This study proposes a bi-level optimization framework for heater placement in 2D manufacturing systems, such as oven configurations, with a focus on achieving uniform heat distribution and energy efficiency. The first level minimizes the maximum absolute deviation of view factors from their average, ensuring uniform thermal management across surface segments. The second level minimizes the number of active heaters while maintaining the thermal uniformity achieved in the first level, promoting energy savings. Computational results across multiple scenarios demonstrate that the framework effectively reduces heater usage by an average of 6% while preserving heat uniformity, using only 45% of the total heater capacity in some cases. By leveraging view factor-based heat transfer models, inverse heat conduction analysis, and bi-level optimization, this work aligns with key Industry 4.0 principles, particularly smart manufacturing and energy-efficient production. The proposed framework offers a data-driven approach to heater placement, enabling intelligent thermal management through computational methods. Its ability to reduce energy consumption while maintaining thermal uniformity supports sustainable manufacturing and creates opportunities for integration with real-time monitoring and process optimization systems.

Keywords

Bi-level optimization, manufacturing system design/reconfiguration, optimization and control, sustainable manufacturing, Industry 4.0.