## 5 Conclusions  
This paper delved into the study of pricing and remanufacturing strategies within a multi-period environment for a decentralized dual-channel supply chain configuration incorporating reverse logistics, focusing on the pharmaceutical sector. The supply chain in question comprised a manufacturer and two distribution channels: a physical pharmacy and an online sales platform. The manufacturer was responsible for both manufacturing and remanufacturing processes, while the distribution channels handled sales to end-consumers. Notably, the pharmacy also offered after-sales services (AS) for products returned from both channels, receiving a unit commission for each online sale in compensation. This investigation covered the forward processes of manufacturing and sales, alongside reverse logistics activities including the collection and refurbishment of used products. A central goal of this paper was to develop the pricing and remanufacturing problem within the framework of [PERSON]'s game theory, identifying the manufacturer as the leader who set wholesale prices and remanufacturing rates, followed by each distribution channel setting their respective retail prices. The key contributions of this study included the creation of a mathematical model for the pricing and remanufacturing issue in a completely decentralized dual-channel supply chain context, taking into account AS and sales commissions between the channels, and exploring the changes and variability of the optimal solutions across multiple periods for a range of significant parameters. A mathematical formulation was elaborated and solved to explore the variations in the obtained optimal pricing and remanufacturing decisions of the manufacturer along with the optimal responsive pricing strategies of both distribution channels according to the parameters of interest. Several numerical results were presented, and sensitivity analyses were conducted to examine the robustness of the proposed model. Numerical results indicated that the pricing and remanufacturing decisions severely depended on the market size and the sensitivity of the demands. In addition, customer preference towards purchasing products via the online channel or the pharmacy dictated the demands, the pricing strategies and consequently the total profits generated by each distribution channel. Furthermore, the optimal remanufacturing strategy adopted by the remanufacturer was extremely affected by the costs related to collecting used products, causing an evolution in the savings, the unit wholesale and selling prices and eventually the total profit of the manufacturer, the pharmacy and the online platform. Moreover, the paper considered a sales commission between the distributors, examined its effect on the transfer of revenues from the online channel to the pharmacy, and investigated the unit sales commission considered as a break-even point allowing both distribution channels to coexist and generate similar profits for different scenarios. This approach highlighted the importance of sharing gains and revenues between online sellers and physical stores, establishing a dynamic of cooperation profitable for everyone. This work endeavored to provide support for decision makers managing either a manufacturer or a vendor in a dual-channel supply chain, allowing them to enhance their operational capabilities. In fact, the developed model offers insights for business managers on their optimal pricing strategies over a planning horizon in response to the pricing decisions of their competitors or the other entities of the supply chain. Moreover, the results of this study constitute a dashboard enabling managers to make more suitable and profitable decisions over a tactical horizon according to several parameters of interest. Furthermore, this work allows decision makers to assess their performance and to evaluate the impact of proposing more services in order to increase their benefits.