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In this paper, we examine the influences of vertical and horizontal cooperation models on the optimal decisions and performance of a low-carbon closed-loop supply chain (CLSC) with a manufacturer and two retailers, and study optimal operation in the competitive pricing, competitive the low-carbon promotion, the carbon emission reduction, the used-products collection and the profits. We consider the completely decentralized model, M-R vertical cooperation model, R-R horizontal cooperation model, M-R-R vertical and horizontal cooperation model and completely centralized model, and also identify the optimal decision results and profits. It can be observed from a systematic comparison and numerical analysis that the completely centralized model is best in all optimal decision results among all models. In semi-cooperation, the M-R vertical cooperation model is positive, the R-R horizontal cooperation model is passive, and the positivity of the M-R-R vertical and horizontal cooperation model decreases with competitive intensity increasing in the used-products returning, carbon emissions reduction level, low-carbon promotion effort and the profits of the manufacturer and the entire supply chain.
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