In the context of carbon neutrality, plastic ban, and green development, this paper aims to maximize the comprehensive interest of manufacturers in building a sustainable logistic network. It proposes a reverse logistics network model of a dual-channel model with multiple objectives and a random environment for the construction of recycling boxes projects and uses a Stackelberg game to develop pricing strategies for dual-channel recyclers and a genetic algorithm to optimize reverse logistics networks. This paper found the following: multi-objective evaluation is more conducive to sustainable development; when consumers are price-sensitive, a stronger rebate can significantly increase revenue; online platform recyclers should invest more in marketing than traditional recyclers; retailers’ willingness to cooperate in recycling has a significant impact on the overall benefits; the impact of government subsidies is marginal and needs to be controlled to a certain extent; the impact of green credit is insignificant, and the strength of commercial banks’ scrutiny of companies has little effect; an increase in environmental uncertainty within a certain range can lead to an overall loss of benefits, and an excessive impact can be out of line with extreme values. It provides a basis for decision-making on strategies for enterprises to build a logistics network of recycling boxes, government subsidies, green credit from banks, and dual-channel recyclers.