Unbounded parallel-batch scheduling under agreeable release and processing to minimize total weighted number of tardy jobs

  • Yuan Gao
  • Jinjiang YuanEmail author


We study the unbounded parallel-batch scheduling problem with the jobs having agreeable release dates and processing times to minimize the total weighted number of tardy jobs. In this problem, we consider two types of jobs: batch jobs and drop-line jobs. For batch jobs, the completion time of a job is given by the completion time of the batch containing this job. For drop-line jobs, the completion time of a job is given by the starting time of the batch containing this job plus the processing time of this job. For both of batch jobs and drop-line jobs, we show that (1) the problems are binary NP-hard, (2) the problems are solvable in pseudo-polynomial times, and when the number of weights is a constant, the problems are solvable in polynomial times, and (3) the problems have a fully polynomial-time approximation scheme.


Parallel-batch scheduling Release dates Drop-line jobs Polynomial-time approximation scheme 



The authors would like to thank the associate editor and two anonymous referees for their constructive comments and helpful suggestions. This research was supported by NSFC (11671368, 11771406, 11571323).


  1. Brucker P, Gladky A, Hoogeveen H, Kovalyov MY, Potts CN, Taut-enhahn T, van de Velde SL (1998) Scheduling a batching machine. J Sched 1:31–54MathSciNetCrossRefzbMATHGoogle Scholar
  2. Cheng TCE, Liu ZH, Yu WC (2001) Scheduling jobs with release dates and deadlines on a batch processing machine. IIE Trans 33:685–690CrossRefGoogle Scholar
  3. Cheng TCE, Ng CT, Yuan JJ, Liu ZH (2004) Single machine parallel batch scheduling subject to precedence constraints. Nav Res Log 51:949–958MathSciNetCrossRefzbMATHGoogle Scholar
  4. Cheng TCE, Ng CT, Yuan JJ (2006) Multi-agent scheduling on a single machine to minimize total weighted number of tardy jobs. Theor Comput Sci 362:273–281MathSciNetCrossRefzbMATHGoogle Scholar
  5. Dobson G, Nambimadom RS (2001) The batch loading and scheduling problem. Oper Res 49:52–65MathSciNetCrossRefzbMATHGoogle Scholar
  6. Gao Y (2018) Min–max scheduling of batch or drop-line jobs under agreeable release and processing. In SubmissionGoogle Scholar
  7. Gao Y, Yuan JJ, Wei ZG (2019) Unbounded parallel-batch scheduling with drop-line jobs. J Sched. Google Scholar
  8. Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. Freeman, San FranciscozbMATHGoogle Scholar
  9. Graham RL, Lawler EL, Lenstra JK, Rinnooy Kan AHG (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann Discrete Math 5:287–326MathSciNetCrossRefzbMATHGoogle Scholar
  10. Lee CY, Uzsoy R (1999) Minimizing makespan on a single batch processing machine with dynamic job arrivals. Int J Prod Res 37:219–236CrossRefzbMATHGoogle Scholar
  11. Lee CY, Uzsoy R, Martin-Vega LA (1992) Efficient algorithms for scheduling semiconductor burn-in operations. Oper Res 40:764–775MathSciNetCrossRefzbMATHGoogle Scholar
  12. Liu ZH, Yuan JJ, Cheng TCE (2003) On scheduling an unbounded batch machine. Oper Res Lett 31:42–48MathSciNetCrossRefzbMATHGoogle Scholar
  13. Mathirajan M, Sivakumar AI (2006) A literature review, classification and simple meta-analysis on scheduling of batch processors in semiconductor. Int J Adv Manuf Technol 29:990–1001CrossRefGoogle Scholar
  14. Potts CN, Kovalyov MY (2000) Scheduling with batching: a review. Eur J Oper Res 120:228–249MathSciNetCrossRefzbMATHGoogle Scholar
  15. Tian J, Fu RY, Yuan JJ (2014) Online over time scheduling on parallel-batch machines: a survey. J Oper Res Soc China 2:445–454MathSciNetCrossRefzbMATHGoogle Scholar
  16. Tian J, Wang Q, Fu RY, Yuan JJ (2016) Online scheduling on the unbounded drop-line batch machines to minimize the maximum delivery completion time. Theor Comput Sci 617:65–68MathSciNetCrossRefzbMATHGoogle Scholar
  17. Wei ZG (2011) Scheduling on a batch machine with item-availability to minimize total weighted completion time. Master Degree Thesis, Zhengzhou UniversityGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsZhengzhou UniversityZhengzhouPeople’s Republic of China

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