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On the availability and changeover cases of the general lot-sizing and scheduling problem with maintenance modelling: a Lagrangian-based heuristic approach

Author

Listed:
  • Mahyar Alimian

    (South Tehran Branch, Islamic Azad University)

  • Vahidreza Ghezavati

    (South Tehran Branch, Islamic Azad University)

  • Reza Tavakkoli-Moghaddam

    (University of Tehran
    Istinye University)

  • Reza Ramezanian

    (K.N. Toosi University of Technology)

Abstract

The present paper proposes a novel concept to integrate maintenance modelling with an integrated lot-sizing and scheduling problem. The maintenance aspect of the problem is studied as age-based maintenance, while the production section is modeled as the General Lot-sizing and Scheduling Problem. The mathematical model aims to minimize the total integrated cost of the manufacturing system by determining the sequence of the products with their optimal lot-size, inventory, and shortage levels in close relation to the specified preventive maintenance plan and the availability of the system. Based on the unique structure of the proposed model, a heuristic solution approach is developed, which includes the Lagrangian relaxation algorithm, decomposition, and valid equalities. The computational result justifies the procedure of the proposed solution method and approves its efficiency in terms of cost and solution time for the range of small to large-scale instances. Furthermore, it is discussed that not only does the integrated model decrease the total cost of the manufacturing system, but it also increases the average availability of the system and improves the feasibility of the production plan. Finally, an extended model is developed to tackle the conflicts of the production and maintenance sub-problems via the bi-objective formulation.

Suggested Citation

  • Mahyar Alimian & Vahidreza Ghezavati & Reza Tavakkoli-Moghaddam & Reza Ramezanian, 2024. "On the availability and changeover cases of the general lot-sizing and scheduling problem with maintenance modelling: a Lagrangian-based heuristic approach," Operational Research, Springer, vol. 24(2), pages 1-43, June.
    • Handle: RePEc:spr:operea:v:24:y:2024:i:2:d:10.1007_s12351-024-00822-z
    DOI: 10.1007/s12351-024-00822-z
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    References listed on IDEAS

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    1. Claudio F. M. Toledo & Alf Kimms & Paulo M. França & Reinaldo Morabito, 2015. "The Synchronized and Integrated Two-Level Lot Sizing and Scheduling Problem: Evaluating the Generalized Mathematical Model," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-18, July.
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    7. Seyed Ahmad Razavi Al-e-hashem & Ali Papi & Mir Saman Pishvaee & Mohammadreza Rasouli, 2022. "Robust maintenance planning and scheduling for multi-factory production networks considering disruption cost: a bi-objective optimization model and a metaheuristic solution method," Operational Research, Springer, vol. 22(5), pages 4999-5034, November.
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    14. Miloš Milenković & Susana Val & Nebojša Bojović, 2023. "Simultaneous lot sizing and scheduling in the animal feed premix industry," Operational Research, Springer, vol. 23(2), pages 1-40, June.
    15. Curcio, Eduardo & Amorim, Pedro & Zhang, Qi & Almada-Lobo, Bernardo, 2018. "Adaptation and approximate strategies for solving the lot-sizing and scheduling problem under multistage demand uncertainty," International Journal of Production Economics, Elsevier, vol. 202(C), pages 81-96.
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