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Consumer preference for product innovation/functionality has become increasingly diverse, therefore firms produce products with distinct versions/generations to satisfy consumers. This paper investigates the decision-making problem for multiple competitive firms considering consumers' diversified preferences for product functionality. This paper develops an optimization model, in which the profit-maximizing firms need to determine the production quantities of their products with different versions. Due to our model's computational complexity, it motivates us to adopt variational inequalities theory, which is applied to convert an original model into a new variational inequality problem. On this basis, the existence and uniqueness of an equilibrium solution are proved, and a high-efficient Euler algorithm is proposed. A case study focused on the 5G smartphone market is conducted. Numerical results show that firms may obtain more profits by producing products with newer versions if the consumer preference for product functionality is high. However, if the preference level of consumer is under a certain level, it is not necessarily beneficial for firms who launch new versions of their products to the demand market. In addition, when the competition in market becomes intensive (due to new entrants), giving up the production of previous-version products may be more conducive to existing firms.

Optimal production strategies of competitive firms considering product innovation