The paper considers a stylized model of a dynamic assortment optimization problem, where given a limited capacity constraint, we must decide the assortment of products to offer to customers to maximize the profit. Our model is motivated by the problem faced by retailers of stocking products on a shelf with limited capacities and by the problem of placing a limited number of ads on a web page. We assume that each customer chooses to purchase the product (or to click on the ad) that maximizes her utility. We use the multinomial logit choice model to represent demand. However, we do not know the demand for each product. We can learn the demand distribution by offering different product assortments, observing resulting selections, and inferring the demand distribution from past selections and assortment decisions. We present an adaptive policy for joint parameter estimation and assortment optimization. To evaluate our proposed policy, we define a benchmark profit as the maximum expected profit that we can earn if we know the underlying demand distribution in advance. We show that the running average expected profit generated by our policy converges to the benchmark profit and establish its convergence rate. Numerical experiments based on sales data from an online retailer indicate that our policy performs well, generating over 90% of the optimal profit after less than two days of sales.

Reliable facility location models consider unexpected failures with site-dependent probabilities, as well as possible customer reassignment. This paper proposes a compact mixed integer program (MIP) formulation and a continuum approximation (CA) model to study the reliable uncapacitated fixed charge location problem (RUFL) which seeks to minimize initial setup costs and expected transportation costs in normal and failure scenarios.The MIP determines the optimal facility locations as well as the optimal customer assignments, and the MIP is solved using a custom-designed Lagrangian Relaxation (LR) algorithm. The CA model predicts the total system cost without details about facility locations and customer assignments, and it provides a fast heuristic to find near-optimum solutions. Our computational results show that the LR algorithm is efficient for mid-sized RUFL problems and that the CA solutions are close to optimal in most of the test instances.For large-scale problems, the CA method is a good alternative to the LR algorithm that avoids prohibitively long running times.

Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions of a convex optimization problem are corrupted by noise. We first provide a formulation for inverse optimization and prove it to be NP-hard. In contrast to existing methods, we show that the parameter estimates produced by our formulation are statistically consistent. Our approach involves combining a new duality-based reformulation for bilevel programs with a regularization scheme that smooths discontinuities in the formulation. Using epi-convergence theory, we show the regularization parameter can be adjusted to approximate the original inverse optimization problem to arbitrary accuracy, which we use to prove our consistency results. Next, we propose two solution algorithms based on our duality-based formulation. The first is an enumeration algorithm that is applicable to settings where the dimensionality of the parameter space is modest, and the second is a semiparametric approach that combines nonparametric statistics with a modified version of our formulation. These numerical algorithms are shown to maintain the statistical consistency of the underlying formulation. Lastly, using both synthetic and real data, we demonstrate that our approach performs competitively when compared with existing heuristics.

E lectric vehicles (EVs) have been proposed as a key technology to help cut down the massive greenhouse gas emissions from the transportation sector. Unfortunately, because of the limited capacity of batteries, typical EVs can only travel for about 100 miles on a single charge and require hours to be recharged. The industry has proposed a novel solution centered around the use of "swapping stations," at which depleted batteries can be exchanged for recharged ones in the middle of long trips. The possible success of this solution hinges on the ability of the charging service provider to deploy a cost-effective infrastructure network, given only limited information regarding adoption rates. We develop robust optimization models that aid the planning process for deploying battery-swapping infrastructure. Using these models, we study the potential impacts of battery standardization and technology advancements on the optimal infrastructure deployment strategy.

The present study developed a fast MEG source imaging technique based on Fast Vector-based Spatio-Temporal Analysis using a L1-minimum-norm (Fast-VESTAL) and then used the method to obtain the source amplitude images of resting-state magnetoencephalography (MEG) signals for different frequency bands. The Fast-VESTAL technique consists of two steps. First, L1-minimum-norm MEG source images were obtained for the dominant spatial modes of sensor-waveform covariance matrix. Next, accurate source time-courses with millisecond temporal resolution were obtained using an inverse operator constructed from the spatial source images of Step 1. Using simulations, Fast-VESTAL’s performance of was assessed for its 1) ability to localize multiple correlated sources; 2) ability to faithfully recover source time-courses; 3) robustness to different SNR conditions including SNR with negative dB levels; 4) capability to handle correlated brain noise; and 5) statistical maps of MEG source images. An objective pre-whitening method was also developed and integrated with Fast-VESTAL to remove correlated brain noise. Fast-VESTAL’s performance was then examined in the analysis of human mediannerve MEG responses. The results demonstrated that this method easily distinguished sources in the entire somatosensory network. Next, Fast-VESTAL was applied to obtain the first whole-head MEG source-amplitude images from resting-state signals in 41 healthy control subjects, for all standard frequency bands. Comparisons between resting-state MEG sources images and known neurophysiology were provided. Additionally, in simulations and cases with MEG human responses, the results obtained from using conventional beamformer technique were compared with those from Fast-VESTAL, which highlighted the beamformer’s problems of signal leaking and distorted source time-courses.

We study several joint facility location and inventory management problems with stochastic retailer demand. In particular, we consider cases with uncapacitated facilities, capacitated facilities, correlated retailer demand, stochastic lead times, and multicommodities. We show how to formulate these problems as conic quadratic mixed-integer problems. Valid inequalities, including extended polymatroid and extended cover cuts, are added to strengthen the formulations and improve the computational results. Compared to the existing modeling and solution methods, the new conic integer programming approach not only provides a more general modeling framework but also leads to fast solution times in general.

The coronavirus/SARS‐CoV‐2 (COVID‐19) outbreak has caused severe supply chain disruptions in practically all industries worldwide. Online e‐commerce platforms, which interact directly with various industries and service numerous consumers, have become remarkable interfaces to observe the impacts of the pandemic on supply chains. Using quantitative operational data obtained from JD.com https://www.jd.com., this study analyzes the impact of the pandemic on supply chain resilience, summarizes the challenging scenarios that retailing supply chains experienced in China, and presents the practical response of JD.com throughout the pandemic. To summarize, the pandemic caused exceptional demand and severe logistical disruptions in China, and JD.com has handled well its supply chain management in response based on its integrated supply chain structure and comprehensive intelligent platforms. In particular, the existing intelligent platforms and the delivery procedures were modified slightly but promptly to deal with specific disruptions. Moreover, the entire market scenario in China was effectively controlled through the joint efforts of multiple firms, the government, and the entire Chinese society. Our study provides an example of using practical operational indicators to analyze supply chain resilience, and suggests firms pay attention to operational flexibility and collaboration beyond supply chains to deal with a large‐scale supply chain disruption, such as the COVID‐19 outbreak.

We study a reliable facility location problem wherein some facilities are subject to failure from time to time. If a facility fails, customers originally assigned to it have to be reassigned to other (operational) facilities. We formulate this problem as a two-stage stochastic program and then as a nonlinear integer program. Several heuristics that can produce near-optimal solutions are proposed for this NP-hard problem. For the special case where the probability that a facility fails is a constant (independent of the facility), we provide an approximation algorithm with a worst-case bound of 4. The effectiveness of our heuristics is tested by extensive computational studies, which also lead to some managerial insights.