## 管理科学代写|决策论代写Management Science Models for Decision Making代考|QBUS3310

2022年10月6日

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
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## 管理科学代写|决策论代写Management Science Models for Decision Making代考|Operations Research: The Science of Better

Operations Research $(O R)$ is the branch of science dealing with tools or techniques for decision making to optimize the performance of systems, that is, to make those systems better. Measures of performance, of which there may be several, are numerical criteria that gauge the quality of some aspect of system’s performance, for example, annual profit or market share of a company, etc. They are of two types: (1) profit measures: (for these, the higher the value the better), (2) cost measures: (for these the lower the value the better).

OR deals with techniques for designing ways to operate the system to maximize profit measures or minimize cost measures as desired. Hence $\mathrm{OR}$ is the science to make systems better.

Linear Programming $(L P)$ is an important branch of OR dealing with decision problems modeled as those of optimizing a linear function of decision variables subject to linear constraints that may include equality constraints, inequality constraints, and bounds in decision variables. In an LP, all decision variables are required to be continuous variables that can assume all possible values within their bounds subject to the constraints. LPs are special instances of mathematical programming. Besides LP, the subject mathematical programming includes network, integer, combinatorial, discrete, quadratic, and nonlinear programming.

The focus of this book is to study important aspects of LP and QP (quadratic programming) and their intelligent applications for decision making.

We refer the reader to Chap. 3 in the Junior-level book (Murty (2005b) of Chap. 1; this book can be downloaded from the website mentioned there), where decisionmaking problems that can be modeled directly as LPs are discussed with many illustrative examples. In this chapter we extend the range of applications of LP to include decision-making problems involving the optimization of a piecewise linear objective function subject to linear constraints. When the objective function satisfies certain properties, these problems can be transformed into LPs in terms of additional variables.

## 管理科学代写|决策论代写Management Science Models for Decision Making代考|Differentiable Convex and Concave Functions

The concepts of convexity of functions, and of sets, are fundamental pillars in optimization theory. We already know that
a subset $K \subset R^n$ is said to be a convex set if for every pair of points $x, y \in K$, every convex combination of $x, y$ (i.e., point of the form $\alpha x+(1-\alpha) y$ for any $0 \leq \alpha \leq 1)$ is also in $K$.
A real-valued function $f(x)$ of decision variables $x=\left(x_1, \ldots, x_n\right)^T \in R^n$ is said to be a linear function if it satisfies the following two properties that together are known as the linearity assumptions:
Proportionality: $f(\alpha x)=\alpha f(x)$ for all $x \in R^n, \alpha \in R^1$
Additivity: $f(x+y)=f(x)+f(y)$ for all $x, y \in R^n$
An equivalent definition is: The real-valued function $f(x)$ defined over $x \in R^n$ is a linear function, iff there exists a row vector of constants $c=\left(c_1, \ldots, c_n\right)$ such that $f(x)=c_1 x_1+\ldots+c_n x_n=c x$ for all $x \in R^n$. In fact, for each $j=1$ to $n$, $c_j=f\left(I_{. j}\right)$, where $I_{. j}$ is the $j$ th column vector of the unit matrix $I$ of order $n$.
A real-valued function $\theta(x)$ of decision variables $x \in R^n$ is said to be an affine function if there exists a constant $c_0$ such that $\theta(x)-c_0$ is a linear function as defined earlier. Actually this constant $c_0=\theta(0)$. Thus equivalently, theta $(x)$ is an affine function iff there exist constants $c_0, c_1, \ldots, c_n$ such that $\theta(x)=c_0+c_1 x_1+\ldots+$ $c_n x_n$.

The concept of convexity of a function is defined by Jensen’s inequality stated below; it is related to the concept of convexity of a set, but we will not discuss this relationship in this book as it is not important for the things we discuss here. A function is said to be concave if its negative is convex, but there is no corresponding concept called “concavity” for sets.

Linear and affine functions are both convex and concave; but convex and concave functions may be nonlinear. In this section, we study important properties of differentiable convex, concave functions, which may be nonlinear. A requirement is that the set on which a convex or concave function is defined must be a convex set. We will study convex, concave functions defined over $R^n$ (or over a convex subset of it) for $n \geq 1$ in this section.

# 决策论代写

## 管理科学代写|决策论代写管理科学决策模型代考|运筹学:更好的科学

OR处理设计操作系统的方法的技术，以便按需要使利润措施最大化或使成本措施最小化。因此$\mathrm{OR}$是使系统更好的科学。

## 管理科学代写|决策论代写管理科学决策模型代考|可微凸凹函数

$f(\alpha x)=\alpha f(x)$ 为所有人 $x \in R^n, \alpha \in R^1$

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。