Data Envelopment Approximation model in the Stochastic Frontier Analysis and Its Application to TV Advertising Planning

这份报告关注的是电视广告的效率。过去对广告的大量研究都集中在广告效果上。另一方面，尽管广告生产率(或效率)已被确定为一个重要的问题，但对广告生产率的研究仍然有限。效率是通过观测产量(S)与从给定投入(S)可获得的最大潜在产量(S)的比率来衡量的。前沿分析涉及广告效率。然而，在一些情况下，很难知道前沿的功能知名度，例如，由于电视广告中的许多因素，给定某一电视广告在一天中重复插入的次数，受众的最大知晓值。在本文中，基于DEA，我们提出了基于DEA的随机前沿模型中优化问题的数据包络近似(DEAP)模型。作为应用，我们描述了在CM-Karte使用过去的电视广告的广告预算约束下，为了最大限度地提高“CM意识”，日间广告的最优位置分配；2.我们还使用了另一种DEA方法来解决某一电视广告重复插入日间时段的问题，以便同时达到每个目标细分市场的最大“可达性”。一般而言，由于时间间隔的精细划分，在广告预算内存在大量的日间组合。因此，通过生成多种个体分配模式，探索DEA逐步定位的有效分配，研究了广告预算约束下的近似最优日间分配问题。

This report is concerned with TV advertising efficiency.The substantial volume of the past research on advertising has focused on advertising effectiveness. On the other hand, although advertising productivity (or efficiency) has been identified as an important issue, research on advertising productivity is still limited. The efficiency is measured by the ratio of observed oulput(s) to maximum potential output(s) obtainable from the given input(s). The frontier analysis addresses advertising efficiency. There are, however, not least situations in which it is difficult to know the functional fame of the frontier, for instance, the maximum awareness value of the audiences given the number of repetitive insertions of a certain TV commercial to dayparts because of many factors in TV advertising.In this report,1. we proposed the data envelopment approximation (DEAP) model for an optimization problem in the stochastic frontier model with unknown functional form of the frontier based on DEA. As an application, we described the optimal allocation of spots to dayparts so as to maximize the "CM- awareness" under the constraint of advertising budget using the past TV commertials by CM-KARTE;2. we also employed another DEA approach to the problem of repetitive insertions of a certain TV commercial to dayparts so as to attain the maximum "reach" of each target segment simultaneously. In general, there are enormous daypart combinations within an advertising budget because of a fine partition of time interval of day. Therefore, generating many individual allocating patterns and exploring efficient allocations which are progressively located by DEA, a near optimal daypart allocation under the constraint of advertising budget is examined.