Mixed Integer Nonlinear Programming Model for Positioning a New Product in a Multiattribute Space with Risk

This is a marketing problem faced by a firm which wishes to position a new brand product in an existing product class. It is natural that an individual choice for his/her most preferred products are influenced essentially by the perceptions and values of the products (e. g. the design of the product). Individuals usually differ in their choice of an object out of an existing set, and they would also differ if asked to specify an ideal object. Due to these differences, the aim of the problem considered here is to optimally design a new product in order to attract the largest number of consumers. This paper addresses a mixed integer nonlinear programming model to formulate the positioning problem. A direct search approach is proposed to solve the model. A computational experience is presented.