An assignment-based lower bound for a class of two-machine flow shop problems

We present an assignment-based lower bound that is valid for a wide class of two-machine flow shop problems with a regular additive performance criterion. We provide empirical evidence that this new bound consistently outperforms state-of-the-art lower bounds in two important special cases: F2@?@?C"j and F2@?@?T"j. Moreover, we illustrate its wide applicability and good performance on two additional problems: F2@?@?C"j and F2@?@?lnC"j.

[1]  A. Volgenant,et al.  A shortest augmenting path algorithm for dense and sparse linear assignment problems , 1987, Computing.

[2]  Jatinder N. D. Gupta,et al.  The two-machine flowshop scheduling problem with total tardiness , 1989, Comput. Oper. Res..

[3]  Ravi Sethi,et al.  The Complexity of Flowshop and Jobshop Scheduling , 1976, Math. Oper. Res..

[4]  Jeffrey E. Schaller,et al.  Note on minimizing total tardiness in a two-machine flowshop , 2005, Comput. Oper. Res..

[5]  Jen-Shiang Chen,et al.  Minimizing tardiness in a two-machine flow-shop , 2002, Comput. Oper. Res..

[6]  William L. Maxwell,et al.  Theory of scheduling , 1967 .

[7]  Zhiyong Xu,et al.  Some results of the worst-case analysis for flow shop scheduling with a learning effect , 2008, Annals of Operations Research.

[8]  S. M. Johnson,et al.  Optimal two- and three-stage production schedules with setup times included , 1954 .

[9]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[10]  Can Akkan,et al.  The two-machine flowshop total completion time problem: Improved lower bounds and a branch-and-bound algorithm , 2004, Eur. J. Oper. Res..

[11]  Han Hoogeveen,et al.  Lower bounds for minimizing total completion time in a two-machine flow shop , 2006, J. Sched..

[12]  Jason Chao-Hsien Pan,et al.  Two-machine flowshop scheduling to minimize total tardiness , 1997, Int. J. Syst. Sci..

[13]  Yeong-Dae Kim,et al.  A new branch and bound algorithm for minimizing mean tardiness in two-machine flowshops , 1993, Comput. Oper. Res..

[14]  Christos Koulamas,et al.  The Total Tardiness Problem: Review and Extensions , 1994, Oper. Res..

[15]  Roberto Tadei,et al.  An improved branch-and-bound algorithm for the two machine total completion time flow shop problem , 2002, Eur. J. Oper. Res..

[16]  M. Aziz Moukrim,et al.  Exact and Heuristic Methods for Variants of the Permutation Flow Shop Problems , 2011 .

[17]  George J. Kyparisis,et al.  Algorithms with performance guarantees for flow shops with regular objective functions , 2005 .

[18]  M. Desrochers,et al.  A Generalized Permanent Labelling Algorithm For The Shortest Path Problem With Time Windows , 1988 .

[19]  E. Ignall,et al.  Application of the Branch and Bound Technique to Some Flow-Shop Scheduling Problems , 1965 .

[20]  F. D. Croce,et al.  The two-machine total completion time flow shop problem , 1996 .

[21]  Jan Karel Lenstra,et al.  Complexity of machine scheduling problems , 1975 .

[22]  Ji-Bo Wang,et al.  Worst-case behavior of simple sequencing rules in flow shop scheduling with general position-dependent learning effects , 2011, Ann. Oper. Res..