Integrated inventory model with multi-retailer and rework process

This paper derives optimal production-shipment policy for a single-producer multi-retailer integrated inventory model with rework. We assume that a product is manufactured by a producer. All items are screened for quality assurance. Random defective items will be picked up and reworked in the same cycle when regular production ends. Upon entire lot is quality assured, multiple shipments are delivered synchronously to m different retailers in each production cycle. Each retailer has its own annual product demand, unit stock holding cost, and fixed and variable delivery costs. Mathematical modeling and analysis is used to derive the expected system cost. The Hessian matrix equations are employed to prove the convexity of cost function. A closed-form optimal production-shipment policy that minimizes total expected costs for such a specific integrated inventory model is obtained.