arXiv subjects

Alvaro Flores

Publications and source records attributed to Alvaro Flores.

4 recordsLinked to original sources

arXiv2021

The Refined Assortment Optimization Problem

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.

econ.TH↗

arXiv2019

Assortment and Price Optimization Under the Two-Stage Luce model

This paper studies assortment and pricing optimization problems under the Two-Stage Luce model (2SLM), a discrete choice model introduced by Echenique and Saito (2018) that generalizes the multinomial logit model (MNL). The model employs an utility function as in the the MNL, and a dominance relation between products. When consumers are offered an assortmentS , they first discard all dominated products in S and then select one of the remaining products using the standard MNL. This model may violate the regularity condition, which states that the probability of choosing a product cannot increase if the offer set is enlarged. Therefore, the 2SLM falls outside the large family of discrete choice models based on random utility which contains almost all choice models studied in revenue management. We prove that the assortment problem under the 2SLM is polynomial-time solvable. Moreover, we show that the capacitated assortment optimization problem is NP-hard and but it admits polynomial-time algorithms for the relevant special cases cases where (1) the dominance relation is attractiveness-correlated and (2) its transitive reduction is a forest. The proofs exploit a strong connection between assortments under the 2SLM and independent sets in comparability graphs. Finally, we study the associated joint pricing and assortment problem under this model. First, we show that well known optimal pricing policy for the MNL can be arbitrarily bad. Our main result in this section is the development of an efficient algorithm for this pricing problem. The resulting optimal pricing strategy is simple to describe: it assigns the same price for all products, except for the one with the highest attractiveness and as well as for the one with the lowest attractiveness.

cs.DM↗

arXiv2018

Assortment Optimization under the Sequential Multinomial Logit Model

We study the assortment optimization problem under the Sequential Multinomial Logit (SML), a discrete choice model that generalizes the multinomial logit (MNL). Under the SML model, products are partitioned into two levels, to capture differences in attractiveness, brand awareness and, or visibility of the products in the market. When a consumer is presented with an assortment of products, she first considers products in the first level and, if none of them is purchased, products in the second level are considered. This model is a special case of the Perception-Adjusted Luce Model (PALM) recently proposed by Echenique et al (2018). It can explain many behavioural phenomena such as the attraction, compromise, similarity effects and choice overload which cannot be explained by the MNL model or any discrete choice model based on random utility. In particular, the SML model allows violations to regularity which states that the probability of choosing a product cannot increase if the offer set is enlarged. This paper shows that the seminal concept of revenue-ordered assortment sets, which contain an optimal assortment under the MNL model, can be generalized to the SML model. More precisely, the paper proves that all optimal assortments under the SML are revenue-ordered by level, a natural generalization of revenue-ordered assortments that contains, at most, a quadratic number of assortments. As a corollary, assortment optimization under the SML is polynomial-time solvable. This result is particularly interesting given that the SML model does not satisfy the regularity condition and, therefore, it can explain choice behaviours that cannot be explained by any choice model based on random utility.

cs.DM↗

arXiv2016

Trial-Offer Markets with Continuation

Trial-offer markets, where customers can sample a product before deciding whether to buy it, are ubiquitous in the online experience. Their static and dynamic properties are often studied by assuming that consumers follow a multinomial logit model and try exactly one product. In this paper, we study how to generalize existing results to a more realistic setting where consumers can try multiple products. We show that a multinomial logit model with continuation can be reduced to a standard multinomial logit model with different appeal and product qualities. We examine the consequences of this reduction on the performance and predictability of the market, the role of social influence, and the ranking policies.

cs.GT↗