An optimal semi-online algorithm for a single machine scheduling problem with bounded processing time

The single machine semi-online scheduling problem is considered with the assumption that the ratio of the longest processing time to the shortest one is not greater than @c. The goal is to minimize the total weighted completion time. We design a semi-online algorithm and prove that it has a competitive ratio of [email protected]^[email protected], which is also shown to be the best performance achieved by any deterministic semi-online algorithm for the problem.

[1]  David Simchi-Levi,et al.  Asymptotic analysis of an on-line algorithm for the single machine completion time problem with release dates , 2001, Oper. Res. Lett..

[2]  Han Hoogeveen,et al.  Optimal On-Line Algorithms for Single-Machine Scheduling , 1996, IPCO.

[3]  Xi Yugeng.  A NOVEL WAY TO ANALYZE COMPETITIVE PERFORMANCE OF ONLINE ALGORITHMS——INSTANCE TRANSFORMATION BASED METHOD , 2009 .

[4]  Chris N. Potts,et al.  On-line scheduling of a single machine to minimize total weighted completion time , 2002, SODA '02.

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

[6]  Yong He,et al.  Semi-online scheduling jobs with tightly-grouped processing times on three identical machines , 2005, Discret. Appl. Math..

[7]  David Simchi-Levi,et al.  The asymptotic performance ratio of an on-line algorithm for uniform parallel machine scheduling with release dates , 2001, Math. Program..

[8]  Cheng-Feng Mabel Chou.  Asymptotic performance ratio of an online algorithm for the single machine scheduling with release dates , 2004, IEEE Transactions on Automatic Control.

[9]  Gerhard J. Woeginger,et al.  Developments from a June 1996 seminar on Online algorithms: the state of the art , 1998 .

[10]  Gerhard J. Woeginger,et al.  Competitive Analysis of Algorithms , 1996, Online Algorithms.

[11]  Michel X. Goemans,et al.  Improved approximation algorthims for scheduling with release dates , 1997, SODA '97.

[12]  David B. Shmoys,et al.  Scheduling to Minimize Average Completion Time: Off-Line and On-Line Approximation Algorithms , 1997, Math. Oper. Res..

[13]  Wayne E. Smith.  Various optimizers for single‐stage production , 1956 .

[14]  Cynthia A. Phillips,et al.  Minimizing average completion time in the presence of release dates , 1998, Math. Program..