考虑负效用问题的新产品定位模型及算法

Model and algorithm for new product positioning with negative utility

在新产品定位的顾客选择行为分析中,概率选择规则更能真实地反映顾客选择行为,然而由于该规则是假设顾客对所有产品的选择概率均为非零,即存在顾客选择效用值为负的产品的情况,因此这一假设在实际中并不合理.目前已经有一些学者认识到这个问题,但是针对负效用这一问题尚没有关于概率选择规则中的多项式分对数规则的研究.本文建立了一个基于多项式分对数规则的新产品定位模型,该模型考虑了顾客选择行为中负效用问题,讨论了小规模问题的精确求解方法.证明了在无细分市场环境下,该模型的目标是一个单峰函数,可以采用标准的非线性优化方法进行求解;在细分市场环境下,可以采用本文设计的基于二分搜索的区间分析算法求得全局最优解.

In the researches related to consumer choice behavior analysis, the probabilistic consumer choice rules can reflect customer choice behavior more truly. However, because this rule assumes that the choice prob- ability is always non-negative which will result in the situation that customers choose the product with negative utility, it is not realistic in practice. Some researchers have realized the problem but there is no research on multinomial logit rule among probabilistic consumer choice rules directing at the problem of negative utility. In this research, a conjoint-analysis-based one-step optimization model for product positioning based on multi- nomial logit rule is established. The negative utility problem in consumer choice behavior is considered in the model. An exact algorithm for small-scale problems is proposed. This research proves that, in an unpartitioned product market, the objective of the model is a unimodal function and therefore the standard non-linear opti- mization algorithms can be applied; a bi-search algorithm based on interval analysis is developed to solve the proposed model in a multi-segment market.