Currently, distributed supply chain production planning (SCPP) is a practical problem affecting global supply chain production. Distributed SCPP is a complex constraint satisfaction problem (CSP) comprising a series of constraints intra- and inter-production members on orders, capacity, and materials. Previous studies have proposed various advanced planning and scheduling (APS) algorithms for companies to solve internal CSPs related to production planning. Distributed SCPP problems additionally require a coordination approach to resolve conflicts among the production plans of individual production members. Several distributed CSP (DCSP) algorithms have been proposed to guide the coordination for various DCSP conditions and objectives. Based on these techniques, we propose a coordination approach for achieving consistency among individual production plans to develop an integral supply chain production plan. First, we employed an APS system to resolve the internal production planning constraints and to develop a feasible production plan for each production member. Next, we developed a hybrid DCSP coordination algorithm based on agent-ordering asynchronous weak-commitment search (AWS) algorithm and asynchronous incremental relaxation (IR) algorithm concepts to facilitate production planning coordination and resolve constraint conflicts among individual production plans. Finally, a thin-film transistor liquid crystal display (TFT-LCD) supply chain was used to illustrate and verify the proposed coordination approach.