skip to main content
Explore Scholarly Publications and Datasets in the NSF-PAR

Title: Dynamic Assortment Optimization for Reusable Products with Random Usage Durations
We consider dynamic assortment problems with reusable products, in which each arriving customer chooses a product within an offered assortment, uses the product for a random duration of time, and returns the product back to the firm to be used by other customers. The goal is to find a policy for deciding on the assortment to offer to each customer so that the total expected revenue over a finite selling horizon is maximized. The dynamic-programming formulation of this problem requires a high-dimensional state variable that keeps track of the on-hand product inventories, as well as the products that are currently in use. We present a tractable approach to compute a policy that is guaranteed to obtain at least 50% of the optimal total expected revenue. This policy is based on constructing linear approximations to the optimal value functions. When the usage duration is infinite or follows a negative binomial distribution, we also show how to efficiently perform rollout on a simple static policy. Performing rollout corresponds to using separable and nonlinear value function approximations. The resulting policy is also guaranteed to obtain at least 50% of the optimal total expected revenue. The special case of our model with infinite usage more » durations captures the case where the customers purchase the products outright without returning them at all. Under infinite usage durations, we give a variant of our rollout approach whose total expected revenue differs from the optimal by a factor that approaches 1 with rate cubic-root of Cmin, where Cmin is the smallest inventory of a product. We provide computational experiments based on simulated data for dynamic assortment management, as well as real parking transaction data for the city of Seattle. Our computational experiments demonstrate that the practical performance of our policies is substantially better than their performance guarantees and that performing rollout yields noticeable improvements. « less
Authors:
; ;
Award ID(s):
1824860 1825406
Publication Date:
NSF-PAR ID:
10172517
Journal Name:
Management science
Volume:
66
Issue:
7
Page Range or eLocation-ID:
2820-2844
ISSN:
0025-1909
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ( , Mathematics of Operations Research)
    We study the dynamic assortment planning problem, where for each arriving customer, the seller offers an assortment of substitutable products and the customer makes the purchase among offered products according to an uncapacitated multinomial logit (MNL) model. Because all the utility parameters of the MNL model are unknown, the seller needs to simultaneously learn customers’ choice behavior and make dynamic decisions on assortments based on the current knowledge. The goal of the seller is to maximize the expected revenue, or, equivalently, to minimize the expected regret. Although dynamic assortment planning problem has received an increasing attention in revenue management, most existing policies require the estimation of mean utility for each product and the final regret usually involves the number of products [Formula: see text]. The optimal regret of the dynamic assortment planning problem under the most basic and popular choice model—the MNL model—is still open. By carefully analyzing a revenue potential function, we develop a trisection-based policy combined with adaptive confidence bound construction, which achieves an item-independent regret bound of [Formula: see text], where [Formula: see text] is the length of selling horizon. We further establish the matching lower bound result to show the optimality of our policy. There aremore »two major advantages of the proposed policy. First, the regret of all our policies has no dependence on [Formula: see text]. Second, our policies are almost assumption-free: there is no assumption on mean utility nor any “separability” condition on the expected revenues for different assortments. We also extend our trisection search algorithm to capacitated MNL models and obtain the optimal regret [Formula: see text] (up to logrithmic factors) without any assumption on the mean utility parameters of items.« less
  2. ; ; ; ( , Operations Research)
    We provide an approximation algorithm for network revenue management problems. In our approximation algorithm, we construct an approximate policy using value function approximations that are expressed as linear combinations of basis functions. We use a backward recursion to compute the coefficients of the basis functions in the linear combinations. If each product uses at most L resources, then the total expected revenue obtained by our approximate policy is at least [Formula: see text] of the optimal total expected revenue. In many network revenue management settings, although the number of resources and products can become large, the number of resources used by a product remains bounded. In this case, our approximate policy provides a constant-factor performance guarantee. Our approximate policy can handle nonstationarities in the customer arrival process. To our knowledge, our approximate policy is the first approximation algorithm for network revenue management problems under nonstationary arrivals. Our approach can incorporate the customer choice behavior among the products, and allows the products to use multiple units of a resource, while still maintaining the performance guarantee. In our computational experiments, we demonstrate that our approximate policy performs quite well, providing total expected revenues that are substantially better than its theoretical performance guarantee.
  3. ; ; ; ; ( , Management Science)
    We examine the revenue–utility assortment optimization problem with the goal of finding an assortment that maximizes a linear combination of the expected revenue of the firm and the expected utility of the customer. This criterion captures the trade-off between the firm-centric objective of maximizing the expected revenue and the customer-centric objective of maximizing the expected utility. The customers choose according to the multinomial logit model, and there is a constraint on the offered assortments characterized by a totally unimodular matrix. We show that we can solve the revenue–utility assortment optimization problem by finding the assortment that maximizes only the expected revenue after adjusting the revenue of each product by the same constant. Finding the appropriate revenue adjustment requires solving a nonconvex optimization problem. We give a parametric linear program to generate a collection of candidate assortments that is guaranteed to include an optimal solution to the revenue–utility assortment optimization problem. This collection of candidate assortments also allows us to construct an efficient frontier that shows the optimal expected revenue–utility pairs as we vary the weights in the objective function. Moreover, we develop an approximation scheme that limits the number of candidate assortments while ensuring a prespecified solution quality. Finally, wemore »discuss practical assortment optimization problems that involve totally unimodular constraints. In our computational experiments, we demonstrate that we can obtain significant improvements in the expected utility without incurring a significant loss in the expected revenue. This paper was accepted by Omar Besbes, revenue management and market analytics.« less
  4. ; ( , Manufacturing & Service Operations Management)
    Problem definition: We consider the assortment optimization problem of a retailer that operates a physical store and an online store. The products that can be offered are described by their features. Customers purchase among the products that are offered in their preferred store. However, customers who purchase from the online store can first test out products offered in the physical store. These customers revise their preferences for online products based on the features that are shared with the in-store products. The full assortment is offered online, and the goal is to select an assortment for the physical store to maximize the retailer’s total expected revenue. Academic/practical relevance: The physical store’s assortment affects preferences for online products. Unlike traditional assortment optimization, the physical store’s assortment influences revenue from both stores. Methodology: We introduce a features tree to organize products by features. The nonleaf vertices on the tree correspond to features, and the leaf vertices correspond to products. The ancestors of a leaf correspond to features of the product. Customers choose among the products within their store’s assortment according to the multinomial logit model. We consider two settings; either all customers purchase online after viewing products in the physical store, or wemore »have a mix of customers purchasing from each store. Results: When all customers purchase online, we give an efficient algorithm to find the optimal assortment to display in the physical store. With a mix of customers, the problem becomes NP-hard, and we give a fully polynomial-time approximation scheme. We numerically demonstrate that we can closely approximate the case where products have arbitrary combinations of features without a tree structure and that our fully polynomial-time approximation scheme performs remarkably well. Managerial implications: We characterize conditions under which it is optimal to display expensive products with underrated features and expose inexpensive products with overrated features.« less
  5. ; ; ; ; ; ; ( , Operations Research)
    We develop a variant of the multinomial logit model with impatient customers and study assortment optimization and pricing problems under this choice model. In our choice model, a customer incrementally views the assortment of available products in multiple stages. The patience level of a customer determines the maximum number of stages in which the customer is willing to view the assortments of products. In each stage, if the product with the largest utility provides larger utility than a minimum acceptable utility, which we refer to as the utility of the outside option, then the customer purchases that product right away. Otherwise, the customer views the assortment of products in the next stage as long as the customer’s patience level allows the customer to do so. Under the assumption that the utilities have the Gumbel distribution and are independent, we give a closed-form expression for the choice probabilities. For the assortment-optimization problem, we develop a polynomial-time algorithm to find the revenue-maximizing sequence of assortments to offer. For the pricing problem, we show that, if the sequence of offered assortments is fixed, then we can solve a convex program to find the revenue-maximizing prices, with which the decision variables are the probabilitiesmore »that a customer reaches different stages. We build on this result to give a 0.878-approximation algorithm when both the sequence of assortments and the prices are decision variables. We consider the assortment-optimization problem when each product occupies some space and there is a constraint on the total space consumption of the offered products. We give a fully polynomial-time approximation scheme for this constrained problem. We use a data set from Expedia to demonstrate that incorporating patience levels, as in our model, can improve purchase predictions. We also check the practical performance of our approximation schemes in terms of both the quality of solutions and the computation times.« less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email