Optimal product positioning with consideration of negative utility effect on consumer choice rule

In most studies related to product positioning, probabilistic consumer choice rules assume that a product always gains some market share no matter how small a product's utility value is or even if the utility value is negative. Some researchers have considered this problem in multidimensional-scaling-based model or share-of-surplus choice rule. In this study, we consider this problem for multinomial logit rule by introducing a piecewise function and establishing a conjoint-analysis-based one-step optimization model for product positioning. Interval analysis is applied to obtain the optimal price of the new product from the model, and the mathematical properties of the profit-maximizing model are analyzed. An interval-analysis-embedded Tabu Search (TS) algorithm is developed for solving the model. An industrial application employing the proposed model and the interval-analysis-based enumeration method is presented and sensitivity analysis is performed. An experiment for randomly created large-scale product positioning problems is carried out to evaluate the feasibility of the proposed TS algorithm. ► A product positioning model is established considering the negative utility. ► The pricing-sub-model in an unpartitioned market has been proved unimodal. ► A bi-search algorithm based on interval analysis is developed.