Abstract

The rise of Industry 4.0 has intensified demand for hybrid production systems delivering both standard and highly customized products. Yet, current production planning models largely overlook modular-structured products in multi-echelon job-shop environments, particularly under uncertainty. This study develops a robust tactical planning framework that captures defect risks, variable processing times, and capacity uncertainty for customized items. A mixed-integer programming model based on the cardinality-constrained robust optimization approach is formulated to jointly optimize order acceptance, machine activation, procurement, production, and inventory decisions, with the objective of maximizing profit across the manufacturing network.
To mitigate the effects of volatile manufacturing conditions, the framework allows the flexible activation of additional machine capacity modules within a budgeted uncertainty set. Computational experiments are conducted using literature-driven data to evaluate the model’s behavior under a range of uncertainty realizations. Sensitivity analysis confirms that the selected uncertain parameters have the largest impact on profit. Complexity analysis shows that the model remains computationally efficient and scalable across different problem sizes.
An out-of-sample performance evaluation demonstrates that the robust approach’s machine capacity module activation decisions outperform conventional deterministic planning by enhancing resilience and profitability under uncertainty, while maintaining operational efficiency with only marginal additional machine use. Most of the profit improvement is driven by reduced delays and cancellations, indicating a higher service level. These results highlight the model’s ability to safeguard profitability and operational stability in complex, customization-driven production systems.