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 | 0.12 | 0.12 | 0.29 | 0.35 | 0.17 | 0.01 |
20 | 0.22 | 1.56 | 1.01 | 2.48 | 0.49 | 0.03 |
50 | 1.52 | 13.92 | 1.53 | 3.69 | 1.14 | 0.07 |
100 | - | - | 4.35 | 6.09 | 1.83 | 0.18 |
200 | - | - | 12.53 | 8.45 | 5.70 | 0.57 |
500 | - | - | 62.70 | - | 20.04 | 3.16 |
1000 | - | - | - | - | 131.32 | 21.66 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.12 | 0.14 | 0.54 | 0.31 | 0.18 | 0.02 |
1 | 0.13 | 0.13 | 0.20 | 0.42 | 0.22 | 0.00 |
2 | 0.12 | 0.14 | 0.21 | 0.43 | 0.09 | 0.01 |
3 | 0.12 | 0.16 | 0.26 | 0.33 | 0.18 | 0.00 |
4 | 0.12 | 0.09 | 0.25 | 0.32 | 0.21 | 0.00 |
5 | 0.07 | 0.09 | 0.52 | 0.41 | 0.20 | 0.01 |
6 | 0.13 | 0.14 | 0.23 | 0.44 | 0.19 | 0.01 |
7 | 0.12 | 0.15 | 0.21 | 0.40 | 0.07 | 0.00 |
8 | 0.12 | 0.09 | 0.22 | 0.25 | 0.19 | 0.02 |
9 | 0.13 | 0.08 | 0.26 | 0.24 | 0.20 | 0.00 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.16 | 1.50 | 1.74 | 1.59 | 0.42 | 0.04 |
1 | 0.17 | 2.02 | 0.58 | 1.83 | 0.19 | 0.03 |
2 | 0.16 | 0.99 | 1.42 | 1.38 | 0.75 | 0.05 |
3 | 0.15 | 0.24 | 0.79 | 3.03 | 0.46 | 0.04 |
4 | 0.25 | 0.45 | 0.65 | 1.41 | 0.79 | 0.03 |
5 | 0.29 | 0.56 | 0.60 | 3.16 | 0.59 | 0.03 |
6 | 0.28 | 3.44 | 1.55 | 5.09 | 0.20 | 0.04 |
7 | 0.29 | 4.30 | 0.56 | 1.52 | 0.63 | 0.03 |
8 | 0.22 | 0.29 | 0.58 | 3.95 | 0.19 | 0.04 |
9 | 0.24 | 1.86 | 1.60 | 1.81 | 0.67 | 0.02 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.44 | 0.33 | 0.45 | 1.08 | 0.13 | 0.03 |
1 | 0.66 | 7.21 | 1.55 | 4.88 | 1.57 | 0.08 |
2 | 2.27 | 25.57 | 0.82 | 2.97 | 0.75 | 0.08 |
3 | 0.67 | 8.25 | 0.80 | 4.07 | 1.39 | 0.08 |
4 | 1.78 | 4.88 | 2.37 | 2.52 | 0.86 | 0.08 |
5 | 0.69 | 2.17 | 1.29 | 3.18 | 1.66 | 0.08 |
6 | 0.42 | 8.39 | 1.64 | 5.29 | 1.50 | 0.08 |
7 | 6.80 | 59.71 | 1.58 | 2.38 | 0.87 | 0.09 |
8 | 0.66 | 9.02 | 1.52 | 5.25 | 1.42 | 0.07 |
9 | 0.86 | 13.68 | 3.32 | 5.29 | 1.25 | 0.08 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | 0.73 | 0.80 | 0.97 | 1.92 | 0.28 | 0.05 |
1 | 16.30 | 270.13 | 4.83 | 8.50 | 1.95 | 0.19 |
2 | 8.28 | 99.05 | 2.31 | 6.59 | 1.84 | 0.19 |
3 | 4.08 | 64.50 | 4.48 | 7.07 | 2.26 | 0.21 |
4 | 14.93 | 107.96 | 10.53 | 3.77 | 2.15 | 0.19 |
5 | 27.95 | 231.40 | 4.99 | 6.03 | 1.86 | 0.18 |
6 | 1.20 | 5.78 | 4.05 | 8.09 | 1.88 | 0.18 |
7 | 286.36 | 285.22 | 3.79 | 7.14 | 2.36 | 0.21 |
8 | - | - | 4.34 | 5.81 | 1.75 | 0.20 |
9 | - | - | 3.23 | 5.94 | 2.01 | 0.20 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | - | - | 15.76 | 5.75 | 4.48 | 0.56 |
1 | - | - | 14.97 | 13.24 | 4.57 | 0.51 |
2 | - | - | 19.02 | 9.10 | 6.71 | 0.47 |
3 | - | - | 8.86 | 7.90 | 6.64 | 0.70 |
4 | - | - | 14.78 | 6.74 | 6.67 | 0.69 |
5 | - | - | 12.73 | 8.23 | 4.31 | 0.48 |
6 | - | - | 4.67 | 7.99 | 5.76 | 0.54 |
7 | - | - | 6.92 | 8.38 | 6.95 | 0.52 |
8 | - | - | 17.08 | 12.90 | 5.77 | 0.56 |
9 | - | - | 10.48 | 4.26 | 5.14 | 0.64 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | - | - | 47.79 | 20.79 | 21.04 | 2.30 |
1 | - | - | 76.58 | 96.86 | 19.94 | 3.20 |
2 | - | - | 64.62 | 55.91 | 29.49 | 3.11 |
3 | - | - | 76.18 | 17.04 | 13.56 | 2.76 |
4 | - | - | 75.10 | 20.36 | 22.07 | 2.73 |
5 | - | - | 11.31 | 27.39 | 4.58 | 1.58 |
6 | - | - | 52.43 | 112.41 | 19.69 | 2.94 |
7 | - | - | 116.01 | 32.70 | 25.93 | 4.34 |
8 | - | - | 70.35 | 279.64 | 26.36 | 6.94 |
9 | - | - | 36.60 | - | 17.76 | 1.72 |
inst | mselect | cc_dis | cc_dis_log | cc_agg | cc_agg_log | sos |
0 | - | - | 288.39 | - | 117.73 | 40.12 |
1 | - | - | - | - | 53.87 | 13.31 |
2 | - | - | - | - | 110.30 | 17.36 |
3 | - | - | - | - | 215.43 | 45.53 |
4 | - | - | - | - | 127.41 | 9.96 |
5 | - | - | - | - | 258.29 | 41.54 |
6 | - | - | - | - | 127.56 | 11.57 |
7 | - | - | - | - | 115.75 | 12.97 |
8 | - | - | - | - | 158.96 | 18.54 |
9 | - | - | - | - | 27.85 | 5.69 |