Demand Estimation under Uncertain Consideration Sets

To estimate customer demand, choice models rely both on what the individuals do and do not purchase. A customer may not purchase a product because it was not offered, but also because it was not considered. To account for this behavior, existing literature has proposed the so-called consider-then-choose (CTC) models, which posit that customers sample a consideration set and then choose the most preferred product from the intersection of the offer set and the consideration set. CTC models have been studied quite extensively in the marketing literature. More recently, they have gained popularity within the Operations Management literature to make assortment and pricing decisions. Despite their richness, CTC models are difficult to estimate in practice because firms do not observe customers’ consideration sets. Therefore, the common assumption in operations has been that customers consider everything on offer, so the offer set is the same as the consideration set. This raises the following question: when firms only collect transaction data, do CTC models offer any predictive advantage over the classic choice models? More precisely, under what conditions do CTC models outperform (if ever) classic choice models in terms of prediction accuracy?

In this work, we study a general class of CTC models. We propose techniques to estimate these models efficiently from sales transaction data. We then compare their performance against the classic approach. We find that CTC models outperform standard choice models when there is noise in the offer set information and the noise is asymmetric across the training and test offer sets, but otherwise offer no particular predictive advantage over the classic approach. We demonstrate the benefits of using the CTC models in real-world retail and online platform settings. In particular, we show that CTC models calibrated on transaction data are better at long-term and warehouse level sales forecasts. We also find that offer sets are difficult to accurately define in online platform settings because customers usually only consider a small subset of all the available listings in the platform. In fact, CTC models significantly outperform standard choice models in online platform settings.