Robust product line pricing under the multinomial logit choice model

Incorporating consumer choice behavior into a product line design optimization model enhances the understanding of consumer choices and improves the opportunities to increase profit. Most product line optimization problems assume that parameters are precisely known in consumer choice model. However, the decision maker does not precisely know the model parameters because of insufficient sample data, measurement problems, and other factors. We investigate the problem of establishing robust product line pricing under a multinomial logit model to account for the uncertainty of the valuation parameter. First, we present a nominal product line model to maximize profit. We then establish a robust product line model to maximize the worst-case expected profit, where the valuation parameter lies in an uncertainty set. We consider both single and multiple products development and derive the optimal prices' closed-form expressions. Through numerical experiments, we illustrate the benefit of robust product line pricing to address parameter uncertainty. We demonstrate that the difference between the expected nominal profit and the worst-case profit increases with the increase of the interval of the uncertainty set, and the robust profit relative to the worst-case nominal profit improves. The robust product line design can ensure steadier, even higher profit.