Decision Forest: A Nonparametric Approach to Modeling Irrational Choice

Customer behavior is often assumed to follow weak rationality, which implies that adding a product to an assortment will not increase the choice probability of another product in that assortment. However, an increasing amount of research has revealed that customers are not necessarily rational when making decisions. In this paper, we propose a new nonparametric choice model that relaxes this assumption and can model a wider range of customer behavior, such as decoy effects between products. In this model, each customer type is associated with a binary decision tree, which represents a decision process for making a purchase based on checking for the existence of specific products in the assortment. Together with a probability distribution over customer types, we show that the resulting model -- a decision forest -- is able to represent any customer choice model, including models that are inconsistent with weak rationality. We theoretically characterize the depth of the forest needed to fit a data set of historical assortments and prove that with high probability, a forest whose depth scales logarithmically in the number of assortments is sufficient to fit most data sets. We also propose two practical algorithms -- one based on column generation and one based on random sampling -- for estimating such models from data. Using synthetic data and real transaction data exhibiting non-rational behavior, we show that the model outperforms both rational and non-rational benchmark models in out-of-sample predictive ability.Comment: The paper is forthcoming in Management Science (accepted on July 25, 2021

Assortment optimization using an attraction model in an omnichannel environment

Making assortment decisions is becoming an increasingly difficult task for many retailers worldwide as they implement omnichannel initiatives. Discrete choice modeling lies at the core of this challenge, yet existing models do not sufficiently account for the complex shopping behavior of customers in an omnichannel environment. In this paper, we introduce a discrete choice model called the multichannel attraction model (MAM). A key feature of the MAM is that it specifically accounts for both the product substitution behavior of customers within each channel and the switching behavior between channels. We formulate the corresponding assortment optimization problem as a mixed integer linear program and provide a computationally efficient heuristic method that can be readily used for obtaining high-quality solutions in large-scale omnichannel environments. We also present three different methods to estimate the MAM parameters based on aggregate sales transaction data. Finally, we describe general effects of the implementation of widely-used omnichannel initiatives on the MAM parameters, and carry out numerical experiments to explore the structure of optimal assortments, thereby gaining new insights into omnichannel assortment optimization. Our work provides the analytical framework for future studies to assess the impact of different omnichannel initiatives

Retail Demand Management: Forecasting, Assortment Planning and Pricing

In the first part of the dissertation, we focus on the retailer\u27s problem of forecasting demand for products in a category (including those that they have never carried before), optimizing the selected assortment, and customizing the assortment by store to maximize chain-wide revenues or profits. We develop algorithms for demand forecasting and assortment optimization, and demonstrate their use in practical applications. In the second part, we study the sensitivity of the optimal assortment to the underlying assumptions made about demand, substitution and inventory. In particular, we explore the impact of choice model mis-specification and ignoring stock-outs on the optimal profits. We develop bounds on the optimality gap in terms of demand variability, in-stock rate and consumer heterogeneity. Understanding this sensitivity is key to developing more robust approaches to assortment optimization. In the third and final part of the dissertation, we study how the seat value perceived by consumers attending an event in a stadium, depends on the location of their seat relative to the field. We develop a measure of seat value, called the Seat Value Index (SVI), and relate it to seat location and consumer characteristics. We apply our methodology to a proprietary dataset collected by a professional baseball franchise in Japan. Based on the observed heterogeneity in SVI, we provide segment-specific pricing recommendations to achieve a service level objective