In this paper, a multi-objective decision-making model with birandom parameters is proposed. A birandom simulation technique is developed to tackle general birandom objective functions and birandom constraints. Combined with a birandom simulation technique, a genetic algorithm is designed for solving a birandom multi-objective decision-making problem. The proposed model and algorithm are applied to a hydropower station operation problem. The stochastic model and fuzzy programming approach are used for comparison to illustrate the usefulness of the proposed model and algorithm.