Effective order allocation has a great impact on improving the efficiency of supply chain operations. This paper investigates a high-dimensional stochastic order allocation problem that assigns uncertain customer orders to heterogeneous parallel machines. Considering the arrival uncertainty of customer orders in the real-world production environment, a mathematical model of the investigated problem is established with the objective of maximizing the expected profit of order processing. A novel intelligent stochastic optimization approach is proposed by combining a modified adaptive large neighborhood search algorithm with a scenario generation technique. In this approach, the modified adaptive large neighborhood search algorithm suitable for the generalized allocation problem is proposed to seek the best solutions, while the scenario generation technique is used to generate the scenarios needed to evaluate the solutions of the high-dimensional stochastic optimization problem. Experimental results demonstrate that the proposed approach outperforms the compared stochastic optimization method in terms of optimization efficiency and optimization ability.