Search tree based approaches for parallel machine scheduling

Parallel machine scheduling with precedence constraints and setup times

“…The efficiency of the lower bounds, the dominance rules and the energetic reasoning proposed in Section 3 are tested on middle and large-size instances (n = 100, m ∈ [2, 4]). We also compare the CDS and the HD-CDDS methods with the results obtained in Néron et al (2008) for the hard instances of the P m|r i , q i |C max problem (without precedence constraints and setup times). And finally, we evaluate and compare the proposed methods on a set of 120 large-size instances with the results obtained with ILOG OPL 6.0.…”

“…However the time consumed to reach the best solution is reduced when we use the dominance rule for most of cases. We compare CDS and HD-CDDS methods against other tree search methods presented in Néron et al (2008). In Néron et al (2008), the authors test two dif-ferent branching schemes, time windows (tw ) and chronological (chr ), and several incomplete tree search techniques (truncated branch-and-bound, LDS, Beam Search and Branch-and-Greed) for the P m|r i , q i |C max problem.…”

“…We compare CDS and HD-CDDS methods against other tree search methods presented in Néron et al (2008). In Néron et al (2008), the authors test two dif-ferent branching schemes, time windows (tw ) and chronological (chr ), and several incomplete tree search techniques (truncated branch-and-bound, LDS, Beam Search and Branch-and-Greed) for the P m|r i , q i |C max problem. We adapt the proposed methods for this problem and we use the heuristic for the initial solution and the upper bounds proposed in their paper.…”

“…We have evaluated the number of times the method has found the best solution (NbBest) and for how many of them the method is the only one to reach the best solution (NbBestStrict) for a set of 50 hard instances (n = 100 and m = 10). The CPU time is limited to 30 seconds as in Néron et al (2008).…”

“…Salem et al (2000) solve the problem with a tree search method. More recently, Néron et al (2008) compare two different branching schemes and several tree search strategies for the problem with release dates and tails for the makespan minimization case.…”