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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
    (Springer Heidelberg, 2024) Alimian, Mahyar; Ghezavati, Vahidreza; Tavakkoli-Moghaddam, Reza; Ramezanian, Reza
    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.