On the product line selection problem under attraction choice models of consumer behavior

Product line design (PLD) involves important decisions at the interface of operations and marketing that are very costly to implement and change, and, simultaneously, determinant for market success. To evaluate the financial performance of a product line, a number of mathematical programming approaches have been proposed. Problem formulations are typically mixed or pure integer non-linear optimization models that are intractable for exact solution - in particular when empirically supported consumer choice models are incorporated. In this note, we present an exact approach for determining a profit-maximizing product line with continuous prices when consumers choose among available products according to a general and widely applied attraction choice model including the MNL, the BTL, the MCI, and approximately the first choice model. In particular, we show how to efficiently exploit the structural properties resulting from attraction models when consumer behavior is (a) modelled at the aggregate level or (b) disaggregated into customer segments in such a way that each segment can be offered a customized price - a strategy that firms more and more engage in, recognizing it to be not only very profitable but also implementable in the era of e-business. Under these assumptions, we can transform the standard MINLP formulation of the PLD problem into a more convenient convex MIP that can be solved globally with current solvers even for large instances with ten-thousands of products in reasonable time. Therefore our work contributes by accommodating a new trend increasingly encountered in practice and by providing an efficient exact approach to profit-driven PLD for real-world applications.