 0.02 | 0.03 | 0.03 | 0.02 |
2 | 0.00 | 0.02 | 0.04 | 0.03 | 0.02 | 0.01 |
3 | 0.01 | 0.02 | 0.01 | 0.02 | 0.02 | 0.01 |
4 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.03 |
5 | 0.02 | 0.02 | 0.02 | 0.03 | 0.03 | 0.02 |
6 | 0.01 | 0.02 | 0.01 | 0.01 | 0.02 | 0.00 |
7 | 0.02 | 0.02 | 0.03 | 0.03 | 0.02 | 0.01 |
8 | 0.02 | 0.01 | 0.01 | 0.01 | 0.02 | 0.02 |
9 | 0.03 | 0.02 | 0.02 | 0.03 | 0.03 | 0.02 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.05 | 0.09 | 0.10 | 0.09 | 0.09 | 0.12 |
1 | 0.04 | 0.14 | 0.10 | 0.10 | 0.12 | 0.10 |
2 | 0.05 | 0.11 | 0.08 | 0.21 | 0.19 | 0.18 |
3 | 0.08 | 0.15 | 0.13 | 0.17 | 0.16 | 0.27 |
4 | 0.07 | 0.09 | 0.09 | 0.08 | 0.06 | 0.08 |
5 | 0.07 | 0.07 | 0.12 | 0.08 | 0.09 | 0.07 |
6 | 0.07 | 0.19 | 0.15 | 0.23 | 0.22 | 0.22 |
7 | 0.05 | 0.08 | 0.10 | 0.09 | 0.09 | 0.11 |
8 | 0.05 | 0.08 | 0.07 | 0.06 | 0.06 | 0.06 |
9 | 0.06 | 0.10 | 0.09 | 0.07 | 0.07 | 0.09 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.54 | 2.09 | 2.01 | 2.23 | 2.06 | 2.41 |
1 | 0.56 | 2.14 | 1.68 | 1.45 | 1.61 | 1.63 |
2 | 0.83 | 2.05 | 2.93 | 2.48 | 2.84 | 2.71 |
3 | 0.65 | 2.01 | 1.83 | 2.03 | 1.94 | 1.64 |
4 | 0.66 | 3.17 | 3.34 | 2.75 | 3.11 | 3.77 |
5 | 0.64 | 0.63 | 0.79 | 0.65 | 0.74 | 0.62 |
6 | 1.01 | 1.48 | 1.75 | 1.48 | 1.20 | 1.72 |
7 | 0.87 | 1.40 | 1.52 | 1.26 | 0.99 | 1.41 |
8 | 0.74 | 0.86 | 0.79 | 0.84 | 0.67 | 1.18 |
9 | 0.72 | 0.92 | 0.78 | 0.78 | 0.73 | 0.85 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 5.58 | 10.99 | 17.53 | 17.29 | 9.69 | 12.16 |
1 | 6.30 | 8.73 | 15.87 | 16.91 | 11.04 | 9.56 |
2 | 5.68 | 10.79 | 16.72 | 18.72 | 21.62 | 14.02 |
3 | 5.18 | 10.14 | 13.17 | 13.86 | 20.41 | 13.20 |
4 | 6.29 | 6.72 | 6.97 | 5.83 | 7.84 | 10.42 |
5 | 7.20 | 6.92 | 6.88 | 8.22 | 9.64 | 13.97 |
6 | 7.09 | 8.28 | 9.03 | 9.79 | 10.44 | 18.61 |
7 | 6.53 | 6.35 | 9.16 | 7.05 | 9.62 | 13.81 |
8 | 8.62 | 13.08 | 11.95 | 16.40 | 17.53 | 19.14 |
9 | 2.93 | 7.96 | 5.94 | 3.77 | 3.66 | 5.03 |