Scheduling with Discretely Compressible Release dates to minimize makespan

In this paper, we address the scheduling model with discretely compressible release dates, where processing any job with a compressed release date incurs a corresponding compression cost. We consider the following problem for the first time: scheduling with discretely compressible release dates to minimize the sum of makespan plus total compression cost. We show its NP-hardness, and design an approximation algorithm with worst-case performance ratio 2, which is the best possible if the processing order of the jobs is pre-specified.

[1]  Eugeniusz Nowicki,et al.  A survey of results for sequencing problems with controllable processing times , 1990, Discret. Appl. Math..

[2]  A. Janiak.  Single machine sequencing with linear models of release dates , 1998 .

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

[4]  T. C. Edwin Cheng,et al.  A permutation flow-shop scheduling problem with convex models of operation processing times , 2000, Ann. Oper. Res..

[5]  T.C.E. Cheng,et al.  Resource optimal control in some single-machine scheduling problems , 1994, IEEE Trans. Autom. Control..

[6]  T. C. Edwin Cheng,et al.  Scheduling with controllable release dates and processing times: Makespan minimization , 2006, Eur. J. Oper. Res..

[7]  T. C. Edwin Cheng,et al.  Bicriterion Single Machine Scheduling with Resource Dependent Processing Times , 1998, SIAM J. Optim..

[8]  Zhi-Long Chen,et al.  Single machine scheduling with discretely controllable processing times , 1997, Oper. Res. Lett..

[9]  Adam Janiak.  Computational Complexity Analysis of Single Machine Scheduling Problems with Job Release Dates Dependent on Resources , 1997 .

[10]  Adam Janiak,et al.  Time-optimal control in a single machine problem with resource constraints , 1986, Autom..

[11]  Wieslaw Kubiak,et al.  Positive half-products and scheduling with controllable processing times , 2005, Eur. J. Oper. Res..

[12]  T. C. Edwin Cheng,et al.  Single Machine Scheduling of Unit-time Jobs with Controllable Release Dates , 2003, J. Glob. Optim..

[13]  Chung-Lun Li,et al.  Scheduling to minimize the total weighted completion time with a constraint on the release time resource consumption , 1994 .

[14]  Yuzhong Zhang,et al.  On Several Scheduling Problems with Rejection or Discretely Compressible Processing Times , 2006, TAMC.

[15]  Adam Janiak,et al.  Single machine scheduling problem with a common deadline and resource dependent release dates , 1991 .