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# 数学代写|运筹学代写Operations Research代考|IND604 HUNGARIAN ALGORITHM

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## 数学代写|运筹学代写Operations Research代考|HUNGARIAN ALGORITHM

Transportation problem is a general-purpose algorithm involving allocation of units available from certain sources to certain destinations. However, it does not provide sufficient resolution for a special structure of transportation problem where all demand and supplies equal to one unit. Hungarian algorithm is a special purpose method to resolve such problems termed as assignment problem. Steps involved in the algorithm have been discussed by using the illustration shown in Table 6.1.
Step 1: Feasibility check: In the assignment problem, the feasibility of model is checked by finding equality between the number of rows and columns. Such problem is called as balanced problem. The example considered is shown in Table 6.4. The number of rows representing teams to be assigned is four, which is equal to the number of columns representing the number of projects.
The next two steps are based on the concept of matrix reduction that implies that if a constant value is subtracted or added from the entire set of values in the matrix, it would yield an optimal solution. The reduced values indicate the opportunity cost (time in this case) indicating the next best opportunity. For instance, for team 1, the best possible assignment would be project 2 as it entails the least cost/time, whereas the next best would be project $1 .$

Step 2: Row reduction: From each row, subtract the minimum cell value (in this case, time) from all other values of that row. In row 1, represented by Team 1, the minimum value is 8 , which is subtracted from other values. This would give us the following result (Table 6.5):
Step 3: Column reduction: From each column, subtract the minimum cell value (in this case, time) from all other values of that column. In column 1 represented by Project 1 , the minimum value is 0 , which is subtracted from other values. This would give values as shown in Table 6.6.
Step 4: Make assignments:
i. Starting from the first row, make assignment or allocations in the row which has only one zero. This would imply assigning an employee to a particular job. The first row has two zeros, so assignment cannot be done as the most optimal assignment for team 1 would be both projects 2 and 4 .

## 数学代写|运筹学代写Operations Research代考|COMPARISON WITH TRANSPORTATION MODEL

The assignment problem is a special case of the transportation model. This is better understood by comparing the assignment model shown in Table $6.1$ with transportation model shown in Table $5.1$ of the chapter on Transportation model. This is reproduced here as Table 6.3.
First, let’s discuss similarities between the two models.
Similarities:

First, both models have a limited and fixed number of suppliers or employees and a limited and known number of demand centres or jobs.

Second, both models deals with aspect of combining resources with demand and tasks. In the case of transportation, the number of units from different supply centres is allocated to fulfil demand of various destinations in a manner to minimize transportation cost. Whereas, in the assignment model, the same kind of allocation is done based on certain criteria of either minimizing cost or minimizing time to do a specific job.
Difference:

But both models have one major difference. In the case of transportation problem, different supply and demand centres can have different capacities of output and requirements respectively, shown by $b_i$ and $c_j$ in Table 6.3. Whereas in the case of assignment problem, all supplies and demands equal to one. This is because of fundamental of assignment problem, i.e. one worker can be assigned to do only job at a time, one geographic area can be assigned only one store or department and so on. Thus, the cost incurred in transporting ‘ $x$ ‘ units from supply centre 1 to demand centre 1 would be $c_{11} x_{11}$. For the assignment model, it would be the same but the value of $x_{11}$ would be either 1 or 0 .The optimality of the transportation model is checked by equating total available units with total requirement. Whereas in the case of assignment, it is checked by equating the number of persons with the number of tasks. Thus, the condition of suppliers/employees to be equal to demand centres/ tasks in assignment is essential, though not a necessary condition.

Finally, feasibility of transportation is checked by equating $m+n-1$ with the number of basic variables (allocated cells). If it is not fulfilled then deficit variables are termed as degenerate. Thus in the case of assignment where $m=n$ number of allocations/assignments should be equal to $2 n-1$. However, because the assignment problem involves assigning $n$ employees to $\mathrm{n}$ jobs so, there would be only $\mathrm{n}$ assignments. So deficit, i.e. $\mathrm{n}-1$ variables would degenerate. This is depicted by $\mathrm{x}_{\mathrm{ij}}=0$, implying no assignment.

## 数学代写|运筹学代写运筹学代考|匈牙利算法

.匈牙利算法

i。从第一行开始，对只有一个0的行进行赋值或分配。这就意味着将一个员工分配到一个特定的工作。第一行有两个0，所以分配不能完成，因为团队1的最优分配将是项目2和项目4

## 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。