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# 数学代写|运筹学代写Operations Research代考|MATH3202 The General Model and a Generic Solution Method

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## 数学代写|运筹学代写Operations Research代考|The General Model and a Generic Solution Method

Throughout this section, we assume that the decision maker has a finite number of possible decisions $d_1, d_2, \ldots, d_m$ that are to be evaluated on a number of criteria $c_1$, $c_2, \ldots, c_n$. All decisions are then evaluated on all criteria in a matrix (not unlike the payoff matrices in decision analysis). Without loss of generality, we assume that all criteria are of the utility type, i.e., more is always better. In case some of the criteria originally denote costs or distances, i.e., criteria for which less is better, we may convert them to utilities by multiplying them by some negative value or subtracting them from some large number.

In order to demonstrate some of the basic concepts, consider the problem of choosing a house. The decision maker has identified some of the criteria most important to him, which include the size of the house, the size of the lot, the taxes charged most recently, the price of the house, and the distance between the house and his place of work. Furthermore, the decision maker has chosen seven possible choices from a multiple listing service that provides some basic information (which is how these actual data have been determined). The information is summarized in Table 11.1.

Often, decision makers will also consider additional criteria, such as the number of bedrooms, bathrooms, and garages. All of these properties have two garages, four or five bedrooms, and $2 \frac{1}{2}$ to 3 baths, so that we have eliminated those criteria from further consideration. In general, decision makers should restrict themselves to, say, no more than six criteria, so as to avoid clutter and correlation. This limitation has been suggested by psychological research.

Clearly, there is usually a correspondence between the size of the house and the number of rooms in it. When considering correlated criteria, it is typically a good idea to include only one of those criteria and thus avoid considering and counting them multiple times.

## 数学代写|运筹学代写Operations Research代考|TOPSIS

The TOPSIS (Technique for $O$ rder of Preference by Similarity to Ideal Solution) was first described by Hwang and Yoon (1981). It evaluates decisions on the basis of the distances between their attributes and some ideal points: the closer a decision’s attributes are to the chosen ideal point, the better a decision is. In other words, we consider the distance as a disutility that we attempt to minimize. Even at this level, it is apparent that at least two user-defined measures will influence the solution: the choice of an ideal point and the yardstick used to measure the distance between the attributes of a decision and the ideal point.

We may explain the concept by means of a simple example. A student is in the process to choose one among four institutions of higher learning for his studies. In five topics, the choices are the “Business Undergraduate Necessary Knowledge” (BUNK), the “Online University of Indeterminate Junior Academics” (OUIJA), the Commonwealth Undergraduate Teaching Education (CUTE), and the “Business Undergraduate Liberal Learning”‘ (BULL). Given these choices (for simplicity, we will refer to them as $\mathrm{d}_1, d_2, d_3$, and $d_4$ ), the student wants to choose one of these institutions to learn about technical issues related to business. The attributes of the four institutions regarding the five programs are shown in Table 11.5, where all scores are expressed on a scale between 0 and 100 , where 100 means that the course perfectly suits our student’s interests, while 0 means that our student is not interested in that academy’s offering at all.

## 数学代写|运筹学代写Operations Research代考|TOPSIS

TOPSIS（技术 $O$ Hwang 和 Yoon (1981) 首次描术了与理想解决方案相似度的偏好。它根据属性与某些理想点之间的距离来评估 决策: 决策的属性越接近所选的理想点，决策就越好。换句话脱，我们将距离视为我们试图最小化的负效用。即使在这个级别，很 明显至少有两个用户定义的度量会影响解决方案：理想点的选择以及用于衡量决策属性与理想点之间距离的标准。

## 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。