Market-System Design Optimization With Consider-Then-Choose Models

Design optimization in market system research commonly relies on Discrete choice analysis (DCA) to forecast sales and revenues for different product variants. Conventional DCA, which represents consumer choice as a compensatory process through maximization of a smooth utility function, has proven to be reasonably accurate at predicting choice and interfaces easily with engineering models. However, the marketing literature has documented significant improvement in modeling choice with the use of models that incorporate both noncompensatory (descriptive) and compensatory (predictive) components. This noncompensatory component can, for example, model a "consider-then-choose" process in which potential customers first narrow their decisions to a small set of products using noncompensatory screening rules and then employ a compensatory evaluation to select from within this consideration set. This article presents solutions to a design optimization challenge that arises when demand is modeled with a consider-then-choose model: the choice probabilities are no longer continuous or continuously differentiable. We examine two different classes of methods to solve optimal design problems-genetic algorithms (GAs) and nonlinear programming (NLP) relaxations based on complementarity constraints-for consider-then-choose models whose screening rules are based on conjunctive (logical "and") rules.