### 统计代写|运筹学作业代写operational research代考|Transportation Models

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• 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

## 统计代写|运筹学作业代写operational research代考|Concept of Transportation Problem

The transportation problem, first described by Hitchcock in 1941 , is a special class of linear programming (LP) problem. The objective is to yield the leastcost means of shipment through a transportation network in which there is a set of origins providing a commodity to a definite number of destinations. Suppose that a number of suppliers $(i=1,2, \ldots, m)$ provides a commodity to a number of customers $(j=1,2, \ldots, n)$. The transportation problem determines to meet each customer’s requirement, $d_{j}$, while not exceeding the capacity of any supplier, $s_{i}$ at minimum cost, $c_{i j}$. By introducing variables $x_{i j}$ to represent the quantity of the commodity sent from supplier $i$ to customer $j$, the transportation model can be written as shown in Model 2.1.1.
Model 2.1.1 Standard transportation model
Minimize $z=\sum_{i=1}^{m} \sum_{j=1}^{n} c_{i j} x_{i j}$
subject to
$$\sum_{j=1}^{n} x_{i j} \leq s_{i} \quad i=1,2, \ldots, m$$

\begin{aligned} \sum_{i=1}^{m} x_{i j} \geq d_{j} \quad j=1,2, \ldots, n \ & \text { All } x_{i j} \geq 0 \end{aligned}
Model 2.1.1 is referred to as the transportation model. Objective function 2.1.1 minimizes the total transportation cost. Unit transportation costs $c_{i j}$ for shipping 1 unit of commodity from supplier $i$ to customer $j$ are known. These costs are often dependent on the travel distances between supplier $i$ to customer $j$. It is assumed that the cost on a particular route of the transportation network is directly proportional to the number of commodities shipped on that route. If supplier $i$ cannot supply customer $j$, the unit transportation cost $c_{i j}$ is considered infinite $(\infty)$. Constraint set $2.1 .2$ is known as a supply constraint or availability constraint, and constraint set 2.1.3 is known as a demand constraint or requirement constraint. It is assumed that the capacity of each supplier, $s_{j}$, and the demand of each customer, $d_{j}$, are known in advance. If the total supply equals the total demand, then the problem is said to be a balanced transportation problem. In this case, constraint sets $2.1 .2$, and $2.1 .3$ are treated as both equal instead of less than or equal to and greater than or equal to, respectively. If the total supply does not equal the total demand, then the problem is referred to as an unbalanced transportation problem. A dummy customer (when the total supply exceeds the total demand) or a dummy supplier (when the total demand exceeds the total supply) is added to balance the transportation model. Because shipments via the dummy supplier or dummy customer are not real shipments, the unit transportation costs assigned to them are 0 .

## 统计代写|运筹学作业代写operational research代考|Example of Transportation Problem

Figure $2.1$ shows a transportation network in which there are four suppliers and five customers. The unit transportation costs are shown above the arcs, or arrows. For example, it costs 3 units of dollars to ship 1 unit of commodity from supplier 1 to customer 1 . The capacity of each supplier, $s_{i}$, and the demand of each customer, $d_{j}$, are also shown.

This transportation network or problem can be represented by a tableau as shown in Table 2.1. The upper-right corner of each cell in the tableau represents the unit transportation cost $c_{i j}$.

By introducing variables $x_{i j}$ to represent the quantity of the commodity shipped from supplier $i$ to customer $j$, this transportation problem can be formulated as shown in Model 2.1.2.

## 统计代写|运筹学作业代写operational research代考|Advanced Options in PROC OPTMODEL

As discussed earlier, PROC OPTMODEL provides a full environment for programming using do-loop, if-then-else, and many other programming statements. We can divide the syntax of PROC OPTMODEL into three types of statements:

1. Options in PROC OPTMODEL
2. Declaration of parameters and variables, as well as objective function and constraints
3. Programming statements
With the option statements, you can control how the optimization model is processed and how results are displayed. The declaration statements define the parameters, variables, constraints, and objectives that describe the model to be solved. All declarations in the PROC OPTMODEL are also saved for later use. The most popular declaration statements are:
• constraint (or con): Defines one or more constraints
• max/min: Declares an objective for the solver
• number (or num): Declares a numeric parameter
• string (or str): Declares a string parameter
• set: Declares a set type parameter
• var: Declares a variable
Parameters and variables can also be initialized using option “init.”

## 统计代写|运筹学作业代写operational research代考|Basic PROC OPTMODEL

PROC OPTMODEL非常强大，所以我们可以很方便的声明变量和参数，定义目标和约束，解决问题。它还为使用 do-loop、if-then-else 和许多其他编程语句进行编程提供了完整的环境。PROC OPTMODEL 的语法在附录 2 中给出。这里我们给出了在 PROC OPTMODEL 中定义线性规划的一些细节。

1. number：用于定义置信度
2. var：用于定义变量
3. 读取：用于将数据从数据集中加载到相应的参数
1. min/max：用于定义目标函数
2. con：用于定义约束
3. solve：使用选定的求解器解决问题
因为在大多数线性规划中，我们有一个变量向量和一个系数矩阵，PROC OPTMODEL 提供了一个索引工具来更有效地处理这些问题。可以使用整数或一组值来定义索引。例如，
数字 c{1..4}；
曾是⁡X1…4;
定义了四个可以称为的数字C[1],C[2],C[3]， 和C[4]并定义了四个变量，可以称为X[1],X[2],X[3]， 和X[4].

s=和⁡一世 在 1..4X[一世];

## 统计代写|运筹学作业代写operational research代考|

PROC OPTMODEL 中将数据初始化为参数的另一种方法是使用“读取”语句并使用数据集中保存的数据填充参数。假设 Program 中的数据1.4保存在银行数据集中；以下程序读取数据集并将其加载到相应的变量中： 在此代码中，我们使用了“读取”语句。第一个“读取”加载银行名称以设置行，而第二个“读取”将资本、劳动力和利润的价值加载到每个银行。

## 统计代写|运筹学作业代写operational research代考|Advanced Options in PROC OPTMODEL

1. PROC OPTMODEL 中的选项
2. 参数和变量的声明，以及目标函数和约束
3. 编程语句
使用选项语句，您可以控制优化模型的处理方式以及结果的显示方式。声明语句定义了描述要求解的模型的参数、变量、约束和目标。PROC OPTMODEL 中的所有声明也被保存以供以后使用。最流行的声明语句是：
• 约束（或con）：定义一个或多个约束
• max/min：为求解器声明一个目标
• number（或 num）：声明一个数字参数
• string（或str）：声明一个字符串参数
• set：声明一个集合类型参数
• var：声明一个变量
参数和变量也可以使用选项“init”进行初始化。

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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。