A two-stage three-machine assembly scheduling problem with a truncation position-based learning effect

Abstract

The two-stage assembly scheduling problem has a lot of applications in industrial and service sectors. Furthermore, truncation-based learning effects have received growing attention in connection with scheduling problems. However, it is relatively unexplored in the two-stage assembly scheduling problem. Therefore, we addressed the two-stage assembly with truncation learning effects with two machines in the first stage and an assembly machine in the second stage. The objective function was to complete all jobs as soon as possible (or to minimize the makespan). Due to the NP-hardness of the considered problem, we proposed several dominance relations and a lower bound for the branch-and-bound method for finding the optimal solution. Moreover, we proposed six versions of hybrids greedy iterative algorithm, where three versions of the local searches algorithm with and without a probability scheme are embedded. They include extraction and backward-shifted reinsertion, pairwise interchange and extraction and forward-shifted reinsertion for searching good-quality solutions. The experimental results of all proposed algorithms are presented on small-size and big-size jobs.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

References

  1. Abualigah LMQ (2019) Feature selection and enhanced Krill Herd algorithm for text document clustering, vol 816. Studies in computational intelligence. Springer, Berlin, pp 1–165

    Google Scholar 

  2. Abualigah LMQ, Hanandeh ES (2015) Applying genetic algorithms to information retrieval using vector space model. Int J Comput Sci Eng Appl 5(1):19

    Google Scholar 

  3. Abualigah LM, Khader AT (2017) Unsupervised text feature selection technique based on hybrid particle swarm optimization algorithm with genetic operators for the text clustering. J Supercomput 73(11):4773–4795

    Google Scholar 

  4. Abualigah LM, Khader AT, Hanandeh ES (2018) A new feature selection method to improve the document clustering using particle swarm optimization algorithm. J Comput Sci 25:456–466

    Google Scholar 

  5. Allahverdi A, Al-Anzi FS (2006) A PSO and a Tabu search heuristics for assembly scheduling problem of the two-stage distributed database application. Comput Oper Res 33:1056–1080

    MATH  Google Scholar 

  6. Arroyo JEC, Leung JYT, Tavares RG (2019) An iterated greedy algorithm for total flow time minimization in unrelated parallel batch machines with unequal job release times. Eng Appl Artif Intell 77:239–254

    Google Scholar 

  7. Azzouz A, Ennigrou M, Ben Said L (2018) Scheduling problems under learning effects: classification and cartography. Int J Prod Res 56(4):1642–1661

    Google Scholar 

  8. Biskup D (1999) Single-machine scheduling with learning considerations. Eur J Oper Res 115(1):173–178

    MathSciNet  MATH  Google Scholar 

  9. Chen P, Chin-Chia W, Lee W-C (2006) A bi-criteria two-machine flowshop scheduling problem with a learning effect. J Oper Res Soc 57(9):1113–1125

    MATH  Google Scholar 

  10. Cheng TCE, Wu CC, Chen JC, Wu WH, Cheng SR (2013) Two-machine flowshop scheduling with a truncated learning function to minimize the makespan. Int J Prod Econ 141(1):79–86

    Google Scholar 

  11. Critchlow DE, Fligner MA (1991) On distribution-free multiple comparisons in one-way analysis of variance. Commun Stat Theory Methods 20:127–139

    MathSciNet  Google Scholar 

  12. Della Croce F, Narayan V, Tadei R (1996) The two-machine total completion time flow shop problem. Eur J Oper Res 90:227–237

    MATH  Google Scholar 

  13. Hollander MD, Wolfe A, Chicken E (2014) Nonparametric statistical methods, 3rd edn. Wiley, Hoboken

    Google Scholar 

  14. Hosseini N, Tavakkoli-Moghaddam R (2013) Two meta-heuristics for solving a new two-machine flowshop scheduling problem with the learning effect and dynamic arrivals. Int J Adv Manuf Technol 65(5–8):771–786

    Google Scholar 

  15. Jacobs LW, Brusco MJ (1995) A local search heuristic for large set-covering problems. Naval Res Logist Q 42(7):1129–1140

    MathSciNet  MATH  Google Scholar 

  16. Lee W-C, Wu C-C (2004) Minimizing total completion time in a two-machine flowshop with a learning effect. Int J Prod Econ 88(1):85–93

    Google Scholar 

  17. Lee CY, Cheng TCE, Lin BMT (1993) Minimizing the makespan in the 3-machine assembly-type flowshop scheduling problem. Manag Sci 39:616–625

    MATH  Google Scholar 

  18. Lee W-C, Wu C-C, Sung H-J (2004) A bi-criterion single-machine scheduling problem with learning considerations. Acta Inform 40:303–315

    MathSciNet  MATH  Google Scholar 

  19. Mahalleh MKK, Ashjari B, Yousefi F, Saberi M (2017) A robust solution to resource-constraint project scheduling problem. Int J Fuzzy Logic Intell Syst 17(3):221–227

    Google Scholar 

  20. Marchiori E, Steenbeek A (2000) An evolutionary algorithm for large scale set covering problems with application to airline crew scheduling. In: Workshops on real-world applications of evolutionary computation. Springer, Berlin, pp 370–384

  21. Nawaz M, Enscore EE Jr, Ham I (1983) A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem. Omega 11(1):91–95

    Google Scholar 

  22. Nouri V, Behdin P, Ramezanian R (2013) Hybrid firefly-simulated annealing algorithm for the flow shop problem with learning effects and flexible maintenance activities. Int J Prod Res 51(12):3501–3515

    Google Scholar 

  23. Park JH, Yu JS, Geem ZW (2018) Genetic algorithm-based optimal investment scheduling for public rental housing projects in South Korea. Int J Fuzzy Logic Intell Syst 18(2):135–145

    Google Scholar 

  24. Potts CN, Sevast’Janov SV, Strusevich VA, Van Wassenhove LN, Zwaneveld CM (1995) The two-stage assembly scheduling problem: complexity and approximation. Oper Res 43:346–355

    MathSciNet  MATH  Google Scholar 

  25. Ribas I, Companys R, Tort-Martorell X (2011) An iterated greedy algorithm for the flowshop scheduling problem with blocking. Omega 39(3):293–301

    Google Scholar 

  26. Ruiz R, Stützle T (2007) A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem. Eur J Oper Res 177(3):2033–2049

    MATH  Google Scholar 

  27. Ruiz R, Stützle T (2008) An iterated greedy heuristic for the sequence dependent setup times flowshop problem with makespan and weighted tardiness objectives. Eur J Oper Res 187(3):1143–1159

    MATH  Google Scholar 

  28. Ruiz R, Pan QK, Naderi B (2019) Iterated Greedy methods for the distributed permutation flowshop scheduling problem. Omega 83:213–222

    Google Scholar 

  29. Shiau Y-R, Tsai M-S, Lee W-C, Cheng TCE (2015) Two-agent two-machine flowshop scheduling with learning effects to minimize the total completion time. Comput Ind Eng 87:580–589

    Google Scholar 

  30. Wang X-Y, Wang J-J (2013) Scheduling problems with past-sequence-dependent setup times and general effects of deterioration and learning. Appl Math Model 37(7):4905–4914

    MathSciNet  MATH  Google Scholar 

  31. Wang X-Y, Zhou Z, Zhang X, Ji P, Wang J-B (2013) Several flow shop scheduling problems with truncated position-based learning effect. Comput Oper Res 40(12):2906–2929

    MathSciNet  MATH  Google Scholar 

  32. Wright TP (1936) Factors affecting the cost of airplanes. J Aeronaut Sci (Inst Aeronaut Sci) 3(4):122–128

    Google Scholar 

  33. Wu CC, Yin Y, Cheng SR (2013) Single-machine and two-machine flowshop scheduling problems with truncated position-based learning functions. J Oper Res Soc 64(1):147–156

    Google Scholar 

  34. Wu CC, Wang DJ, Cheng SR, Chung IH, Lin WC (2018) A two-stage three-machine assembly scheduling problem with a position-based learning effect. Int J Prod Res 56(9):3064–3079

    Google Scholar 

  35. Wu CC, Yang TH, Zhang X, Kang CC, Chung IH, Lin WC (2019) Using heuristic and iterative greedy algorithms for the total weighted completion time order scheduling with release times. Swarm Evol Comput 44:913–926

    Google Scholar 

  36. Yele LE (1979) The learning curve: historical review and comprehensive survey. Decis Sci 10(2):302–328

    Google Scholar 

  37. Yin Y, Wu W-H, Wu W-H, Wu C-C (2014) A branch-and-bound algorithm for a single machine sequencing to minimize the total tardiness with arbitrary release dates and position-dependent learning effects. Inf Sci 256:91–108

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This article was supported in part by Ministry of Science and Technology of Taiwan (No. MOST 108-2410-H-035-046).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Ameni Azzouz.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Communicated by V. Loia.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Azzouz, A., Pan, P., Hsu, P. et al. A two-stage three-machine assembly scheduling problem with a truncation position-based learning effect. Soft Comput 24, 10515–10533 (2020). https://doi.org/10.1007/s00500-019-04561-8

Download citation

Keywords

  • Two-stage assembly
  • Greedy iterative algorithm
  • Branch-and-bound
  • Flowshop