The Refined Assortment Optimization Problem

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 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.

Bounds, Heuristics, and Prophet Inequalities for Assortment Optimization

“…Finally, let R p−taop denote the optimal personalized revenue when the firm offers the optimal assortment to each segment and let R o be the best revenue using revenue-ordered assortments. We then have: The first inequality follows from Theorem 3, and the second inequality follows from a result in Berbeglia et al [2021b] (Theorem 1 in their paper) who proved that the revenue ordered bound holds against the personalized refined assortment optimization which yields at least R p−taop .…”

“…Recently, Lei et al [2020] considers the personalized assortment optimization problem when the firm must ensure that the assortment policy doesn't reveal private information using the differential privacy framework [Dwork, 2006]. Berbeglia et al [2021b] provides tight revenue guarantees on the performance of the well-known revenue-ordered assortment strategy with respect to the optimal personalized assortment solution. Their result holds for regular choice models (which includes all RUMs) and works even under personalized refined assortment optimization where the firm may reduce the product utilities to some consumer segments.…”

“…The p-TAOP has been the subject of recent attention, see e.g. El Housni and Topaloglu [2021], Chen et al [2021]) and is also related to the personalized refined assortment optimization problem (p-RAOP) introduced by Berbeglia et al [2021b]. Under the RAOP a firm is allowed to make some products less attractive to avoid demand cannibalization.…”