銷售力之數學模型

Abstract

銷售力一直是一個企業關切的主要議題，借助Vidale-Wolfe數學模型，我們提出一個銷售力數學模型。藉由熱傳導方程，刻畫由資訊交流產生的自身銷售力。在資訊交流及商品促銷下產生的銷售力，可經由非齊次熱傳導方程描繪。然而，我們無法以單一非齊次熱傳導方程描繪所有情況，因此，模型建立與問題解決須於不同情況下逐一地討論。\n 透過充分的數據，銷售力是可以被預估的；另外，我們也可以利用此模型，對於行銷策略加以評估。\n 異於以往大部分的研究，此模型加入了空間上的概念，對於傳導現象而言，這是相當重要的。

Sale intensity is always one of the major subjects that business is concerned\nabout. We propose a mathematical model based on the concept given by\nVidale-Wolfe to characterize the behavior of sale intensity.\n Using the sense of diffusion in heat equation, we could characterize the\nbehavior of sale intensity starting from the spontaneous sale intensity caused\nby the circulating of information. The behavior of changing on sale intensity under the effect of diffusing by\nthe circulating of information and the promoting activities can be generally\nmodeled as nonhomogeneous heat equations. However, because of the great difference between cases, the problem\nformulating and model solving cannot be generally modeled as one certain\nnonhomogeneous heat equation and are restricted to be discussed case by case.%\n The further sale intensity is predictable possibly with sufficient data, but\nwithout sufficient data, we can also use the model to appraise the\nspontaneous sale intensity and the benefit of each advertising strategy in\npractical.\n Different from most previous relevant studies, the model supports the studies of sale\nintensity diffusing over geographic regions, which is especially of significance\nin spontaneous sale intensity.