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| Title: | 銷售力之數學模型
A Mathematical Model Model on Sale Intensity |
| Authors: | 林雨農 |
| Contributors: | 李明融
林雨農 |
| Keywords: | 傳導方程
銷售力
擴散係數
heat equation
sale intensity
diffusion coefficient |
| Date: | 2006 |
| Issue Date: | 2009-09-17 13:47:00 (UTC+8) |
| 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。
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。
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
about. We propose a mathematical model based on the concept given by
Vidale-Wolfe to characterize the behavior of sale intensity.
Using the sense of diffusion in heat equation, we could characterize the
behavior of sale intensity starting from the spontaneous sale intensity caused
by the circulating of information. The behavior of changing on sale intensity under the effect of diffusing by
the circulating of information and the promoting activities can be generally
modeled as nonhomogeneous heat equations. However, because of the great difference between cases, the problem
formulating and model solving cannot be generally modeled as one certain
nonhomogeneous heat equation and are restricted to be discussed case by case.%
The further sale intensity is predictable possibly with sufficient data, but
without sufficient data, we can also use the model to appraise the
spontaneous sale intensity and the benefit of each advertising strategy in
practical.
Different from most previous relevant studies, the model supports the studies of sale
intensity diffusing over geographic regions, which is especially of significance
in spontaneous sale intensity. |
| Reference: | [1] Vidale, M.L., and Wolfe, H.B., An Operation Research Study for Sale Responce
to Advertising , Operations Research 5 (1957), 370-381.
[2] Nerlove, M., and J.K. Arrow, Optimal Advertising Policy Under Dynamic Conditions
, Econamica, 29 (1962), 129-142.
[3] Kaliappan, P., nonlinear heat equations: An exact solution for travelling waves
of ut = Duxx + u ¡ uk: , Physica D. 11 (1984), 368-374.
[4] Marinelli Carlo, and Savin Sergei, Optimal distributed dynamic advertising,
eprint arXiv:math, 0406435 (2004).
[5] Agmon,S., Lectures on Elliptic Boundary Value Problems , D. Van Nostrand
Co., Princeton,1965. 29 (1965).
[6] Nerlove, M., and J.K. Arrow, Mathmetical Methods in Optimization of Differential
Systems, Kluwer,Dorrecht, (1995).
[7] Bronnenberg, B.J., and V. Mahajan, Unobserved Retailer Behavior in Multi-
Market data:Joint Spatial Dependence in Market Shares and Promotion Variables
, Marketing Science, 20 (2001), 284-299.
[8] Dube, J.P., and P. Manchanda, Difference in Dynamic Brand Competition
across Markets: An Empirical Analysis, Forthcoming Marketing Science, (2004).
[9] Feichtinger, G., Hartl, R.F., and S.P. Sethi, Dynamic Optimal Control Model in
Advertising: Resent Developments, Management Science, 40 (1994),195-226. |
| Description: | 碩士
國立政治大學
應用數學研究所
93751008
95 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0093751008 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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