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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 finished 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. [ABSTRACT FROM AUTHOR]

Vendor managed inventory (VMI) is a partnership between a supplier and buyers whereby supplier makes inventory replenishment decisions on behalf of buyers. A (z, Z) VMI contract is one of the strategies that protect the buyers from dispatching a lot of inventory by the supplier using lower bound z and upper bound Z on the buyer's inventory level. This paper develops a model for a single vendor and multiple retailers supply chain under (z, Z) VMI contracts by considering the time value of money and also introduces a novel approach designated as "secondary negotiations" in order to improve manufacturer's cost or retailers' profits. Numerical analysis is designed to compare the performance (z, Z) VMI contract and independent system (without VMI) that both consider the time value of money. Furthermore, computational results show that how secondary negotiation changes in both upper bounds and replenishment quantity and cause to absorb and keep important retailers and increase their level of satisfaction for developing more mutual cooperation. [ABSTRACT FROM AUTHOR]