A linear time approximation algorithm for permutation flow shop scheduling

In the last 40 years, the permutation flow shop scheduling (PFS) problem with makespan minimization has been a central problem, known for its intractability, that has been well studied from both theoretical and practical aspects. The currently best performance ratio of a deterministic approximation algorithm for the PFS was recently presented by Nagarajan and Sviridenko, using a connection between the PFS and the longest increasing subsequence problem. In a different and independent way, this paper employs monotone subsequences in the approximation analysis techniques. To do this, an extension of the Erdos-Szekeres theorem to weighted monotone subsequences is presented. The result is a simple deterministic algorithm for the PFS with a similar approximation guarantee, but a much lower time complexity.

[1]  Chris N. Potts,et al.  Permutation vs. non-permutation flow shop schedules , 1991, Oper. Res. Lett..

[2]  Klaus W. Wagner,et al.  Monotonic Coverings of Finite Sets , 1984, J. Inf. Process. Cybern..

[3]  Sergey Vasil'evich Sevast'janov,et al.  on Some Geometric Methods in Scheduling Theory: A Survey , 1994, Discret. Appl. Math..

[4]  Alexander Schrijver,et al.  Combinatorial optimization. Polyhedra and efficiency. , 2003 .

[5]  Eugeniusz Nowicki,et al.  Worst-case analysis of Dannenbring's algorithm for flow-shop scheduling , 1991, Oper. Res. Lett..

[6]  Reuven Bar-Yehuda,et al.  Partitioning a sequence into few monotone subsequences , 1998, Acta Informatica.

[7]  Klaus Jansen,et al.  Makespan Minimization in Job Shops: A Linear Time Approximation Scheme , 2003, SIAM J. Discret. Math..

[8]  Teofilo F. Gonzalez,et al.  Flowshop and Jobshop Schedules: Complexity and Approximation , 1978, Oper. Res..

[9]  G. Szekeres,et al.  A combinatorial problem in geometry , 2009 .

[10]  Maxim Sviridenko,et al.  Tight Bounds for Permutation Flow Shop Scheduling , 2008, Math. Oper. Res..

[11]  Eugeniusz Nowicki,et al.  Worst-case analysis of an approximation algorithm for flow-shop scheduling , 1989 .

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

[13]  Leslie A. Hall.  Approximability of flow shop scheduling , 1998, Math. Program..

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

[15]  Jatinder N. D. Gupta,et al.  Performance guarantees for flowshop heuristics to minimize makespan , 2006, Eur. J. Oper. Res..

[16]  Maxim Sviridenko.  A Note on Permutation Flow Shop Problem , 2004, Ann. Oper. Res..

[17]  J. Michael Steele,et al.  Variations on the Monotone Subsequence Theme of Erdös and Szekeres , 1995 .

[18]  Harold N. Gabow,et al.  Algorithms for Edge Coloring Bipartite Graphs and Multigraphs , 1982, SIAM J. Comput..

[19]  Eugeniusz Nowicki,et al.  New Results in the Worst-Case Analysis for Flow-Shop Scheduling , 1993, Discret. Appl. Math..