An MILP Model for Optimizing Quality Inspection Allocation with Technology Selection and Variable Sampling Rates

Quality inspection is critical for ensuring efficiency and compliance in assembly lines. The increasing adoption of AI-driven technologies, such as machine vision systems, offers significant potential to enhance detection performance and reduce inspection costs. However, these technologies are often integrated with human operators in hybrid inspection systems, posing complex design challenges. Motivated by gaps in the existing research, this paper proposes a novel MILP model that introduces several previously unaddressed capabilities in inspection planning. Specifically, it simultaneously optimizes the inspection method selection, sampling rate, and detection rate across multi-product systems featuring multiple inspection technologies with varying costs and accuracies. This unified formulation represents a substantive advancement over existing models, which typically address only isolated aspects of the problem. The model minimizes the total quality-related costs-comprising investment, inspection, penalty, and rework costs-while considering operational constraints such as workforce availability, inspection and rework time limits, and equipment capacity. Key modeling assumptions include heterogeneous inspection accuracies, product-specific defect probabilities, and the feasibility of partial inspections. The approach is validated on both synthetic datasets and a real-world automotive case study, demonstrating its ability to significantly reduce costs and to highlight the benefits of effectively combining human and machine-based inspections.