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Using a branch-and-bound and a genetic algorithm for a single-machine total late work scheduling problem

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Abstract

Scheduling with learning effects has received a lot of research attention lately. On the other hand, it is commonly seen that time restrictions are usually modeled by due dates or deadlines and the quality of schedules is estimated with reference to these parameters. One of the performance measures involving due dates is the late work criterion, which is relatively unexplored. Thus, we study a single-machine scheduling problem with a position-based learning effect. The objective is to minimize the total late work, where the late work for a job is the amount of processing of this job that is performed after its due date. We attempt to develop a branch-and-bound algorithm incorporating with some dominance rules and a lower bound for the optimal solution. For saving computational time, we also propose three heuristic-based genetic algorithms for the near-optimal solution. Finally, the computational results of proposed algorithms are also provided.

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References

  • Bachman A, Janiak A (2004) Scheduling jobs with position-dependent processing times. J Oper Res Soc 55:257–264

    Article  MATH  Google Scholar 

  • Beasley D, Bull D, Martin RR (1993) An overview of genetic algorithms, part 1: fundamentals. J Univ Comput 15:58–69

    Google Scholar 

  • Bean JC (1994) Genetic algorithms and random keys for sequencing and optimization. ORSA J Comput 6:154–160

    Article  MATH  Google Scholar 

  • Besbes W, Teghem J, Loukil T (2010) Scheduling hybrid flow shop problem with non-fixed availability constraint. Eur J Ind Eng 4(4):413–433

    Article  MATH  Google Scholar 

  • Biskup D (1999) Single-machine scheduling with learning considerations. Eur J Oper Res 115:173–178

    Article  MATH  Google Scholar 

  • Biskup D (2008) A state-of-the-art review on scheduling with learning effect. Eur J Oper Res 188:315–329

    Article  MathSciNet  MATH  Google Scholar 

  • Blazewicz J (1984) Scheduling preemptible tasks on parallel processors with information loss. Technique et Science Informatiques 3:415–420

    MathSciNet  MATH  Google Scholar 

  • Blazewicz J, Pesch E, Sterna M, Werner F (2005) A comparison of solution procedures for two-machine flow shop scheduling with late work criterion. Comput Ind Eng 49:611–624

    Article  MATH  Google Scholar 

  • Blazewicz J, Pesch E, Sterna M, Werner F (2008) Metaheuristic approaches for the two-machine flow-shop problem with weighted late work criterion and common due date. Comput Oper Res 35:574–599

    Article  MATH  Google Scholar 

  • Bryan Kethley R, Alidaee B (2002) Single machine scheduling to minimize total weighted late work: a comparison of scheduling rules and search algorithms. Comput Ind Eng 43:509–528

    Article  Google Scholar 

  • Chen CL, Vempati VS, Aljaber N (1995) An application of genetic algorithms for flow shop problems. Eur J Oper Res 80:389–396

    Article  Google Scholar 

  • Chen JS, Pan JCH, Lin CM (2008) A hybrid genetic algorithm for the reentrant flow-shop scheduling problem. Expert Syst Appl 34:570–577

    Article  Google Scholar 

  • Chen Z-Y, Tsai C-F, Eberle W, Lin W-C, Ke S-W (2014) Instance selection by genetic-based biological algorithm. Soft Comput. doi:10.1007/s00500-014-1339-0

  • Cheng TCE, Wang G (2000) Single machine scheduling with learning effect considerations. Ann Oper Res 98:273–290

    Article  MathSciNet  MATH  Google Scholar 

  • Cheng TCE, Cheng S-R, Wu W-H, Hsu P-H, Wu C-C (2011) A two-agent single-machine scheduling problem with truncated sum-of-processing- times-based learning considerations. Comput Ind Eng 60:534–541

    Article  Google Scholar 

  • Essafi I, Matib Y, Dauzere-Peres S (2008) A genetic local search algorithm for minimizing total weighted tardiness in the job-shop scheduling problem. Comput Oper Res 35:2599–2616

    Article  MathSciNet  MATH  Google Scholar 

  • Etiler O, Toklu B, Atak M, Wilson J (2004) A genetic algorithm for flow shop scheduling problems. J Oper Res Soc 55(8):830–835

    Article  MATH  Google Scholar 

  • Fisher ML (1971) A dual algorithm for the one-machine scheduling problem. Math Progr 11:229–251

    Article  MathSciNet  MATH  Google Scholar 

  • French S (1982) Sequencing and scheduling: an introduction to the mathematics of the job-shop. Ellis Horwood Ltd., Chichester

    MATH  Google Scholar 

  • Falkenauer E, Bouffoix S (1991) A genetic algorithm for job shop. In: Proceedings of the 1991 IEEE international conference on robotics and automation

  • Iyer SK, Saxena BS (2004) Improved genetic algorithm for the permutation flowshop scheduling problem. Comput Oper Res 31:593–606

    Article  MathSciNet  MATH  Google Scholar 

  • Janiak A, Rudek R (2010) A note on a makespan minimization problem with a multi-ability learning effect. Omega 38(3–4):213–217

    Article  Google Scholar 

  • Karthikeyan P, Baskar S, Alphones A (2013) Improved genetic algorithm using different genetic operator combinations (GOCs) for multicast routing in ad hoc networks. Soft Comput 17:1563–1572

    Article  Google Scholar 

  • Koulamas C, Kyparisis GJ (2007) Single-machine and two-machine flowshop scheduling with general learning functions. Eur J Oper Res 178:402–407

    Article  MathSciNet  MATH  Google Scholar 

  • Kuo WH, Yang DL (2006) Minimizing the total completion time in a single-machine scheduling problem with a time- dependent learning effect. Eur J Oper Res 174(2):1184–1190

    Article  MathSciNet  MATH  Google Scholar 

  • Li J, Song Y (2013) Community detection in complex networks using extended compact genetic algorithm. Soft Comput. doi:10.1007/s00500-012-0942-1

  • Manaa A, Chu C (2010) Scheduling multiprocessor tasks to minimise the makespan on two dedicated processors. Eur J Ind Eng 4(3):265–279

    Article  Google Scholar 

  • Moore JM (1968) An n-job, one machine sequencing algorithm for minimizing the number of late jobs. Manag Sci 15:102–109

    Article  MATH  Google Scholar 

  • Mosheiov G (2001) Scheduling problem with a learning effect. Eur J Oper Res 130:638–652

    Article  MathSciNet  MATH  Google Scholar 

  • Nawaz M, Enscore EE, Ham I (1983) A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem. Omega 11:91–95

    Article  Google Scholar 

  • Pesch E, Sterna M (2009) Late work minimization in flow shops by a genetic algorithm. Comput Ind Eng 57:1202–1209

    Article  Google Scholar 

  • Potts CN, Van Wassenhove LN (1992) Single machine scheduling to minimize total late work. Oper Res 40(3):586–595

    Article  MathSciNet  MATH  Google Scholar 

  • Sterna M (2007a) Late work minimization in a small flexible manufacturing system. Comput Ind Eng 52:210–228

    Article  Google Scholar 

  • Sterna M (2007b) Dominance relations for two-machine flow shop problem with late work criterion. Bull Pol Acad Sci Tech Sci 55(1):59–69

    MATH  Google Scholar 

  • Sterna M (2011) A survey of scheduling problems with late work criteria. Omega 39:120–129

    Article  Google Scholar 

  • Sterna M, Blazewicz J (2007) Genetic algorithm for late work minimization in a flow shop system. MISTA, pp 455–462

  • Toksari MD, Oron D, Güner E (2009) Single machine scheduling problems under the effects of nonlinear deterioration and time-dependent learning. Math Comput Model 50:401–406

    Article  MathSciNet  MATH  Google Scholar 

  • Wang JB (2010) Single-machine scheduling with a sum-of-actual-processing-time-based learning effect. J Oper Res Soc 61:172–177

  • Wang J-B, Sun L-H, Sun L-Y (2010a) Single machine scheduling with a learning effect and discounted costs. Int J Adv Manuf Technol 49:1141–1149

    Article  Google Scholar 

  • Wang J-B, Sun L-H, Sun L-Y (2010b) Scheduling jobs with an exponential sum-of-actual-processing-time based learning effect. Comput Math Appl 60:2673–2678

    Article  MathSciNet  MATH  Google Scholar 

  • Wang J-B, Wang M-Z (2010) Single machine multiple common due dates scheduling with learning effects. Comput Math Appl 60:2998–3002

    Article  MathSciNet  MATH  Google Scholar 

  • Wang J-B, Li J-X (2011) Single machine past-sequence-dependent setup times scheduling with general position-dependent and time-dependent learning effects. Appl Math Model 35:1388–1395

    Article  MathSciNet  MATH  Google Scholar 

  • Wang J-B, Wang C (2011a) Single-machine due-window assignment problem with learning effect and deteriorating jobs. Appl Math Model 35:4017–4022

    Article  MathSciNet  MATH  Google Scholar 

  • Wang J-B, Guo Q (2010) A due-date assignment problem with learning effect and deteriorating jobs. Appl Math Model 34:309–313

    Article  MathSciNet  MATH  Google Scholar 

  • Wang J-B, Wang M-Z (2011b) Worst-case behavior of simple sequencing rules in flow shop scheduling with general position-dependent learning effects. Ann Oper Res 191:155–169

    Article  MathSciNet  MATH  Google Scholar 

  • Wang J-B, Wang M-Z, Ji P (2012) Scheduling jobs with processing times dependent on position, starting time and allotted resource. Asia Pac J Oper Res 29(5):1250030 (p 15 )

    Article  MathSciNet  MATH  Google Scholar 

  • Wang J-B, Wang J-J (2013) Scheduling jobs with a general learning effect model. Appl Math Model 37:2364–2373

    Article  MathSciNet  Google Scholar 

  • Wang J-B, Liu L, Wang C (2013a) Single machine SLK/DIF due window assignment problem with learning effect and deteriorating jobs. Appl Math Model 37:8394–8400

    Article  MathSciNet  Google Scholar 

  • Wang X-Y, Zhou Z, Zhang X, Ji P, Wang J-B (2013b) Several flow shop scheduling problems with truncated position-based learning effect. Comput Oper Res 40:2906–2929

    Article  MathSciNet  Google Scholar 

  • Wright TP (1936) Factors affecting the cost of airplanes. J Aeronaut Sci 3:122–128

    Article  Google Scholar 

  • Wu C-C, Hsu P-H, Chen J-C, Wang N-S (2011) Genetic algorithm for minimizing the total weighted completion time scheduling problem with learning and release times. Comput Oper Res 38:1025–1034

    Article  MathSciNet  MATH  Google Scholar 

  • Yang SJ, Hsu CJ, Yang DL (2010) Parallel-machine scheduling with setup and removal times under consideration of the learning effect. J Chin Inst Ind Eng 27(5):372–378

    Google Scholar 

  • Yang S-J, Yang D-L (2011) Single-machine scheduling simultaneous with position-based and sum-of-processing-times-based learning considerations under group technology assumption. Appl Math Model 35:2068–2074

    Article  MathSciNet  MATH  Google Scholar 

  • Yang S-J, Yang D-L (2012) Scheduling problems with past-sequence-dependent delivery times and learning effects. J Oper Res Soc 63:1508–1515

    Article  Google Scholar 

  • Yin N, Wang X-Y (2011) Single machine scheduling with controllable processing times and learning effect. Int J Adv Manuf Technol 54:743–748

    Article  Google Scholar 

  • Yin Y, Xu D, Wang J (2010) Single-machine scheduling with a general sum-of-actual-processing-times-based and job-position-based learning effect. Appl Math Model 34(11):3623–3630

    Article  MathSciNet  MATH  Google Scholar 

  • Ying K-C, Lin S-W, Lu C-C (2011) Cell formation using a simulated annealing algorithm with variable neighbourhood. Eur J Ind Eng 5(1):22–42

    Article  Google Scholar 

Download references

Acknowledgments

We are grateful to the Editor, Associate Editor, and two anonymous referees for their constructive comments on the earlier version of our paper. This paper was supported in part by the National Natural Science Foundation of China (No. 71301022); in part by the MOST of Taiwan under Grant numbers NSC 102-2221-E-035-070-MY3 and NSC 102-2221-E-252-007, and MOST 103-2410-H-035-022-MY2.

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Authors and Affiliations

  1. Department of Statistics, Feng Chia University, Taichung, Taiwan

    Chin-Chia Wu & Hung-Ming Chen

  2. Faculty of Science, Kunming University of Science and Technology, Kunming, 650093, China

    Yunqiang Yin

  3. Department of Healthcare Management, Yuanpei University, Hsinchu, Taiwan

    Wen-Hsiang Wu

  4. Graduate Institute of Business Administration, Cheng Shiu University, Kaohsiung City, Taiwan

    Shuenn-Ren Cheng

Authors
  1. Chin-Chia Wu
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  2. Yunqiang Yin
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  3. Wen-Hsiang Wu
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  4. Hung-Ming Chen
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Correspondence to Shuenn-Ren Cheng.

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Communicated by V. Loia.

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Wu, CC., Yin, Y., Wu, WH. et al. Using a branch-and-bound and a genetic algorithm for a single-machine total late work scheduling problem. Soft Comput 20, 1329–1339 (2016). https://doi.org/10.1007/s00500-015-1590-z

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