CPU time for the lot sizing instances without considering the constraint for maximum resource consumption: capacity limits $Q_{max} \in \{10,50,100\}$ and $T_{max}=\infty$
number of periods ($n$) | inventory capacity limit ($Q_{max}$) | method | seed = 100 | 101 | 102 | 103 | 104 | 105 | 106 | 107 | 108 | 109 | 110 |
10 | small Qmax | DP | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
10 | small Qmax | GUROBI | 0.010 | 0.040 | 0.010 | 0.010 | 0.020 | 0.010 | 0.010 | 0.030 | 0.020 | 0.030 | 0.010 |
10 | medium Qmax | DP | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
10 | medium Qmax | GUROBI | 0.030 | 0.030 | 0.020 | 0.030 | 0.030 | 0.030 | 0.020 | 0.020 | 0.020 | 0.050 | 0.020 |
10 | large Qmax | DP | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
10 | large Qmax | GUROBI | 0.030 | 0.030 | 0.030 | 0.030 | 0.040 | 0.070 | 0.020 | 0.020 | 0.020 | 0.040 | 0.020 |
20 | small Qmax | DP | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
20 | small Qmax | GUROBI | 0.050 | 0.060 | 0.050 | 0.060 | 0.100 | 0.070 | 0.050 | 0.060 | 0.040 | 0.090 | 0.050 |
20 | medium Qmax | DP | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
20 | medium Qmax | GUROBI | 0.090 | 0.050 | 0.050 | 0.060 | 0.070 | 0.100 | 0.050 | 0.070 | 0.070 | 0.140 | 0.060 |
20 | large Qmax | DP | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
20 | large Qmax | GUROBI | 0.080 | 0.050 | 0.050 | 0.060 | 0.040 | 0.100 | 0.040 | 0.060 | 0.070 | 0.110 | 0.050 |
30 | small Qmax | DP | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
30 | small Qmax | GUROBI | 0.080 | 0.120 | 0.100 | 0.120 | 0.090 | 0.180 | 0.120 | 0.110 | 0.120 | 0.110 | 0.130 |
30 | medium Qmax | DP | 0.001 | 0.001 | 0.001 | 0.002 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
30 | medium Qmax | GUROBI | 0.350 | 0.140 | 0.100 | 0.640 | 0.180 | 0.100 | 0.150 | 0.170 | 0.280 | 0.160 | 0.170 |
30 | large Qmax | DP | 0.002 | 0.002 | 0.003 | 0.001 | 0.002 | 0.002 | 0.002 | 0.002 | 0.001 | 0.001 | 0.002 |
30 | large Qmax | GUROBI | 0.180 | 0.110 | 0.150 | 0.220 | 0.150 | 0.110 | 0.100 | 0.160 | 0.270 | 0.150 | 0.160 |
40 | small Qmax | DP | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
40 | small Qmax | GUROBI | 0.310 | 0.260 | 0.150 | 0.250 | 0.410 | 0.980 | 0.200 | 0.220 | 0.170 | 0.120 | 0.180 |
40 | medium Qmax | DP | 0.002 | 0.001 | 0.001 | 0.002 | 0.001 | 0.001 | 0.002 | 0.002 | 0.002 | 0.001 | 0.002 |
40 | medium Qmax | GUROBI | 0.330 | 0.960 | 0.150 | 0.300 | 1.220 | 1.350 | 1.020 | 0.380 | 0.310 | 0.500 | 0.210 |
40 | large Qmax | DP | 0.002 | 0.003 | 0.002 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.004 | 0.002 | 0.003 |
40 | large Qmax | GUROBI | 0.120 | 0.250 | 0.120 | 0.370 | 0.220 | 1.040 | 0.820 | 0.280 | 0.220 | 0.200 | 0.130 |
50 | small Qmax | DP | 0.002 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
50 | small Qmax | GUROBI | 0.170 | 0.270 | 0.390 | 0.190 | 0.320 | 0.310 | 0.390 | 0.350 | 0.160 | 0.330 | 0.340 |
50 | medium Qmax | DP | 0.002 | 0.002 | 0.003 | 0.002 | 0.003 | 0.003 | 0.002 | 0.002 | 0.002 | 0.002 | 0.003 |
50 | medium Qmax | GUROBI | 1.590 | 1.210 | 0.380 | 1.750 | 1.620 | 1.500 | 1.850 | 1.390 | 0.890 | 1.780 | 2.290 |
50 | large Qmax | DP | 0.004 | 0.003 | 0.004 | 0.004 | 0.004 | 0.006 | 0.005 | 0.004 | 0.004 | 0.004 | 0.006 |
50 | large Qmax | GUROBI | 1.040 | 0.380 | 0.170 | 1.440 | 1.780 | 0.420 | 0.490 | 1.230 | 0.920 | 0.530 | 3.530 |