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Sequencing a tri-criteria multiple job classes and customer orders problem on a single machine by using heuristics and simulated annealing method

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Abstract

Multiple-job-class sequencing problems solve a group of jobs belonging to multiple classes, where to decrease the processing time, jobs in the same class tend to be performed together with the same setup time. In contrast, customer order scheduling problems focus on completing all jobs (belonging to different classes) in the same order at the same time to reduce shipping costs. Because related studies on multiple-job-class sequencing problems with more than one criterion are quite limited in the current research community, this study investigates tri-criteria scheduling problems with multiple job classes and customer orders on a single machine, where the goal is to minimize a linear combination of the makespan, total completion times of all jobs, and sum of the ranges of all orders. Due to the high complexity of the proposed problem, mixed integer programming is developed to formulate the problem, and a branch-and-bound method along with a lower bound and a property is utilized for finding the optimal schedules. Then, two heuristics and a simulated annealing algorithm are proposed to solve the problem approximately. The simulation results of the proposed heuristics and algorithm are evaluated through statistical methods.

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Data availability

The corresponding author will provide the relevant datasets upon request.

Code availability

The corresponding author will provide the Fortran programming code upon request.

References

  • Allahverdi A, Gupta JND, Aldowaisan T (1999) A review of scheduling research involving setup considerations. Omega 27(2):219–239

    Article  Google Scholar 

  • Allahverdi A, Ng CT, Cheng TCE, Kovalyov MY (2008) A survey of scheduling problems with setup times or costs. Eur J Oper Res 187(3):985–1032

    Article  MathSciNet  Google Scholar 

  • Allahverdi A (2015) The third comprehensive survey on scheduling problems with setup times/costs. Eur J Oper Res 246(2):345–378

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • Dileepan P, Sen T (1988) Bicriterion static scheduling research for a single machine. Omega 16:53–59

    Article  Google Scholar 

  • Erel E, Ghosh JB (2007) Customer order scheduling on a single machine with family setup times: complexity and algorithms. Appl Math Comput 185:11–18

    MathSciNet  Google Scholar 

  • Framinan JM, Perez-Gonzalez P, Fernandez-Viagas V (2019) Deterministic assembly scheduling problems: a review and classification of concurrent-type scheduling models and solution procedures. Eur J Oper Res 273:401–417

    Article  MathSciNet  Google Scholar 

  • Fry TD, Armstrong RD, Lewis H (1989) A framework for single machine multiple objective sequencing research. Omega 17:595–607

    Article  Google Scholar 

  • Gupta JND, Ho JC, van der Veen JA (1997) Single machine hierarchical scheduling with customer orders and multiple job classes. Ann Oper Res 70:127–143

    Article  MathSciNet  Google Scholar 

  • Hassan DA, Amiri NM, Ramadan AM (2022) Solving three objectives single-machine scheduling problem using fuzzy multi-objective linear programming. Tikrit J Pure Sci 27(6):82–87

    Article  Google Scholar 

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

    Google Scholar 

  • Hosseinzadeh MR, Heydari M, Mazdeh MM (2022) Mathematical modeling and two metaheuristic algorithms for integrated process planning and group scheduling with sequence-dependent setup time. Oper Res Int J 22:5055–5105

    Article  Google Scholar 

  • Hsu SY, Liu CH (2009) Improving the delivery efficiency of the customer order scheduling problem in a job shop. Comput Ind Eng 57:856–866

    Article  Google Scholar 

  • Kirkpatrick S, Gellat CD, Vecchi MP (1983) Optimization by simulated annealing algorithm. Science 220:671–680

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  • Kim SC, Bobrowski PM (1997) Scheduling jobs with uncertain setup times and sequence dependency. Omega 25(4):437–447

    Article  Google Scholar 

  • Klamroth K, Wiecek MM (2001) A time-dependent multiple criteria single-machine scheduling problem. Eur J Oper Res 135:17–26

    Article  MathSciNet  Google Scholar 

  • Kovalenko YV, Zakharov AO (2020) The Pareto set reduction in bicriteria customer order scheduling on a single machine with setup times. In: Journal of physics: conference series, IOP Publishing. p 012087

  • Liaee MM, Emmons H (1997) Scheduling families of jobs with setup times. Int J Prod Econ 51(3):165–176

    Article  Google Scholar 

  • Liao CJ (1993) Tradeoff between setup times and carrying costs for finished items. Comput Oper Res 20:697–705

    Article  Google Scholar 

  • Li LY, Lin WC, Bai D, Zhang X, Azzouz A, Cheng SR, Wu YL, Wu CC (2023) Composite heuristics and water wave optimality algorithms for tricriteria multiple job classes and customer order scheduling on a single machine. Int J Ind Eng Comput 14(2):265–274

    Google Scholar 

  • Lin BMT, Yin PY, Liu YS (2013) Sequence-dependent scheduling with order deliveries. Appl Math Comput 222:58–71

    MathSciNet  Google Scholar 

  • Lin BMT, Kononov AV (2007) Customer order scheduling to minimize the number of tardy jobs. Eur J Oper Res 183(2):944–948

    Article  Google Scholar 

  • Lin WC, Zhang X, Liu X, Hu KX, Cheng SR, Azzouz A, Wu CC (2023) Sequencing single machine multiple-class customer order jobs using heuirstics and improved simulated annealing algorithms. RAIRO Op Res 57:1417–1441

    Article  Google Scholar 

  • Liu CH (2009) Lot streaming for customer order scheduling problem in job shop environments. Int J Comput Integr Manuf 22(9):890–907

    Article  Google Scholar 

  • Liu CH (2010) A coordinated scheduling system for customer orders scheduling problem in job shop environments. Expert Syst Appl 37:7831–7837

    Article  Google Scholar 

  • Qian J, Lin H, Kong Y, Wang Y (2020) Tri-criteria single machine scheduling model with release times and learning factor. Appl Math Comput 387:124543

    MathSciNet  Google Scholar 

  • Shi Z, Wang L, Liu P, Shi L (2017) Minimizing completion time for order scheduling: formulation and heuristic algorithm. IEEE Trans Autom Sci Eng 14(4):1558–1569

    Article  Google Scholar 

  • Shi Z, Huang Z, Shi L (2018) Customer order scheduling on batch processing machines with incompatible job families. Int J Prod Res 56(1–2):795–808

    Article  Google Scholar 

  • Soltani R, Jolai F, Zandieh M (2010) Two robust meta-heuristics for scheduling multiple job classes on a single machine with multiple criteria. Expert Syst Appl 37:5951–5959

    Article  Google Scholar 

  • Suma T, Murugesan R (2019) Mathematical model and heuristic based subtask scheduling algorithm for order scheduling. AIP Conf Proc 2095:030026-1–030026-9

    Google Scholar 

  • Suerie C (2006) Modeling of period overlapping setup times. Eur J Oper Res 174(2):874–886

    Article  Google Scholar 

  • Suerie C, Stadtler H (2003) The capacitated lot-sizing problem with linked lot-sizes. Manag Sci 49:1039–1054

    Article  Google Scholar 

  • van Donk DP, van Doorne R (2016) The impact of the customer order decoupling point on type and level of supply chain Integration. Int J Prod Res 54(9):2572–2584

    Article  Google Scholar 

  • Xu X, Ma Y, Zhou Z, Zhao Y (2015) Customer order scheduling on unrelated parallel machines to minimize total completion time. IEEE Trans Autom Sci Eng 12(1):244–257

    Article  Google Scholar 

  • Yang WH (1999) Survey of scheduling research involving setup times. Int J Syst Sci 30(2):143–155

    Article  Google Scholar 

  • Yang J (2011) Customer order scheduling in a two machine flowshop. Int J Manag Sci 17(1):95–116

    Google Scholar 

  • Yedidsion L (2012) Bi-criteria and tri-criteria analysis to minimize maximum lateness makespan and resource consumption for scheduling a single machine. J Sched 15:665–679

    MathSciNet  Google Scholar 

  • Ying KC, Pourhejazy P, Cheng CY, Syu RS (2020) Supply chain-oriented permutation flowshop scheduling considering flexible assembly and setup times. Int J Prod Res 61(1):258–281

    Article  Google Scholar 

  • Zangwill WI (1987) From EOQ towards ZI. Manag Sci 33:1209–1223

    Article  MathSciNet  Google Scholar 

  • Zhao Y, Xu X, Li H, Liu Y (2018) Stochastic customer order scheduling with setup times to minimize expected cycle time. Int J Prod Res 56(7):2684–2706

    Article  CAS  Google Scholar 

Download references

Acknowledgements

Authors thank the editor and two reviewers for their useful suggestions and positive comments. This article was supported in part by the Ministry of Science and Technology of Taiwan, MOST 110-2221-E-035-082- MY2, and National Science and Technology Council of Taiwan (NSTC) under Grant No. NSTC 112-2221-E-035- 060-MY2. and in part by the Major Program of the National Natural Science Foundation of China\ (11991022), the National Natural Science Foundation of China (11971443.

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Authors and Affiliations

  1. Department of Statistics, Feng Chia University, No.100, Wenhwa Road, Seatwen District, Taichung City, 40724, Taiwan

    Chin-Chia Wu, Xin-Rong Chen & Win-Chin Lin

  2. College of Mathematics Science, Chongqing Normal University, Chongqing, 401331, China

    Xingong Zhang

  3. School of Maritime Economics and Management, Dalian Maritime University, Dalian, 116026, China

    Danyu Bai

  4. SMART Laboratory, Institut supérieur de gestion de Tunis, Université de Tunis, Tunis, Tunisia

    Ameni Azzouz

  5. Tunis Business School, University of Tunis, Tunis, Tunisia

    Ameni Azzouz

  6. Department of Healthcare Management, Yuanpei University of Medical Technology, Hsinchu City, 30015, Taiwan

    Wen-Hsiang Wu

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  1. Chin-Chia Wu
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  2. Xingong Zhang
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  3. Danyu Bai
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  4. Ameni Azzouz
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  5. Wen-Hsiang Wu
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  7. Win-Chin Lin
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Correspondence to Win-Chin Lin.

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Wu, CC., Zhang, X., Bai, D. et al. Sequencing a tri-criteria multiple job classes and customer orders problem on a single machine by using heuristics and simulated annealing method. Oper Res Int J 24, 2 (2024). https://doi.org/10.1007/s12351-023-00809-2

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  • DOI: https://doi.org/10.1007/s12351-023-00809-2

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