Operations Research

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• Technical Note-Global Robust Stability in a General Price and Assortment Competition Model AI翻译
  作者：Federgruen, Awi; Hu, Ming
  作者单位：Columbia University; University of Toronto
  摘要：We analyze a general but parsimonious price competition model for an oligopoly in which each firm offers any number of products. The demand volumes are general piecewise affine functions of the full price vector, generated as the regular extension of a base set of affine functions. The model specifies a product assortment, along with their prices and demand volumes, in contrast to most commonly used demand models, such as the multinomial logit model or any of its variants. We show that a speci...
• Technical Note-A Stochastic Assignment Problem with Unknown Eligibility Probabilities AI翻译
  作者：Ross, Sheldon M.; Weiss, Gideon; Zhang, Zhengyu
  作者单位：University of Southern California; University of Haifa
  摘要：Consider n initially empty boxes, numbered 1 through n. Balls arrive sequentially. Each ball has a binary n-vector attached to it, with the interpretation that the ball is eligible to be put in box i if component i of its vector is equal to 1. An arriving ball can be put in any empty box for which it is eligible. Assuming that components of the vector are independent Bernoulli random variables with initially unknown probabilities, our primary interest is to compare several policies to determin...
• Global Convergence of Stochastic Gradient Hamiltonian Monte Carlo for Nonconvex Stochastic Optimization: Nonasymptotic Performance Bounds and Momentum-Based Acceleration AI翻译
  作者：Gao, Xuefeng; Gurbuzbalaban, Mert; Zhu, Lingjiong
  作者单位：Chinese University of Hong Kong; Rutgers University System; Rutgers University New Brunswick; State University System of Florida; Florida State University
  摘要：Stochastic gradient Hamiltonian Monte Carlo (SGHMC) is a variant of stochastic gradients with momentum where a controlled and properly scaled Gaussian noise is added to the stochastic gradients to steer the iterates toward a global minimum. Many works report its empirical success in practice for solving stochastic nonconvex optimization problems; in particular, it has been observed to outperform overdamped Langevin Monte Carlo-based methods, such as stochastic gradient Langevin dynamics (SGLD)...
• Assortment Optimization and Pricing Under the Multinomial Logit Model with Impatient Customers: Sequential Recommendation and Selection AI翻译
  作者：Gao, Pin; Ma, Yuhang; Chen, Ningyuan; Gallego, Guillermo; Li, Anran; Rusmevichientong, Paat; Topaloglu, Huseyin
  作者单位：The Chinese University of Hong Kong, Shenzhen; University of Toronto; University Toronto Mississauga; University of London; London School Economics & Political Science; University of Southern California
  摘要：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 min...
• Always Valid Inference: Continuous Monitoring of A/B Tests AI翻译
  作者：Johari, Ramesh; Koomen, Pete; Pekelis, Leonid; Walsh, David
  作者单位：Stanford University
  摘要：A/B tests are typically analyzed via frequentist p-values and confidence intervals, but these inferences are wholly unreliable if users endogenously choose samples sizes by continuously monitoring their tests. We define always valid p-values and confidence intervals that let users try to take advantage of data as fast as it becomes available, providing valid statistical inference whenever they make their decision. Always valid inference can be interpreted as a natural interface for a sequentia...
• Improving the Chilean College Admissions System AI翻译
  作者：Rios, Ignacio; Larroucau, Tomas; Parra, Giorgiogiulio; Cominetti, Roberto
  作者单位：University of Texas System; University of Texas Dallas; University of Pennsylvania; Universidad de Chile; Universidad Adolfo Ibanez
  摘要：In this paper we present the design and implementation of a new system to solve the Chilean college admissions problem. We develop an algorithm that obtains all applicant/program pairs that can be part of a stable allocation when preferences are not strict and when all students tied in the last seat of a program (if any) must be allocated. We use this algorithm to identify which mechanism was used in the past to perform the allocation, and we propose a new method to incorporate the affirmative...
• How Service Quality Variability Hurts Revenue When Customers Learn: Implications for Dynamic Personalized Pricing AI翻译
  作者：DeCroix, Gregory; Long, Xiaoyang; Tong, Jordan
  作者单位：University of Wisconsin System; University of Wisconsin Madison
  摘要：We formalize an understudied mechanism through which quality variability hurts firm revenues, analyze when and why this mechanism is important, and generate new insight into how dynamic personalized pricing strategies can mitigate the negative effects of quality variability. To do so, we model a firm that sells a service repeatedly with variable but stationary quality. Customers update their quality beliefs based on their experiences (exponential smoothing), and their purchase probability in e...
• Bayesian Decision Making in Groups is Hard AI翻译
  作者：Hazla, Jan; Jadbabaie, Ali; Mossel, Elchanan; Rahimian, M. Amin
  作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
  摘要：We study the computations that Bayesian agents undertake when exchanging opinions over a network. The agents act repeatedly on their private information and take myopic actions that maximize their expected utility according to a fully rational posterior belief. We show that such computations are NP-hard for two natural utility functions: one with binary actions and another where agents reveal their posterior beliefs. In fact, we show that distinguishing between posteriors that are concentrated...
• Risk Arbitrage Opportunities for Stock Index Options AI翻译
  作者：Post, Thierry; Longarela, Inaki Rodriguez
  作者单位：Nazarbayev University; Stockholm University
  摘要：To analyze the economic significance of pricing errors of stock index options, a system of linear inequalities is developed that completely characterizes all risk arbitrage opportunities that arise if a well-behaved pricing kernel does not exist. The stochastic arbitrage system can account for market imperfections in the form of transactions costs and general portfolio restrictions. An active trading strategy based on the stochastic arbitrage system for front-month S&P500 stock index options y...
• Finding Minimum Volume Circumscribing Ellipsoids Using Generalized Copositive Programming AI翻译
  作者：Mittal, Areesh; Hanasusanto, Grani A.
  作者单位：University of Texas System; University of Texas Austin
  摘要：We study the problem of finding the Liiwner-John ellipsoid (i.e., an ellipsoid with minimum volume that contains a given convex set). We reformulate the problem as a generalized copositive program and use that reformulation to derive tractable semidefinite programming approximations for instances where the set is defined by affine and quadratic inequalities. We prove that, when the underlying set is a polytope, our method never provides an ellipsoid of higher volume than the one obtained by sc...