Research Article

A Two-Stage Assembly-Type Flowshop Scheduling Problem for Minimizing Total Tardiness

Table 1

Results of the test on the B&B algorithm and CPLEX.

(, )B&BCPLEX
ACPUTMCPUTNI#ACPUTMCPUTNI

8(0.1, 0.8)<0.01<0.01100.040.0310
(0.1, 1.3)<0.01<0.01100.050.0510
(0.1, 1.8)<0.01<0.01100.060.0610
(0.3, 0.8)<0.01<0.01100.050.0310
(0.3, 1.3)<0.01<0.01100.040.0410
(0.3, 1.8)<0.01<0.01100.070.0610
(0.5, 0.8)<0.01<0.01100.050.0510
(0.5, 1.3)<0.01<0.01100.050.0510
(0.5, 1.8)<0.01<0.01100.070.0610

12(0.1, 0.8)0.040.00100.130.0610
(0.1, 1.3)0.000.00100.110.0510
(0.1, 1.8)0.020.00100.550.4210
(0.3, 0.8)0.030.02100.240.0910
(0.3, 1.3)0.030.02100.710.4010
(0.3, 1.8)0.020.02101.140.7210
(0.5, 0.8)0.050.04100.260.1710
(0.5, 1.3)0.050.02100.970.3510
(0.5, 1.8)0.060.02100.660.6510

16(0.1, 0.8)0.000.00100.070.0610
(0.1, 1.3)0.060.00100.250.0810
(0.1, 1.8)0.120.09104.571.1510
(0.3, 0.8)1.210.91100.620.6510
(0.3, 1.3)0.100.06104.051.5310
(0.3, 1.8)0.850.171077.7910.8210
(0.5, 0.8)2.101.20104.103.7410
(0.5, 1.3)1.261.07108.804.7910
(0.5, 1.8)1.090.8710208.3480.9910

20(0.1, 0.8)0.000.00100.120.1110
(0.1, 1.3)0.440.00108.820.1110
(0.1, 1.8)0.850.131032.972.6610
(0.3, 0.8)34.4224.091018.431.8810
(0.3, 1.3)7.680.6610758.1610.908
(0.3, 1.8)14.576.41101804.621817.275
(0.5, 0.8)151.5171.9210239.5640.8210
(0.5, 1.3)61.4811.0810386.61180.4610
(0.5, 1.8)32.537.96101230.12275.377

24(0.1, 0.8)0.000.00100.200.1910
(0.1, 1.3)7.150.001018.100.4010
(0.1, 1.8)5.711.0210514.3896.669
(0.3, 0.8)292.9581.57103.342.2310
(0.3, 1.3)692.239.7091248.93255.207
(0.3, 1.8)304.4034.13102905.163600.002
(0.5, 0.8)1210.80431.4481209.62135.647
(0.5, 1.3)946.30166.1382129.493055.505
(0.5, 1.8)669.19161.9692634.283600.003

Average CPU time (3600 seconds was used as the CPU time for the instances that were not solved to optimality in 3600 seconds).
Median CPU time.
#Number of instances (out of 10 instances) that were solved within 3600 seconds.