Approximation algorithms for precedence-constrained identical machine scheduling with rejection

We study a precedence-constrained identical parallel machine scheduling problem with rejection. There is a communication delay between any two jobs connected in the precedence network where jobs may be rejected with penalty. The goal is to minimize the sum of the makespan and the rejection cost. We propose two 3-approximation algorithms for this problem under linear and submodular rejection costs respectively. These two algorithms are both based on linear programming rounding technique.

[1]  Han Hoogeveen,et al.  Three, four, five, six, or the complexity of scheduling with communication delays , 1994, Oper. Res. Lett..

[2]  Gur Mosheiov,et al.  Scheduling on parallel identical machines with job-rejection and position-dependent processing times , 2012, Inf. Process. Lett..

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

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

[5]  Jean-Claude König,et al.  A Heuristic for a Scheduling Problem with Communication Delays , 1997, Oper. Res..

[6]  C. Hanen,et al.  An approximation algorithm for scheduling dependent tasks on m processors with small communication delays , 1995, Proceedings 1995 INRIA/IEEE Symposium on Emerging Technologies and Factory Automation. ETFA'95.

[7]  Jing Liu,et al.  Semi-online scheduling on two identical machines with rejection , 2013, J. Comb. Optim..

[8]  Susan A. Slotnick,et al.  Order acceptance and scheduling: A taxonomy and review , 2011, Eur. J. Oper. Res..

[9]  Leah Epstein,et al.  Preemptive online scheduling with rejection of unit jobs on two uniformly related machines , 2014, J. Sched..

[10]  David R. Karger,et al.  Techniques for scheduling with rejection , 2003, J. Algorithms.

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

[12]  Christophe Picouleau.  New Complexity Results on Scheduling with Small Communication Delays , 1995, Discret. Appl. Math..

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

[14]  James E. Kelley,et al.  Critical-Path Planning and Scheduling: Mathematical Basis , 1961 .

[15]  Y. He,et al.  Solving second order ordinary differential equations with maximal symmetry group , 1999 .

[16]  Jinjiang Yuan,et al.  Parallel-machine scheduling with deteriorating jobs and rejection , 2010, Theor. Comput. Sci..

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

[18]  Leah Epstein,et al.  Online scheduling with rejection and withdrawal , 2011, Theor. Comput. Sci..

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