Predicting Demand for New Products Using Polytope Volume and Benchmarking

This paper addresses the challenge of evaluating existing product alternatives and predicting demand for new entries. We target settings in which historical demand data for the entrant are unavailable or non-analogous, limiting the usefulness of fitted econometric or machine-learning demand models. To this end, two alternative approaches are proposed: the volume-based approach and the benchmarking-based approach. The former, serving as the theoretical backbone of both approaches, forms weight sets that represent the range of attribute weights under which an alternative is preferred over others. By calculating the volumes of these sets – a process involving the Double Description Method and the Quickhull algorithm – we quantify potential demand shifts from new product introductions. The latter approach – less computationally demanding – uses Data Envelopment Analysis as a core component to assess the efficiency of existing products. We also formulate super-efficiency programs to extend the analysis by measuring the degree to which a product alternative surpasses the efficiency frontier. This enables us to predict how the introduction of a new product will reshape the demand landscape. Graphical examples and an empirical illustration within the pharmaceutical industry, specifically focusing on the rather concentrated but competitive market for diabetes medications in Denmark, demonstrate the practical application and the similarity of the results of these approaches.