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A Make-to-Order Capacitated Lot-Sizing Model with Parallel Machines, Eligibility Constraints, Extra Shifts, and Backorders

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Publicado en:Mathematics vol. 13, no. 11 (2025), p. 1798
Autor principal: Muñoz, Felipe T
Otros Autores: Ulloa-Navarro, Juan
Publicado:
MDPI AG
Materias:
Cold-rolled steel
Cold
Linear programming
Forming machines
Performance evaluation
Integer programming
Mathematical models
Solvers
Production planning
Metal sheets
Operating costs
Manufacturing
Workloads
Lot sizing
Cost effectiveness
Mathematical programming
Scheduling
Cold-formed steel
Raw materials
Galvanized steel
Decision making
Optimization
Produce to order
Construction costs
Mixed integer
Complexity
Metalworking industry
Constraints
Inventory
Backorders
Cold working
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Resumen:This study addresses the multi-period, multi-item, single-stage capacitated lot sizing problem (CLSP) in a parallel machine environment with machine eligibility constraints under a make-to-order production policy. A mixed-integer linear programming (MILP) model is developed to minimize total operational costs, including production, overtime, extra shifts, inventory holding, and backorders. The make-to-order setting introduces additional complexity by requiring individualized customer orders, each with specific due dates and product combinations, to be scheduled under constrained capacity and setup requirements. The model’s performance is evaluated in the context of a real-world production planning problem faced by a manufacturer of cold-formed steel profiles. In this setting, parallel forming machines process galvanized sheets of cold-rolled steel into a variety of profiles. The MILP model is solved using open-source optimization tools, specifically the HiGHS solver. The results show that optimal solutions can be obtained within reasonable computational times. For more computationally demanding instances, a runtime limit of 300 s is shown to improve solution quality while maintaining efficiency. These findings confirm the viability and cost-effectiveness of free software for solving complex industrial scheduling problems. Moreover, experimental comparisons reveal that solution times and performance can be further improved by using commercial solvers such as CPLEX, highlighting the potential trade-off between cost and computational performance.
ISSN:2227-7390
DOI:10.3390/math13111798
Fuente:Engineering Database