Online scheduling on a single machine with rejection under an agreeable condition to minimize the total completion time plus the total rejection cost

We consider the single-machine online scheduling with job rejection to minimize the total completion time of the scheduled jobs plus the total rejection cost of the rejected jobs under an agreeable condition on the processing times and rejection penalties of the jobs. In the problem, a set of independent jobs arriving online over time has to be scheduled on the machine with the flexibility of rejecting some of the jobs, where preemption is not allowed and the information of each job J"j, including its processing time p"j, release date r"j and rejection penalty e"j, is not known in advance. The agreeable condition means that, for every two jobs J"i and J"j, p"i=e"j, and furthermore, p"i=p"j and r"i=e"j. For this problem, we provide an online algorithm with the best possible competitive ratio of 2. As a consequence, the online algorithm is also best possible when the jobs have identical rejection penalties.

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

[2]  Apa Arjen Vestjens.  On-line machine scheduling , 1997 .

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

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

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

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

[7]  C. T. Ng,et al.  Optimal algorithms for single-machine scheduling with rejection to minimize the makespan , 2011 .

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

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

[10]  Dvir Shabtay,et al.  A survey on offline scheduling with rejection , 2013, J. Sched..

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

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

[13]  Dvir Shabtay,et al.  A bicriteria approach to scheduling a single machine with job rejection and positional penalties , 2012, J. Comb. Optim..

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

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

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