Online algorithms for scheduling on batch processing machines with interval graph compatibilities between jobs

Abstract We consider the online (over time) scheduling problem of minimizing the makespan on m unbounded parallel-batch machines, in which jobs in the same batch have to be pairwise compatible. Compatibility is a symmetric binary relation, which is represented by an interval compatibility graph. The processing time of a batch is equal to the maximum processing time of the jobs in it, and all jobs in the same batch start and finish at the same time. For this problem, firstly, we show that there exists no online algorithm with a competitive ratio less than 2. Then we provide an online algorithm with a competitive ratio 2 + m − 1 m + 1 , which is optimal for the case m = 1 . When all jobs have the same processing times, we also give an optimal online algorithm.

[1]  S HochbaumDorit,et al.  Scheduling with batching , 1994 .

[2]  Gerd Finke,et al.  Batch processing with interval graph compatibilities between tasks , 2005, Discret. Appl. Math..

[3]  Xiaoqiang Cai,et al.  On‐line algorithms for minimizing makespan on batch processing machines , 2001 .

[4]  Chung Keung Poon,et al.  A Flexible On-line Scheduling Algorithm for Batch Machine with Infinite Capacity , 2005, Ann. Oper. Res..

[5]  T. C. Edwin Cheng,et al.  An optimal online algorithm for single parallel-batch machine scheduling with incompatible job families to minimize makespan , 2013, Oper. Res. Lett..

[6]  Ruyan Fu,et al.  An optimal online algorithm for the parallel-batch scheduling with job processing time compatibilities , 2017, J. Comb. Optim..

[7]  Ruyan Fu,et al.  Online Over Time Scheduling on Parallel-Batch Machines: A Survey , 2014 .

[8]  Gregory Dobson,et al.  The Batch Loading and Scheduling Problem , 2001, Oper. Res..

[9]  T. C. Edwin Cheng,et al.  The unbounded single machine parallel batch scheduling problem with family jobs and release dates to minimize makespan , 2004, Theor. Comput. Sci..

[10]  Yuzhong Zhang,et al.  Approximation Algorithms in Batch Processing , 1999, ISAAC.

[11]  Reha Uzsoy,et al.  Efficient Algorithms for Scheduling Semiconductor Burn-In Operations , 1992, Oper. Res..

[12]  T. C. Edwin Cheng,et al.  The bounded single-machine parallel-batching scheduling problem with family jobs and release dates to minimize makespan , 2004, Oper. Res. Lett..

[13]  T. C. Edwin Cheng,et al.  Single-machine batch scheduling with job processing time compatibility , 2015, Theor. Comput. Sci..

[14]  Xiwen Lu,et al.  A best possible deterministic on-line algorithm for minimizing makespan on parallel batch machines , 2012, J. Sched..

[15]  Mourad Boudhar,et al.  Scheduling a batch processing machine with bipartite compatibility graphs , 2003, Math. Methods Oper. Res..

[16]  Gerd Finke,et al.  Batch Processing with Graph Compatibilities between Tasks , 2008 .

[17]  Adam Janiak,et al.  Scheduling an unbounded batching machine with job processing time compatibilities , 2012, Discret. Appl. Math..

[18]  Chris N. Potts,et al.  Scheduling with batching: A review , 2000, Eur. J. Oper. Res..

[19]  Ronald L. Graham,et al.  Bounds on Multiprocessing Timing Anomalies , 1969, SIAM Journal of Applied Mathematics.

[20]  Mourad Boudhar.  Dynamic Scheduling on a Single Batch Processing Machine with Split Compatibility Graphs , 2003, J. Math. Model. Algorithms.