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A mathematical model for simultaneous personnel shift planning and unrelated parallel machine scheduling (2402.15670v1)

Published 24 Feb 2024 in cs.AI and cs.DM

Abstract: This paper addresses a production scheduling problem derived from an industrial use case, focusing on unrelated parallel machine scheduling with the personnel availability constraint. The proposed model optimizes the production plan over a multi-period scheduling horizon, accommodating variations in personnel shift hours within each time period. It assumes shared personnel among machines, with one personnel required per machine for setup and supervision during job processing. Available personnel are fewer than the machines, thus limiting the number of machines that can operate in parallel. The model aims to minimize the total production time considering machine-dependent processing times and sequence-dependent setup times. The model handles practical scenarios like machine eligibility constraints and production time windows. A Mixed Integer Linear Programming (MILP) model is introduced to formulate the problem, taking into account both continuous and district variables. A two-step solution approach enhances computational speed, first maximizing accepted jobs and then minimizing production time. Validation with synthetic problem instances and a real industrial case study of a food processing plant demonstrates the performance of the model and its usefulness in personnel shift planning. The findings offer valuable insights for practical managerial decision-making in the context of production scheduling.

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References (30)
  1. Abbasi, Mostafa, Mir Saman Pishvaee, and Samira Bairamzadeh. 2020. “Land suitability assessment for Paulownia cultivation using combined GIS and Z-number DEA: A case study.” Computers and Electronics in Agriculture 176: 105666.
  2. Afzalirad, Mojtaba, and Javad Rezaeian. 2016. “Resource-constrained unrelated parallel machine scheduling problem with sequence dependent setup times, precedence constraints and machine eligibility restrictions.” Computers & Industrial Engineering 98: 40–52.
  3. Ahang, Maryam, Todd Charter, Oluwaseyi Ogunfowora, Maziyar Khadivi, Mostafa Abbasi, and Homayoun Najjaran. 2024. “Intelligent Condition Monitoring of Industrial Plants: An Overview of Methodologies and Uncertainty Management Strategies.” arXiv preprint arXiv:2401.10266 .
  4. AIMMS 4.92.7 software. 2023. “.” https://www.aimms.com/. Version 4.92.7.
  5. Al-Harkan, Ibrahim M, and Ammar A Qamhan. 2019. “Optimize unrelated parallel machines scheduling problems with multiple limited additional resources, sequence-dependent setup times and release date constraints.” IEEE Access 7: 171533–171547.
  6. Arnaout, Jean-Paul, Ghaith Rabadi, and Rami Musa. 2010. “A two-stage ant colony optimization algorithm to minimize the makespan on unrelated parallel machines with sequence-dependent setup times.” Journal of Intelligent Manufacturing 21: 693–701.
  7. Avalos-Rosales, Oliver, Francisco Angel-Bello, and Ada Alvarez. 2015. “Efficient metaheuristic algorithm and re-formulations for the unrelated parallel machine scheduling problem with sequence and machine-dependent setup times.” The International Journal of Advanced Manufacturing Technology 76: 1705–1718.
  8. Avgerinos, Ioannis, Ioannis Mourtos, Stavros Vatikiotis, and Georgios Zois. 2023. “Scheduling unrelated machines with job splitting, setup resources and sequence dependency.” International Journal of Production Research 61 (16): 5502–5524.
  9. Bektur, Gulcin, and Tugba Saraç. 2019. “A mathematical model and heuristic algorithms for an unrelated parallel machine scheduling problem with sequence-dependent setup times, machine eligibility restrictions and a common server.” Computers & Operations Research 103: 46–63.
  10. Bitar, Abdoul, Stéphane Dauzère-Pérès, and Claude Yugma. 2021. “Unrelated parallel machine scheduling with new criteria: Complexity and models.” Computers & Operations Research 132: 105291.
  11. Burdett, Robert L, Paul Corry, Colin Eustace, and Simon Smith. 2021. “Scheduling pre-emptible tasks with flexible resourcing options and auxiliary resource requirements.” Computers & Industrial Engineering 151: 106939.
  12. Castro, Pedro M, Ignacio E Grossmann, and Augusto Q Novais. 2006. “Two new continuous-time models for the scheduling of multistage batch plants with sequence dependent changeovers.” Industrial & engineering chemistry research 45 (18): 6210–6226.
  13. Chen, Haichao, Peng Guo, Jesus Jimenez, Zhijie Sasha Dong, and Wenming Cheng. 2022. “Unrelated parallel machine photolithography scheduling problem with dual resource constraints.” IEEE Transactions on Semiconductor Manufacturing 36 (1): 100–112.
  14. Costa, A, FA Cappadonna, and S Fichera. 2013. “A hybrid genetic algorithm for job sequencing and worker allocation in parallel unrelated machines with sequence-dependent setup times.” The International Journal of Advanced Manufacturing Technology 69: 2799–2817.
  15. Daniels, Richard L, Barbara J Hoopes, and Joseph B Mazzola. 1996. “Scheduling parallel manufacturing cells with resource flexibility.” Management science 42 (9): 1260–1276.
  16. Daniels, Richard L, Barbara J Hoopes, and Joseph B Mazzola. 1997. “An analysis of heuristics for the parallel-machine flexible-resource scheduling problem.” Annals of Operations Research 70 (0): 439–472.
  17. Edis, Emrah B, Ceyda Oguz, and Irem Ozkarahan. 2013. “Parallel machine scheduling with additional resources: Notation, classification, models and solution methods.” European Journal of Operational Research 230 (3): 449–463.
  18. Fanjul-Peyro, Luis. 2020. “Models and an exact method for the unrelated parallel machine scheduling problem with setups and resources.” Expert Systems with Applications: X 5: 100022.
  19. Fanjul-Peyro, Luis, Rubén Ruiz, and Federico Perea. 2019. “Reformulations and an exact algorithm for unrelated parallel machine scheduling problems with setup times.” Computers & Operations Research 101: 173–182.
  20. Gurobi 10.0.2 software. 2023. “.” https://www.gurobi.com/. Version 10.0.2.
  21. Khadivi, Maziyar, Todd Charter, Marjan Yaghoubi, Masoud Jalayer, Maryam Ahang, Ardeshir Shojaeinasab, and Homayoun Najjaran. 2023. “Deep reinforcement learning for machine scheduling: Methodology, the state-of-the-art, and future directions.” arXiv preprint arXiv:2310.03195 .
  22. Liang, Yi, Zan Sun, Tianheng Song, Qiang Chou, Wei Fan, Jianping Fan, Yong Rui, et al. 2022. “Lenovo Schedules Laptop Manufacturing Using Deep Reinforcement Learning.” INFORMS Journal on Applied Analytics 52 (1): 56–68.
  23. Ogunfowora, Oluwaseyi, and Homayoun Najjaran. 2023. “Reinforcement and deep reinforcement learning-based solutions for machine maintenance planning, scheduling policies, and optimization.” Journal of Manufacturing Systems 70: 244–263.
  24. Shojaeinasab, Ardeshir, Todd Charter, Masoud Jalayer, Maziyar Khadivi, Oluwaseyi Ogunfowora, Nirav Raiyani, Marjan Yaghoubi, and Homayoun Najjaran. 2022. “Intelligent manufacturing execution systems: A systematic review.” Journal of Manufacturing Systems 62: 503–522.
  25. Słowiński, Roman. 1980. “Two approaches to problems of resource allocation among project activities—a comparative study.” Journal of the Operational Research Society 31 (8): 711–723.
  26. Tableau Desktop 2023.1.2 Professional Edition. 2023. “.” https://www.tableau.com/products/desktop/download. Version 2023.1.2.
  27. Tahmassebi, T. 1999. “Vehicle routing problem (VRP) formulation for continuous-time packing hall design/operations.” Computers & Chemical Engineering 23: S1011–S1014.
  28. Tran, Tony T, Arthur Araujo, and J Christopher Beck. 2016. “Decomposition methods for the parallel machine scheduling problem with setups.” INFORMS Journal on Computing 28 (1): 83–95.
  29. Yepes-Borrero, Juan C, Fulgencia Villa, Federico Perea, and Juan Pablo Caballero-Villalobos. 2020. “GRASP algorithm for the unrelated parallel machine scheduling problem with setup times and additional resources.” Expert Systems with Applications 141: 112959.
  30. Yunusoglu, Pinar, and Seyda Topaloglu Yildiz. 2022. “Constraint programming approach for multi-resource-constrained unrelated parallel machine scheduling problem with sequence-dependent setup times.” International Journal of Production Research 60 (7): 2212–2229.

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