The optimal pricing of dual-channel supply chain with the third party product recovery and sales effort is considered in this paper. The optimal selling pricing of direct channel and retail channel in the forward supply chain and the optimal collection pricing of retail channel and the third party in the backward supply chain are given for the general case under the centralized and decentralized model. Then, the effect of sales effort of the retailer and the optimal pricing strategy with sales effort under the centralized and decentralized model are provided and analyzed. Finally, the comparative analysis of four situations is carried out by numerical results.

中文翻译：

---

通过第三方产品回收和销售努力实现双渠道供应链的最优定价

本文考虑了具有第三方产品回收和销售努力的双渠道供应链的最优定价。在集中和分散模型下，给出了一般情况下前向供应链中直接渠道和零售渠道的最优销售价格，以及后向供应链中零售渠道和第三方的最优集合价格。然后，提供并分析了在集中和分散模式下零售商的销售努力的效果和具有销售努力的最优定价策略。最后，通过数值结果对四种情况进行了比较分析。