Posted on Categories:Operations Research, 数学代写, 运筹学

数学代写|运筹学代写Operations Research代考|KMA255 Modeling Fixed Charges

avatest™

avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

数学代写|运筹学代写Operations Research代考|Modeling Fixed Charges

The purpose of this section is to introduce decision models, which provide options regarding the choice of machines. One of the pertinent tasks is to ensure that machine-related constraints apply only to those machines that are purchased or leased. As an example, consider a publishing company that intends to produce its annual lineup of operations research texts. This year, they have the books by Gabby and Blabby $(G B)$, Huff, Fluff, and Stuff (HFS), and the “Real OR” (ROR) texts. As usual nowadays, authors are required to do everything except for the printing, binding, and the subsequent marketing. A number of different machines are available for printing and binding, and from each type of machine, exactly one must be chosen. The three printing machines under consideration are $P_1, P_2$, and $P_3$, while the two binding machines are $B_4$ and $B_5$. The processing times for the different books on the respective machines in minutes per book are shown in Table 5.10.

The capacities of the three printing machines are 120,100 , and $110 \mathrm{hrs}(7200$, 6000 , and $6600 \mathrm{~min}$ ), respectively, in the planning period. Similarly, the capacities of the binding machines are $3331 / 3$ and $300 \mathrm{hrs}$, respectively (or 20,000 and $18,000 \mathrm{~min}$ ). The costs to lease the machines are independent of the number of books made with them. They are $\$ 10,000, \$8000, \$ 9000, \$20,000$, and $\$ 23,000$, respectively. The profit contributions of the three books (other than the leasing costs) have been identified as$\$40, \$ 60$, and$\$70$, respectively. It has also been determined that the publishing house should produce at least 500 copies of the landmark $R O R$ book in order to maintain a good academic image.

The problem presented in this subsection deals with the allocation of tasks to employees, so as to ensure that none of the employees is overworked, while others are partially idle. We assume that tasks cannot be split, meaning that once an employee starts a job, he will have to finish it. (This scenario is reminiscent of the bin packing problem, see, e.g., Chap. 17.) Due to their different backgrounds and training, a job will take different amounts of time if different employees perform it. There are three workers $W_1, W_2$, and $W_3$, who will have to perform tasks $T_1, \ldots$, $T_5$. Table $5.11$ shows the processing times (in hours) for all worker-task combinations.

In order to formulate the problem, we need to introduce zero-one variables, which are defined as $y_{i j}=1$, if employee $W_i$ is assigned to task $T_j$, and zero otherwise. The only constraints of the model ensure that each task is assigned to exactly one employee. Formally, we can write
$$y_{1 j}+y_{2 j}+y_{3 j}=1 \text { for all } j=1, \ldots, 5 .$$
The more contentious issue concerns the objective function. First, we note that the actual working time of the employees can be written as
$$\begin{gathered} w_1=5 y_{11}+1 y_{12}+9 y_{13}+4 y_{14}+9 y_{15}, \ w_2=4 y_{21}+3 y_{22}+8 y_{23}+3 y_{24}+8 y_{25}, \text { and } \ w_3=7 y_{31}+5 y_{32}+6 y_{33}+4 y_{34}+7 y_{35}, \end{gathered}$$
where the new variables $w_1, w_2$, and $w_3$ denote that time that employees $W_1, W_2$, and $W_3$ are busy working on the tasks. One possibility to ensure fairness in the solution is to attempt to make the longest working time as short as possible. In other words, the employee who works longest should have the shortest working hours possible. Formally for our problem, we can write this objective as
$$\operatorname{Min} z=\max \left{w_1, w_2, w_3\right} .$$

数学代写运筹学代写Operations Research代考|Modeling Fixed Charges

$$y_{1 j}+y_{2 j}+y_{3 j}=1 \text { for all } j=1, \ldots, 5 .$$

$$w_1=5 y_{11}+1 y_{12}+9 y_{13}+4 y_{14}+9 y_{15}, w_2=4 y_{21}+3 y_{22}+8 y_{23}+3 y_{24}+8 y_{25}, \text { and } w_3=7 y_{31}+5 y_{32}+6 y_{33}+4 y_{34}+7 y_{35},$$

\eft 的分隔符缺失或无法识别

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。