PAPERS
Discrete Choice Modeling:
"Category Choice Model and Loss Leaders”, with Guillermo Gallego
- Manufacturing & Service Operations Management, Major revision
Abstract: Multiple purchases, where a consumer purchases multiple products at one time, is an important and common feature in retailing and other industries. One limitation of traditional choice models is that it can not accommodate the multiple purchases feature. Moreover, the practice of loss leaders, where some products are priced intentionally below their costs, is closely related to the multiple purchase feature. The goal of this paper is to develop a choice model that accommodates the multiple purchase feature with the ability to justify loss leaders. We propose and study a random utility-based category choice model where a store offers multiple categories of products and consumers purchase at most one product within each category. We investigate the multi-product pricing problem for the category choice model under both monopoly and competition. We show that loss leaders, if any, should be products with the largest price sensitivity and that the optimal profit without loss leaders can be arbitrarily small relative to the optimal profit with loss leaders. Our model is robust to possible correlations between categories, and can be extended to consumers with limited attention. Our results provide important managerial insights and suggest that there are three driving forces for loss leaders: (1) inertia against visiting the store; (2) heterogeneity in price sensitivity parameter; (3) competition.
"Redirecting Consumer Demand: Managing Product Substitutions with Coupons", with Guillermo Gallego
- Manufacturing & Service Operations Management, Major revision
Abstract: When their preferred product is unavailable, consumers often substitute to an available alternative. Understanding demand substitutions between products is a central topic in discrete choice modeling, revenue management and assortment optimization. We consider the problem of managing demand substitution through the use of coupons. Specifically, we study how coupons help redirect consumer choices to improve expected revenues. We incorporate coupons into the discrete choice modeling framework and investigate the associated assortment optimization problem. We find that the benefit of using coupons can be arbitrarily large relative to assortment optimization without coupons. When the underlying choice model is governed by the multinomial logit (MNL) choice model, we show that optimal assortments can be found in polynomial time. For the pricing problem with coupons, we find that all products share the same markup at optimality and coupons serve as a tool for price discrimination. In contrast to assortment optimization, we find that the ratio for optimal profits with coupon is at most twice the
optimal profits without coupon when firms can optimize over prices. Coupons are an effective tool for redirecting consumer demand that can significantly increase profit for sellers, particularly in the context of assortment optimization with exogenously determined prices.
Assortment Optimization:
"Efficient Local-Search Heuristics for Online and Offline Assortment Optimization”, with Guillermo Gallego and Srikanth Jagabathula
- Operations Research, submitted
Abstract: We consider the key operational problem of optimizing the mix of offered products to maximize revenues when product prices are exogenous, and product demand follows a general discrete choice model. The key challenge is the computational difficulty of finding the best assortment, which may require an exhaustive search. Existing approaches address the challenge by either deriving efficient algorithms for specific parametric choice models or by studying the performance of general-purpose heuristics. The former approach results in algorithms that lack portability to other structures; whereas the latter approach has resulted in algorithms that may have poor performance in practice. We study a portable and easy-to-implement local search heuristic. We show that it efficiently finds the global optimum for the Markov chain model with performance guarantees for general choice structures. Empirically, it is better than prevailing heuristics when no efficient algorithms exist. It is within 0.02% of optimality in our numerical studies for non-MC choice models. Moreover, we propose a learning algorithm based on our local search heuristic and show that the learning algorithm enjoys minimal learning regret for the Markov chain model. Our learning algorithm can also be employed for more general choice models.
"Online Assortment Optimization for Random Consideration Set Choice Model", Solo author paper
- Production and Operations Management, Reject and resubmit
Abstract: Assortment optimization is a key operational problem in revenue management. One practical challenge for assortment optimization is the lack of information regarding model parameters, which gives rise to the online assortment optimization problem. In this paper, we investigate the online assortment optimization problem for the random consideration set choice model, where there is a preference order over products and each product is equipped with an attention probability. We first propose learning algorithms when the environment is stationary, i.e., the preference order and attention probabilities stay the same during the selling period. In particular, we consider three different cases: 1) when the preference order is unknown; 2) when the attention probabilities are unknown; 3) both the preference order and attention probabilities are unknown. We propose learning algorithms for all these three cases and show that our algorithms enjoy minimal regret. We then consider the case where the preference order and attention probabilities could change during the selling period. We then propose a learning algorithm that can adapt to the non-stationary environment using the idea of random testing. The essential idea of our learning algorithms is to learn a series of binary relations instead of estimating parameters. This technique avoids the difficulty of establishing concentration inequalities for parameter estimations and allows for an efficient learning algorithm within the classic first explore then commit structure.
"Bounds on Revenue for the Random Consideration Set Choice Model", Solo author paper
- Operations Research Letters, 2024:107070 Link
"Online Assortment Optimization for Markov Chain Model with the UCB Algorithm",
- work in progress
Social Learning:
"The Economics of Bestsellers: Consumer Search, Sales Ranking, and Social Learning”, with Man Yu
- Manufacturing & Service Operations Management, Major revision
Abstract: Motivated by major e-commerce platforms' diverse practices in bestseller information provision, this paper examines consumers' learning, searching, and purchasing behavior under uncertainty about products' values, while a platform strategically decides whether and, if so, how to disclose the products' past sales information to consumers. We build an analytical model that embeds consumers' sequential search in a social-learning framework and shows how the interaction between bestseller information and consumer search impacts on a platform's optimal information-provision strategy. We find that a bestseller list constitutes an informative, and yet noisy, signal about the products' values. The informativeness of the signal is determined by the granularity of the bestseller information. By evaluating bestseller information of two levels of granularity, sales ranking and sales volume, we discover that although consumers benefit more from information of a higher granularity (i.e., sales volume), the platform may prefer providing information of a lower granularity (i.e., sales ranking), suggesting that the platform may withhold some information at the cost of consumers. In particular, an inference effect unique to multi-product Bayesian learning gives rise to the possibility that disclosure of past sales volume backfires and hurts the platform. We identify conditions under which displaying bestseller rankings without revealing sales volumes is optimal to the platform. Furthermore, we show that bestseller information provision may lead to lower purchased value or higher search cost, the latter of which implies that public learning may stimulate rather than substitute private learning.
Fairness:
" A Simple Way to Fair Assortment Planning: Market Exposure and Welfare Implications”, with Ozge Sahin and Ruxian Wang
- Management Science, submitted
Abstract: Large online retailers and department stores function as marketplaces for many other sellers in addition to themselves, and consumers rely on the platform's assortment and display decisions to examine different sellers (or products) and make purchase decisions. Traditionally, the primary objective of these marketplaces for assortment planning is to maximize revenue (or profit), which may create unfairness among sellers. This is because only a single assortment with the highest expected revenue is chosen resulting in some sellers being excluded from recommendations or assortments, with minimal market exposure and revenue. To address this issue, we incorporate fairness constraints that ensure fair market exposures for all sellers. These constraints ensure each seller has a minimum market exposure, which may depend on the seller's reputation, product quality, and price, among other features. We show that the optimal solution with fairness constraints is to randomize over at most $n$ nested assortments, where n is the number of sellers (or products), and the optimal solution can be found in polynomial time. For cases in which there are other business constraints including imposing cardinality constraints on the assortments and limiting the number of different assortments, we characterize the structure of the optimal solutions and propose efficient heuristics. We further investigate the impact of fairness constraints on consumer welfare, and show that it always increases when such constraints are imposed. Our analysis reveals that when fairness constraints induce new sellers with high-quality products to enter the platform, all involved parties are better-off resulting in a win-win-win situation. Even when there is no new seller entry, we identify cases in which the total welfare improves and therefore propose a revenue redistributing mechanism to achieve a win-win-win solution.
"Fair Ranking with the Cascade Model", with Ozge Sahin and Ruxian Wang
- work in progress
Supply Chain Management:
" Store Brand Production in a Diffusion Model”, with Maqbool Dada and Aditya Jain
- work in progress