Optimizing multi-item EPQ under defect and rework: A case in the plastic molding industry

Product availability is a key indicator of service performance and is closely linked to production planning. Inaccurate decisions in lot sizing may lead to either overstock or stockout, resulting in substantial financial losses. Classical Economic Production Quantity (EPQ) models generally assume perfect quality and ignore real-world factor such as defects, rework, and backorders. This study proposes an extended EPQ model for multi-item production systems that integrates random defect rates, rework, and backordering within a single framework. Unlike previous studies that focus on single-item scenarios or deterministic defect rates, this model reflects a more realistic setting faced by companies by accounting for stochastic defects, the cost of crushing and rework, and customer backorder fulfillment. The model aims to determine the optimal lot size and production cycle that minimize the total inventory-related costs. The proposed model is validated using real case data from a plastic molding company. Results show that the model yields cost savings of 0.19% compared to the current company policy. Although modest, these savings are significant when scaled across production periods. More importantly, the model demonstrates strong adaptability to operational constraints and provides a practical decision-support tool for industries managing multiple products, quality variation, and uncertain demand.