Skip to main content
SpringerLink
Log in

A scenario-based robust optimization model for the sustainable distributed permutation flow-shop scheduling problem

  • Original Research
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

Sustainable production scheduling considers economic, environmental, and social criteria while generating the schedule of jobs in a factory. This paper formulates a Sustainable Distributed Permutation Flow-shop Scheduling Problem (SDPFSP) by considering that each machine used to process the jobs can be operated under different operating modes ranging from manual to automatic. In addition, the energy consumption as well as the number of operators required and the number of working days lost to train them have been taken into account in the proposed SDPFSP. Most importantly, this study considers multiple uncertainties including machine breakdowns, variable processing times, and random arrivals of new jobs. These uncertainties are formulated by a scenario-based robust optimization model as the main significant contribution of this research where the goal is to minimize the expected makespan and its deviations from probabilistic scenarios. To deal with this complex optimization problem, another innovation of this research is to propose a new metaheuristic algorithm named Adaptive Large Neighborhood Search (ALNS). The proposed algorithm uses four constructive heuristics to identify an initial solution. Then, the current solution is destroyed and repaired efficiently by the use of removal and construction heuristics to explore the search space. Thus, a local search algorithm is developed to exploit new solutions in this search space. After implementing the proposed ALNS, an extensive computational study is provided to analyze the calibration of parameters and components of the proposed algorithm. Then, a comparison of the results with those obtained using the exact solver and state-of-the-art metaheuristics found in the literature is provided. The SDPFSP is validated through a numerical example of a flow-shop production system. Based on the results derived from our numerical example, we can conclude that our solution holds the potential to improve energy consumption by 24%, bolster job opportunities by 67%, and decrease lost workdays by 18%. Moreover, the impact of robust optimization parameters and uncertainties on optimality is investigated by performing sensitivity analysis. Finally, an in-depth discussion is provided to identify the main findings and recommendations of this research for flow-shop production systems to highlight the performance of our scenario-based robust model and the ALNS algorithm.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Notes

  1. https://www.ibm.com/analytics/cplex-optimizer

  2. https://www.mathworks.com/products/matlab.html

References

  • Abreu, L. R., Cunha, J. O., Prata, B. A., & Framinan, J. M. (2020). A genetic algorithm for scheduling open shops with sequence-dependent setup times. Computers & Operations Research, 113, 104793.

    Article  Google Scholar 

  • Al-Behadili, M., Ouelhadj, D., & Jones, D. (2020). Multi-objective biased randomised iterated greedy for robust permutation flow shop scheduling problem under disturbances. Journal of the Operational Research Society, 71(11), 1847–1859.

    Article  Google Scholar 

  • Ali, S. M., Fathollahi-Fard, A. M., Ahnaf, R., & Wong, K. Y. (2023). A multi-objective closed-loop supply chain under uncertainty: An efficient Lagrangian relaxation reformulation using a neighborhood-based algorithm. Journal of Cleaner Production, 423, 138702.

  • Bargaoui, H., Driss, O. B., & Ghédira, K. (2017). A novel chemical reaction optimization for the distributed permutation flowshop scheduling problem with makespan criterion. Computers & Industrial Engineering, 111, 239–250.

    Article  Google Scholar 

  • Bellio, R., Ceschia, S., Di Gaspero, L., & Schaerf, A. (2021). Two-stage multi-neighborhood simulated annealing for uncapacitated examination timetabling. Computers & Operations Research, 132, 105300.

    Article  Google Scholar 

  • Che, A., Wu, X., Peng, J., & Yan, P. (2017). Energy-efficient bi-objective single-machine scheduling with power-down mechanism. Computers & Operations Research, 85, 172–183.

    Article  Google Scholar 

  • Corbett, C. J., & Kirsch, D. A. (2001). International diffusion of ISO 14000 certification. Production and Operations Management, 10(3), 327–342.

    Article  Google Scholar 

  • Conti, J., Holtberg, P., Diefenderfer, J., LaRose, A., Turnure, J. T., & Westfall, L. (2016). International energy outlook 2016 with projections to 2040 (No. DOE/EIA-0484 (2016)). USDOE Energy Information Administration (EIA), Washington, DC (United States). Office of Energy Analysis.

  • Dalenogare, L. S., Benitez, G. B., Ayala, N. F., & Frank, A. G. (2018). The expected contribution of Industry 4.0 technologies for industrial performance. International Journal of Production Economics, 204, 383–394.

    Article  Google Scholar 

  • Fard, A. M. F., & Hajaghaei-Keshteli, M. (2018). A tri-level location-allocation model for forward/reverse supply chain. Applied Soft Computing, 62, 328–346.

    Article  Google Scholar 

  • Fathollahi-Fard, A. M., Woodward, L., & Akhrif, O. (2024). A distributed permutation flow-shop considering sustainability criteria and real-time scheduling. Journal of Industrial Information Integration, 39, 100598.

  • Fathollahi-Fard, A. M., Woodward, L., & Akhrif, O. (2021). Sustainable distributed permutation flow-shop scheduling model based on a triple bottom line concept. Journal of Industrial Information Integration, 24, 100233.

    Article  Google Scholar 

  • Fathollahi-Fard, A. M., Ahmadi, A., & Karimi, B. (2022). Sustainable and robust home healthcare logistics: A response to the covid-19 pandemic. Symmetry, 14(2), 193.

    Article  Google Scholar 

  • Fu, Y., Ding, J., Wang, H., & Wang, J. (2018). Two-objective stochastic flow-shop scheduling with deteriorating and learning effect in Industry 4.0-based manufacturing system. Applied Soft Computing, 68, 847–855.

    Article  Google Scholar 

  • Fu, Y., Tian, G., Fathollahi-Fard, A. M., Ahmadi, A., & Zhang, C. (2019). Stochastic multi-objective modelling and optimization of an energy-conscious distributed permutation flow shop scheduling problem with the total tardiness constraint. Journal of Cleaner Production, 226, 515–525.

    Article  Google Scholar 

  • Fernandez-Viagas, V., Perez-Gonzalez, P., & Framinan, J. M. (2018). The distributed permutation flow shop to minimise the total flowtime. Computers & Industrial Engineering, 118, 464–477.

    Article  Google Scholar 

  • Framinan, J. M., Fernandez-Viagas, V., & Perez-Gonzalez, P. (2019). Using real-time information to reschedule jobs in a flowshop with variable processing times. Computers & Industrial Engineering, 129, 113–125.

    Article  Google Scholar 

  • Gahm, C., Denz, F., Dirr, M., & Tuma, A. (2016). Energy-efficient scheduling in manufacturing companies: A review and research framework. European Journal of Operational Research, 248(3), 744–757.

    Article  Google Scholar 

  • Gao, J., & Chen, R. (2011). A hybrid genetic algorithm for the distributed permutation flowshop scheduling problem. International Journal of Computational Intelligence Systems, 4(4), 497–508.

    Google Scholar 

  • Ghaleb, M., Zolfagharinia, H., & Taghipour, S. (2020). Real-time production scheduling in the Industry-4.0 context: Addressing uncertainties in job arrivals and machines breakdowns. Computers & Operations Research, 123, 105031.

    Article  Google Scholar 

  • Gmys, J., Mezmaz, M., Melab, N., & Tuyttens, D. (2020). A computationally efficient branch-and-bound algorithm for the permutation flow-shop scheduling problem. European Journal of Operational Research, 284(3), 814–833.

    Article  Google Scholar 

  • Han, Y., Li, J., Sang, H., Liu, Y., Gao, K., & Pan, Q. (2020). Discrete evolutionary multi-objective optimization for energy-efficient blocking flow shop scheduling with setup time. Applied Soft Computing, 93, 106343.

    Article  Google Scholar 

  • Hamzadayı, A. (2020). An effective benders decomposition algorithm for solving the distributed permutation flowshop scheduling problem. Computers & Operations Research, 123, 105006.

    Article  Google Scholar 

  • Huang, J., & Gu, X. (2021). Distributed assembly permutation flow-shop scheduling problem with sequence-dependent set-up times using a novel biogeography-based optimization algorithm. Engineering Optimization. https://doi.org/10.1080/0305215X.2021.1886289

    Article  Google Scholar 

  • Jing, X. L., Pan, Q. K., & Gao, L. (2021). Local search-based metaheuristics for the robust distributed permutation flowshop problem. Applied Soft Computing, 105, 107247.

    Article  Google Scholar 

  • Llach, J., Marimon, F., & del Mar Alonso-Almeida, M. (2015). Social Accountability 8000 standard certification: Analysis of worldwide diffusion. Journal of Cleaner Production, 93, 288–298.

    Article  Google Scholar 

  • Leung, S. C., Tsang, S. O., Ng, W. L., & Wu, Y. (2007). A robust optimization model for multi-site production planning problem in an uncertain environment. European Journal of Operational Research, 181(1), 224–238.

    Article  Google Scholar 

  • Li, D. C., & Hsu, P. H. (2012). Solving a two-agent single-machine scheduling problem considering learning effect. Computers & Operations Research, 39(7), 1644–1651.

    Article  Google Scholar 

  • Lin, S. W., Ying, K. C., & Huang, C. Y. (2013). Minimising makespan in distributed permutation flowshops using a modified iterated greedy algorithm. International Journal of Production Research, 51(16), 5029–5038.

    Article  Google Scholar 

  • Liu, F., Wang, S., Hong, Y., & Yue, X. (2017a). On the robust and stable flowshop scheduling under stochastic and dynamic disruptions. IEEE Transactions on Engineering Management, 64(4), 539–553.

    Article  Google Scholar 

  • Liu, X., Laporte, G., Chen, Y., & He, R. (2017b). An adaptive large neighborhood search metaheuristic for agile satellite scheduling with time-dependent transition time. Computers & Operations Research, 86, 41–53.

    Article  Google Scholar 

  • Lu, C., Gao, L., Gong, W., Hu, C., Yan, X., & Li, X. (2020). Sustainable scheduling of distributed permutation flow-shop with non-identical factory using a knowledge-based multi-objective memetic optimization algorithm. Swarm and Evolutionary Computation, 60, 100803.

    Article  Google Scholar 

  • Moldavska, A., & Welo, T. (2019). A Holistic approach to corporate sustainability assessment: Incorporating sustainable development goals into sustainable manufacturing performance evaluation. Journal of Manufacturing Systems, 50, 53–68.

  • Karna, S. K., & Sahai, R. (2012). An overview on Taguchi method. International Journal of Engineering and Mathematical Sciences, 1(1), 1–7.

    Google Scholar 

  • Marchi, B., & Zanoni, S. (2017). Supply chain management for improved energy efficiency: Review and opportunities. Energies, 10(10), 1618.

    Article  Google Scholar 

  • Mara, S. T. W., Norcahyo, R., Jodiawan, P., Lusiantoro, L., & Rifai, A. P. (2022). A survey of adaptive large neighborhood search algorithms and applications. Computers & Operations Research, 146, 105903.

    Article  Google Scholar 

  • Meng, T., Pan, Q. K., & Wang, L. (2019). A distributed permutation flowshop scheduling problem with the customer order constraint. Knowledge-Based Systems, 184, 104894.

    Article  Google Scholar 

  • Mulvey, J. M., Vanderbei, R. J., & Zenios, S. A. (1995). Robust optimization of large-scale systems. Operations Research, 43(2), 264–281.

    Article  Google Scholar 

  • Naderi, B., & Ruiz, R. (2010). The distributed permutation flowshop scheduling problem. Computers & Operations Research, 37(4), 754–768.

    Article  Google Scholar 

  • Naderi, B., & Ruiz, R. (2014). A scatter search algorithm for the distributed permutation flowshop scheduling problem. European Journal of Operational Research, 239(2), 323–334.

    Article  Google Scholar 

  • Mladenović, N., & Hansen, P. (1997). Variable neighborhood search. Computers & Operations Research, 24(11), 1097–1100.

    Article  Google Scholar 

  • Pan, Q. K., Gao, L., Wang, L., Liang, J., & Li, X. Y. (2019). Effective heuristics and metaheuristics to minimize total flowtime for the distributed permutation flowshop problem. Expert Systems with Applications, 124, 309–324.

    Article  Google Scholar 

  • Parente, M., Figueira, G., Amorim, P., & Marques, A. (2020). Production scheduling in the context of Industry 4.0: Review and trends. International Journal of Production Research, 58(17), 5401–5431.

    Article  Google Scholar 

  • Pasha, J., Nwodu, A. L., Fathollahi-Fard, A. M., Tian, G., Li, Z., Wang, H., & Dulebenets, M. A. (2022). Exact and metaheuristic algorithms for the vehicle routing problem with a factory-in-a-box in multi-objective settings. Advanced Engineering Informatics, 52, 101623.

    Article  Google Scholar 

  • Rossit, D. A., Tohmé, F., & Frutos, M. (2019). Industry 4.0: Smart scheduling. International Journal of Production Research, 57(12), 3802–3813.

    Article  Google Scholar 

  • Ross, M. S. (2019). Introduction to probability models. Elsevier books.

    Google Scholar 

  • Ruiz, R., Pan, Q. K., & Naderi, B. (2019). Iterated Greedy methods for the distributed permutation flowshop scheduling problem. Omega, 83, 213–222.

    Article  Google Scholar 

  • Schrimpf, G., Schneider, J., Stamm-Wilbrandt, H., & Dueck, G. (2000). Record breaking optimization results using the ruin and recreate principle. Journal of Computational Physics, 159(2), 139–171.

    Article  Google Scholar 

  • Shao, W., Shao, Z., & Pi, D. (2020). Modeling and multi-neighborhood iterated greedy algorithm for distributed hybrid flow shop scheduling problem. Knowledge-Based Systems, 194, 105527.

    Article  Google Scholar 

  • Shaw, P. (1998). Using constraint programming and local search methods to solve vehicle routing problems. In International conference on principles and practice of constraint programming (pp. 417–431). Springer, Berlin, Heidelberg.

  • Soleimani, H., Chhetri, P., Fathollahi-Fard, A. M., Mirzapour Al-e-Hashem, S. M. J., & Shahparvari, S. (2022). Sustainable closed-loop supply chain with energy efficiency: Lagrangian relaxation, reformulations and heuristics. Annals of Operations Research. https://doi.org/10.1007/s10479-022-04661-z

    Article  Google Scholar 

  • Varelmann, T., Erwes, N., Schäfer, P., & Mitsos, A. (2022). Simultaneously optimizing bidding strategy in pay-as-bid-markets and production scheduling. Computers & Chemical Engineering, 157, 107610.

    Article  Google Scholar 

  • Van Laarhoven, P. J., & Aarts, E. H. (1987). Simulated annealing. In Simulated annealing: Theory and applications (pp. 7-15). Springer, Dordrecht.

  • Wang, J. J., & Wang, L. (2018). A knowledge-based cooperative algorithm for energy-efficient scheduling of distributed flow-shop. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 99, 1–15.

    Google Scholar 

  • Wang, G., Gao, L., Li, X., Li, P., & Tasgetiren, M. F. (2020). Energy-efficient distributed permutation flow shop scheduling problem using a multi-objective whale swarm algorithm. Swarm and Evolutionary Computation, 57, 100716.

    Article  Google Scholar 

  • Zhang, J., Ding, G., Zou, Y., Qin, S., & Fu, J. (2019). Review of job shop scheduling research and its new perspectives under Industry 4.0. Journal of Intelligent Manufacturing, 30(4), 1809–1830.

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to declare that this work was financially supported by the discovery grant program from the National Sciences and Engineering Research Council of Canada (NSERC), grant number RGPIN-2019–05853.

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, École de Technologie Supérieure, University of Québec, 1100, Notre-Dame St. W., Montréal, Canada

    Amir M. Fathollahi-Fard, Lyne Woodward & Ouassima Akhrif

  2. Department of Engineering Science, Faculty of Innovation Engineering, Macau University of Science and Technology, Macau, 999078, China

    Amir M. Fathollahi-Fard

Authors
  1. Amir M. Fathollahi-Fard
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lyne Woodward
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ouassima Akhrif
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Amir M. Fathollahi-Fard.

Ethics declarations

Conflict of interest

There is no conflict of interest between the authors to be declared.

Human and animals rights

This research has no financial and non-financial interest in human participants and or animals.

Informed consent

All the authors have read and agreed to the publication of this research in Annals of Operations Research.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fathollahi-Fard, A.M., Woodward, L. & Akhrif, O. A scenario-based robust optimization model for the sustainable distributed permutation flow-shop scheduling problem. Ann Oper Res (2024). https://doi.org/10.1007/s10479-024-05940-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10479-024-05940-7

Keywords

Search

Navigation