新产品分销密度的动态优化

本文讨论了新产品上市过程中的分销密度的动态诊断问题，旨在识别分销密度是否偏离最优的动态演化路径，进而帮助厂商获取最大化的新产品利润。从控制理论模型构建的角度出发，分销密度被视为控制变量，新产品销售量被视为状态变量，并基于泛函极值的动态规划方法，推导了分销密度的最优路径解。然后，以两组家电新产品的市场销售数据为样本，进行了应用算例分析。研究结果表明，本文推导的分销密度最优路径解，不仅能够有效提升制造商的销售利润，而且其形态会随着参数取值的差异，发生明显的变化。当分销密度导数对销售量的影响系数不断增大时，分销密度的最优路径会逐步收敛到一条直线。所以，在假设条件成立的前提下，本文的研究结果揭示出分销密度的动态演化规律，进而为制造商的新产品分销密度规划提供定量的决策依据。

Dynamic Optimization of Distribution Density of New Product

Issue of planning distribution density during the new product commercialization process for manufactures is discussed in this paper to diagnose the evolution of distribution density and therefore optimize the profit of new products. Based upon control theory, distribution density is set as a control variable, and sales as a state variable. Then, the optimization issue of new product distribution density is solved based on dynamic programming method. Further the optimization procedure for sales data of two electronic apparatus is applied to get the optimization trajectory. The type of sales data is time series which records distribution density, sales, and sales cost. The numerical result indicates that the optimization trajectory of new product distribution density can substantially improve the profit of new products and the shape of the optimization result is contingent on the parameters of the optimization procedure. As the impact coefficient of distribution density on sales increases, the optimization trajectory of distribution density will eventually converge to a straight line. Thus, if the assumptions of this paper are valid, the deduced optimization trajectory can uncover the dynamic regularities of distribution density and be a quantitative decision criterion of distribution density planning for manufactures.