This paper develops a supply chain optimization model comprising multiple firms who compete in an oligopolistic manner. Each firm provides both non-green and green products to satisfy stochastic demand under consideration of consumer preference. With the goal of profit maximization, this paper assesses equilibrium decisions that firms face to determine production quantities and prices for these two types of products. An Euler algorithm is proposed with good characteristics for computation by applying variational inequality theory. Some numerical examples focusing on the doorbell market is conducted. The results show that if consumer green preference is high, producing more green products with higher prices while greatly improving their green levels are not necessarily conducive to firms. When green level achieves a certain level, firms may suffer a loss of their profits, even if green preference continues to improve. Thus, a well-designed green level can lead to firms obtaining more profits, while also benefit consumers. Furthermore, an increase of competition intensity brings disadvantage for firms, but this may yield a larger market share of green products. It is more advantageous if firms differentiate products with their rivals to reduce competition.