IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i19p3446-d921821.html
   My bibliography  Save this article

The Permutation Flow Shop Scheduling Problem with Human Resources: MILP Models, Decoding Procedures, NEH-Based Heuristics, and an Iterated Greedy Algorithm

Author

Listed:
  • Victor Fernandez-Viagas

    (Department of Industrial Organization and Business Management I, School of Engineering, University of Seville, 41091 Seville, Spain
    Grupo de Informática de la Salud Computacional, Hospital Universitario Virgen del Rocío, 41013 Seville, Spain)

  • Luis Sanchez-Mediano

    (Department of Industrial Organization and Business Management I, School of Engineering, University of Seville, 41091 Seville, Spain)

  • Alvaro Angulo-Cortes

    (Department of Industrial Organization and Business Management I, School of Engineering, University of Seville, 41091 Seville, Spain)

  • David Gomez-Medina

    (Department of Industrial Organization and Business Management I, School of Engineering, University of Seville, 41091 Seville, Spain
    Grupo de Informática de la Salud Computacional, Hospital Universitario Virgen del Rocío, 41013 Seville, Spain)

  • Jose Manuel Molina-Pariente

    (Department of Industrial Organization and Business Management I, School of Engineering, University of Seville, 41091 Seville, Spain
    Grupo de Informática de la Salud Computacional, Hospital Universitario Virgen del Rocío, 41013 Seville, Spain)

Abstract

In this paper, we address the permutation flow shop scheduling problem with sequence-dependent and non-anticipatory setup times. These setups are performed or supervised by multiple servers, which are renewable secondary resources (typically human resources). Despite the real applications of this kind of human supervision and the growing attention paid in the scheduling literature, we are not aware of any previous study on the problem under consideration. To cover this gap, we start theoretically addressing the problem by: proposing three mixed-integer linear programming models to find optimal solutions in the problem; and proposing different decoding procedures to code solutions in approximated procedures. After that, the best decoding procedure is used to propose a new mechanism that generates 896 different dispatching rules, combining different measures, indicators, and sorting criteria. All these dispatching rules are embedded in the traditional NEH algorithm. Finally, an iterated greedy algorithm is proposed to find near-optimal solutions. By doing so, we provide academics and practitioners with efficient methods that can be used to obtain exact solutions of the problem; applied to quickly schedule jobs and react under changes; used for initialisation or embedded in more advanced algorithms; and/or easily updated and implemented in real manufacturing scenarios.

Suggested Citation

  • Victor Fernandez-Viagas & Luis Sanchez-Mediano & Alvaro Angulo-Cortes & David Gomez-Medina & Jose Manuel Molina-Pariente, 2022. "The Permutation Flow Shop Scheduling Problem with Human Resources: MILP Models, Decoding Procedures, NEH-Based Heuristics, and an Iterated Greedy Algorithm," Mathematics, MDPI, vol. 10(19), pages 1-32, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3446-:d:921821
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/19/3446/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/19/3446/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yenisey, Mehmet Mutlu & Yagmahan, Betul, 2014. "Multi-objective permutation flow shop scheduling problem: Literature review, classification and current trends," Omega, Elsevier, vol. 45(C), pages 119-135.
    2. Rajendran, Chandrasekharan, 1993. "Heuristic algorithm for scheduling in a flowshop to minimize total flowtime," International Journal of Production Economics, Elsevier, vol. 29(1), pages 65-73, February.
    3. M S Nagano & J V Moccellin, 2002. "A high quality solution constructive heuristic for flow shop sequencing," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(12), pages 1374-1379, December.
    4. Liu, Weibo & Jin, Yan & Price, Mark, 2017. "A new improved NEH heuristic for permutation flowshop scheduling problems," International Journal of Production Economics, Elsevier, vol. 193(C), pages 21-30.
    5. Brucker, Peter & Knust, Sigrid & Wang, Guoqing, 2005. "Complexity results for flow-shop problems with a single server," European Journal of Operational Research, Elsevier, vol. 165(2), pages 398-407, September.
    6. Rad, Shahriar Farahmand & Ruiz, Rubén & Boroojerdian, Naser, 2009. "New high performing heuristics for minimizing makespan in permutation flowshops," Omega, Elsevier, vol. 37(2), pages 331-345, April.
    7. Fernandez-Viagas, Victor & Talens, Carla & Framinan, Jose M., 2022. "Assembly flowshop scheduling problem: Speed-up procedure and computational evaluation," European Journal of Operational Research, Elsevier, vol. 299(3), pages 869-882.
    8. Ruiz, Ruben & Stutzle, Thomas, 2007. "A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem," European Journal of Operational Research, Elsevier, vol. 177(3), pages 2033-2049, March.
    9. Rios-Mercado, Roger Z. & Bard, Jonathan F., 1998. "Heuristics for the flow line problem with setup costs," European Journal of Operational Research, Elsevier, vol. 110(1), pages 76-98, October.
    10. Missaoui, Ahmed & Ruiz, Rubén, 2022. "A parameter-Less iterated greedy method for the hybrid flowshop scheduling problem with setup times and due date windows," European Journal of Operational Research, Elsevier, vol. 303(1), pages 99-113.
    11. Nawaz, Muhammad & Enscore Jr, E Emory & Ham, Inyong, 1983. "A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem," Omega, Elsevier, vol. 11(1), pages 91-95.
    12. Jun-Ho Lee & Hyun-Jung Kim, 2022. "Reinforcement learning for robotic flow shop scheduling with processing time variations," International Journal of Production Research, Taylor & Francis Journals, vol. 60(7), pages 2346-2368, April.
    13. Ying Ji & Huanhuan Li & Huijie Zhang, 2022. "Risk-Averse Two-Stage Stochastic Minimum Cost Consensus Models with Asymmetric Adjustment Cost," Group Decision and Negotiation, Springer, vol. 31(2), pages 261-291, April.
    14. Fernandez-Viagas, Victor & Ruiz, Rubén & Framinan, Jose M., 2017. "A new vision of approximate methods for the permutation flowshop to minimise makespan: State-of-the-art and computational evaluation," European Journal of Operational Research, Elsevier, vol. 257(3), pages 707-721.
    15. Kalczynski, Pawel J. & Kamburowski, Jerzy, 2009. "An empirical analysis of the optimality rate of flow shop heuristics," European Journal of Operational Research, Elsevier, vol. 198(1), pages 93-101, October.
    16. Framinan, Jose M. & Perez-Gonzalez, Paz, 2015. "On heuristic solutions for the stochastic flowshop scheduling problem," European Journal of Operational Research, Elsevier, vol. 246(2), pages 413-420.
    17. Hatami, Sara & Ruiz, Rubén & Andrés-Romano, Carlos, 2015. "Heuristics and metaheuristics for the distributed assembly permutation flowshop scheduling problem with sequence dependent setup times," International Journal of Production Economics, Elsevier, vol. 169(C), pages 76-88.
    18. Ammar Oulamara & Djamal Rebaine & Mehdi Serairi, 2013. "Scheduling the two-machine open shop problem under resource constraints for setting the jobs," Annals of Operations Research, Springer, vol. 211(1), pages 333-356, December.
    19. Vallada, Eva & Ruiz, Rubén, 2011. "A genetic algorithm for the unrelated parallel machine scheduling problem with sequence dependent setup times," European Journal of Operational Research, Elsevier, vol. 211(3), pages 612-622, June.
    20. Rune Larsen & Marco Pranzo, 2019. "A framework for dynamic rescheduling problems," International Journal of Production Research, Taylor & Francis Journals, vol. 57(1), pages 16-33, January.
    21. Yepes-Borrero, Juan C. & Perea, Federico & Ruiz, Rubén & Villa, Fulgencia, 2021. "Bi-objective parallel machine scheduling with additional resources during setups," European Journal of Operational Research, Elsevier, vol. 292(2), pages 443-455.
    22. Meenakshi Sharma & Manisha Sharma & Sameer Sharma, 2022. "Desert sparrow optimization algorithm for the bicriteria flow shop scheduling problem with sequence-independent setup time," Operational Research, Springer, vol. 22(4), pages 4353-4396, September.
    23. E F Stafford & F T Tseng & J N D Gupta, 2005. "Comparative evaluation of MILP flowshop models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(1), pages 88-101, January.
    24. Bish, Ebru K., 2003. "A multiple-crane-constrained scheduling problem in a container terminal," European Journal of Operational Research, Elsevier, vol. 144(1), pages 83-107, January.
    25. Hamed Samarghandi, 2015. "Studying the effect of server side-constraints on the makespan of the no-wait flow-shop problem with sequence-dependent set-up times," International Journal of Production Research, Taylor & Francis Journals, vol. 53(9), pages 2652-2673, May.
    26. Ruiz, Rubén & Pan, Quan-Ke & Naderi, Bahman, 2019. "Iterated Greedy methods for the distributed permutation flowshop scheduling problem," Omega, Elsevier, vol. 83(C), pages 213-222.
    27. Pan, Quan-Ke & Ruiz, Rubén, 2014. "An effective iterated greedy algorithm for the mixed no-idle permutation flowshop scheduling problem," Omega, Elsevier, vol. 44(C), pages 41-50.
    28. Abdelhak Elidrissi & Rachid Benmansour & Mohammed Benbrahim & David Duvivier, 2021. "Mathematical formulations for the parallel machine scheduling problem with a single server," International Journal of Production Research, Taylor & Francis Journals, vol. 59(20), pages 6166-6184, October.
    29. Miltenburg, John, 2001. "U-shaped production lines: A review of theory and practice," International Journal of Production Economics, Elsevier, vol. 70(3), pages 201-214, April.
    30. Kalczynski, Pawel Jan & Kamburowski, Jerzy, 2007. "On the NEH heuristic for minimizing the makespan in permutation flow shops," Omega, Elsevier, vol. 35(1), pages 53-60, February.
    31. Horst Tempelmeier & Karina Copil, 2016. "Capacitated lot sizing with parallel machines, sequence-dependent setups, and a common setup operator," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(4), pages 819-847, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Benavides, Alexander J. & Vera, Antony, 2022. "The reversibility property in a job-insertion tiebreaker for the permutational flow shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 297(2), pages 407-421.
    2. Fernando Luis Rossi & Marcelo Seido Nagano, 2022. "Beam search-based heuristics for the mixed no-idle flowshop with total flowtime criterion," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(4), pages 1311-1346, December.
    3. Yong Wang & Yuting Wang & Yuyan Han, 2023. "A Variant Iterated Greedy Algorithm Integrating Multiple Decoding Rules for Hybrid Blocking Flow Shop Scheduling Problem," Mathematics, MDPI, vol. 11(11), pages 1-25, May.
    4. Fernandez-Viagas, Victor & Ruiz, Rubén & Framinan, Jose M., 2017. "A new vision of approximate methods for the permutation flowshop to minimise makespan: State-of-the-art and computational evaluation," European Journal of Operational Research, Elsevier, vol. 257(3), pages 707-721.
    5. Ruiz, Rubén & Pan, Quan-Ke & Naderi, Bahman, 2019. "Iterated Greedy methods for the distributed permutation flowshop scheduling problem," Omega, Elsevier, vol. 83(C), pages 213-222.
    6. Liu, Weibo & Jin, Yan & Price, Mark, 2017. "A new improved NEH heuristic for permutation flowshop scheduling problems," International Journal of Production Economics, Elsevier, vol. 193(C), pages 21-30.
    7. Perez-Gonzalez, Paz & Framinan, Jose M., 2024. "A review and classification on distributed permutation flowshop scheduling problems," European Journal of Operational Research, Elsevier, vol. 312(1), pages 1-21.
    8. Libralesso, Luc & Focke, Pablo Andres & Secardin, Aurélien & Jost, Vincent, 2022. "Iterative beam search algorithms for the permutation flowshop," European Journal of Operational Research, Elsevier, vol. 301(1), pages 217-234.
    9. Said Aqil & Karam Allali, 2021. "On a bi-criteria flow shop scheduling problem under constraints of blocking and sequence dependent setup time," Annals of Operations Research, Springer, vol. 296(1), pages 615-637, January.
    10. Fernandez-Viagas, Victor & Talens, Carla & Framinan, Jose M., 2022. "Assembly flowshop scheduling problem: Speed-up procedure and computational evaluation," European Journal of Operational Research, Elsevier, vol. 299(3), pages 869-882.
    11. K Sheibani, 2010. "A fuzzy greedy heuristic for permutation flow-shop scheduling," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(5), pages 813-818, May.
    12. Gmys, Jan & Mezmaz, Mohand & Melab, Nouredine & Tuyttens, Daniel, 2020. "A computationally efficient Branch-and-Bound algorithm for the permutation flow-shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 284(3), pages 814-833.
    13. Pagnozzi, Federico & Stützle, Thomas, 2019. "Automatic design of hybrid stochastic local search algorithms for permutation flowshop problems," European Journal of Operational Research, Elsevier, vol. 276(2), pages 409-421.
    14. Lin, Shih-Wei & Ying, Kuo-Ching, 2016. "Optimization of makespan for no-wait flowshop scheduling problems using efficient matheuristics," Omega, Elsevier, vol. 64(C), pages 115-125.
    15. Kalczynski, Pawel J. & Kamburowski, Jerzy, 2009. "An empirical analysis of the optimality rate of flow shop heuristics," European Journal of Operational Research, Elsevier, vol. 198(1), pages 93-101, October.
    16. Pan, Quan-Ke & Ruiz, Rubén, 2014. "An effective iterated greedy algorithm for the mixed no-idle permutation flowshop scheduling problem," Omega, Elsevier, vol. 44(C), pages 41-50.
    17. Pan, Quan-Ke & Ruiz, Rubén, 2012. "An estimation of distribution algorithm for lot-streaming flow shop problems with setup times," Omega, Elsevier, vol. 40(2), pages 166-180, April.
    18. Vallada, Eva & Ruiz, Rubén, 2010. "Genetic algorithms with path relinking for the minimum tardiness permutation flowshop problem," Omega, Elsevier, vol. 38(1-2), pages 57-67, February.
    19. Pagnozzi, Federico & Stützle, Thomas, 2021. "Automatic design of hybrid stochastic local search algorithms for permutation flowshop problems with additional constraints," Operations Research Perspectives, Elsevier, vol. 8(C).
    20. Mario Levorato & David Sotelo & Rosa Figueiredo & Yuri Frota, 2024. "Efficient solutions to the m-machine robust flow shop under budgeted uncertainty," Annals of Operations Research, Springer, vol. 338(1), pages 765-799, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3446-:d:921821. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.