关键词: 报童问题, 技术创新, 生产决策, 联合优化

Abstract: Technological innovation can reduce unit manufacturing costs, which in turn influences production decisions. Changes in production quantities can also affect the level of technological innovation. In this context, we address the joint decision-making problem of technology innovation intensity and product output for a manufacturing firm by constructing a newsvendor model involving two decision variables. First, we prove the existence of an optimal solution to this problem. Subsequently, we establish a sufficient condition-by imposing a mild restriction on the demand distribution function-that ensures the uniqueness of the solution. We then analyze the impact of the firm’s innovation capability, retail price and unit production cost on its strategic decisions with the following key findings:
   The firm’s innovation capability significantly influences both the intensity of technological innovation and its output strategy. Generally, higher innovation capability-up to a certain threshold-leads to greater output and stronger innovation intensity. Beyond this threshold, further increases in innovation capability no longer impact output or innovation intensity. Notably, if the firm has no innovation capability, no technological innovation will be undertaken.
   Retail price and unit production cost also play a critical role in determining both the intensity of technological innovation and the firm’s production strategy. Output and innovation intensity increase with retail price, though their relationship with unit production cost is more complex. As retail prices rise, output continues to increase, while innovation intensity grows until it reaches a maximum point. However, the relationship between innovation intensity and unit cost is not monotonic. There are two key exceptions: (1) when innovation capability is particularly strong, optimal innovation intensity will rise with production costs; and (2) output decreases as unit costs rise, especially when production costs at least double the minimum cost achievable with current technology. From an industry-wide perspective, firms with higher pre-innovation costs continue to face higher post-innovation costs than those with lower initial costs, despite adopting more intensive innovation strategies.
   Additionally, we propose a hypothesis regarding the demand distribution function that guarantees the uniqueness of the optimal solution. This hypothesis can serve as a reference for future research. Furthermore, we provide criteria to determine whether this hypothesis holds for uniform, negative exponential and normal distributions. Notably, the methods outlined in this paper, particularly for normal distribution, can be extended to other continuous distributions, such as the power, Weibull, gamma and beta distributions.

Key words: newsvendor problem, technological innovation, production decision, joint optimization