Abstract: Under the carbon trading mechanism, the impacts of outsourcing or not outsourcing the manufacturer's emission reduction and the choice of outsourcing mode on the operation of the low-carbon supply chain are investigated for a low-carbon supply chain consisting of a manufacturer engaging in low-carbon production, a retailer and a third-party emission reduction service provider. The study shows that: when the abatement cost coefficient meets specific conditions, there is a unique interior equilibrium under both autonomous abatement (IE) and outsourced ordering abatement (OE); when the service provider has a stronger abatement capability, the manufacturer's choice of the OE mode can effectively enhance carbon abatement; there exists an interval of abatement capability coefficient, which makes the manufacturer's profit higher under the OE than under the IE mode; and the manufacturer's choice of the customized outsourcing (CE) mode due to a lack of willingness to reduce emissions, resulting in the system obtaining a boundary equilibrium. Subsequently, an abatement cost-sharing contract is introduced between the manufacturer and the service provider, and it is found that when the abatement cost coefficients and cost-sharing ratios satisfy specific conditions, there is a unique interior equilibrium under both types of improved outsourcing modes (OEC and CEC); compared to the IE mode, strong abatement capacity or high cost-sharing ratios under OEC and CEC contribute to the enhancement of carbon abatement, and the retailer indirectly benefits from the rise in demand, the The manufacturer prefers the IE model under high cost-sharing ratio or high abatement cost coefficient; compared with the OE model, the OEC model is more conducive to incentivizing service providers to increase the amount of carbon emission reductions and the price of services, which benefits both service providers and retailers, but the manufacturer suffers from the abatement cost sharing; comparing the two types of improvement outsourcing models, it is found that service providers and retailers unanimously prefer the OEC model, but the manufacturer's preference is related to the cost-sharing ratio, and its preference is also correlated with the cost-sharing ratio. Comparing the two types of improved outsourcing models, it is found that both service providers and retailers consistently prefer the OEC model, but the manufacturer's preference is related to the cost-sharing ratio, and its preference reverses with the increase of the cost-sharing ratio. Numerical simulation reveals that OEC (IE) is superior among all models in terms of improving system profitability and social welfare when the service provider's ability to reduce emissions is very strong (very weak).

Key words: low carbon supply chain, third party abatement service provider, outsourcing abatement, outsourcing model