数学代写|运筹学作业代写Operational Research代考|TIE2110

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。

数学代写|运筹学作业代写operational research代考|Encoding and evaluating the network reliability by $B D D$

The K-terminal network reliability function can be represented by a boolean function $f$ defined as follows:
$$\left{\begin{array}{l} f\left(x_1, x_2, \ldots, x_m\right)=1 \text { if nodes in } K \text { are linked by edges } e_i \text { with } x_i=1 \ f\left(x_1, x_2, \ldots, x_m\right)=0 \text { otherwise } \end{array}\right.$$
where boolean variable $x_i$ stands for the state of the link $e_i(1 \leq i \leq m)$. For instance, the boolean formula encoded by the BDD structure in figure 3 is:
$$x_1\left(\bar{x}_2\left(\bar{x}_3 x_4 x_5 x_6+x_3\left(\bar{x}_4 x_5 x_6+x_4\right)\right)+x_2\left(\bar{x}_4 x_5 x_6+x_4\right)\right)+\bar{x}_1 x_2\left(x_3\left(\bar{x}_4 x_5 x_6+x_4\right)+\bar{x}_3 x_5 x_6\right)$$
Our aim is to encode this reliability function by BDD. The algorithm is developed in Section 3.3. In figure 3(b), we explain the definition of BDD through an example of BDD representing the K-terminal reliability of network $\mathrm{G}$ (see figure

2). The BDD can represent the SDP implicitly avoiding huge storage for large number of SDP. A useful property of BDD is that all the paths from the root to the leaves are disjoint. If $f$ represents the system reliability expression, based on this property, the K-terminal network reliability $R_K$ of $G$ can be recursively evaluated by:
\begin{aligned} & \forall i \in{1, \ldots, m}: \ & R_K(p ; G)=\operatorname{Pr}(f=1) \ & R_K(p ; G)=\operatorname{Pr}\left(x_i \cdot f_{x_i=1}=1\right)+\operatorname{Pr}\left(\bar{x}i, f{x_i=0}=1\right) \ & R_K(p ; G)=p_i \cdot \operatorname{Pr}\left(f_{x_i=1}=1\right)+q_i \cdot \operatorname{Pr}\left(f_{x_i=0}=1\right) \ & \end{aligned}
with $p=\left(p_1, \ldots, p_m\right)$.
For instance, in figure $3(\mathrm{~b})$, the K-terminal network reliability is then defined as follows:
$$R_K(p ; G)=p_1\left(q_2\left(q_3 p_4 p_5 p_6+p_3\left(q_4 p_5 p_6+p_4\right)\right)+p_2\left(q_4 p_5 p_6+p_4\right)\right)+q_1 p_2\left(p_3\left(q_4 p_5 p_6+p_4\right)+q_3 p_5 p_6\right)$$
The next section presents our BDD-based algorithm for the K-terminal network reliability problem.

数学代写|运筹学作业代写operational research代考|Construction of the $B D D$ representing the $K$-terminal reliability function

We remind that the order of the variables is very important for BDD generation (see Section 2). Time and space complexity of BDD closely depend on variable ordering. This paper is not concerned with this kind of problem and we use a breadth-first-search (BFS) ordering.
In short, our algorithm follows three steps:

• 1 The edges are ordered by using a heuristic.
• 2 The BDD is generated to encode the network reliability. The following shows the construction of the BDD encoding the K-terminal network reliability.
• 3 From this BDD structure, we obtain the K-terminal network reliabilities (whatever $p_i, i \in[1 \ldots m]$ ) as shown in the previous section.

The top-down construction process can be represented as a binary tree such that the root corresponds to the original graph $G$ and children correspond to graphs obtained by deletion /contraction of edges. Nodes in the binary tree correspond to subgraphs of $G$. At the root, we consider the edge $e_1$, construct the subgraph $G_{-1}$, that is $G$ with $e_1$ deleted and the subgraph $G_{* 1}$ that is $G$ with $e_1$ contracted. Then at the second step, from $G_{-1}$, we construct $G_{-1-2}$ where $e_2$ is deleted and $G_{-1 * 2}$ where $e_2$ is contracted and so on from each created subgraphs until the vertices of $K$ are fully connected or at least one vertex of $K$ is disconnected. There are $2^n$ possible states and isomorphic graphs appear in the computation process. For the graph $G$ pictured in Fig. 2, its subgraphs $G_{* 1 * 2}$ and $G_{-1 * 2 * 3}$ are isomorphic. Our aim is to provide an efficient method in order to avoid redundant computation due to the appearance of isomorphic subproblems during the process. We use the method introduced by Carlier and Lucet ${ }^{15}$ for representing graph by partition which is an efficient way for solving this kind of problem. By identifying the isomorphic subgraphs an expansion tree is modified as a rooted acyclic graph which is a BDD (see figure $3(\mathrm{~b})$ ).

运筹学代考

数学代写|运筹学作业代写operational research代考|Encoding and evaluating the network reliability by $B D D$

k端网络可靠性函数可以用布尔函数$f$表示，定义如下:
$$\left{\begin{array}{l} f\left(x_1, x_2, \ldots, x_m\right)=1 \text { if nodes in } K \text { are linked by edges } e_i \text { with } x_i=1 \ f\left(x_1, x_2, \ldots, x_m\right)=0 \text { otherwise } \end{array}\right.$$

$$x_1\left(\bar{x}_2\left(\bar{x}_3 x_4 x_5 x_6+x_3\left(\bar{x}_4 x_5 x_6+x_4\right)\right)+x_2\left(\bar{x}_4 x_5 x_6+x_4\right)\right)+\bar{x}_1 x_2\left(x_3\left(\bar{x}_4 x_5 x_6+x_4\right)+\bar{x}_3 x_5 x_6\right)$$

2). BDD可以隐式地表示SDP，避免大量SDP占用巨大的存储空间。BDD的一个有用的性质是从根到叶的所有路径都是不相交的。若$f$表示系统可靠性表达式，则根据该性质，$G$的k端网络可靠性$R_K$可递归求出:
\begin{aligned} & \forall i \in{1, \ldots, m}: \ & R_K(p ; G)=\operatorname{Pr}(f=1) \ & R_K(p ; G)=\operatorname{Pr}\left(x_i \cdot f_{x_i=1}=1\right)+\operatorname{Pr}\left(\bar{x}i, f{x_i=0}=1\right) \ & R_K(p ; G)=p_i \cdot \operatorname{Pr}\left(f_{x_i=1}=1\right)+q_i \cdot \operatorname{Pr}\left(f_{x_i=0}=1\right) \ & \end{aligned}

$$R_K(p ; G)=p_1\left(q_2\left(q_3 p_4 p_5 p_6+p_3\left(q_4 p_5 p_6+p_4\right)\right)+p_2\left(q_4 p_5 p_6+p_4\right)\right)+q_1 p_2\left(p_3\left(q_4 p_5 p_6+p_4\right)+q_3 p_5 p_6\right)$$

数学代写|运筹学作业代写operational research代考|Construction of the $B D D$ representing the $K$-terminal reliability function

2生成BDD对网络可靠性进行编码。BDD编码k端网络可靠性的构造如下图所示。

有限元方法代写

tatistics-lab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。

数学代写|运筹学作业代写operational research代考|MGSC373

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。

数学代写|运筹学作业代写operational research代考|Binary Decision Diagram (BDD)

Akers ${ }^1$ first introduced BDD for representing boolean function. Bryant popularized the use of BDD by introducing a set of algorithms for efficient construction and manipulation of the BDD structure ${ }^2$. Nowadays, BDD are used in a wide range of area, including hardware synthesis and verification, model checking and protocol validation. Their use in the reliability analysis framework has been introduced by Madre and Coudert ${ }^5 4$ and developped by Odeh ${ }^6$ and Rauzy ${ }^3$. Sekine and Imai have introduced the BDD structure in network reliability ${ }^{10} 11$. The BDD structure provides compact representations of boolean expressions. A BDD is a directed acyclic graph (DAG) based on Shannon’s decomposition. The Shannon’s decomposition for a boolean function $f$ is defined as follows:
$$f=x f_{x=1}+\bar{x} f_{x=0}$$
where $x$ is one of decision variables and $f_{x=i}$ is the boolean function $f$ evaluated at $x=i$.

The graph has two sink nodes labeled with 0 and 1 representing the two corresponding constant expressions. Each internal node is labeled with a boolean variable $x$ and has two out-edges called 0 -edge and 1-edge. The node linked by 1-edge represents the boolean expression when $x=1$, i.e. $f_{x=1}$ while the node linked by 0 -edge represents the boolean expression when $x=0$, i.e. $f_{x=0}$. An ordered binary decision diagram (OBDD) is a BDD where variables are ordered according to a known total ordering and every path visits variables in an ascending order. Afterwards, BDDs will be considered as ordered. Leaves of the BDD give the value of $f$ for the assignment corresponding to a path from the root to the leaf.

The size of a BDD structure (the number of nodes) depends critically on the chosen variable ordering. Figure 1 shows the effect of the variable ordering on the BDD size. If we consider the expression $\left(x_1 \Leftrightarrow x_3\right) \wedge\left(x_2 \Leftrightarrow x_4\right)$ the resulting BDD using the ordering $x_1<x_2<x_3<x_4$ consists of 11 nodes (figure 1(a)) and not 8 nodes as for the ordering $x_1<x_3<x_2<x_4$ (figure 1(b)). Finding an ordering that minimizes the size of BDD is also a NP-complete problem ${ }^7$. Several heuristics relying on different principles have been proposed in many domains. However, they both try to put close in the order the variables that are close in the formula as illustrated in figure 1 .

数学代写|运筹学作业代写operational research代考|Definitions and notations

The K-terminal reliability computation is the most general network reliability problem found in the literature. It consists in evaluating the probability that net work components of a specified subset $K$ remain connected when the components are subject to failure.

Our network model is an undirected stochastic graph $G=(V, E)$, with $V$ its set of vertex (representing workstations, servers, routers …) and $E \subseteq V \times V$ its set of edges (representing the links between these nodes). Each edge $e_i$ of the stochastic graph is subject to failure with known probability $q_i$. We denote $p_i=1-q_i$ the probability that edge $e_i$ functions, and assume that all the failure events are statistically independent. In the following, we consider the vertices as perfect, but the proposed algorithms are still functioning for such problem. In classical enumerative method, all the states of the graph are generated, evaluated as a fail state or a functioning state, and then probabilistic methods are used for computing the associated reliability. So, as there are two states for each edge, there are $2^m$ (with $m=|E|$ ) possible states for the graph. A state $\mathcal{G}$ of the stochastic graph $G$ is denoted by $\left(x_1, x_2 \ldots, x_m\right)$ where $x_i$ stands for the state of edge $e_i$, i.e. $x_i=0$ when edge $e_i$ fails and $x_i=1$ when it functions. The associated probability of $\mathcal{G}$ is defined as:
$$\operatorname{Pr}(\mathcal{G})=\prod_{i=1}^m\left(x_i \cdot p_i+\left(1-x_i\right) \cdot q_i\right)$$
At each state $\mathcal{G}$ is associated a partial graph $G(\mathcal{G})=\left(V, E^{\prime}\right)$ such that $e_i \in E^{\prime}$ if and only if $e_i \in E$ and $x_i=1$. A path is defined as a set of edges such that if these edges are all up, the system is up. A path is minimal if it has no proper subpaths. We define a subset of the nodes $K \subseteq V$ to be the “terminals” (with $2 \leq|K| \leq|V|)$. If $|K|=2$ this problem is well-known as the 2 -terminal reliability problem and if $|K|=|V|$ it deals with the all-terminal reliability problem. The terminal nodes are essential to the system function and have to communicate with each other, i.e. the network is up if and only if there exists at least one path made of functioning edges linking nodes in $K$. The K-terminal reliability, denoted by $R_K(p ; G)\left(p=\left(p_1, \ldots, p_m\right)\right)$, is the probability that all vertices in $K$ are connected and can be defined as follows:
$$R_K(p ; G)=\sum_{\text {K-nodes are connected by working links in } G(\mathcal{G})} \operatorname{Pr}(\mathcal{G})$$

运筹学代考

数学代写|运筹学作业代写operational research代考|Binary Decision Diagram (BDD)

Akers ${ }^1$首先引入BDD来表示布尔函数。Bryant通过引入一套有效构建和操作BDD结构${ }^2$的算法，推广了BDD的使用。目前，BDD已广泛应用于硬件综合与验证、模型检验和协议验证等领域。它们在可靠性分析框架中的使用已由Madre和Coudert ${ }^5 4$引入，并由Odeh ${ }^6$和Rauzy ${ }^3$开发。Sekine和Imai在网络可靠性方面引入了BDD结构${ }^{10} 11$。BDD结构提供了布尔表达式的紧凑表示。BDD是基于香农分解的有向无环图(DAG)。布尔函数$f$的香农分解定义如下:
$$f=x f_{x=1}+\bar{x} f_{x=0}$$

BDD结构的大小(节点数量)主要取决于所选择的变量排序。图1显示了变量排序对BDD大小的影响。如果我们考虑表达式$\left(x_1 \Leftrightarrow x_3\right) \wedge\left(x_2 \Leftrightarrow x_4\right)$，那么使用顺序$x_1<x_2<x_3<x_4$得到的BDD由11个节点组成(图1(a))，而不是顺序$x_1<x_3<x_2<x_4$的8个节点(图1(b))。找到最小化BDD大小的排序也是一个np完全问题${ }^7$。许多领域都提出了基于不同原理的启发式方法。然而，它们都试图按照公式中接近的变量的顺序排列，如图1所示。

数学代写|运筹学作业代写operational research代考|Definitions and notations

k端可靠性计算是文献中发现的最普遍的网络可靠性问题。它包括评估特定子集$K$的网络组件在组件发生故障时保持连接的概率。

$$\operatorname{Pr}(\mathcal{G})=\prod_{i=1}^m\left(x_i \cdot p_i+\left(1-x_i\right) \cdot q_i\right)$$

$$R_K(p ; G)=\sum_{\text {K-nodes are connected by working links in } G(\mathcal{G})} \operatorname{Pr}(\mathcal{G})$$

有限元方法代写

tatistics-lab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。

数学代写|运筹学作业代写operational research代考|MATH3901

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。

数学代写|运筹学作业代写operational research代考|The Markov Chain Monte Carlo Method

In this section, we present the utilisation of Markov chain Monte Carlo method (see Chen, Shao and Ibrahim $^6$ ) for estimating $\tau$ and the parameters of the initial lifetime distribution. To simplify the matter, we assume that the first two lifetimes are observed and the repair type is known to be WTNBTU.

The McMC methods enable us to simulate a Markov chain whose stationary distribution is our “target” distribution, for instance, the posterior distribution of the parameter of interest. We will use the Gibbs sampler which is one of the McMC methods. Under our model, the Gibbs sampler can be described as follows:
(1) Start with an arbitrary initial vector $\theta^{(0)}=\left(\tau^{(0)}, \alpha^{(0)}, \beta^{(0)}\right)$ and set $k=0$.
(2) Sample $\tau^{(k+1)}$ from $\pi\left(\tau \mid \alpha^{(k)}, \beta^{(k)}, x_1, x_2\right)$.
(3) Sample $\alpha^{(k+1)}$ from $\pi\left(\alpha \mid \tau^{(k+1)}, \beta^{(k)}, x_1, x_2\right)$.
(4) Sample $\beta^{(k+1)}$ from $\pi\left(\beta \mid \tau^{(k+1)}, \alpha^{(k+1)}, x_1, x_2\right)$.
(5) Set $\theta^{(k+1)}=\left(\tau^{(k+1)}, \alpha^{(k+1)}, \beta^{(k+1)}\right)$ and $k=k+1$. Go back to the second step.

Here, $\pi(\cdot \mid \cdot)$ denotes a full conditional density function. For instance,
$$\pi\left(\tau \mid \alpha^{(k)}, \beta^{(k)}, x_1, x_2\right)$$

denotes the conditional density function of $\tau$ given current values of all the other parameters as well as two failure times. One can obtain each full conditional density up to a proportionality constant as follows by, firstly, obtaining the joint density function of all the parameters and failure times, i.e.,
$$L\left(\tau, \alpha, \beta \mid x_1, x_2\right) \pi(\tau) \pi(\alpha) \pi(\beta),$$
and then viewing (5) as a function of the parameter of interest. With our model assumptions, direct sampling from each full conditional cannot be easily done due to the indexing parameter $\tau$ (see Gilks ${ }^5$ ). MetropolisHastings algorithms (see Metropolis et al. ${ }^8$ and Hastings ${ }^9$ ) can be used to draw samples from the full conditionals. The Metropolis-Hastings method is an McMC methods that includes the Gibbs sampler as a special case (see Chib and Greenberg $\left.{ }^7\right)$. Under certain regularity conditions, for sufficiently large $k,\left{\theta^{(m)}: k \leq m \leq(k+n-1)\right}$ is approximately an i.i.d. sample of size $n$ from the posterior distribution of $\tau, \alpha, \beta$ given $\left(x_1, x_2\right)$. Numerical examples will illustrate our approach.

数学代写|运筹学作业代写operational research代考|Example

In this section we will reconsider the example discussed in ${ }^{12}$ and summarize the findings on the estimation of $\tau$ using maximum likelihood approach. Further, we will estimate $\tau$ from Bayesian prospective and compare the results of the two approaches. As in ${ }^{12}$, we will restrict our attention on the comparison of two consecutive lifetime distributions by using corresponding failure rate functions.
We will begin with the following assumptions:

• The item, $S$, subject to failures/repairs, has a complex structure comprising $m$ subsystems, i.e., $S=\left{S_1, S_2, \ldots S_m\right}$.
• A failure of a particular subsystem requires a type of repair which is known in advance.

For example, let us consider a car. If the failure affects the tires of a car (say subsystem $S_1$ ), usually a complete repair is required. On the other hand, if the charging system of the car (say subsystem $S_2$ ) fails, worse than new, better than used (WTNBTU) repair is performed. The information on warranty failures and repairs is usually strictly confidential and it is very difficult to obtain real warranty data even for research purposes. For this reason we demonstrate how one might estimate the parameters of our model using simulated data.

运筹学代考

数学代写|运筹学作业代写operational research代考|The Markov Chain Monte Carlo Method

McMC方法使我们能够模拟一个马尔可夫链，其平稳分布是我们的“目标”分布，例如，感兴趣的参数的后验分布。我们将使用Gibbs采样器，这是McMC方法之一。在我们的模型下，吉布斯采样器可以描述为:
(1)从任意初始向量$\theta^{(0)}=\left(\tau^{(0)}, \alpha^{(0)}, \beta^{(0)}\right)$开始，设置$k=0$。
(2)样本$\tau^{(k+1)}$来自$\pi\left(\tau \mid \alpha^{(k)}, \beta^{(k)}, x_1, x_2\right)$。
(3)从$\pi\left(\alpha \mid \tau^{(k+1)}, \beta^{(k)}, x_1, x_2\right)$获取$\alpha^{(k+1)}$样本。
(4)从$\pi\left(\beta \mid \tau^{(k+1)}, \alpha^{(k+1)}, x_1, x_2\right)$获取$\beta^{(k+1)}$样本。
(5)设置$\theta^{(k+1)}=\left(\tau^{(k+1)}, \alpha^{(k+1)}, \beta^{(k+1)}\right)$和$k=k+1$。回到第二步。

$$\pi\left(\tau \mid \alpha^{(k)}, \beta^{(k)}, x_1, x_2\right)$$

$$L\left(\tau, \alpha, \beta \mid x_1, x_2\right) \pi(\tau) \pi(\alpha) \pi(\beta),$$

有限元方法代写

tatistics-lab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。

数学代写|运筹学作业代写operational research代考|MTH2105

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。

数学代写|运筹学作业代写operational research代考|A BRANCH-AND-BOUND ALGORITHM FOR MIXED INTEGER PROGRAMMING

We shall now consider the general MIP problem, where some of the variables (say, $I$ of them) are restricted to integer values (but not necessarily just 0 and 1) but the rest are ordinary continuous variables. For notational convenience, we shall order the variables so that the first $I$ variables are the integer-restricted variables. Therefore, the general form of the problem being considered is
$$\text { Maximize } \quad Z=\sum_{j=1}^n c_j x_j,$$
subject to
$$\sum_{j=1}^n a_{i j} x_j \leq b_i, \quad \text { for } i=1,2, \ldots, m,$$
and
\begin{aligned} & x_j \geq 0, \quad \text { for } j=1,2, \ldots, n, \ & x_j \text { is integer, for } j=1,2, \ldots, I ; I \leq n . \end{aligned}
(When $I=n$, this problem becomes the pure IP problem.)
We shall describe a basic branch-and-bound algorithm for solving this problem that, with a variety of refinements, has provided a standard approach to MIP. The structure of this algorithm was first developed by R. J. Dakin, ${ }^1$ based on a pioneering branch-andbound algorithm by A. H. Land and A. G. Doig. ${ }^2$

This algorithm is quite similar in structure to the BIP algorithm presented in the preceding section. Solving LP relaxations again provides the basis for both the bounding and fathoming steps. In fact, only four changes are needed in the BIP algorithm to deal with the generalizations from binary to general integer variables and from pure IP to mixed IP.
One change involves the choice of the branching variable. Before, the next variable in the natural ordering $-x_1, x_2, \ldots, x_n$-was chosen automatically. Now, the only variables considered are the integer-restricted variables that have a noninteger value in the optimal solution for the LP relaxation of the current subproblem. Our rule for choosing among these variables is to select the first one in the natural ordering. (Production codes generally use a more sophisticated rule.)

数学代写|运筹学作业代写operational research代考|OTHER DEVELOPMENTS IN SOLVING BIP PROBLEMS

Integer programming has been an especially exciting area of OR since the mid-1980s because of the dramatic progress being made in its solution methodology.
Background
To place this progress into perspective, consider the historical background. One big breakthrough had come in the 1960 s and early 1970 s with the development and refinement of the branch-and-bound approach. But then the state of the art seemed to hit a plateau. Relatively small problems (well under 100 variables) could be solved very efficiently, but even a modest increase in problem size might cause an explosion in computation time beyond feasible limits. Little progress was being made in overcoming this exponential growth in computation time as the problem size was increased. Many important problems arising in practice could not be solved.

Then came the next breakthrough in the mid-1980s, as reported largely in four papers published in 1983, 1985, 1987, and 1991. (See Selected References 3, 6, 10, and 5.)

In the 1983 paper, Harlan Crowder, Ellis Johnson, and Manfred Padberg presented a new algorithmic approach to solving pure BIP problems that had successfully solved problems with no apparent special structure having up to 2,756 variables! This paper won the Lanchester Prize, awarded by the Operations Research Society of America for the most notable publication in operations research during 1983. In the 1985 paper, Ellis Johnson, Michael Kostreva, and Uwe Suhl further refined this algorithmic approach.

However, both of these papers were limited to pure BIP. For IP problems arising in practice, it is quite common for all the integer-restricted variables to be binary, but a large proportion of these problems are mixed BIP problems. What was critically needed was a way of extending this same kind of algorithmic approach to mixed BIP. This came in the 1987 paper by Tony Van Roy and Laurence Wolsey of Belgium. Once again, problems of very substantial size (up to nearly 1,000 binary variables and a larger number of continuous variables) were being solved successfully. And once again, this paper won a very prestigious award, the Orchard-Hays Prize given triannually by the Mathematical Programming Society.

In the 1991 paper, Karla Hoffman and Manfred Padberg followed up on the 1983 and 1985 papers by developing improved techniques for solving pure BIP problems. Using the name branch-and-cut algorithm for this algorithmic approach, they reported successfully solving problems with as many as 6,000 variables!

运筹学代考

数学代写|运筹学作业代写operational research代考|A BRANCH-AND-BOUND ALGORITHM FOR MIXED INTEGER PROGRAMMING

$$\text { Maximize } \quad Z=\sum_{j=1}^n c_j x_j,$$

$$\sum_{j=1}^n a_{i j} x_j \leq b_i, \quad \text { for } i=1,2, \ldots, m,$$

\begin{aligned} & x_j \geq 0, \quad \text { for } j=1,2, \ldots, n, \ & x_j \text { is integer, for } j=1,2, \ldots, I ; I \leq n . \end{aligned}
(当$I=n$时，这个问题变成了纯粹的IP问题。)

有限元方法代写

tatistics-lab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。

数学代写|运筹学作业代写operational research代考|MAT2200

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。

数学代写|运筹学作业代写operational research代考|SOME PERSPECTIVES ON SOLVING INTEGER PROGRAMMING PROBLEMS

It may seem that IP problems should be relatively easy to solve. After all, linear programming problems can be solved extremely efficiently, and the only difference is that IP problems have far fewer solutions to be considered. In fact, pure IP problems with a bounded feasible region are guaranteed to have just a finite number of feasible solutions.
Unfortunately, there are two fallacies in this line of reasoning. One is that having a finite number of feasible solutions ensures that the problem is readily solvable. Finite numbers can be astronomically large. For example, consider the simple case of BIP problems. With $n$ variables, there are $2^n$ solutions to be considered (where some of these solutions can subsequently be discarded because they violate the functional constraints). Thus, each time $n$ is increased by 1 , the number of solutions is doubled. This pattern is referred to as the exponential growth of the difficulty of the problem. With $n=10$, there are more than 1,000 solutions $(1,024)$; with $n=20$, there are more than $1,000,000$; with $n=30$, there are more than 1 billion; and so forth. Therefore, even the fastest computers are incapable of performing exhaustive enumeration (checking each solution for feasibility and, if it is feasible, calculating the value of the objective value) for BIP problems with more than a few dozen variables, let alone for general IP problems with the same number of integer variables. Sophisticated algorithms, such as those described in subsequent sections, can do somewhat better. In fact, Sec. 12.8 discusses how some algorithms have successfully solved certain vastly larger BIP problems. The best algorithms today are capable of solving many pure BIP problems with a few hundred variables and some considerably larger ones (including certain problems with several tens of thousands of variables). Nevertheless, because of exponential growth, even the best algorithms cannot be guaranteed to solve every relatively small problem (less than a hundred binary or integer variables). Depending on their characteristics, certain relatively small problems can be much more difficult to solve than some much larger ones.

The second fallacy is that removing some feasible solutions (the noninteger ones) from a linear programming problem will make it easier to solve. To the contrary, it is only because all these feasible solutions are there that the guarantee can be given (see Sec. 5.1) that there will be a corner-point feasible (CPF) solution [and so a corresponding basic feasible (BF) solution] that is optimal for the overall problem. This guarantee is the key to the remarkable efficiency of the simplex method. As a result, linear programming problems generally are тисh easier to solve than IP problems.

Consequently, most successful algorithms for integer programming incorporate the simplex method (or dual simplex method) as much as they can by relating portions of the IP problem under consideration to the corresponding linear programming problem (i.e., the same problem except that the integer restriction is deleted). For any given IP problem, this corresponding linear programming problem commonly is referred to as its LP relaxation. The algorithms presented in the next two sections illustrate how a sequence of LP relaxations for portions of an IP problem can be used to solve the overall IP problem effectively.

数学代写|运筹学作业代写operational research代考|THE BRANCH-AND-BOUND TECHNIQUE AND ITS APPLICATION TO BINARY INTEGER PROGRAMMING

Because any bounded pure IP problem has only a finite number of feasible solutions, it is natural to consider using some kind of enumeration procedure for finding an optimal solution. Unfortunately, as we discussed in the preceding section, this finite number can be, and usually is, very large. Therefore, it is imperative that any enumeration procedure be cleverly structured so that only a tiny fraction of the feasible solutions actually need be examined. For example, dynamic programming (see Chap. 11) provides one such kind of procedure for many problems having a finite number of feasible solutions (although it is not particularly efficient for most IP problems). Another such approach is provided by the branch-and-bound technique. This technique and variations of it have been applied with some success to a variety of OR problems, but it is especially well known for its application to IP problems.

The basic concept underlying the branch-and-bound technique is to divide and conquer. Since the original “large” problem is too difficult to be solved directly, it is divided into smaller and smaller subproblems until these subproblems can be conquered. The dividing (branching) is done by partitioning the entire set of feasible solutions into smaller and smaller subsets. The conquering (fathoming) is done partially by bounding how good the best solution in the subset can be and then discarding the subset if its bound indicates that it cannot possibly contain an optimal solution for the original problem.

We shall now describe in turn these three basic steps – branching, bounding, and fathoming-and illustrate them by applying a branch-and-bound algorithm to the prototype example (the California Manufacturing Co. problem) presented in Sec. 12.1 and repeated here (with the constraints numbered for later reference).
Maximize $Z=9 x_1+5 x_2+6 x_3+4 x_4$,
subject to
(1) $6 x_1+3 x_2+5 x_3+2 x_4 \leq 10$
(2) $\quad x_3+x_4 \leq 1$
(3) $-x_1+x_3 \leq 0$
(4) $-x_2+x_4 \leq 0$
and
(5) $\quad x_j$ is binary, for $j=1,2,3,4$.

运筹学代考

数学代写|运筹学作业代写operational research代考|SOME PERSPECTIVES ON SOLVING INTEGER PROGRAMMING PROBLEMS

IP问题似乎相对容易解决。毕竟，线性规划问题可以非常有效地解决，唯一的区别是IP问题需要考虑的解决方案要少得多。事实上，具有有界可行域的纯IP问题保证只有有限个可行解。

A somewhat similar application on a vastly larger scale occurred in China recently (January-February 1995 issue of Interfaces). China was facing at least $\$ 240$billion in new investments over a 15-year horizon to meet the energy needs of its rapidly growing economy. Shortages of coal and electricity required developing new infrastructure for transporting coal and transmitting electricity, as well as building new dams and plants for generating thermal, hydro, and nuclear power. Therefore, the Chinese State Planning Commission and the World Bank collaborated in developing a huge mixed BIP model to guide the decisions on which projects to approve and when to undertake them over the 15-year planning period to minimize the total discounted cost. It is estimated that this OR application is saving China about$\$6.4$ billion over the 15 years.

数学代写|运筹学作业代写operational research代考|Scheduling Asset Divestitures

This next application actually is another example of the preceding one (scheduling interrelated activities). However, rather than dealing with such activities as constructing office buildings or investing in hydroelectric plants, the activities now are selling (divesting) assets to generate income. The assets can be either financial assets, such as stocks and bonds, or physical assets, such as real estate. Given a group of assets, the problem is to determine when to sell each one to maximize the net present value of total profit from these assets while generating the desired income stream.
In this case, each yes-or-no decision has the following form.
Should a certain asset be sold in a certain time period?
Its decision variable $= \begin{cases}1 & \text { if yes } \ 0 & \text { if no. }\end{cases}$
One company that deals with these kinds of yes-or-no decisions is Homart Development Company (January-February 1987 issue of Interfaces), which ranks among the largest commercial land developers in the United States. One of its most important strategic issues is scheduling divestiture of shopping malls and office buildings. At any particular time, well over 100 assets will be under consideration for divestiture over the next 10 years. Applying BIP to guide these decisions is credited with adding $\$ 40$million of profit from the divestiture plan. Airline Applications The airline industry is an especially heavy user of OR throughout its operations. For example, one large consulting firm called SABRE (spun off by American Airlines) employs several hundred OR professionals solely to focus on the problem of companies involved with transportation, including especially airlines. We will mention here just two of the applications which specifically use BIP. One is the fleet assignment problem. Given several different types of airplanes available, the problem is to assign a specific type to each flight leg in the schedule so as to maximize the total profit from meeting the schedule. The basic trade-off is that if the airline uses an airplane that is too small on a particular flight leg, it will leave potential customers behind, while if it uses an airplane that is too large, it will suffer the greater expense of the larger airplane to fly empty seats. For each combination of an airplane type and a flight leg, we have the following yesor-no decision. Should a certain type of airplane be assigned to a certain flight leg? $$\text { Its decision variable }= \begin{cases}1 & \text { if yes } \ 0 & \text { if no. }\end{cases}$$ 运筹学代考 数学代写|运筹学作业代写operational research代考|Scheduling Interrelated Activities 我们在日常生活中都会安排相关的活动，即使只是安排什么时候开始做各种家庭作业。因此，管理者也必须安排各种相互关联的活动。我们什么时候开始生产各种新订单?我们什么时候开始销售各种新产品?我们什么时候应该进行各种资本投资来扩大产能? 对于任何这样的活动，关于何时开始的决定可以用一系列是或否的决定来表示，每个可能开始的时间段都有一个决定，如下所示。 某项活动是否应该在某个时间段开始?$ $\text{其决策变量}= \begin{cases}1 & \text{如果是的话}\ 0 & \text{如果不是的话。} \结束{病例}$ $由于特定的活动只能在一个时间段内开始，因此对各个时间段的选择提供了一组互斥的备选方案，因此仅针对一个时间段的决策变量的值可以为1。 例如，这种方法被用于在德克萨斯州体育场(达拉斯牛仔队的主场)附近的一系列办公大楼的规划，规划周期为7年。在这种情况下，模型有49个二元决策变量，每个办公楼对应于其建设可能开始的7年中的每一年。BIP的应用使利润增加了630万美元。(参见1983年10月号的《接口》。) 最近在中国出现了一个规模大得多的类似应用程序(1995年1 – 2月的《界面》)。中国在15年的时间里面临着至少2400亿美元的新投资，以满足其快速增长的经济的能源需求。煤炭和电力的短缺需要发展新的基础设施来运输煤炭和传输电力，以及建造新的水坝和发电厂来产生热能、水力和核能。因此，中国国家计划委员会和世界银行合作开发了一个巨大的混合BIP模型，以指导在15年规划期内批准哪些项目以及何时实施这些项目的决策，以最大限度地降低总贴现成本。据估计，这一应用在15年内为中国节省了大约64亿美元。 数学代写|运筹学作业代写operational research代考|Scheduling Asset Divestitures 下一个应用程序实际上是前一个应用程序(调度相互关联的活动)的另一个示例。然而，现在的活动不是处理诸如建造办公楼或投资水力发电厂之类的活动，而是出售(剥离)资产以产生收入。这些资产可以是金融资产，如股票和债券，也可以是实物资产，如房地产。给定一组资产，问题是确定何时出售每一项资产，以最大化这些资产总利润的净现值，同时产生期望的收入流。 在这种情况下，每个是或否的决定有以下形式。 某项资产是否应该在某段时间内出售? 它的决策变量$= \begin{cases}1 & \text{如果是的话}\ 0 & \text{如果不是的话。} {病例}$美国最大的商业用地开发商之一的Homart Development company(1987年1月至2月的《界面》杂志)就是处理这类“是或否”决策的公司之一。其最重要的战略问题之一是安排剥离购物中心和办公楼的时间表。在未来10年的任何时候，都有超过100项资产将被考虑剥离。应用BIP来指导这些决策，从剥离计划中增加了4000万美元的利润。 航空公司应用程序 在整个运营过程中，航空业尤其大量使用手术室。例如，一家名为SABRE的大型咨询公司(由美国航空公司剥离)雇佣了数百名OR专业人员，专门研究与运输有关的公司，特别是航空公司的问题。我们在这里只提到两个专门使用BIP的应用程序。 一个是舰队分配问题。给定几种不同类型的可用飞机，问题是为时间表中的每个航段分配特定类型，以使满足时间表的总利润最大化。基本的权衡是，如果航空公司在特定的航班上使用太小的飞机，它会把潜在的客户抛在后面，而如果它使用太大的飞机，它将承受更大的飞机运送空座位的成本。 统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。 金融工程代写 金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。 非参数统计代写 非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。 广义线性模型代考 广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。 术语 广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。 有限元方法代写 有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。 有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。 tatistics-lab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。 随机分析代写 随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。 时间序列分析代写 随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。 随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。 回归分析代写 多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。 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。 数学代写|运筹学作业代写operational research代考|MATH208 如果你也在 怎样代写运筹学Operations Research 这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。运筹学Operations Research为管理者、工程师和任何有更好解决方案的实践者提供更好的解决方案。这门科学诞生于第二次世界大战期间。虽然它最初用于军事行动，但它的应用以某种形式扩展到地球上的任何领域。 运筹学Operations Research是将科学方法应用于解决复杂问题，指导和管理工业、商业、政府和国防中由人、机器、材料和资金组成的大型系统。独特的方法是开发一个系统的科学模型，包括诸如变化和风险等因素的测量，以此来预测和比较不同决策、战略或控制的结果。其目的是帮助管理层科学地确定其政策和行动。 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。 数学代写|运筹学作业代写operational research代考|DETERMINISTIC DYNAMIC PROGRAMMING This section further elaborates upon the dynamic programming approach to deterministic problems, where the state at the next stage is completely determined by the state and policy decision at the current stage. The probabilistic case, where there is a probability distribution for what the next state will be, is discussed in the next section. Deterministic dynamic programming can be described diagrammatically as shown in Fig. 11.3. Thus, at stage$n$the process will be in some state$s_n$. Making policy decision$x_n$then moves the process to some state$s_{n+1}$at stage$n+1$. The contribution thereafter to the objective function under an optimal policy has been previously calculated to be$f_{n+1}^\left(s_{n+1}\right)$. The policy decision$x_n$also makes some contribution to the objective function. Combining these two quantities in an appropriate way provides$f_n\left(s_n, x_n\right)$, the contribution of stages$n$onward to the objective function. Optimizing with respect to$x_n$then gives$f_n^\left(s_n\right)=f_n\left(s_n, x_n^\right)$. After$x_n^$and$f_n^*\left(s_n\right)$are found for each possible value of$s_n$, the solution procedure is ready to move back one stage. One way of categorizing deterministic dynamic programming problems is by the form of the objective function. For example, the objective might be to minimize the sum of the contributions from the individual stages (as for the stagecoach problem), or to maximize such a sum, or to minimize a product of such terms, and so on. Another categorization is in terms of the nature of the set of states for the respective stages. In particular, states$s_n$might be representable by a discrete state variable (as for the stagecoach problem) or by a continuous state variable, or perhaps a state vector (more than one variable) is required. Several examples are presented to illustrate these various possibilities. More importantly, they illustrate that these apparently major differences are actually quite inconsequential (except in terms of computational difficulty) because the underlying basic structure shown in Fig. 11.3 always remains the same. The first new example arises in a much different context from the stagecoach problem, but it has the same mathematical formulation except that the objective is to maximize rather than minimize a sum. 数学代写|运筹学作业代写operational research代考|A Prevalent Problem Type—The Distribution of Effort Problem The preceding example illustrates a particularly common type of dynamic programming problem called the distribution of effort problem. For this type of problem, there is just one kind of resource that is to be allocated to a number of activities. The objective is to determine how to distribute the effort (the resource) among the activities most effectively. For the World Health Council example, the resource involved is the medical teams, and the three activities are the health care work in the three countries. Assumptions. This interpretation of allocating resources to activities should ring a bell for you, because it is the typical interpretation for linear programming problems given at the beginning of Chap. 3. However, there also are some key differences between the distribution of effort problem and linear programming that help illuminate the general distinctions between dynamic programming and other areas of mathematical programming. One key difference is that the distribution of effort problem involves only one resource (one functional constraint), whereas linear programming can deal with thousands of resources. (In principle, dynamic programming can handle slightly more than one resource, as we shall illustrate in Example 5 by solving the three-resource Wyndor Glass Co. problem, but it quickly becomes very inefficient when the number of resources is increased.) On the other hand, the distribution of effort problem is far more general than linear programming in other ways. Consider the four assumptions of linear programming presented in Sec. 3.3: proportionality, additivity, divisibility, and certainty. Proportionality is routinely violated by nearly all dynamic programming problems, including distribution of effort problems (e.g., Table 11.1 violates proportionality). Divisibility also is often violated, as in Example 2, where the decision variables must be integers. In fact, dynamic programming calculations become more complex when divisibility does hold (as in Examples 4 and 5). Although we shall consider the distribution of effort problem only under the assumption of certainty, this is not necessary, and many other dynamic programming problems violate this assumption as well (as described in Sec. 11.4). 运筹学代考 数学代写|运筹学作业代写operational research代考|DETERMINISTIC DYNAMIC PROGRAMMING 本节进一步阐述了确定性问题的动态规划方法，其中下一阶段的状态完全由当前阶段的状态和政策决策决定。下一节将讨论概率情况，即存在下一状态的概率分布。 确定性动态规划的描述如图11.3所示。因此，在阶段$n$时，进程将处于某种状态$s_n$。制定策略决策$x_n$然后将流程移动到阶段$n+1$的某个状态$s_{n+1}$。在最优策略下，此后对目标函数的贡献先前已计算为$f_{n+1}^\left(s_{n+1}\right)$。决策$x_n$也对目标函数有一定的贡献。以一种适当的方式结合这两个量可以得到$f_n\left(s_n, x_n\right)$，即阶段$n$对目标函数的贡献。然后对$x_n$进行优化，得到$f_n^\left(s_n\right)=f_n\left(s_n, x_n^\right)$。在为$s_n$的每个可能值找到$x_n^$和$f_n^*\left(s_n\right)$之后，求解过程准备向后移动一个阶段。 对确定性动态规划问题进行分类的一种方法是通过目标函数的形式。例如，目标可能是最小化来自各个阶段的贡献的总和(就像公共马车问题一样)，或者最大化这样的总和，或者最小化这样的项的乘积，等等。另一种分类是根据各个阶段的状态集的性质进行的。特别是，状态$s_n$可以用离散状态变量表示(就像驿站马车问题一样)，也可以用连续状态变量表示，或者可能需要一个状态向量(多个变量)。 本文给出了几个例子来说明这些不同的可能性。更重要的是，它们说明了这些明显的主要差异实际上是相当无关紧要的(除了计算难度方面)，因为图11.3所示的底层基本结构总是保持不变。 第一个新例子出现的背景与公共马车问题大不相同，但它具有相同的数学公式，只是目标是最大化而不是最小化总和。 数学代写|运筹学作业代写operational research代考|A Prevalent Problem Type—The Distribution of Effort Problem 前面的例子说明了一种特别常见的动态规划问题，称为工作量分配问题。对于这类问题，只需要将一种资源分配给若干活动。目标是确定如何在活动之间最有效地分配工作(资源)。以世界卫生理事会为例，所涉及的资源是医疗队，三个活动是三个国家的卫生保健工作。 假设。这种将资源分配给活动的解释应该对您有所帮助，因为它是第3章开头给出的线性规划问题的典型解释。然而，在工作量分配问题和线性规划之间也有一些关键的区别，这些区别有助于阐明动态规划和其他数学规划领域之间的一般区别。 一个关键的区别是，工作量分配问题只涉及一种资源(一个功能约束)，而线性规划可以处理数千种资源。(原则上，动态规划可以处理一个以上的资源，正如我们将在例5中通过解决三个资源的winddor Glass Co.问题来说明的那样，但是当资源数量增加时，它很快就会变得非常低效。) 另一方面，努力分配问题在其他方面远比线性规划更为普遍。考虑第3.3节中提出的线性规划的四个假设:比例性、可加性、可除性和确定性。几乎所有的动态规划问题都经常违反比例原则，包括工作量分配问题(例如，表11.1违反了比例原则)。可除性也经常被违反，如在例2中，其中决策变量必须是整数。事实上，当可整除性成立时，动态规划计算变得更加复杂(如例4和5所示)。尽管我们将仅在确定性假设下考虑努力分配问题，但这是不必要的，许多其他动态规划问题也违反了这一假设(如第11.4节所述)。 统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。 金融工程代写 金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。 非参数统计代写 非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。 广义线性模型代考 广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。 术语 广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。 有限元方法代写 有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。 有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。 tatistics-lab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。 随机分析代写 随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。 时间序列分析代写 随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。 随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。 回归分析代写 多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。 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。 数学代写|运筹学作业代写operational research代考|MATH318 如果你也在 怎样代写运筹学Operations Research 这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。运筹学Operations Research为管理者、工程师和任何有更好解决方案的实践者提供更好的解决方案。这门科学诞生于第二次世界大战期间。虽然它最初用于军事行动，但它的应用以某种形式扩展到地球上的任何领域。 运筹学Operations Research是将科学方法应用于解决复杂问题，指导和管理工业、商业、政府和国防中由人、机器、材料和资金组成的大型系统。独特的方法是开发一个系统的科学模型，包括诸如变化和风险等因素的测量，以此来预测和比较不同决策、战略或控制的结果。其目的是帮助管理层科学地确定其政策和行动。 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。 数学代写|运筹学作业代写operational research代考|CONSIDERING TIME-COST TRADE-OFFS Mr. Perty now wants to investigate how much extra it would cost to reduce the expected project duration down to 40 weeks (the deadline for the company earning a bonus of$\$150,000$ for early completion). Therefore, he is ready to address the next of his questions posed at the end of Sec. 10.1 .

Question 8: If extra money is spent to expedite the project, what is the least expensive way of attempting to meet the target completion time (40 weeks)?

Mr. Perty remembers that CPM provides an excellent procedure for using linear programming to investigate such time-cost trade-offs, so he will use this approach again to address this question.
We begin with some background.
The first key concept for this approach is that of crashing.
Crashing an activity refers to taking special costly measures to reduce the duration of an activity below its normal value. These special measures might include using overtime, hiring additional temporary help, using special time-saving materials, obtaining special equipment, etc. Crashing the project refers to crashing a number of activities in order to reduce the duration of the project below its normal value.
The CPM method of time-cost trade-offs is concerned with determining how much (if any) to crash each of the activities in order to reduce the anticipated duration of the project to a desired value.

The data necessary for determining how much to crash a particular activity are given by the time-cost graph for the activity. Figure 10.11 shows a typical time-cost graph. Note the two key points on this graph labeled Normal and Crash.
The normal point on the time-cost graph for an activity shows the time (duration) and cost of the activity when it is performed in the normal way. The crash point shows the time and cost when the activity is fully crashed, i.e., it is fully expedited with no cost spared to reduce its duration as much as possible. As an approximation, CPM assumes that these times and costs can be reliably predicted without significant uncertainty.
For most applications, it is assumed that partially crashing the activity at any level will give a combination of time and cost that will lie somewhere on the line segment between these two points. (For example, this assumption says that half of a full crash will give a point on this line segment that is midway between the normal and crash points.) This simplifying approximation reduces the necessary data gathering to estimating the time and cost for just two situations: normal conditions (to obtain the normal point) and a full crash (to obtain the crash point).

Using this approach, Mr. Perty has his staff and crew supervisors working on developing these data for each of the activities of Reliable’s project. For example, the supervisor of the crew responsible for putting up the wallboard indicates that adding two temporary employees and using overtime would enable him to reduce the duration of this activity from 8 weeks to 6 weeks, which is the minimum possible. Mr. Perty’s staff then estimates the cost of fully crashing the activity in this way as compared to following the normal 8-week schedule, as shown below.
Activity $J$ (put up the wallboard):
Normal point: time $=8$ weeks, $\operatorname{cost}=\$ 430,000$. Crash point: time$=6$weeks, cost$=\$490,000$.
Maximum reduction in time $=8-6=2$ weeks.
\begin{aligned} \text { Crash cost per week saved } & =\frac{\ 490,000-\ 430,000}{2} \ & =\ 30,000 . \end{aligned}
Table 10.7 gives the corresponding data obtained for all the activities.

数学代写|运筹学作业代写operational research代考|Which Activities Should Be Crashed?

Summing the normal cost and crash cost columns of Table 10.7 gives
Sum of normal costs $=\$ 4.55$million, Sum of crash costs$=\$6.15$ million.

Recall that the company will be paid $\$ 5.4$million for doing this project. (This figure excludes the$\$150,000$ bonus for finishing within 40 weeks and the $\$ 300,000$penalty for not finishing within 47 weeks.) This payment needs to cover some overhead costs in addition to the costs of the activities listed in the table, as well as provide a reasonable profit to the company. When developing the (winning) bid of$\$5.4$ million, Reliable’s management felt that this amount would provide a reasonable profit as long as the total cost of the activities could be held fairly close to the normal level of about $\$ 4.55$million. Mr. Perty understands very well that it is now his responsibility to keep the project as close to both budget and schedule as possible. As found previously in Fig. 10.7, if all the activities are performed in the normal way, the anticipated duration of the project would be 44 weeks (if delays can be avoided). If all the activities were to be fully crashed instead, then a similar calculation would find that this duration would be reduced to only 28 weeks. But look at the prohibitive cost ($\$6.15$ million) of doing this! Fully crashing all activities clearly is not an option that can be considered.
However, Mr. Perty still wants to investigate the possibility of partially or fully crashing just a few activities to reduce the anticipated duration of the project to 40 weeks.
The problem: What is the least expensive way of crashing some activities to reduce the (estimated) project duration to the specified level (40 weeks)?
One way of solving this problem is marginal cost analysis, which uses the last column of Table 10.7 (along with Fig. 10.7 in Sec. 10.3) to determine the least expensive way to reduce project duration 1 week at a time. The easiest way to conduct this kind of analysis is to set up a table like Table 10.8 that lists all the paths through the project network and the current length of each of these paths. To get started, this information can be copied directly from Table 10.2.

运筹学代考

For some applications of minimum cost flow problems, all the transshipment nodes are processing facilities rather than intermediate storage facilities. This is the case for solid waste management, as indicated in the second row of Table 9.3. Here, the flow of materials through the network begins at the sources of the solid waste, then goes to the facilities for processing these waste materials into a form suitable for landfill, and then sends them on to the various landfill locations. However, the objective still is to determine the flow plan that minimizes the total cost, where the cost now is for both shipping and processing.

运筹学代考

数学代写|运筹学作业代写operational research代考|Some Applications

Woodlands $\right tarrow$ wooddyards $\right tarrow$锯木厂
$\右箭头$造纸厂$\右箭头$转换厂
$\右箭头$仓库$\右箭头$顾客。

有限元方法代写

tatistics-lab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。

数学代写|运筹学作业代写operational research代考|PROTOTYPE EXAMPLE

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。

数学代写|运筹学作业代写operational research代考|PROTOTYPE EXAMPLE

SEERVADA PARK has recently been set aside for a limited amount of sightseeing and backpack hiking. Cars are not allowed into the park, but there is a narrow, winding road system for trams and for jeeps driven by the park rangers. This road system is shown (without the curves) in Fig. 9.1, where location $O$ is the entrance into the park; other letters designate the locations of ranger stations (and other limited facilities). The numbers give the distances of these winding roads in miles.

The park contains a scenic wonder at station $T$. A small number of trams are used to transport sightseers from the park entrance to station $T$ and back.

The park management currently faces three problems. One is to determine which route from the park entrance to station $T$ has the smallest total distance for the operation of the trams. (This is an example of the shortest-path problem to be discussed in Sec. 9.3.)
A second problem is that telephone lines must be installed under the roads to establish telephone communication among all the stations (including the park entrance). Because the installation is both expensive and disruptive to the natural environment, lines will be installed under just enough roads to provide some connection between every pair of stations. The question is where the lines should be laid to accomplish this with a minimum total number of miles of line installed. (This is an example of the minimum spanning tree problem to be discussed in Sec. 9.4.)

The third problem is that more people want to take the tram ride from the park entrance to station $T$ than can be accommodated during the peak season. To avoid unduly disturbing the ecology and wildlife of the region, a strict ration has been placed on the number of tram trips that can be made on each of the roads per day. (These limits differ for the different roads, as we shall describe in detail in Sec. 9.5.) Therefore, during the peak season, various routes might be followed regardless of distance to increase the number of tram trips that can be made each day. The question pertains to how to route the various trips to maximize the number of trips that can be made per day without violating the limits on any individual road. (This is an example of the maximum flow problem to be discussed in Sec. 9.5.)

数学代写|运筹学作业代写operational research代考|THE TERMINOLOGY OF NETWORKS

A relatively extensive terminology has been developed to describe the various kinds of networks and their components. Although we have avoided as much of this special vocabulary as we could, we still need to introduce a considerable number of terms for use throughout the chapter. We suggest that you read through this section once at the outset to understand the definitions and then plan to return to refresh your memory as the terms are used in subsequent sections. To assist you, each term is highlighted in boldface at the point where it is defined.

A network consists of a set of points and a set of lines connecting certain pairs of the points. The points are called nodes (or vertices); e.g., the network in Fig. 9.1 has seven nodes designated by the seven circles. The lines are called arcs (or links or edges or branches); e.g., the network in Fig. 9.1 has 12 arcs corresponding to the 12 roads in the road system. Arcs are labeled by naming the nodes at either end; for example, $A B$ is the $\operatorname{arc}$ between nodes $A$ and $B$ in Fig. 9.1.

The arcs of a network may have a flow of some type through them, e.g., the flow of trams on the roads of Seervada Park in Sec. 9.1. Table 9.1 gives several examples of flow in typical networks. If flow through an arc is allowed in only one direction (e.g., a oneway street), the arc is said to be a directed arc. The direction is indicated by adding an arrowhead at the end of the line representing the arc. When a directed arc is labeled by listing two nodes it connects, the from node always is given before the to node; e.g., an arc that is directed from node $A$ to node $B$ must be labeled as $A B$ rather than $B A$. Alternatively, this arc may be labeled as $A \rightarrow B$.

If flow through an arc is allowed in either direction (e.g., a pipeline that can be used to pump fluid in either direction), the arc is said to be an undirected arc. To help you distinguish between the two kinds of arcs, we shall frequently refer to undirected arcs by the suggestive name of links.

运筹学代考

数学代写|运筹学作业代写operational research代考|PROTOTYPE EXAMPLE

SEERVADA公园最近被划为有限数量的观光和背包徒步旅行。汽车不允许进入公园，但有一条狭窄蜿蜒的道路供有轨电车和公园护林员驾驶的吉普车通行。该道路系统如图9.1所示(没有曲线)，其中位置$O$为进入公园的入口;其他字母标明了护林站(和其他有限设施)的位置。这些数字以英里为单位给出了这些蜿蜒道路的距离。

有限元方法代写

tatistics-lab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。