On generating multivariate Poisson data in management science applications

Generating multivariate Poisson random variables is essential in many applications, such as multi echelon supply chain systems, multi‐item/multi‐period pricing models, accident monitoring systems, etc. Current simulation methods suffer from limitations ranging from computational complexity to restrictions on the structure of the correlation matrix, and therefore are rarely used in management science. Instead, multivariate Poisson data are commonly approximated by either univariate Poisson or multivariate Normal data. However, these approximations are often not adequate in practice. In this paper, we propose a conceptually appealing correction for NORTA (NORmal To Anything) for generating multivariate Poisson data with a flexible correlation structure and rates. NORTA is based on simulating data from a multivariate Normal distribution and converting it into an arbitrary continuous distribution with a specific correlation matrix. We show that our method is both highly accurate and computationally efficient. We also show the managerial advantages of generating multivariate Poisson data over univariate Poisson or multivariate Normal data. Copyright © 2011 John Wiley & Sons, Ltd.     

THE ENSEMBLE KALMAN FILTER FOR MULTIDIMENSIONAL BIOECONOMIC MODELS

To integrate economic considerations into management decisions in ecosystem frameworks, we need to build models that capture observed system dynamics and incorporate existing knowledge of ecosystems, while at the same time accommodating economic analysis. The main constraint for models to serve in economic analysis is dimensionality. In addition, to apply in long‐term management analysis, models should be stable in terms of adjustments to new observations. We use the ensemble Kalman filter to fit relatively simple models to ecosystem or foodweb data and estimate parameters that are stable over the observed variability in the data. The filter also provides a lower bound on the noise terms that a stochastic analysis requires. In this paper, we apply the filter to model the main interactions in the Barents Sea ecosystem. In a comparison, our method outperforms a regression‐based approach.     

A MIXED CONTROL PROBLEM OF THE MANAGEMENT OF NATURAL RESOURCES

In this paper, we study the optimal solutions of a model of natural resource management which allows for both impulse and continuous harvesting policies. This type of model is known in the literature as mixed optimal control problem. In the resource management context, each type of control represents a different harvesting technology, which has a different cost. In particular, we want to know when the following conjecture made by Clark is an optimal solution to this mixed optimal control problem: if the harvesting capacity is unlimited, it is optimal to jump immediately to the steady state of the continuous time problem and then to stay there. We show that under a particular relationship between the continuous and the impulse profit function, the conjecture made by Clark is true. In other cases, however, it is either better to use only continuous control variables or to jump to resource levels which are smaller than the steady state and then let the resource grow back to the steady state. These results emphasize the importance of the cost functions in the modeling of natural resource management.     

Imputation of Mixed Data With Multilevel Singular Value Decomposition

Statistical analysis of large datasets offers new opportunities to better understand underlying processes. Yet, data accumulation often implies relaxing acquisition procedures or compounding diverse sources. As a consequence, datasets often contain mixed data, that is, both quantitative and qualitative, and many missing values. Furthermore, aggregated data present a natural multilevel structure, where individuals or samples are nested within different sites, such as countries or hospitals. Imputation of multilevel data has therefore drawn some attention recently, but current solutions are not designed to handle mixed data, and suffer from important drawbacks, such as their computational cost. In this article, we propose a single imputation method for multilevel data, which can be used to complete either quantitative, categorical, or mixed data. The method is based on multilevel singular value decomposition (SVD), which consists in decomposing the variability of the data into two components, the between and within groups variability, and performing an SVD on both parts. We show on a simulation study that in comparison to competitors, the method has the advantages of handling datasets of various size, and being computationally faster. Furthermore, it is the first so far to handle mixed data. We apply the method to impute a medical dataset resulting from the aggregation of several hospitals datasets. This application falls in the framework of a larger project on Trauma patients. To overcome obstacles associated to the aggregation of medical data, we turn to distributed computation. The method is implemented in the R package missMDA. Supplementary materials for this article are available online.     

The present value of resources with large discount rates

This paper describes a method to detect limit cycles for optimal control problems in the plain. The procedure includes two steps. First, the solution paths are analytically studied for large discount rates. Second, we demonstrate by means of computer simulations how the dynamics found can be traced back to small discount rates. We apply this method to two specific examples from resource management: a taxation problem and an exploited system of predator-prey interaction which show that the limit cycles may grow as the discount rates decrease. The principle that small discount rates are more conservative than large ones is therefore questionable. The relation of our results to theorems in optimal growth theory is also discussed. This paper is part of a research project on “Cyclical Resource Management” financially supported by the German Science Foundation (DFG).     

Compression and denoising using <Emphasis Type="Italic">l</Emphasis><Subscript>0</Subscript>-norm

In this paper, we deal with l ₀-norm data fitting and total variation regularization for image compression and denoising. The l ₀-norm data fitting is used for measuring the number of non-zero wavelet coefficients to be employed to represent an image. The regularization term given by the total variation is to recover image edges. Due to intensive numerical computation of using l ₀-norm, it is usually approximated by other functions such as the l ₁-norm in many image processing applications. The main goal of this paper is to develop a fast and effective algorithm to solve the l ₀-norm data fitting and total variation minimization problem. Our idea is to apply an alternating minimization technique to solve this problem, and employ a graph-cuts algorithm to solve the subproblem related to the total variation minimization. Numerical examples in image compression and denoising are given to demonstrate the effectiveness of the proposed algorithm.     

APPLICATION OF BAYESIAN STATISTICAL INFERENCE AND DECISION THEORY TO A FUNDAMENTAL PROBLEM IN NATURAL RESOURCE SCIENCE: THE ADAPTIVE MANAGEMENT OF AN ENDANGERED SPECIES

Abstract A fundamental problem of interest to contemporary natural resource scientists is that of assessing whether a critical population parameter such as population proportion p has been maintained above (or below) a specified critical threshold level p_c. This problem has been traditionally analyzed using frequentist estimation of parameters with confidence intervals or frequentist hypothesis testing. Bayesian statistical analysis provides an alternative approach that has many advantages. It has a more intuitive interpretation, providing probability assessments of parameters. It provides the Bayesian logic of “if (data), then probability (parameters)” rather than the frequentist logic of “if (parameters), then probability (data).” It provides a sequential, cumulative, scientific approach to analysis, using prior information and reassessing the probability distribution of parameters for adaptive management decision making. It has been integrated with decision theory and provides estimates of risk. Natural resource scientists have the opportunity of using Bayesian statistical analysis to their advantage now that this alternative approach to statistical inference has become practical and accessible.     

Multistage stochastic portfolio optimisation in deregulated electricity markets using linear decision rules

The deregulation of electricity markets increases the financial risk faced by retailers who procure electric energy on the spot market to meet their customers’ electricity demand. To hedge against this exposure, retailers often hold a portfolio of electricity derivative contracts. In this paper, we propose a multistage stochastic mean-variance optimisation model for the management of such a portfolio. To reduce computational complexity, we apply two approximations: we aggregate the decision stages and solve the resulting problem in linear decision rules (LDR). The LDR approach consists of restricting the set of recourse decisions to those affine in the history of the random parameters. When applied to mean-variance optimisation models, it leads to convex quadratic programs. Since their size grows typically only polynomially with the number of periods, they can be efficiently solved. Our numerical experiments illustrate the value of adaptivity inherent in the LDR method and its potential for enabling scalability to problems with many periods.     

Randomized allocation processes

Many dynamic resource allocation and on‐line load balancing problems can be modeled by processes that sequentially allocate balls into bins. The balls arrive one by one and are to be placed into bins on‐line without using a centralized controller. If n balls are sequentially placed into n bins by placing each ball in a randomly chosen bin, then it is widely known that the maximum load in bins is ln n /ln ln n?(1+o(1)) with high probability. Azar, Broder, Karlin, and Upfal extended this scheme, so that each ball is placed sequentially into the least full of d randomly chosen bins. They showed that the maximum load of the bins reduces exponentially and is ln ln n/In d+Θ(1) with high probability, provided d<2. In this paper we investigate various extensions of these schemes that arise in applications in dynamic resource allocation and on‐line load balancing. Traditionally, the main aim of allocation processes is to place balls into bins to minimize the maximum load in bins. However, in many applications it is equally important to minimize the number of choices performed (the allocation time). We study adaptive allocation schemes that achieve optimal tradeoffs between the maximum load, the maximum allocation time, and the average allocation time. We also investigate allocation processes that may reallocate the balls. We provide a tight analysis of a natural class of processes that each time a ball is placed in one of d randomly chosen bins may move balls among these d bins arbitrarily. Finally, we provide a tight analysis of the maximum load of the off‐line process in which each ball may be placed into one of d randomly chosen bins. We apply this result to competitive analysis of on‐line load balancing processes. ©2001 John Wiley & Sons, Inc. Random Struct. Alg., 18: 297–331, 2001     

Monte Carlo methods for mean-risk optimization and portfolio selection

Stochastic programming is a well-known instrument to model many risk management problems in finance. In this paper we consider a stochastic programming model where the objective function is the variance of a random function and the constraint function is the expected value of the random function. Instead of using popular scenario tree methods, we apply the well-known sample average approximation (SAA) method to solve it. An advantage of SAA is that it can be implemented without knowing the distribution of the random data. We investigate the asymptotic properties of statistical estimators obtained from the SAA problem including examining the rate of convergence of optimal solutions of the SAA problem as sample size increases. By using the classical penalty function technique and recent results on uniform exponential convergence of sample average random functions, we show that under some mild conditions the statistical estimator of the optimal solution converges to its true counterpart at an exponential rate. We apply the proposed model and the numerical method to a portfolio management problem and present some numerical results.     

基于教育部评价指标的高校发展仿真模型建立与应用研究

高校管理是一项涉及多层面、多要素变量的复杂系统,教育部建立高校评价指标体系对各高校现发展水平进行评价,促进国家教育发展.如何建立科学的评价指标体系?如何提高评价效应已有很多研究.但,未来发展仿真研究很少,因此,进行依据评价指标建立仿真方程、建立可靠性高的仿真模型研究很有意义.本文运用逐树设撤关联数结构行为检验建模法,基于教育部高校评价指标体系建立6个流位流率对构成的流位流率系;分别应用流率历史枝、主撑枝、条件枝法构建6棵流率入树基本结构,基于历史数据建立流率历史枝变量仿真方程;基于教育部高校评价指标的内涵等式建立刻画未来发展的主撑枝变量的仿真方程,基于表函数、延迟函数等建立条件枝变量仿真方程;通过设撤关联数分别进行T1(t)、T1(t)T2(t)、…、T1(t)T2(t)T3(t)…T6(t)各入树组合的结构行为检验,提高模型的可靠性,构建了高校管理系统的系统动力学(SD)评价仿真模型.通过高校最重要人力资源教师发展规划实施调控函数的不同调控参数下分别进行全系统仿真,分别揭示十二五、十三五期间各年满足教育部评价指标的教师数、在校生数、校建面积、教学设备、专业、收支差的数据复杂定量变化结果.为典型高校未来发展提供了具普遍意义的决策依据,为基于评价指标建立仿真方程,为提高仿真模型可靠性提供了新方法.     

基于关键链方法的多项目共享人力资源均衡问题及其遗传算法

通过对多项目管理瓶颈的分析,结合关键链方法,设置了瓶颈缓冲,建立了基于关键链方法的多项目管理,为多项目管理提供了一种新的管理方法.将基于关键链方法的多项目管理方法应用于并行多项目共享人力资源冲突管理,建立了基于遗传算法的多项目共享人力资源均衡模型,为缓解多项目共享人力资源供求矛盾提供了一种具体的量化管理方法,并进行了算例分析,证明了模型的有效性、实用性.     

企业库存问题研究－离散事件的动态模拟

本文在详细占有统计数据的基础上，对玻壳厂的库存问题进行了研究，并用统计实验方法作了动态模拟，得到了可供选择的较优解。本文的方法和度序原则上也适用于其它生产企业和商业机构甚至后勤部门。     

Epi-convergent discretizations of stochastic programs via integration quadratures

Summary. The simplest and the best-known method for numerical approximation of high-dimensional integrals is the Monte Carlo method (MC), i.e. random sampling. MC has also become the most popular method for constructing numerically solvable approximations of stochastic programs. However, certain modern integration quadratures are often superior to crude MC in high-dimensional integration, so it seems natural to try to use them also in discretization of stochastic programs. This paper derives conditions that guarantee the epi-convergence of the resulting objectives to the original one. Our epi-convergence result is closely related to some of the existing ones but it is easier to apply to discretizations and it allows the feasible set to depend on the probability measure. As examples, we prove epi-convergence of quadrature-based discretizations of three different models of portfolio management and we study their behavior numerically. Besides MC, our discretizations are the only existing ones with guaranteed epi-convergence for these problem classes. In our tests, modern quadratures seem to result in faster convergence of optimal values than MC.Mathematics Subject Classification (2000): 90C15, 49M25The work of this author was partially supported by The Finnish Foundation for Economic Education under grant no. 21599 and by Finnish Academy under contract no. 3385     

Scheduling data transfers in a network and the set scheduling problem

In this paper we consider the online ftp problem. The goal is to service a sequence of file transfer requests given bandwidth constraints of the underlying communication network. The main result of the paper is a technique that leads to algorithms that optimize several natural metrics, such as max-stretch, total flow time, max flow time, and total completion time. In particular, we show how to achieve optimum total flow time and optimum max-stretch if we increase the capacity of the underlying network by a logarithmic factor. We show that the resource augmentation is necessary by proving polynomial lower bounds on the max-stretch and total flow time for the case where online and offline algorithms are using same-capacity edges. Moreover, we also give polylogarithmic lower bounds on the resource augmentation factor necessary in order to keep the total flow time and max-stretch within a constant factor of optimum.     

Random orthogonal matrix simulation

This paper introduces a method for simulating multivariate samples that have exact means, covariances, skewness and kurtosis. We introduce a new class of rectangular orthogonal matrix which is fundamental to the methodology and we call these matrices L matrices. They may be deterministic, parametric or data specific in nature. The target moments determine the L matrix then infinitely many random samples with the same exact moments may be generated by multiplying the L matrix by arbitrary random orthogonal matrices. This methodology is thus termed “ROM simulation”. Considering certain elementary types of random orthogonal matrices we demonstrate that they generate samples with different characteristics. ROM simulation has applications to many problems that are resolved using standard Monte Carlo methods. But no parametric assumptions are required (unless parametric L matrices are used) so there is no sampling error caused by the discrete approximation of a continuous distribution, which is a major source of error in standard Monte Carlo simulations. For illustration, we apply ROM simulation to determine the value-at-risk of a stock portfolio.     

企业库存问题研究－离散事件的动态模拟

本文在详细占有统计数据的基础上，对玻壳厂的库存问题进行了研究，并用统计实验方法作了动态模拟，得到了可供选择的较优解。本文的方法和度序原则上也适用于其它生产企业和商业机构甚至后勤部门。     

Simulation of Stationary Gaussian Processes in [0, 1] d

Abstract

A method for simulating a stationary Gaussian process on a fine rectangular grid in [0, 1]^d ??^d is described. It is assumed that the process is stationary with respect to translations of ?^d, but the method does not require the process to be isotropic. As with some other approaches to this simulation problem, our procedure uses discrete Fourier methods and exploits the efficiency of the fast Fourier transform. However, the introduction of a novel feature leads to a procedure that is exact in principle when it can be applied. It is established that sufficient conditions for it to be possible to apply the procedure are (1) the covariance function is summable on ?^d, and (2) a certain spectral density on the d-dimensional torus, which is determined by the covariance function on ?^d, is strictly positive. The procedure can cope with more than 50,000 grid points in many cases, even on a relatively modest computer. An approximate procedure is also proposed to cover cases where it is not feasible to apply the procedure in its exact form.     

A puzzle rhyme from 1782

A puzzle of thirty birds, known in many ancient cultures, is found in an Icelandic spelling book for children from 1782, transposed into Icelandic context so well that it seemed genuinely domestic. Its form is a three-verse rhyme governed by complex Old-Germanic rules of prosody. The birds are sold for units typical for Icelandic middle-age trade commodities, used up to recent times. The composition is completely adjusted to the Icelandic culture and may therefore be considered as Icelandic ethnomathematics of early modern times.     

基于小波神经网络的海上突发事件应急资源动态需求预测

近年来海洋综合开发势头迅猛,海上船舶运输业的发展迅速,然而在创造可观的经济效益和社会效益的同时,海上险情事故频发,应急资源需求复杂多变。本文尝试将小波理论应用于海上应急管理领域,运用小波神经网络模型预测未来周期内的海域险情事故数。在海域险情事故预测的基础上,结合应急资源种类、海域的风险程度等影响因素,引入平均风险月度系数,构建了海上突发事件应急资源动态需求概念模型,间接预测应急资源需求,并提出部分可替代应急资源需求的预测思路。并以山东海事辖区为例,验证了该方法的有效性和可行性。