Greedy-Like Algorithms for Dynamic Assortment Planning Under Multinomial Logit Preferences

We study the joint assortment planning and inventory management problem, where stock-out events elicit dynamic substitution effects, described by the multinomial logit (MNL) choice model. Special cases of this setting have been extensively studied in recent literature, notably the static assortment planning problem. Nevertheless, to our knowledge, the general formulation is not known to admit efficient algorithms with analytical performance guarantees before this work, and most of its computational aspects are still wide open. In this paper, we devise what is, to our knowledge, the first provably good approximation algorithm for dynamic assortment planning under the MNL model. We derive a constant-factor guarantee for a broad class of demand distributions that satisfy the increasing failure rate property. Our algorithm relies on a combination of greedy procedures, where stocking decisions are restricted to specific classes of products and the objective function takes modified forms. We demonstrate that our approach substantially outperforms state-of-the-art heuristic methods in terms of performance and speed, leading to an average revenue gain of 4% to 12% in computational experiments. In the course of establishing our main result, we develop new algorithmic ideas that may be of independent interest. These include weaker notions of submodularity and monotonicity, shown sufficient to obtain constant-factor worst-case guarantees, despite using noisy estimates of the objective functio

Dynamic Assortment Optimization with Changing Contextual Information

In this paper, we study the dynamic assortment optimization problem under a finite selling season of length $T$. At each time period, the seller offers an arriving customer an assortment of substitutable products under a cardinality constraint, and the customer makes the purchase among offered products according to a discrete choice model. Most existing work associates each product with a real-valued fixed mean utility and assumes a multinomial logit choice (MNL) model. In many practical applications, feature/contexutal information of products is readily available. In this paper, we incorporate the feature information by assuming a linear relationship between the mean utility and the feature. In addition, we allow the feature information of products to change over time so that the underlying choice model can also be non-stationary. To solve the dynamic assortment optimization under this changing contextual MNL model, we need to simultaneously learn the underlying unknown coefficient and makes the decision on the assortment. To this end, we develop an upper confidence bound (UCB) based policy and establish the regret bound on the order of $\widetilde O(d\sqrt{T})$, where $d$ is the dimension of the feature and $\widetilde O$ suppresses logarithmic dependence. We further established the lower bound $\Omega(d\sqrt{T}/K)$ where $K$ is the cardinality constraint of an offered assortment, which is usually small. When $K$ is a constant, our policy is optimal up to logarithmic factors. In the exploitation phase of the UCB algorithm, we need to solve a combinatorial optimization for assortment optimization based on the learned information. We further develop an approximation algorithm and an efficient greedy heuristic. The effectiveness of the proposed policy is further demonstrated by our numerical studies.Comment: 4 pages, 4 figures. Minor revision and polishing of presentatio

A review of choice-based revenue management : theory and methods

Over the last fifteen years, the theory and practice of revenue management has experienced significant developments due to the need to incorporate customer choice behavior. In this paper, we portray these developments by reviewing the key literature on choice-based revenue management, specifically focusing on methodological publications of availability control over the years 2004–2017. For this purpose, we first state the choice-based network revenue management problem by formulating the underlying dynamic program, and structure the review according to its components and the resulting inherent challenges. In particular, we first focus on the demand modeling by giving an overview of popular choice models, discussing their properties, and describing estimation procedures relevant to choice-based revenue management. Second, we elaborate on assortment optimization, which is a fundamental component of the problem. Third, we describe recent developments on tackling the entire control problem. We also discuss the relation to dynamic pricing. Finally, we give directions for future research

Online Joint Assortment-Inventory Optimization under MNL Choices

We study an online joint assortment-inventory optimization problem, in which we assume that the choice behavior of each customer follows the Multinomial Logit (MNL) choice model, and the attraction parameters are unknown a priori. The retailer makes periodic assortment and inventory decisions to dynamically learn from the realized demands about the attraction parameters while maximizing the expected total profit over time. In this paper, we propose a novel algorithm that can effectively balance the exploration and exploitation in the online decision-making of assortment and inventory. Our algorithm builds on a new estimator for the MNL attraction parameters, a novel approach to incentivize exploration by adaptively tuning certain known and unknown parameters, and an optimization oracle to static single-cycle assortment-inventory planning problems with given parameters. We establish a regret upper bound for our algorithm and a lower bound for the online joint assortment-inventory optimization problem, suggesting that our algorithm achieves nearly optimal regret rate, provided that the static optimization oracle is exact. Then we incorporate more practical approximate static optimization oracles into our algorithm, and bound from above the impact of static optimization errors on the regret of our algorithm. At last, we perform numerical studies to demonstrate the effectiveness of our proposed algorithm

Product Line Design, Pricing and Framing under General Choice Models

This thesis handles fundamental problems faced by retailers everyday: how do consumers make choices from an enormous variety of products? How to design a product portfolio to maximize the expected profit given consumers’ choice behavior? How to frame products if consumers’ choices are influenced by the display location? We solve those problems by first, constructing mathematical models to describe consumers’ choice behavior from a given offer set, i.e., consumer choice models; second, by designing efficient algorithms to optimally select the product portfolio to maximize the expected profit, i.e., assortment optimization. This thesis consists of three main parts: the first part solves assortment optimization problem under a consideration set based choice model proposed by Manzini and Mariotti (2014) [Manzini, Paola, Marco Mariotti. 2014. Stochastic choice and consideration sets. Econometrica 82(3) 1153-1176.]; the second part proposes an approximation algorithm to jointly optimize products’ selection and display; the third part works on optimally designing a product line under the Logit family choice models when a product’s utility depends on attribute-level configurations

An Exact Method for Assortment Optimization under the Nested Logit Model

We study the problem of finding an optimal assortment of products maximizing the expected revenue, in which customer preferences are modeled using a Nested Logit choice model. This problem is known to be polynomially solvable in a specific case and NP-hard otherwise, with only approximation algorithms existing in the literature. For the NP-hard cases, we provide a general exact method that embeds a tailored Branch-and-Bound algorithm into a fractional programming framework. Contrary to the existing literature, in which assumptions are imposed on either the structure of nests or the combination and characteristics of products, no assumptions on the input data are imposed, and hence our approach can solve the most general problem setting. We show that the parameterized subproblem of the fractional programming scheme, which is a binary highly non-linear optimization problem, is decomposable by nests, which is a main advantage of the approach. To solve the subproblem for each nest, we propose a two-stage approach. In the first stage, we identify those products that are undoubtedly beneficial to offer, or not, which can significantly reduce the problem size. In the second stage, we design a tailored Branch-and-Bound algorithm with problem-specific upper bounds. Numerical results show that the approach is able to solve assortment instances with up to 5,000 products per nest. The most challenging instances for our approach are those in which the dissimilarity parameters of nests can be either less or greater than one