Explainable Data-driven Share-of-choice Product Line Design Optimization

TL;DR

This paper introduces an explainable, robust optimization approach for share-of-choice product line design that integrates survey data estimation, enhances interpretability, and suggests new survey questions for improved decision-making.

Contribution

It integrates polyhedral utility estimation into PLD optimization, providing explainability and a method to identify impactful survey questions.

Findings

Robust model maximizes worst-case share-of-choice with out-of-sample guarantees.

Dual reformulation enables attribution of product line decisions to survey data.

Column generation identifies survey questions that improve model performance.

Abstract

The share-of-choice (SOC) problem is a widely studied problem for product line design (PLD) where representative customers are sampled from a target population and the percentage of the ones who choose the offered products over outside options over the sample is maximized. The utility maximization framework captures individual choices. A significant challenge is that these utilities are not directly observable and must be estimated from other primitive data. Conjoint analysis is a commonly applied technique for generating such data, where sampled customers rate, rank, or choose between different product alternatives. With the responses, various methods, such as the hierarchical Bayesian method and polyhedral estimation, are employed to estimate the utilities. However, this " estimate-then-optimize" procedure disconnects the decision-making process from the primitive data and thus cannot attribute the PLD decision to the unresolved survey data. To fill the gap, we integrate the polyhedral estimation method into the PLD optimization, which constructs a polyhedron set containing all utilities consistent with the responses. Specifically, we proposed a robust model that maximizes the share-of-choice calculated by the worst-case utility over the polyhedron. The model brings threefold explainability to the PLD problem. First, it enables us to explore the influence of both estimation error and the number of sampled customers through an out-of-sample performance guarantee of the proposed model. Secondly, the linearly tractable equivalent reformulation constructed by the duality allows us to attribute the optimal product line to the survey data through the dual variables. Third, inspired by the fact that the survey questions are associated with columns in the dual reformulation, we propose a column generation approach to identify new questions that most effectively improve the model's objective.