Product line optimisation based on semiparametric choice model

Consumer choice behaviour is important in the product line optimisation problem. The extant literature on product line optimisation is mostly based on traditional consumer choice models, such as the multinomial logit and multinomial probit models. These models either assume that the utility errors are independent from irrelevant alternatives (IIA) or are limited by complex calculation processes or pre-given, specific distributions of measuring errors. The marginal moment model (MMM), which is classified as a semiparametric choice model, does not require specific distributions of errors; thus, it can overcome the IIA shortcoming. This study focuses on the concavity of the profit functions of a product line optimisation model based on MMM. We prove that the profit function based on MMM is concave in market share under a monopoly or oligopoly. Numerical experiments show that the choice probabilities obtained from the MMM, multinomial logit, and multinomial probit models are similar although they are obtained under different assumptions. Experimental results under monopolistic, Cournot, and Bertrand competition based on MMM are compared. Some interesting managerial insights are summarised based on the sensitivity analysis of the various model parameters.