The advancement of Industrial Internet of Things (IIoT), blockchain, and cyber-physical systems technologies has brought new possibilities for achieving information sharing and traceability. Due to this, in customized manufacturing, enterprises typically address challenges in inventory management, production, and delivery through external supplier warehouses, capacity adjustment, and third-party logistics companies, respectively. However, the independent optimization of these three components often results in significant efficiency losses and resource waste. Moreover, the inherent demand uncertainty in customized manufacturing, such as uncertainties in product variety, material requirements, and delivery specifications, further complicates the efficient coordination among order picking, production, and delivery phases. Therefore, in this paper, under the condition of uncertain demand, this paper constructs a three-stage integrated optimization model for order picking, production, and delivery as a mixed-integer linear programming (MILP) model, aiming to maximize profit, then achieving efficient scheduling across multiple stages. Furthermore, this study develops an improved genetic algorithm (GA) combined with a greedy algorithm and 2-opt algorithm to solve large-scale problems effectively. By comparing the improved GA with CPLEX, the effectiveness and flexibility of the proposed model and algorithm under conditions of demand uncertainty can be validated.