Integration between Cutting Problems and Batch Sizing in Multistage Production Systems

This work addresses the production planning inspired by a metal-mechanical industry that operates in the manufacture of products to order, focusing on the critical stages of cutting, bending and welding. Traditionally, these steps are handled in a hierarchical manner, which can result in suboptimal or unfeasible solutions. To overcome this limitation, an integrated model is proposed that combines two-dimensional cutting decisions of irregular parts with multi-stage capable batch sizing with parallel machines and setups. The model explicitly captures the interdependencies between stages through coupling constraints and considers costs of production, preparation, and intermediate inventories along the production chain. Instances based on real data were generated to assess the applicability of the approach, allowing for the analysis of metrics such as capacity utilization, throughput rate, and load balancing between stages.