The Refined Assortment Optimization Problem

TL;DR

This paper introduces the refined assortment optimization problem, allowing firms to restrict product access rather than remove products, leading to significantly higher potential revenue and new heuristic strategies with proven performance guarantees.

Contribution

It formulates the refined assortment optimization problem, analyzes its benefits over traditional methods, and develops improved heuristics with performance bounds.

Findings

Refined assortment can yield up to min(n,m) times more revenue.

Revenue-ordered heuristics maintain similar guarantees in refined settings.

Tight bounds are established for revenue ratios under various choice models.

Abstract

We introduce the refined assortment optimization problem where a firm may decide to make some of its products harder to get instead of making them unavailable as in the traditional assortment optimization problem. Airlines, for example, offer fares with severe restrictions rather than making them unavailable. This is a more subtle way of handling the trade-off between demand induction and demand cannibalization. For the latent class MNL model, a firm that engages in refined assortment optimization can make up to $\min(n,m)$ times more than one that insists on traditional assortment optimization, where $n$ is the number of products and $m$ the number of customer types. Surprisingly, the revenue-ordered assortment heuristic has the same performance guarantees relative to {\em personalized} refined assortment optimization as it does to traditional assortment optimization. Based on this finding, we construct refinements of the revenue-order heuristic and measure their improved performance relative to the revenue-ordered assortment and the optimal traditional assortment optimization problem. We also provide tight bounds on the ratio of the expected revenues for the refined versus the traditional assortment optimization for some well known discrete choice models.