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数学代写|运筹学代写Operations Research代考|MATH3830 The Critical Path Method

如果你也在 怎样代写运筹学Operations Research MATH3830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(英式英语:operational research),通常简称为OR,是一门研究开发和应用先进的分析方法来改善决策的学科。它有时被认为是数学科学的一个子领域。管理科学一词有时被用作同义词。

运筹学Operations Research采用了其他数学科学的技术,如建模、统计和优化,为复杂的决策问题找到最佳或接近最佳的解决方案。由于强调实际应用,运筹学与许多其他学科有重叠之处,特别是工业工程。运筹学通常关注的是确定一些现实世界目标的极端值:最大(利润、绩效或收益)或最小(损失、风险或成本)。运筹学起源于二战前的军事工作,它的技术已经发展到涉及各种行业的问题。

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我们在数学Mathematics代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的数学Mathematics代写服务。我们的专家在运筹学Operations Research代写方面经验极为丰富,各种运筹学Operations Research相关的作业也就用不着 说。

数学代写|运筹学代写Operations Research代考|MATH3830 The Critical Path Method

数学代写|运筹学代写Operations Research代考|The Critical Path Method

Before getting into details, the planner will have to decide on what level the planning will take place. We may be interested in planning on the macro level in order to get the “bigger picture.” As an example, when building a house, we may have “foundation work” as a single task, another one is “electrical work,” another is “plumbing,” another is “roofing,” and so forth. Zooming in closer, we may look at each such task as a project in itself. For instance, plumbing may include subtasks such as the installation of pipes, connections to outside lines or septic systems, etc. Zooming in even further, the installation of lavatories may be further subdivided into the mounting of the washbasin, the connection of the faucet to the pipes, and so forth. We can construct project networks on each of these levels.

Once the level has been decided upon, the task in its entirety-the building of the house, design and planting of a public or private garden, an individual’s university studies-will be referred to as a project. Each project can now be subdivided into individual tasks or activities. Planting a bed of grape hyacinths, installing the flashing on the roof, or taking a specific course in a university program are typical examples of such activities. Associated with each activity is a duration that indicates how long it takes to complete the activity. In $C P M$, the durations of all activities are assumed to be known with certainty (which is the only distinction to PERT, where the durations have underlying probability distributions).

In addition to the activities and their durations, we also need to have precedence relations. Such relations indicate which activities must be completely finished before another activity can take place. For example, in order to start the activity “drive with the car to grandmother,” the activities “gas up the car,” “pack the gifts (wine and cheese) for grandmother,” and “lock the house” must be completely finished. A complete set of precedence relations will specify the (immediate) predecessors of each activity.

In the analysis in this section, we are only concerned about time. There is no optimization that takes place here, the goal is to determine the earliest time by which the project can be completed. And while making these calculations, we can also find out when each task can and must be started and finished. That allows us to determine bottleneck activities in the project, whose delay will delay the entire project. In subsequent sections, we will include other components in the basic network, including money and other resources.

数学代写|运筹学代写Operations Research代考|Project Acceleration

So far, we have considered time as the only criterion in project networks. Also note that the technique described in the previous section did not involve any optimization, all we have done is determined when the project can be finished by finding the length of the longest path and which of the activities are bottlenecks in the system. In this section, we will return to the basic model, but allow the possibility to accelerate, at a cost, individual activities, so as to be able to finish the project earlier. The result will be a list that shows possible finishing times of the project and the amounts that will have to be paid to reach them. This will enable the planner to decide what combination of money spent and project duration best fits the specific situation.

In order to describe the situation, consider a single activity. As before, the activity will have what we now call a normal duration. Since we will engage in a marginal analysis, the cost of the activity at its normal duration is immaterial (we will have to engage in the activity in any case), and the only costs we consider are those that are incurred due to the acceleration of the activity. Suppose that the normal duration of our activity is 7 hrs. It is now possible to use more resources (e.g., more manpower, more tools, contracting out part of the activity, or any similar measure) to accelerate this activity. Suppose that it costs $\$ 20$ to reduce the duration of the activity to 6 hrs. Using more resources still, additional money can reduce the duration of the activity further. For simplicity, we assume that the cost function of the acceleration is linear, meaning that reducing the duration by another hour to $5 \mathrm{hrs}$ costs another $\$ 20$ for a total of $\$ 40$. Note that normally the cost function is superlinear, meaning that reducing the duration by $1 \mathrm{hr}$ costs, say $\$ x$, reducing it by another hour costs more than $\$ x$, yet another reduction is more expensive still, and so forth.

It is quite apparent that the reduction has some limitations, below which we cannot reduce the duration of the activity any further. The shortest activity duration of an activity that can be achieved is customarily referred to as crash time, and the process of acceleration is sometimes called crashing. Our task is now to determine which activities should be accelerated or crashed, so as to achieve the desired result at the lowest possible cost.

As an illustration of the concept, consider the numerical example shown in Fig. 8.4.

The project has four activities $A, B, C$, and $D$, whose normal times, crash times, and unit acceleration costs are shown next to the nodes. For example, activity $D$ normally takes 8 hrs (there are no costs incurred at this duration), but we can reduce the duration down to 7,6 , or $5 \mathrm{hrs}$. Each hour of acceleration costs $\$ 200$. Note that activity $B$ cannot be accelerated.

数学代写|运筹学代写Operations Research代考|MATH3830 The Critical Path Method

运筹学代写

数学代写运筹学代写OPERATIONS RESEARCH代考|PCENTER PROBLEMS


位置理论的起源笼置在历史之中。第一个讨论位置模型andhere, weusetheterminthewidestpossiblesense是数学家。著名的基于位置的谜题之一
regardingthepointinthetrianglefromwhichthesumofdistancestothetriangles’verticesisminimal17世纪托里切利和岪马研究并解决了这个问题。地理
学家 von Thunen 写了关于他著名的“von Thunen 圏子”关于中心地区经济活动的位置,德国地理学家韦伯在 20世纪早期写了一篇关于位置模型的论文。哈基米1964
将位置模型引入运筹学领域。我们将在下面遇到他的若名定理。从那时起,来自数学、计算机科学、地理、工商管理和经济学等不同领域的研究人员做出了数千项 贡南。
虽然我们中的许多人都非常清楚什么是位置问题,但让我们退后一步,检荁它的主要组成部分。每个位置模型的三个主要组成部分是空间、客户和设施。供应存在 于设施中,需求出现在客户现场,货物 “以某种方式”从设施运送到㟯户。现在让我们更详细地看一下这些组件。
我们区分了两大类位置模型,即发生在平面上的位置模型orsometimesinthree-dimensionalspace,以及发生在交通网络中的那些。虽然不完全正确,但飞 机中的位置模型倾向于从宏观角度看待问题,而交通网絡中的模型则从微观角度研究场景。平面内的定位问题称为连续定位模型
asthefacilitiesthataretobelocatedcanbesitedanywhereinthespaceunderconsideration 与离散位置模型相反,其中许多发生在网络中。在离散位置模型 中,设施只能位于有限数量的点。
这两类问题也与定义变量的方式不同:确定变量在二维平面连续模型中的位置,需要定义变量 $\left(x_1, y_1\right),\left(x_2, y_2\right), \ldots$ 象征设施的坐标 $1,2, \ldots$ 另一方面,在网络模 型中,我们需要一个变量 $y_j$ 对于每个将假定值为 1 的潜在位置,如果我们确实在现场定位 $j$ ,如果我们不这样做,则为 0 。这将连续位置模型置于线性或非线性优化 领域,而网络位置模型通常被制定和解决为整数规划问题。


数学代写|运筹学代写OPERATIONS RESEARCH代考|MEDIAN PROBLEMS


与上一节讨论的具有极小极大目标的中心问题相反,本节专门讨论具有极小目标的中位数问题。换句话说,他们将定位设施,以尽量减少到宕户的距离总和。这一 特性使得这种类型的物镜适用于公共和私荣部门的应用。例如,考虑图书馆等公共设施的位置。市政规划者将努力使图书馆屈可能地向所有潜在顾客开放。这可以 通过最小化图书馆与其㝒户之间的平均距离来实现。不难证明,只要需求量保持不变,

数学代写|运筹学代写Operations Research代考

数学代写|运筹学代写Operations Research代考 请认准UprivateTA™. UprivateTA™为您的留学生涯保驾护航。

微观经济学代写

微观经济学是主流经济学的一个分支,研究个人和企业在做出有关稀缺资源分配的决策时的行为以及这些个人和企业之间的相互作用。my-assignmentexpert™ 为您的留学生涯保驾护航 在数学Mathematics作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的数学Mathematics代写服务。我们的专家在图论代写Graph Theory代写方面经验极为丰富,各种图论代写Graph Theory相关的作业也就用不着 说。

线性代数代写

线性代数是数学的一个分支,涉及线性方程,如:线性图,如:以及它们在向量空间和通过矩阵的表示。线性代数是几乎所有数学领域的核心。

博弈论代写

现代博弈论始于约翰-冯-诺伊曼(John von Neumann)提出的两人零和博弈中的混合策略均衡的观点及其证明。冯-诺依曼的原始证明使用了关于连续映射到紧凑凸集的布劳威尔定点定理,这成为博弈论和数学经济学的标准方法。在他的论文之后,1944年,他与奥斯卡-莫根斯特恩(Oskar Morgenstern)共同撰写了《游戏和经济行为理论》一书,该书考虑了几个参与者的合作游戏。这本书的第二版提供了预期效用的公理理论,使数理统计学家和经济学家能够处理不确定性下的决策。

微积分代写

微积分,最初被称为无穷小微积分或 “无穷小的微积分”,是对连续变化的数学研究,就像几何学是对形状的研究,而代数是对算术运算的概括研究一样。

它有两个主要分支,微分和积分;微分涉及瞬时变化率和曲线的斜率,而积分涉及数量的累积,以及曲线下或曲线之间的面积。这两个分支通过微积分的基本定理相互联系,它们利用了无限序列和无限级数收敛到一个明确定义的极限的基本概念 。

计量经济学代写

什么是计量经济学?
计量经济学是统计学和数学模型的定量应用,使用数据来发展理论或测试经济学中的现有假设,并根据历史数据预测未来趋势。它对现实世界的数据进行统计试验,然后将结果与被测试的理论进行比较和对比。

根据你是对测试现有理论感兴趣,还是对利用现有数据在这些观察的基础上提出新的假设感兴趣,计量经济学可以细分为两大类:理论和应用。那些经常从事这种实践的人通常被称为计量经济学家。

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。

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