Abstract: Recently supply chain industry experiences a significant energy consumption growth drawing the attention of government, academia, and industry to its environmental impacts and the issue of low-carbon supply chain management. Supply chain businesses not only face the competitive market with uncertain demand but also realize the low-carbon competitiveness under the carbon emission compliance scenario. Thus, a green-focusedtwo-stage stochastic location-inventory model is required to integrate the inventory control decisions with the 3-stage network (i.e., supplier-DC-retailer) design decisions to deal with nonstationary demand, whose objective maximize the profits of the supply chain business including the sales profit and the low-carbon reward (i.e., trade extra carbon allowances).To be specific, given the allocated carbon-capΦ^cap, the carbon emissions associated with DC implementation (CE_L), DC operations (CE_O), and transportation (CE_T) are considered, then the carbon-cap difference is calculated as CE_L+ CE_O+ CE_T-Φ^cap. Thenegative difference reflects the low-carbon emitter can sell extra allowances to obtain incomes; otherwise, buy emission allowances to comply with the carbon-cap. To make inventory control decisions under the (t,s,S)policy, we explicit the formulations of optimal parameters based on the Newsboy adjustment method and linearization technique. Because the problem is of the NP-hard, a three-step hierarchical matheuristic algorithm is proposed, which features different initial solution construction modes, simulated annealing (SA) and intensification after SA. The case study from a supply chain company in China facilitates the verification of model validation and algorithm effectiveness. After investigate the impact of cost structures, demand uncertainty, and different carbon-caps on supply chain network design, costs, and profits of the supply chain business, managerial insights include: (1) integrated decision-making at strategic and tactical levels in supply chain management is necessary, separating them can only reach to sub-optimal results thus higher costs. (2) When facing nonstationary demand, supply chain businesses open more DCs to enhance the level of service; while the back-ordering cost is high, supply chain businesses alsoopen more DCs to reduce the probability of out-of-stocks. (3) The emission trading system encourages enterprises to achieve low-carbon through better operations to obtain the low-carbon reward, which is the most flexible and beneficial emission regulation; however, the most suitable caps and carbon prices depend on the environmental targets and the economic benefits. As the climate change is at issue around the globe nowadays, this model and algorithm provide solutions to supply chain industry’s operations and emission compliance also cast light on future carbon emission regulation schemes to be implemented in China.

Key words: location-inventory problem, carbon emission allowance, two-stage stochastic programming, three-step hierarchical matheuristic