### 统计代写|运筹学作业代写operational research代考|Operational Research, Algorithms, and Methods

statistics-lab™ 为您的留学生涯保驾护航 在代写运筹学operational research方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写运筹学operational research代写方面经验极为丰富，各种代写运筹学operational research相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• 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

## 统计代写|运筹学作业代写operational research代考|Operational Research, Algorithms, and Methods

The term operations research (or operational research as appears in this book) was introduced in England during World War II when British military leaders ordered scientists to make decisions concerning the optimal use and allocation of limited war material and resources such as radar and bombing. After the war, the success of operational research was extensively recognized.
Operational research is a scientific decision-making tool that involves the use of a mathematical programming model. A mathematical programming model is a mathematical representation of the actual situation that may be used to make better decisions or simply to understand the actual situation better (Winston and Venkataramanan 2003). The common feature that mathematical programming models have is that they all involve optimization (Williams 1999), which includes the minimization of something (e.g., delivery time and production cost) or the maximization of something (e.g., customer service level and profit) under certain constraints (e.g., budget and human resources).

A set of fixed computational rules for solving a particular class of problems or models is known as an algorithm. It applies the rules repetitively to the problem or the model, and each iteration moves the solution closer to the optimum. In operational research, there is no algorithm that solves all types of mathematical models. For example, the simplex method is the general method for solving linear programming models, whereas the branch-andbound algorithm is the general technique for solving integer linear programming models.

In the following sections, attention is confined to the algorithms and methods for the linear programming model, integer linear programming model, and goal programming model. They are discussed because the practical examples, to be examined in Chapters 2 to 9 , can be formulated with these types of models.

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

A linear programming ( $L P)$ model comprises three basic elements: decision variables, objectives, and constraints. A model is defined as LP when the

objective function and the constraints involve linear expressions and the decision variables are continuous. The transportation model, to be presented in Section 2.1, is a special class of LP. Comparatively, LP models are given extensive attention in comparison with nonlinear programming models because they are much easier to solve and they have been applied successfully in many contexts, including agriculture, business, economics, environmental studies, government, higher education, logistics, manufacturing, and military planning.

The first step in formulating the LP model is to define the decision variables. They can be expressed in any form except nonlinear functions, such as $x_{1}^{2}$ and $x_{1} x_{2}$. Decision variables are the objects that the user needs to determine. For example, the decision variables in the transportation model are the quantities of commodities sent from a set of origins to a set of destinations.
After defining the decision variables, the user has to define an objective, which is the goal that they aim to optimize. Some prevalently used objectives include maximization of profit, maximization of workload balance, maximization of efficiency, maximization of customer satisfaction, minimization of cost, minimization of travelling distance, minimization of cycle time, and minimization of vehicles used.

The last elements of LP models are the constraints, which are the conditions that the user needs to satisfy. Some of the most common types of constraints used in LP models include customer demands, available workforce, available raw material, production time, available machinery, budget constraints, and subtour elimination constraints.
The general LP model can be formulated as shown in Model 1.1.1.

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

The simplex method, introduced by G. B. Dantzig, has proved highly efficient in practice and therefore was widely adopted in commercial optimization packages for solving any LP model (Jensen and Bard 2003). Its development was based on the graphical method, which states that the optimal solution is always associated with a corner point of the solution space. The idea of the simplex method is to move the solution to a new corner that has the potential to improve the value of the objective function in each iteration. The process terminates when the optimal solution is found (Taha 2003).

Before applying the method, an LP must be converted into a standard form. The conditions of the standard form are that all constraints must be transformed into equality constraints and that all variables must be nonnegative. If the constraint of an LP is a less-than-or-equal-to constraint, it can be converted into an equality constraint by adding a slack variable. If it is a greater-than-or-equal-to constraint, a surplus variable should be subtracted from the original constraint to become an equality constraint. A standard LP form aims at finding the basic solutions of the simultaneous linear equations. These basic solutions are exactly the corner point solutions of the solution space. The simplex method is then executed iteratively to search for the optimum from among these basic solutions.

The formal iterative steps of the simplex method are listed as (Winston and Venkataramanan 2003):

• Step 1: Obtain a basic feasible solution from the standard form.
• Step 2: Determine whether the current basic feasible solution is optimal.
• Step 3: If the current basic feasible solution is not optimal, then determine which nonbasic variable should become a basic variable and which basic variable should become a nonbasic variable to find a new basic feasible solution with a better objective function value.
• Step 4: Use elementary row operations to find the new basic feasible solution with the better objective function value. Return to Step $2 .$

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

LP 模型的最后一个元素是约束，即用户需要满足的条件。LP 模型中使用的一些最常见的约束类型包括客户需求、可用劳动力、可用原材料、生产时间、可用机器、预算约束和子旅游消除约束。

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

GB Dantzig 引入的单纯形法在实践中证明是高效的，因此在商业优化包中被广泛采用以解决任何 LP 模型（Jensen 和 Bard 2003）。它的发展是基于图解法，它指出最优解总是与解空间的一个角点相关联。单纯形法的思想是将解决方案移动到一个新的角落，该角落有可能在每次迭代中提高目标函数的值。当找到最佳解决方案时，该过程终止（Taha 2003）。

• 第一步：从标准表格中得到一个基本可行的解。
• 第二步：判断当前基本可行解是否最优。
• 第三步：如果当前的基本可行解不是最优的，则确定哪个非基本变量应该成为基本变量，哪个基本变量应该成为非基本变量，以找到具有更好目标函数值的新基本可行解。
• 第四步：利用初等行操作，找到目标函数值更好的新的基本可行解。返回步骤2.

## 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。