Reexamining a single-producer multi-retailer integrated inventory model with rework using algebraic method

In this study, a single-producer multi-retailer integrated inventory model with rework is reexamined using mathematical modeling and an algebraic method. It is assumed that a product is manufactured through an imperfect production process, and the reworking of random defective items is done right after the regular process in each cycle. After the entire lot is quality assured, multiple shipments will be delivered synchronously to m different retailers in each production cycle. The objective is to find the optimal production lot size and optimal number of shipments that minimizes total expected costs for such a specific supply chains system. The conventional approach uses differential calculus on system cost function to derive the optimal production- shipment policy (Chiu et al. [1]); in contrast, the proposed algebraic approach is a straightforward method that enables practitioners who may not have sufficient knowledge of calculus to understand and manage real-world systems more effectively