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.