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Two-agent scheduling of time-dependent jobs

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Abstract

We consider the problem of scheduling deteriorating jobs or shortening jobs with two agents A and B. We are interested in generating all Pareto-optimal schedules for the two criteria: (1) the total completion time of the jobs in A and the maximum cost of the jobs in B, and (2) the maximum cost of the jobs in A and the maximum cost of the jobs in B. We show that all Pareto-optimal schedules for both problems can be generated in polynomial time, whether the jobs are deteriorating or shortening.

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References

  • Agnetis A, Mirchani PB, Pacciarelli D, Pacifici A (2004) Scheduling problems with two competing agents. Oper Res 52:229–242

    Article  MathSciNet  MATH  Google Scholar 

  • Agnetis A, Pacciarelli D, Pacifici A (2007) Multi-agent single machine scheduling. Ann Oper Res 150:3–15

    Article  MathSciNet  MATH  Google Scholar 

  • Agnetis A, Billaut JC, Gawiejnowicz S, Pacciarelli D, Soukhal A (2014) Multiagent scheduling: models and algorithms. Springer, Berlin

    Book  MATH  Google Scholar 

  • Alidaee B, Womer NK (1999) Scheduling with time dependent processing times: review and extensions. J Oper Res Soc 50:711–720

    Article  MATH  Google Scholar 

  • Baker KR, Smith JC (2003) A multiple criterion model for machine scheduling. J Sched 6:7–16

    Article  MathSciNet  MATH  Google Scholar 

  • Browne S, Yechiali U (1990) Scheduling deteriorating jobs on a single processor. Oper Res 38:495–498

    Article  MATH  Google Scholar 

  • Brucker P (2001) Scheduling algorithms, 3rd edn. Springer, Berlin

    Book  MATH  Google Scholar 

  • Cheng TCE, Ding Q, Lin BMT (2004) A concise survey of scheduling with time-dependent processing times. Eur J Oper Res 152:1–13

    Article  MathSciNet  MATH  Google Scholar 

  • 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 362:273–281

    Article  MathSciNet  MATH  Google Scholar 

  • Cheng TCE, Ng CT, Yuan JJ (2008) Multi-agent scheduling on a single machine with max-form criteria. Eur J Oper Res 188:603–609

    Article  MathSciNet  MATH  Google Scholar 

  • Graham RL, Lawler EL, Lenstra JK, Rinnooy Kan AHG (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann Discrete Math 5:287–326

    Article  MathSciNet  MATH  Google Scholar 

  • Gupta JND, Gupta SK (1988) Single facility scheduling with nonlinear processing times. Comput Ind Eng 14:387–393

    Article  MathSciNet  Google Scholar 

  • Ho KIJ, Leung JY-T, Wei W-D (1993) Complexity of scheduling tasks with time-dependent execution times. Inf Process Lett 48:315–320

    Article  MathSciNet  MATH  Google Scholar 

  • Hoogeveen H (2005) Multicriteria scheduling. Eur J Oper Res 167:592–623

    Article  MathSciNet  MATH  Google Scholar 

  • Leung JY-T, Pinedo M, Wan G (2010) Competitive two-agent scheduling and its applications. Oper Res 58:458–469

    Article  MathSciNet  MATH  Google Scholar 

  • Liu P, Tang L (2008) Two-agent scheduling with linear deteriorating jobs on single-machine. Lect Notes Comput Sci 5029:642–650

    Article  MathSciNet  MATH  Google Scholar 

  • Liu P, Yi N, Zhou XY (2011) Two-agent single-machine scheduling problems under increasing linear deterioration. Appl Math Model 35:2290–2296

    Article  MathSciNet  MATH  Google Scholar 

  • Ng CT, Cheng TCE, Bachman A, Janiak A (2002) Three scheduling problems with deteriorating jobs to minimize the total completion time. Inf Process Lett 81:327–333

    Article  MathSciNet  MATH  Google Scholar 

  • Ng CT, Cheng TCE, Yuan JJ (2006) A note on the complexity of the problem of two-agent scheduling on a single machine. J Comb Optim 12:387–394

    Article  MathSciNet  MATH  Google Scholar 

  • Wan G, Vakati SR, Leung JY-T, Pinedo M (2010) Scheduling two agents with controllable processing times. Eur J Oper Res 205:528–539

    Article  MathSciNet  MATH  Google Scholar 

  • Wang JB (2010) A note on single-machine scheduling with decreasing time-dependent job processing times. Appl Math Model 34:294–300

    Article  MathSciNet  MATH  Google Scholar 

  • Yin YQ, Cheng SR, Wu CC (2012) Scheduling problems with two agents and a linear non-increasing deterioration to minimize earliness penalties. Inf Sci 189:282–292

    Article  MathSciNet  MATH  Google Scholar 

  • Yuan JJ, Shang WP, Feng Q (2005) A note on the scheduling with two families of jobs. J Sched 8:537–542

    Article  MathSciNet  MATH  Google Scholar 

  • Zhao CL, Zhang QL, Tang HY (2003) Scheduling problems under linear deterioration. Acta Autom Sin 29:531–535

    MathSciNet  Google Scholar 

Download references

Acknowledgments

The work of the first author was supported in part by the NSFC Grants 11201121, (11571323) CSC 201309895008 and young backbone teachers of Henan colleges 2013GGJS-079. The authors would like to thank the two referees whose comments and suggestions have greatly improve the readability of the paper.

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Authors and Affiliations

  1. School of Science, Henan University of Technology, Zhengzhou, 450001, Henan, China

    Cheng He

  2. Department of Computer Science, New Jersey Institute of Technology, Newark, NJ, 07102, USA

    Joseph Y.-T. Leung

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  1. Cheng He
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  2. Joseph Y.-T. Leung
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Correspondence to Joseph Y.-T. Leung.

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He, C., Leung, J.YT. Two-agent scheduling of time-dependent jobs. J Comb Optim 34, 362–377 (2017). https://doi.org/10.1007/s10878-016-9994-y

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  • DOI: https://doi.org/10.1007/s10878-016-9994-y

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