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In order to obtain customer satisfaction and promote the overall revenue of the supply chain system, offline purchase and online return strategy, called a new kind of cross channel return strategy (hereinafter referred to as &#x201C;cross channel return&#x201D;), has been gradually adopted by more and more enterprises in China. Moreover, free riding behavior is always inevitable in supply chain system. When a supply chain system includes free riding behavior and cross channel return strategy, the system is complex so that its stability can&#x2019;t be ensured easily. Hence, the management of the complex supply chain system mentioned above is a major challenge. In this article, the inventory and profit control strategy for a dual channel supply chain (DCSC) with cross channel return and free riding behavior is developed. Firstly, the mathematical model of the supply chain is set up based on the discrete state space equation. Secondly, utilizing the Lyapunov stability theory and the linear matrix inequality (LMI) method, a robust H &#x221E;  control strategy is designed to suppress the bullwhip effect caused by customer random demand. Thirdly, the impact of consumer channel preference, cross channel return and free riding behavior on inventory, production/ordering and profit in the supply chain system is studied by analyzing four different models, such as N-FC(without free riding behavior or cross channel return), Y-C(with cross channel return only), Y-F(with free riding behavior only), Y-FC(with both free riding behavior and cross channel return). Finally, the simulation tests are carried out to verify the performance of the robust control strategy, and some management insights and conclusions are summarized.

Robust Control Strategy for Dual-Channel Supply Chain with Free Riding Behavior and Cross-Channel Return