SAA-regularized methods for multiproduct price optimization under the pure characteristics demand model

Utility-based choice models are often used to determine a consumer’s purchase decision among a list of available products; to provide an estimate of product demands; and, when data on purchase decisions or market shares are available, to infer consumers’ preferences over observed product characteristics. These models also serve as a building block in modeling firms’ pricing and assortment optimization problems. We consider a firm’s multiproduct pricing problem, in which product demands are determined by a pure characteristics model. A sample average approximation (SAA) method is used to approximate the expected market share of products and the firm profit. We propose an SAA-regularized method for the multiproduct price optimization problem. We present convergence analysis and numerical examples to show the efficiency and the effectiveness of the proposed method.     

Multiscale agent‐based consumer market modeling

Consumer markets have been studied in great depth, and many techniques have been used to represent them. These have included regression‐based models, logit models, and theoretical market‐level models, such as the NBD‐Dirichlet approach. Although many important contributions and insights have resulted from studies that relied on these models, there is still a need for a model that could more holistically represent the interdependencies of the decisions made by consumers, retailers, and manufacturers. When the need is for a model that could be used repeatedly over time to support decisions in an industrial setting, it is particularly critical. Although some existing methods can, in principle, represent such complex interdependencies, their capabilities might be outstripped if they had to be used for industrial applications, because of the details this type of modeling requires. However, a complementary method—agent‐based modeling—shows promise for addressing these issues. Agent‐based models use business‐driven rules for individuals (e.g., individual consumer rules for buying items, individual retailer rules for stocking items, or individual firm rules for advertizing items) to determine holistic, system‐level outcomes (e.g., to determine if brand X's market share is increasing). We applied agent‐based modeling to develop a multi‐scale consumer market model. We then conducted calibration, verification, and validation tests of this model. The model was successfully applied by Procter & Gamble to several challenging business problems. In these situations, it directly influenced managerial decision making and produced substantial cost savings. © 2010 Wiley Periodicals, Inc. Complexity, 2010     

Modeling job shop scheduling with batches and setup times by timed Petri nets

Batch and setup times are two important factors in practical job shop scheduling. This paper proposes a method to model job shop scheduling problems including batches and anticipatory sequence-dependent setup times by timed Petri nets. The general modeling method is formally presented. The free choice property of the model is proved. A case study extracted from practical scheduling is given to show the feasibility of the modeling method. Comparison with some previous work shows that our model is more compact and effective in finding the best solution.     

High order asymptotic approach to the evaluation of near field,radiated by ultrasonic transducer to the layered elastic plates

It is well known that one of the most time consuming problem in non-destructive evaluation (NDE) is the near-field modeling. In our approach the near field radiated by an ultrasonic transducer (UT) to the first Fresnel zone is approximated in the frequency domain by a closed form asymptotic solution based on the 3-D generalized orthogonality conditions of Lamb waves and on the stationary phase method. As shown, these asymptotics permit us to elucidate the physics and to work out a numerical algorithm which is about 10⁴ times faster than any direct way of computation. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A novel modeling method for in-plane eigenproblem estimation of the cable-stayed bridges

A novel modeling method is proposed and used to overcome the in-plane eigenproblem of cable-stayed bridges (CSBs). The modeling method is divided into three steps. Firstly, according to the multi-tower configuration and mechanical characteristics of the CSB, the entire CSB is divided into multiple substructures, namely, a single-tower CSB. Secondly, the substructure is treated by a novel method to make it be a chain-like system and the dynamic triple-beam model with discrete springs is developed. The eigenproblem of the substructure is solved by transfer matrix method (TMM). Then, the entire multi-beam model with discrete springs of the CSB can be obtained by assembling all substructures with consideration of the matching conditions, and the eigenvalue and eigenvector of the CSB can be solved by TMM considering the boundary conditions. The above method is demonstrated by four examples of two kinds of CSBs, namely, semi-floating and rigid-frame CSBs, which are also verified by finite element method (FEM). The proposed model and solution method can be used to calculate the natural frequency and mode shape and evaluate the vertical bending stiffness of the CSB.     

The role of processing-by-attribute noncompensatory choice models

Research work on modeling consumer multiple choice problems using logit, regression, and probit is gaining more attention. However, in their work, Russ (1971), Tversky (1972), Newell and Simon (1972), Tversky and Sattath (1979), and Gensch and Svestka (1979; 1984) indicate that for many problems, choice behavior appears to be context dependent and hierarchical. With this specific issue in mind, this paper discusses a mathematical model which estimates threshold tolerances, eliminates nonchosen alternatives, provides choice probabilities and finally offers diagnostic information regarding the key attributes that are responsible for making a final decision. The use of other individual specific models such as: lexicographic, conjunctive, etc., have been briefly explicated.     

Determining Economic Maintenance Frequency for a Family of Machines

This paper deals with the problem of determining economic maintenance frequency for a group of machines. The operating cost for each machine is assumed to increase with time since the last maintenance work carried out on the machine. The cost of carrying out maintenance work is known and assumed constant. A fixed cost is incurred whenever maintenance work is carried out, and this fixed cost is assumed to be independent of the number of machines on which maintenance work is carried out. The total cost of the system is given by the sum of maintenance and operating costs for all the machines. A heuristic method is proposed for determining the economic maintenance frequency of each machine. An example is given to illustrate the method.     

A holistic methodology for modeling consumer response to innovation

A general structural equation model for representing consumer response to innovation is derived and illustrated. The approach both complements and extends an earlier model proposed by Hauser and Urban. Among other benefits, the model is able to take measurement error into account explicitly, to estimate the intercorrelation among exogenous factors if these exist, to yield a unique solution in a statistical sense, and to test complex hypotheses (e.g., systems of relations, simultaneity, feedback) associated with the measurement of consumer responses and their impact on actual choice behavior. In addition, the procedures permit one to model environmental and managerially controllable stimuli as they constrain and influence consumer choice. Limitations of the procedures are discussed and related to existing approaches. Included in the discussion is a development of four generic response models designed to provide a framework for modeling how consumers behave and how managers might better approach the design of products, persuasive appeals, and other controllable factors in the marketing mix.     

Probabilities for Queueing Systems with Embedded Markov Chains

Abstract

Transition probabilities of embedded Markov chain for single-server queues are considered when the distribution of the inter-arrival time or that of the service time is specified. A comprehensive collection of formulas is derived for the transition probabilities, covering some seventeen flexible families. The corresponding estimation procedures are also derived by the method of moments. It is expected that this work could serve as a useful reference for the modeling of queuing systems with embedded Markov chains.     

Multiscale failure Modeling of composites using generalized finite element method

In this work multiscale failure modeling of composites is made using generalized finite element method (GFEM). In this method the global approximation are constructed by combining the local basis with partition of unity functions. The enrichment functions for the GFEM approximation are computed using a proper orthogonal decomposition (POD) technique. The approximation is then used in a two scale Galerkin scheme for failure modeling of composites. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A framework for solving network revenue management problems with customer choice behavior

Revenue management is the process of understanding, anticipating and influencing consumer behavior in order to maximize revenue. Network revenue management models attempt to maximize revenue when customers buy bundles of multiple resources. The dependence among the resources in such cases is created by customer demand. Network revenue management can be formulated as a stochastic dynamic programming problem whose exact solution is computationally intractable. Solutions are based on approximations of various types. Customer choice behavior modeling has been gaining increasing attention in the revenue management. A framework for solving network revenue management problems with customer choice behavior is proposed. The modeling and solving framework is composed from three inter-related network structures: basic network model, Petri net, and neural net.     

Unscented Kalman filter for time varying spectral analysis of earthquake ground motions

A novel parametric time-domain method for time varying spectral analysis of earthquake ground motions is presented. Based upon time varying autoregressive moving average (ARMA) modeling of earthquake ground motion, unscented Kalman filter (UKF) is used to estimate the time varying ARMA coefficients. Then, time varying spectrum is yielded according to the time varying ARMA coefficients. Analysis of the ground motion record El Centro (1940, N–S) shows that compared to Kalman filter (KF) based method, short-time Fourier transform (STFT) and wavelet transform (WT), UKF based method can more reasonably represent the distribution of the seismic energy in time–frequency plane, which ensures its better ability to track the local properties of earthquake ground motions and to identify the systems with nonlinearity. Analysis of the seismic response of a building during the 1994 Northridge earthquake shows that UKF based method can be potentially a useful tool for structural damage detection and health monitoring. Lastly, it is found that the theoretical frequency resolving power of ARMA models usually neglected in some studies has considerable effect on time varying spectrum and it is one of the key factors for ARMA modeling of earthquake ground motion.     

基于灰色系统建模的上海城市居民可支配收入与消费支出关系的实证研究

按不同收入层次可支配收入水平与相应的消费支出关系分别建立GM(0,2)模型,分析不同层次收入群体的灰边际消费倾向变化规律;通过GM(1,2)建模,进一步分析了可支配收入对消费支出的驱动作用,研究了可支配收入与消费支出关系系统的协调性;通过对不同时段收入与支出关系的建模比较,进一步分析了不同层次收入群体灰边际消费倾向的动态变化,有效地改善了模型研究的局限性。     

Bifurcation-free design method of pulse energy converter controllers

In this paper, a design method of pulse energy converter (PEC) controllers is proposed. This method develops a classical frequency domain design, based on the small signal modeling, by means of an addition of a nonlinear dynamics analysis stage. The main idea of the proposed method consists in fact that the PEC controller, designed with an application of the small signal modeling, is tuned after with taking into the consideration an essentially nonlinear nature of the PEC that makes it possible to avoid bifurcation phenomena in the PEC dynamics at the design stage (bifurcation-free design). Also application of the proposed method allows an improvement of the designed controller performance. The application of this bifurcation-free design method is demonstrated on an example of the controller design of direct current–direct current (DC–DC) buck converter with an input electromagnetic interference filter.     

Frequency response analysis of laminated composite beams

Conclusions The modeling of laminated composite beams has been derived systematically from the three-dimensional elasticity relations. The correctness of the solution found by using the present finite element model is verified by comparison with the results obtained by analytical solutions and other results presented in the literature. Numerical results indicate that the present technique can given accurate results for frequency response analysis for laminated composite beams. Loss factors of structures obtained by the method of complex eigenvalues and the direct frequency response method exhibit very good agreement. Optimum design of a laminated composite beam by the finite element method and the method of experiment planning has been successfully presented.Published in Mekhanika Kompozitnykh Materialov, Vol. 30, No. 5, pp. 664–674, September–October, 1994.     

The Emergence of Mathematical Modeling Competencies: An Investigation of Prospective Secondary Mathematics Teachers

A study with prospective teachers without prior mathematical modeling experience sheds light on how their newly developed conceptual understanding of modeling manifested itself in their work on the final task of a modeling module within a pedagogy course in secondary mathematics curriculum and assessment. The main purpose of the module was to provide opportunity for the prospective teachers to experience the Common Core Mathematical Practice Model with Mathematics and begin to develop competency in modeling. Their work and reflections displayed a range of proficiency in several competencies associated with the modeling process. Examples of their work illustrating these ranges are provided. The prospective teachers expressed both struggle and rewards during the process, and reflected on challenges for teaching modeling. The results suggest that infusing modules in existing courses can be an effective way to elevate prospective teachers from unfamiliarity with modeling to noticeable levels of proficiency in various modeling sub-competencies.     

企业声誉在电子商务消费者信任建立过程的作用机制

声誉是企业的一项重要无形资产,能够增进企业对消费者的吸引力。本文从消费者视野探索企业声誉在电子商务消费者信任建立过程的作用机制。将感知的安全性引入技术接受模型,建立了理论模型及假设,并应用结构方程模型分析软件进行了检验。结果表明,企业声誉通过消费者感知的安全性、有用性和易用性正向影响消费者信任,消费者感知的安全性、易用性也通过感知的有用性影响消费者信任。     

A projection method for phase field models in micromagnetics

Magnetic materials have been finding increasingly wider areas of application in industry and therefore, as indicated by the reviews [1], [2] and [3], there is an increased interest in the efficient modeling of such materials that have an inherent coupling between the magnetic and mechanical characteristics. A particular challenge in the modeling of such materials is the algorithmic preservation of the geometric constraint on the magnetization field, that remains constant in magnitude [4]. In earlier works, [5] and [6], we presented a phase field model within a geometrically exact incremental variational framework where the geometric property of the magnetization director is exactly preserved pointwise by nonlinear rotational updates at the nodes. In the current work however, we present an alternative approach that involves an operator split along with a projection step for the magnetization vector. This method provides significant advantages in terms of speed and ease of implementation at the cost of the maximum time step size used. The current work therefore presents comparative study of the the two methods. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Prediction of the dynamic response of a mini-cantilever beam partially submerged in viscous media using finite element method

In this work, the use of mini cantilever beams for characterization of rheological properties of viscous materials is demonstrated. The dynamic response of a mini cantilever beam partially submerged in air and water is measured experimentally using a duel channel PolyTec scanning vibrometer. The changes in dynamic response of the beam such as resonant frequency, and frequency amplitude are compared as functions of the rheological properties (density and viscosity) of fluid media. Next, finite element analysis (FEA) method is adopted to predict the dynamic response of the same cantilever beam. The numerical prediction is then compared with experimental results already performed to validate the FEA modeling scheme. Once the model is validated, further numerical analysis was conducted to investigate the variation in vibration response with changing fluid properties. Results obtained from this parametric study can be used to measure the rheological properties of any unknown viscous fluid.