Study on the impact of value density on profits of closed-loop supply chain with nonlinear demand

In connection with a secondary closed-loop supply chain composed of one manufacturer and one retailer, when on the basic of considering value density of waste products, the paper compares the profits of the open-loop chain and the closed-loop chain with manufacturer as a leader and analyzes the impact of value density of the wasted production on closed-loop supply chain. And then discusses the conditions that the value density should be satisfied when enterprises develop closed-loop supply chain. The results show that the manufacturer is more profits for developing closed-loop supply chain along with the growth of value density, when the other parameters are static and the value density meets a certain threshold. And only when value density is more than a particular value, the developing closed-loop supply chain can be possible.