Product Line Design with Interdependent Products

In this paper, we propose a method based on semidefinite programming to solve a product line design problem, and obtain a new discrete choice model as a by-product. Our choice model termed as the Cross Moment (CMM) model is parsimonious in that it uses only the mean and covariance information of the utility functions. It is computationally tractable using semidefinite optimization and does not have the inherent behavioral limitations of the classical Multinomial Logit (MNL) model, nor the associated complexity in the Probit or the Random Coefficient model. We use the CMM model to solve a flexible packaging design problem confronting a local service parts supplier. The strength of the model lies in its ability to deal with situations where the products share many common attributes. We compare the performance of the MNL and CMM model in this product line design problem. Experimental results using real data suggests that our approach can lead to a better product line design, and can perform significantly better than the direct approach using the MNL model.