Multiple-Purchase Choice Model : Estimation and Optimization

Although multiple-purchase behavior is typical in retail practice, the choice model to portray such behavior is rare in existing research. This paper presents a new multiple-purchase (MP) choice model based on the multinomial logit (MNL) choice model, which allows customers to purchase more than one item in a single visit. We first prove that the log-likelihood function based on our MP choice model has a nice concave property such that we can efficiently estimate the parameters in the model with data. Then, we identify that a revenue-ordered assortment may not be optimal for an assortment optimization problem under the MP choice model. Moreover, there may be no inclusion between the optimal solutions obtained from the assortment problem based on our model and the MNL model. Next, we present an equivalent mixed-integer program for the multiple-purchase assortment optimization, which can be solved by state-of-the-art commercial solvers. Finally, we conduct extensive numerical experiments to evaluate the benefits from the MP choice model in both estimation and optimization problems. We first conduct a case study on a real-world dataset. The numerical results show that our MP choice model performs better in three estimation metrics and one revenue metric than the MNL choice model. Then, we demonstrate the advantage of the MP choice model on simulated data. Our model can provide significant realized revenue improvement compared with that obtained by the single-purchase MNL choice model in numerical results