Single-machine scheduling under the job rejection constraint

In this paper, we consider single-machine scheduling problems under the job rejection constraint. A job is either rejected, in which case a rejection penalty has to be paid, or accepted and processed on the single machine. However, the total rejection penalty of the rejected jobs cannot exceed a given upper bound. The objective is to find a schedule such that a given criterion f is minimized, where f is a non-decreasing function on the completion times of the accepted jobs. We analyze the computational complexities of the problems for distinct objective functions and present pseudo-polynomial-time algorithms. In addition, we provide a fully polynomial-time approximation scheme for the makespan problem with release dates. For other objective functions related to due dates, we point out that there is no approximation algorithm with a bounded approximation ratio.

[1]  Leen Stougie,et al.  Multiprocessor scheduling with rejection , 1996, SODA '96.

[2]  P. Pardalos.  Complexity in numerical optimization , 1993 .

[3]  J. M. Moore,et al.  A Functional Equation and its Application to Resource Allocation and Sequencing Problems , 1969 .

[4]  Dieter Jungnickel,et al.  Approximate minimization algorithms for the 0/1 Knapsack and Subset-Sum Problem , 2000, Oper. Res. Lett..

[5]  Eugene L. Lawler,et al.  Optimal Sequencing of a Single Machine Subject to Precedence Constraints , 1973 .

[6]  David R. Karger,et al.  Techniques for scheduling with rejection , 1998, J. Algorithms.

[7]  Joseph Y.-T. Leung,et al.  Minimizing Total Tardiness on One Machine is NP-Hard , 1990, Math. Oper. Res..

[8]  J. M. Moore.  An n Job, One Machine Sequencing Algorithm for Minimizing the Number of Late Jobs , 1968 .

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

[10]  Gerhard J. Woeginger,et al.  On-line scheduling of unit time jobs with rejection: minimizing the total completion time , 2002, Oper. Res. Lett..

[11]  Steven S. Seiden.  Preemptive multiprocessor scheduling with rejection , 2001, Theor. Comput. Sci..

[12]  Shijie Sun,et al.  Scheduling linear deteriorating jobs with rejection on a single machine , 2009, Eur. J. Oper. Res..

[13]  Yong He,et al.  Scheduling with machine cost and rejection , 2006, J. Comb. Optim..

[14]  Han Hoogeveen,et al.  Multicriteria scheduling , 2005, Eur. J. Oper. Res..

[15]  T. C. Edwin Cheng,et al.  Bounded single-machine parallel-batch scheduling with release dates and rejection , 2009, Comput. Oper. Res..

[16]  E. Lawler.  A “Pseudopolynomial” Algorithm for Sequencing Jobs to Minimize Total Tardiness , 1977 .

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

[18]  Han Hoogeveen,et al.  Preemptive scheduling with rejection , 2000, Math. Program..

[19]  Sudipta Sengupta,et al.  Algorithms and Approximation Schemes for Minimum Lateness/Tardiness Scheduling with Rejection , 2003, WADS.

[20]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[21]  Jinjiang Yuan,et al.  Single machine scheduling with release dates and rejection , 2009, Eur. J. Oper. Res..

[22]  J. A. Hoogeveen,et al.  Single-machine bicriteria scheduling , 1992 .

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

[24]  Jinjiang Yuan,et al.  The unbounded parallel batch machine scheduling with release dates and rejection to minimize makespan , 2008, Theor. Comput. Sci..