A joint economic lot-size model for sustainable industries of recycled content products

Coupling forward and reverse operations in closed-loop supply chains (CLSCs) can lead to a higher degree of sustainability. Previous studies on CLSCs have focused on the products that are either purely remanufactured or purely new. The emphasis on recycling necessitates research that considers recycled content products, which are made from a mix of virgin and recycled material. We study a CLSC consisting of a manufacturer, a retailer, a supplier, a material recovery facility (MRF) and a recycling facility. The supplier and the recycling facility provide the virgin and recycled raw materials, respectively, to the manufacturer who mixes them based on a predefined proportion known as the recycled content level to produce the ?nished products for the retailer. The recycling facility recovers the manufacturer's production waste as well as the used products collected by the MRF. We aim at maximising the chain-wide profit by optimising the shipments among the supply chain parties. We propose a Branch-and-Bound algorithm to obtain the optimal solution, and a heuristic procedure, which provides the optimal solution in 96% of all tested instances. In addition, we prove the optimality of a bang-bang policy for the recycled content level in most cases.