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|KMA355 DEGENERACY

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## 数学代写|运筹学代写Operations Research代考|DEGENERACY

The chapter on simplex explained that if in a solution there is a tie in the right-hand side values leading to making one or more basic variables as zero in a subsequent iteration, then the solution is termed as degenerate. In the transportation model, degeneracy is identified by comparing the number of allocated or occupied cells after initial solution with one less number of constraint functions, i.e. number of allocations $=m+n-1$. Basic variables in the transportation model are represented by occupied cells. Now if the above-stated condition is not satisfied, then a transportation solution would be termed as degenerate. For reaching a basic feasible solution, out of remaining unoccupied cells one of the cost cells would be part of the solution, making it a basic variable that would satisfy the condition of the number of allocated cells. These remaining cells are considered to have allocation of zero units, substantiating the concept of basic variable becoming zero in the case of degeneracy. Thus, any of these cells which would be incoming cell would have an allocation of zero units. It is important to remember that this cell is artificially created with a flow of zero units.

Now the question is which of the cell from all of the unoccupied cells would be an artificial cell. For this, two considerations should be met. First, as the purpose is to minimize total transportation costs, so cell with least per unit transportation cost from unoccupied cells should be selected. In the case of a tie, then the cell with the maximum allocation is selected. Second and more importantly, the selected cell should be able to compute the remaining row (u) and column (v) variables.

To illustrate the solution procedure, Table $5.4$ has been reproduced here in the form of Table 5.28.

## 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。