RM BB LB-BK LB-BK-E LB-BK-E-PREC Instance cpu LB UB cpu lbBK cpu lbBK cpu lbBK cpu --------------------------------------------------------------------------------------------- BL_20_01 0 16 16 0,63 BL_20_02 0 16 16 3,25 BL_20_03 0 15 15 5,95 BL_20_04 0 18 18 0,11 BL_20_05 0 17 19 90,01 17 0,29 17 0,15 17 0,22 BL_20_06 0 16 16 2,02 BL_20_07 0 19 19 17,05 BL_20_08 0 20 20 4,51 BL_20_09 0 14 14 2,52 BL_20_10 0 16 16 1,86 BL_20_11 0 17 17 0,02 BL_20_12 0 18 18 7,57 BL_20_13 0 17 17 0,91 BL_20_14 0 17 18 90,01 17 0,11 17 0,11 17 0,17 BL_20_15 0 13 13 1,05 BL_20_16 0 19 19 2,31 BL_20_17 0 14 15 90,01 14 0,1 14 0,14 14 0,18 BL_20_18 0,1 17 18 90,01 17 0,1 17 0,12 17 0,17 BL_20_19 0 14 14 0,30 BL_20_20 0 15 15 2,79 BL_25_01 0 27 27 19,02 BL_25_02 0 29 29 15,28 BL_25_03 0 23 23 2,59 BL_25_04 0 22 22 0,06 BL_25_05 0 28 28 2,40 BL_25_06 0,1 33 33 0,30 BL_25_07 0 24 28 90,01 24 0,381 24 0,26 24 0,29 BL_25_08 0 24 24 0,70 BL_25_09 0 27 27 1,52 BL_25_10 0 23 23 0,23 BL_25_11 0,1 24 24 26,62 BL_25_12 0 29 30 90,02 29 0,19 29 0,33 29 0,41 BL_25_13 0 17 17 0,18 BL_25_14 0 30 30 0,27 BL_25_15 0 20 20 1,27 BL_25_16 0,1 20 20 0,14 BL_25_17 0 26 26 0,55 BL_25_18 0 23 23 7,98 BL_25_19 0 23 23 1,34 BL_25_20 0 27 28 90,01 27 0,11 27 0,15 27 0,2 ----------------------------------------------------------------------------------------------------------------------------------- cpu RM: cpu time (in seconds) to generate redundant machines (MIP solved by Cplex) LB BB: lower bound computed by the initial branch and bound UB BB: upper bound computed by the initial branch and bound cpu BB: cpu time (in seconds) to run the initial branch and bound (time-limit of 90 seconds, CP solved using Scheduler) If the branch and bound has not prove optimality: LB-BK: lower bound computed by the column generation of Brucker and Knust cpu LB-BK: additional cpu time (in seconds) to run the column generation LB-BK-E: LB-BK + energetic cuts cpu LB-BK-E: additional cpu time (in seconds) to run LB-BK-E LB-BK-E-PREC: LB-BK-E + precedence cuts cpu LB-BK-E-PREC: additional cpu time (in seconds) to run LB-BK-E-PREC