This paper addresses the production scheduling and inventory management in a closed‐loop supply chain that recycles both high‐quality and low‐quality cores and makes products using cores and new raw materials. The manufacturing/remanufacturing supply chain consists of a vendor and a buyer, and they collaborate under a consignment stock (CS) agreement. We investigate and compare three operation policies under the CS agreement, covering continuous and intermittent production manners and shipments of equal and unequal batch sizes. For each operation policy, we develop a mixed integer nonlinear programming model to jointly optimize the production sequence of two classes of cores, production cycle length, shipment frequency, and shipment batch sizes, with the objective of minimizing the cost rate. By analyzing the respective decisions and conducting an extensive numerical study with various scenarios, we explore the advantages and applications of each operation policy. Based on our research findings, we provide general guidelines and criteria for operation policy selection.