Demand modeling in the presence of unobserved lost sales data

We present an integrated mixed-integer programming (MIP) approach to parameter estimation for discrete choice demand models where data for one or more choice alternatives are censored. We jointly determine the prediction parameters associated with a time-varying customer arrival rate and their substitutive choices and recover (near-) optimal parameter values with respect to the chosen loss-minimization objective. We propose a dual-layer estimation model extension that learns the unobserved market shares of competitors. We test these models on simulated and real data, and present results for a variety of demand prediction scenarios: single-item, multi item, and large-scale instances.