The unbounded single machine parallel batch scheduling problem with family jobs and release dates to minimize makespan

We consider the problem of scheduling family jobs with release dates on a bounded batching machine. Our objective is to minimize the maximum completion time of the jobs (i.e., the makespan). We deal with two variants of the problem. One is the identical job size model, in which the machine can process up to b jobs simultaneously as a batch. The other is the non-identical job size model, in which each job has a size no more than 1 and the machine can handle a number of jobs simultaneously as a batch as long as the total size of the jobs does not exceed 1. In this paper we first present a 2-approximation algorithm for the former model and a polynomial time approximation scheme (PTAS) for the case when the number of distinct families is constant; and then derive an approximation algorithm with a worst-case ratio of 5/2 for the latter model.

[1]  Guochuan Zhang,et al.  Minimizing makespan on a single batch processing machine with nonidentical job sizes , 2001 .

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

[3]  Reha Uzsoy,et al.  Minimizing makespan on a single batch processing machine with dynamic job arrivals , 1999 .

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

[5]  Mihalis Yannakakis,et al.  Batch sizing and job sequencing on a single machine , 1991 .

[6]  T. C. Edwin Cheng,et al.  Scheduling Jobs with Release Dates and Deadlines on a Batch Processing Machine , 2001 .

[7]  Yuzhong Zhang,et al.  Minimizing Mean Response Time in Batch Processing System , 1999, COCOON.

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

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

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

[11]  D. Atkin.  OR scheduling algorithms. , 2000, Anesthesiology.

[12]  J. Yuana,et al.  The unbounded single machine parallel batch scheduling problem with family jobs and release dates to minimize makespan , 2004 .

[13]  Xiaoli Wang,et al.  Minimizing makespan on a single batching machine with release times and non-identical job sizes , 2005, Oper. Res. Lett..

[14]  Evripidis Bampis,et al.  Approximation schemes for minimizing average weighted completion time with release dates , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[15]  Zhaohui Liu,et al.  Scheduling one batch processor subject to job release dates , 2000, Discret. Appl. Math..

[16]  T. C. Edwin Cheng,et al.  On scheduling an unbounded batch machine , 2003, Oper. Res. Lett..

[17]  R. Uzsoy.  Scheduling a single batch processing machine with non-identical job sizes , 1994 .

[18]  Jan Karel Lenstra,et al.  Computing near-optimal schedules , 1995 .

[19]  J. A. Hoogeveen,et al.  Scheduling a batching machine , 1998 .

[20]  Shuguang Li,et al.  Minimizing makespan with release times on identical parallel batching machines , 2005, Discret. Appl. Math..