Two-echelon closed-loop supply chain deterministic inventory models in a batch production environment

This paper considers a two-echelon closed-loop supply chain consisting of a manufacturer and a remanufacturer at the upper echelon and a retailer at the lower echelon. The retailer faces a constant demand from customers, which is satisfied through recovered and new products received from the remanufacturer and the manufacturer, respectively. The manufacturer produces the product with finite rate, whereas the recovery of returned product is instantaneous at the remanufacturer. We develop three models to determine the optimal production-inventory policy of the players for minimizing the joint total cost of the system. In the first model, the retailer receives the product in batches from the manufacturer and the remanufacture simultaneously, whereas in the second and third models, the batches are received alternatively. In the third model, however, the procurement of raw material at the manufacturer is also considered. Numerical illustration is presented to examine the impact of certain key parameters.