assignmentutor™您的专属作业导师

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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

Multiple-attribute decision-making (MADM) concerns in making decisions when there are multiple but a finite list of alternatives and criteria. This differs from analysis where we have alternatives and only one criterion such as cost. We address problems as in the DHS scenario where we have seven alternatives and six criteria that impact the decision.

Consider a problem where management needs to prioritize or rank order alternative choices such as identifying key nodes in a business network, picking a contractor or subcontractor, choosing an airport, ranking recruiting efforts, ranking banking facilities, and ranking schools or colleges. How does one proceed to accomplish this analytically?

In this chapter, we will present four methodologies to rank order or prioritize alternatives based on multiple criteria. These four methodologies include the following:

1. Data envelopment analysis (DEA)
2. Simple average weighting (SAW)
3. Analytical hierarchy process (AHP)
4. Technique of order preference by similarity to ideal solution (TOPSIS)
For each method, we describe the method and provide a methodology, discuss some strengths and limitations to the method, discuss tips for conducting sensitivity analysis, and present several illustrative examples.

The model, in simplest terms, may be formulated and solved as a linear programming problem (Callen, 1991; Winston, 1995). Although several formulations for DEA exist, we seek the most straightforward formulation in order to maximize an efficiency of a DMU as constrained by inputs and outputs as shown in Equation 4.1. As an option, we might normalize the metric inputs and outputs for the alternatives if the values are poorly scaled within the data. We will call this data matrix, X, with entries $x_{i i}$. We define an efficiency unit as $E_{i}$ for $i=1,2, \ldots$, nodes. Let $w_{i}$ be the weights or coefficients for the linear combinations. Further, we restrict any efficiency from being larger than one. Thus, the largest efficient DMU will be 1 . This gives the following linear programming formulation for single output but multiple inputs:
$\operatorname{Max} E_{i}$
subject to
$$\begin{gathered} \sum_{i=1}^{n} w_{i} x_{i j}-E_{i}=0, j=1,2, \ldots \ E_{i} \leq 1 \text { for all } i \end{gathered}$$
For multiple inputs and outputs, we recommend the formulations provided by Winston (1995) and Trick (2014) using Equation 4.2.

For any $\mathrm{DMU}{0}$, let $X{i}$ be the inputs and $Y_{i}$ be the outputs. Let $X_{0}$ and $Y_{0}$ be the DMUs being modeled.
$\operatorname{Min} \theta$
subject to
$$\begin{gathered} \sum \lambda_{i} X_{i} \leq \theta X_{0} \ \sum \lambda_{i} Y_{i} \leq Y_{0} \ \lambda_{l}>0 \end{gathered}$$
Nonnegativity

商业数学代考

1. 数据包络分析（DEA）
2. 简单平均加权 (SAW)
3. 层次分析法（AHP）
4. 通过与理想解决方案相似的顺序偏好技术 (TOPSIS)
对于每种方法，我们描述了该方法并提供了一种方法，讨论了该方法的一些优势和局限性，讨论了进行敏感性分析的技巧，并提供了几个说明性示例。

$\operatorname{Max} E_{i}$

$$\sum_{i=1}^{n} w_{i} x_{i j}-E_{i}=0, j=1,2, \ldots E_{i} \leq 1 \text { for all } i$$

$\operatorname{Min} \theta$

$$\sum \lambda_{i} X_{i} \leq \theta X_{0} \sum \lambda_{i} Y_{i} \leq Y_{0} \lambda_{l}>0$$

有限元方法代写

assignmentutor™作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师