Events & Seminars

We examine the impact of assortment size on consumer choice behavior with both empirical evidence and theoretical explanation. We first conduct a large-scale field experiment in online retail to causally examine how consumers' click and purchase behavior changes as the number of products in a choice set increases. There, we document a non-monotonic relationship between the assortment size and consumer choice. We then develop a two-stage choice model that incorporates consumers’ search cost and anticipated regret to explain our findings in the field experiment. We also conduct numerical experiments to investigate the implications of our model for companies' optimal assortment decisions. Our results suggest that our two-stage choice model leads to smaller optimal assortments containing products of higher expected utilities and lower prices on average than the classical multinomial logit (MNL) choice model.

The boom of e-commerce in the globe in recent years has expedited the expansion of fulfillment infrastructures by e-retailers. While e-retailers are building more and more mini-warehouses close to end customers to offer faster delivery service than ever, the associated fulfillment costs have skyrocketed. In this paper, we study a real-time fulfillment problem in a two-layer RDC-FDC distribution network that has been implemented in practice by major e-retailers. In such a network, the upper layer contains larger regional distribution centers (RDCs) and the lower layer contains smaller front distribution centers (FDCs). We allow order split: an order can be split and fulfilled from multiple warehouses at an additional cost. The objective is to minimize the routine fulfillment costs. We study real-time algorithms with performance guarantees in both settings with and without demand forecasts. We also complement our theoretical results by conducting a numerical study by using real data from Alibaba.

This is joint work with Xinshang Wang (Alibaba) and Yanyang Zhao (Chicago Booth).

We consider the problem faced by an e-retailer that needs to display a limited set of products to a customer with no prior information. In this context, the e-retailer is allowed to query preferences in order to inform its display. A standard approach to this problem follows a two-step approach: First, estimate the preferences of the customer using a choice model, and then optimize the product display. While this approach is applicable to many settings with stationary customer preferences, this is not applicable to scenarios with changing customer preferences. In this paper, we develop a novel product-driven online framework for efficiently learning customer preferences using a structured questionnaire design. We demonstrate that our approach provably outperforms state-of-the-art methods which focus on eliciting the preference vector. Further, we formulate a robust algorithm for eliciting the optimal display set when the customer responses are noisy.

We establish theoretical foundations for our question-design mechanism and develop efficiency guarantees for our product-driven algorithm. We also present results of our implementation on a real data set obtained from a major fashion retailer. We demonstrate that we are able to efficiently and customer preferences to inform the optimal product display, and outperform existing approaches based on "estimate, then optimize".

Joint work with Yam Huo (NU), and based on work with Jonathan Amar and Nikos Trichakis (MIT).

This paper presents a novel high-dimensional forecast combination estimator in the presence of many forecasts and potential latent group structures. The new algorithm, which we call ℓ2-relaxation, minimizes the squared ℓ2-norm of the weight vector subject to a relaxed version of the first-order conditions, instead of minimizing the mean squared forecast error as those standard optimal forecast combination procedures. A proper choice of the tuning parameter achieves bias and variance trade-off, and incorporates as special cases the simple average (equal-weight) strategy and the conventional optimal weighting scheme. When the variance-covariance (VC) matrix of the individual forecast errors exhibits latent group structures -- a block equicorrelation matrix plus a VC for idiosyncratic noises, ℓ2-relaxation delivers combined forecasts with roughly equal within-group weights. Asymptotic optimality of the new method is established by exploiting the duality between the sup-norm restriction and the high-dimensional sparse ℓ1-norm penalization. Excellent finite sample performance of our method is demonstrated in Monte Carlo simulations. Its wide applicability is highlighted in three real data examples concerning empirical applications of microeconomics, macroeconomics, and finance.

Based on joint work with Liangjun Su, Tian Xie.

We consider an online retailer selling multiple products to multiple zones over a single period. The retailer orders the products from a single supplier and stores them at multiple warehouses. At the start of the selling period, the retailer determines the order quantities of the products and their storage quantities at each warehouse subject to its capacity constraint. At the end of the period, after knowing the demands, the retailer determines the retrieval quantities from each warehouse to fulfill the demands. The retailer's objective is to maximize her expected profit. For the single- zone case, we solve the problem optimally. The optimal retrieval policy is a greedy policy. We design a polynomial-time algorithm to determine the optimal storage policy, which preserves a nested property: Among all non-empty warehouses, a smaller-index warehouse contains all the products stored in a larger-index warehouse. The optimal ordering policy is a newsvendor-type policy. The problem becomes intractable analytically if there are multiple zones and we propose an efficient heuristic to solve it. This heuristic involves a non-trivial hybrid approximation of the second- stage expected profit. Numerical experiments using both synthetic data and real data from a major fashion online retailer in Asia suggest that our heuristic outperforms state-of-the-art approaches with significantly less computational time. With flexible fulfillment, our heuristic improves the efficiency by 28% on average compared to a dedicated policy adopted by theretailer.

Motivated by the issues of fraudulent clicks in online recommendation systems and contaminated samples in medical trials, we consider a best arm identification (BAI) problem for stochastic bandits with adversarial corruptions. The goal is to identify the best arm with a fixed number of pulls (which are also known as time steps), in the presence of an adversary who can corrupt the stochastic outcomes of the arms.

We design a novel randomized algorithm, PROBABILISTIC SEQUENTIAL SHRINKING (PSS), which is agnostic to the amount of corruptions. In the absence of corruptions, our proposed algorithm achieves the state-of- the-art performance guarantee. In the presence of corruptions, we construct settings where the state-of- the-art BAI algorithm (Karnin et al. 2013) fails to identify the best arm with probability at least 0.5, whereas PSS identifies the best arm with high probability. En route, we demonstrate the importance of randomized sampling for mitigating the impact of corruptions.

In addition, we identify the amount of corruptions per step (CPS) to be a crucial parameter that characterizes the possibility of BAI. When the CPS is below a certain threshold, PSS identifies the best arm with high probability. Otherwise, the optimality gap of the identified arm degrades gracefully with the CPS, while there is no guarantee on the probability of identifying the best arm. We demonstrate the necessity of such a bifurcation, by showing that BAI is impossible when the CPS is above a certain threshold.