Online Demand Fulfillment Under Limited Flexibility

2020 ◽  
Vol 66 (10) ◽  
pp. 4667-4685
Author(s):  
Zhen Xu ◽  
Hailun Zhang ◽  
Rachel Q. Zhang
Keyword(s):  
Numerical Experiments ◽  
Real Data ◽  
Market Size ◽  
Performance Bound ◽  
Performance Gap ◽  
Allocation Rules ◽  
Demand Fulfillment ◽  
Inventory Allocation ◽  
Sparse Networks ◽  
Necessary And Sufficient

We study online demand fulfillment in a class of networks with limited flexibility and arbitrary numbers of resources and request types. We show analytically that such a network is both necessary and sufficient to guarantee a performance gap independent of the market size compared with networks with full flexibility, extending the previous literature from the long chains to more general sparse networks. Inspired by the performance bound, we develop simple inventory allocation rules and guidelines for designing such network structures. Numerical experiments including one using some real data from Amazon China are conducted to confirm our findings as well as some of the flexibility principles conjectured in the literature. This paper was accepted by Chung Piaw Teo, optimization.

scholarly journals Stiffness Analysis to Predict the Spread Out of Fake Information

2021 ◽  
Vol 13 (9) ◽  
pp. 222
Author(s):  
Raffaele D'Ambrosio ◽  
Giuseppe Giordano ◽  
Serena Mottola ◽  
Beatrice Paternoster
Keyword(s):  
Numerical Experiments ◽  
Real Data ◽  
Sir Model ◽  
Stiffness Index ◽  
Fake News ◽  
Stiffness Analysis ◽  
Data Support

This work highlights how the stiffness index, which is often used as a measure of stiffness for differential problems, can be employed to model the spread of fake news. In particular, we show that the higher the stiffness index is, the more rapid the transit of fake news in a given population. The illustration of our idea is presented through the stiffness analysis of the classical SIR model, commonly used to model the spread of epidemics in a given population. Numerical experiments, performed on real data, support the effectiveness of the approach.

Consumer Choice and Market Expansion: Modeling, Optimization, and Estimation

2021 ◽  
Author(s):  
Ruxian Wang
Keyword(s):  
Operations Management ◽  
Expectation Maximization ◽  
Consumer Choice ◽  
Choice Behavior ◽  
Real Data ◽  
Market Size ◽  
Solution Approach ◽  
Pricing Decisions ◽  
Market Expansion ◽  
Consumer Choice Behavior

The growth of market size is crucially important to firms, although researchers often assume that market size is constant in assortment and pricing management. I develop a model that incorporates the market expansion effects into discrete consumer choice models and investigate various operations problems. Market size, measured by the number of people who are interested in the products from the same category, is largely influenced by firms’ operations strategy, and it also affects assortment planning and pricing decisions. Failure to account for market expansion effects may lead to substantial losses in demand estimation and operations management. Based on real data, this paper uses an alternating-optimization expectation-maximization method that separates the estimation of consumer choice behavior and market expansion effects to calibrate the new model. The end-to-end solution approach on modeling, operations, and estimation is readily applicable in real business.

Composite optimization for robust rank one bilinear sensing

2020 ◽  
Author(s):  
Vasileios Charisopoulos ◽  
Damek Davis ◽  
Mateo Díaz ◽  
Dmitriy Drusvyatskiy
Keyword(s):  
Numerical Experiments ◽  
Lipschitz Continuity ◽  
Blind Deconvolution ◽  
Real Data ◽  
Local Search Algorithms ◽  
Composite Optimization ◽  
Statistical Assumptions ◽  
Rank One ◽  
Initialization Procedure ◽  
Initialization Strategy

Abstract We consider the task of recovering a pair of vectors from a set of rank one bilinear measurements, possibly corrupted by noise. Most notably, the problem of robust blind deconvolution can be modeled in this way. We consider a natural nonsmooth formulation of the rank one bilinear sensing problem and show that its moduli of weak convexity, sharpness and Lipschitz continuity are all dimension independent, under favorable statistical assumptions. This phenomenon persists even when up to half of the measurements are corrupted by noise. Consequently, standard algorithms, such as the subgradient and prox-linear methods, converge at a rapid dimension-independent rate when initialized within a constant relative error of the solution. We complete the paper with a new initialization strategy, complementing the local search algorithms. The initialization procedure is both provably efficient and robust to outlying measurements. Numerical experiments, on both simulated and real data, illustrate the developed theory and methods.

scholarly journals Data Assimilation Method, its Application and Stability

2019 ◽  
Vol 292 ◽  
pp. 03012
Author(s):  
Konstantin Belyaev ◽  
Andrey Kuleshov ◽  
Ilya Smirnov ◽  
Natalia Tuchkova
Keyword(s):  
Markov Chain ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Dynamic System ◽  
Numerical Experiments ◽  
Sufficient Conditions ◽  
Ocean Model ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Generalized Kalman Filter

The authors data assimilation method, namely, generalized Kalman filter (GKF) method, its application and stability is considered. The problem of stability of a dynamic system with data assimilation formulated for a sequence of random variables forming a Markov chain is considered. The stability formulation for this problem is suggested as the problem of the convergence of the corresponding Markov chain when the number of its members goes to infinity. Necessary and sufficient conditions of this convergence are proved. A number of numerical experiments with the specific dynamic system, namely with the ocean model circulation HYCOM and the GKF method are conducted and discussed. The stability of the GKF method was proofed.

AN IMPRECISE BOOSTING-LIKE APPROACH TO CLASSIFICATION

2013 ◽  
Vol 27 (08) ◽  
pp. 1351005 ◽  
Author(s):  
LEV V. UTKIN
Keyword(s):  
Statistical Models ◽  
Numerical Experiments ◽  
Extreme Points ◽  
Real Data ◽  
Training Data ◽  
Data Sets ◽  
New Approach

A new approach for ensemble construction based on restricting a set of weights of examples in training data to avoid overfitting is proposed in the paper. The algorithm called EPIBoost (Extreme Points Imprecise Boost) applies imprecise statistical models to restrict the set of weights. The updating of the weights within the restricted set is carried out by using its extreme points. The approach allows us to construct various algorithms by applying different imprecise statistical models for producing the restricted set. It is shown by various numerical experiments with real data sets that the EPIBoost algorithm may outperform the standard AdaBoost for some parameters of imprecise statistical models.

On the computational estimation of high order GARCH model

2021 ◽  
Vol 8 (4) ◽  
pp. 797-806
Author(s):  
A. Settar ◽  
◽  
N. I. Fatmi ◽  
M. Badaoui ◽  
◽  
...  
Keyword(s):  
Monte Carlo ◽  
Kalman Filter ◽  
Monte Carlo Simulations ◽  
Garch Model ◽  
Real Data ◽  
Conditional Variance ◽  
High Order ◽  
Computational Estimation ◽  
Necessary And Sufficient ◽  
The Garch Model

To guarantee the non-negativity of the conditional variance of the GARCH process, it is sufficient to assume the non-negativity of its parameters. This condition was empirically violated besides rendering the GARCH model more restrictive. It was subsequently relaxed for some GARCH orders by necessary and sufficient constraints. In this paper, we generalized an approach for the QML estimation of the GARCH(p,q) parameters for all orders $p\geq 1$ and $q\geq1$ using a constrained Kalman filter. Such an approach allows a relaxed QML estimation of the GARCH without the need to identify and/or apply the relaxed constraints to the parameters. The performance of our method is demonstrated through Monte Carlo simulations and empirical applications to real data.

scholarly journals Stability Analysis ofθ-Methods for Neutral Multidelay Integrodifferential System

2007 ◽  
Vol 2007 ◽  
pp. 1-8
Author(s):  
Y. Xu ◽  
J. J. Zhao ◽  
Z. N. Sui
Keyword(s):  
Numerical Stability ◽  
Numerical Experiments ◽  
Analytic Solutions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Neutral Delay ◽  
Integrodifferential System ◽  
System A ◽  
The Stability ◽  
Necessary And Sufficient

This paper studies the stability of a class of neutral delay integrodifferential system. A necessary and sufficient condition of stability for its analytic solutions is considered. The improvedθ-methods are developed. Some numerical stability properties are obtained and numerical experiments are given.

scholarly journals COMPARISON OF TWO DATA ASSIMILATION METHODS USED TO ACCOUNT FOR OPEN BOUNDARIES IN SEA AREA HYDROTHERMODYNAMICS MODELING

2021 ◽  
Vol 49 (4) ◽  
pp. 86-101
Author(s):  
T. O. Sheloput ◽  
V. I. Agoshkov
Keyword(s):  
Observational Data ◽  
Numerical Experiments ◽  
Real Data ◽  
Open Boundary ◽  
Comparison Of Methods ◽  
Simple Shape ◽  
Variational Assimilation ◽  
Open Boundaries ◽  
Simulation Results ◽  
Sea Area

The problems of modeling hydrothermodynamics of particular sea and coastal areas are of current interest, since the results of this modeling are often used in many applications. One of the methods allowing to take into account open boundaries and bring the simulation results closer to real data is the variational assimilation of observational data. In this paper the following approach is considered: it is supposed that there are observational data at a certain moment in time; the problem is considered as an inverse problem, in which the functions of fluxes across the open boundary are treated as additional unknowns. Comparison of methods for reconstructing unknown functions in boundary conditions at an open boundary using sea level and velocity observational data in a number of numerical experiments for a region of a simple shape is carried out.

scholarly journals Spontaneous Clustering via Minimum Gamma-Divergence

2014 ◽  
Vol 26 (2) ◽  
pp. 421-448 ◽  
Author(s):  
Akifumi Notsu ◽  
Osamu Komori ◽  
Shinto Eguchi
Keyword(s):  
Data Structure ◽  
Local Minimum ◽  
Real Data ◽  
New Method ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Number Of Clusters ◽  
Model Based Clustering ◽  
Necessary And Sufficient ◽  
Minimum Points

We propose a new method for clustering based on local minimization of the gamma-divergence, which we call spontaneous clustering. The greatest advantage of the proposed method is that it automatically detects the number of clusters that adequately reflect the data structure. In contrast, existing methods, such as K-means, fuzzy c-means, or model-based clustering need to prescribe the number of clusters. We detect all the local minimum points of the gamma-divergence, by which we define the cluster centers. A necessary and sufficient condition for the gamma-divergence to have local minimum points is also derived in a simple setting. Applications to simulated and real data are presented to compare the proposed method with existing ones.

scholarly journals Fast, robust and non-convex subspace recovery

2017 ◽  
Vol 7 (2) ◽  
pp. 277-336 ◽  
Author(s):  
Gilad Lerman ◽  
Tyler Maunu
Keyword(s):  
Computational Complexity ◽  
Stationary Point ◽  
Numerical Experiments ◽  
Global Minimum ◽  
Real Data ◽  
Dimensional Subspace ◽  
Iteration Complexity ◽  
Higher Dimensional ◽  
Low Dimensional ◽  
Speed And Accuracy

Abstract This work presents a fast and non-convex algorithm for robust subspace recovery. The datasets considered include inliers drawn around a low-dimensional subspace of a higher dimensional ambient space and a possibly large portion of outliers that do not lie nearby this subspace. The proposed algorithm, which we refer to as fast median subspace (FMS), is designed to robustly determine the underlying subspace of such datasets, while having lower computational complexity than existing accurate methods. We prove convergence of the FMS iterates to a stationary point. Further, under two special models of data, FMS converges to a point which is near to the global minimum with overwhelming probability. Under these models, we show that the iteration complexity is globally sublinear and locally $r$-linear. For one of the models, these results hold for any fixed fraction of outliers (< 1). Numerical experiments on synthetic and real data demonstrate its competitive speed and accuracy.

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