A Random Consideration Set Model for Demand Estimation, Assortment Optimization, and Pricing

In this paper, we operationalize the random consideration set (RCS) choice model proposed by Manzini and Mariotti which assumes that consumers make purchase decisions based on a fixed preference ordering and random consideration sets drawn from independent attention probabilities. We provide a necessary condition, a sufficient condition, and a fast algorithm to estimate preference ordering and attention probabilities from sales transaction data, thereby uniquely identifying the model parameters. Additionally, we propose a greedy-like algorithm to find an assortment that maximizes total expected revenues. This algorithm can be easily adapted to handle cardinality constraints or to discover all efficient sets. Additionally, we explore profit optimization for a price-aware version of the RCS model and demonstrate that optimal profit margins and consumer surplus have the same ordering as the value gaps. Furthermore, we expand the model to include a random consideration-utility maximization framework, where consumers can have random preferences for products once consideration sets are formed. We develop an approximation algorithm with a 1/2 performance guarantee for this extended model. To validate our findings, we conduct a computational study using data provided by a major United States-based airline. The data set comprises 107 different flights serving various markets over a period of 120 days. By testing our models on this airline partner’s data, we demonstrate that the RCS model outperforms the mixed multinomial logit model in nearly half of the markets. These results align with the insights obtained from our synthetic study, indicating that the RCS model exhibits greater robustness when applied to input data sets with limited variations and smaller sizes.