On the optimal product line selection problem with price discrimination

Product line design decisions are determinant for a firm's market success and, simultaneously, very costly to implement and change. To evaluate the profitability of a design, a number of mathematical programming approaches have been proposed in the last three decades–typically nonlinear integer optimization problems that can only be tackled heuristically for real-world instances. Recently, Chen and Hausman (2000) efficiently exploited the fractional programming properties of a stylized model for product line and price selection with the objective to maximize contribution given homogeneous customer behavior by an aggregate multinomial logit choice model. We extend the approach of Chen and Hausman (2000) to determine an optimal product line under a personalized or group pricing strategy in markets with multiple heterogeneous consumers such that total profit (including fixed costs) is maximized. Personalized/group pricing is a growing discrimination strategy that more and more businesses are realizing is not only very profitable, but also often implementable in the era of e-business. Our problem formulation allows to incorporate commonly applied attraction choice models including the multinomial logit, the Bradley–Terry–Luce, and approximately the first choice model. Though the problem is generally nonlinear, we show that the fractional substructure resulting from attraction choice models can still be exploited to globally solve real-world instances in reasonable time.