Hungarian method of assignment

简明释义

匈牙利分配法［运输问题］

英英释义

例句

1.In our operations meeting, we discussed how the Hungarian method of assignment can improve efficiency.

在我们的运营会议上，我们讨论了匈牙利分配法如何提高效率。

2.The logistics manager recommended the Hungarian method of assignment for better route planning.

物流经理建议使用匈牙利分配法来更好地规划路线。

3.The team decided to use the Hungarian method of assignment to optimize their resource allocation.

团队决定使用匈牙利分配法来优化资源分配。

4.By applying the Hungarian method of assignment, we were able to minimize costs in our project.

通过应用匈牙利分配法，我们能够将项目成本降到最低。

5.Using the Hungarian method of assignment, we assigned tasks to team members based on their strengths.

使用匈牙利分配法，我们根据团队成员的优势分配任务。

作文

The Hungarian method of assignment is a combinatorial optimization algorithm that solves the assignment problem in polynomial time. This method is particularly useful in various fields such as operations research, economics, and computer science. The assignment problem involves assigning a set of tasks to a set of agents in such a way that the total cost is minimized or the total profit is maximized. One classic example is assigning jobs to workers where each worker has a different efficiency level for each job. By employing the Hungarian method of assignment, one can efficiently determine the optimal allocation of resources.The origins of the Hungarian method of assignment date back to the early 20th century and are attributed to Hungarian mathematicians, which is how it got its name. The algorithm operates on a cost matrix, where each element represents the cost of assigning a specific task to a specific agent. The process begins by reducing the matrix, which involves subtracting the smallest value in each row and column from all the other values in that row or column. This step ensures that there is at least one zero in each row and each column, which is crucial for the next steps.Once the matrix is reduced, the algorithm proceeds to cover all the zeros with the minimum number of lines. If the number of lines used equals the number of rows (or columns), an optimal assignment can be made using the current set of zeros. If not, the algorithm continues by finding the smallest uncovered value, subtracting it from all uncovered elements, and adding it to the elements covered by two lines. This iterative process continues until an optimal assignment is found.The efficiency of the Hungarian method of assignment makes it a preferred choice for solving assignment problems in many practical applications. For instance, in logistics, companies often need to assign delivery trucks to routes in a way that minimizes fuel costs. Similarly, in project management, tasks must be allocated to team members based on their skills and availability to ensure timely project completion.Moreover, the Hungarian method of assignment is not limited to just minimizing costs; it can also be adapted to maximize profits or optimize other metrics depending on the specific requirements of the problem at hand. This versatility is one of the reasons why it remains a popular algorithm in both academic research and industry applications.In conclusion, understanding the Hungarian method of assignment is essential for anyone involved in fields that require resource allocation or optimization. Its systematic approach not only provides solutions to complex problems but also enhances decision-making processes. As industries continue to evolve and become more data-driven, the relevance of this algorithm will likely increase, making it a valuable tool in the arsenal of professionals across various sectors.

匈牙利分配法是一种组合优化算法，用于在多项式时间内解决分配问题。该方法在运筹学、经济学和计算机科学等多个领域特别有用。分配问题涉及将一组任务分配给一组代理，以最小化总成本或最大化总利润。一个经典的例子是将工作分配给工人，其中每个工人在每项工作上的效率水平不同。通过使用匈牙利分配法，可以有效地确定资源的最佳分配。匈牙利分配法的起源可以追溯到20世纪初，归功于匈牙利数学家，这就是它得名的原因。该算法在一个成本矩阵上操作，其中每个元素表示将特定任务分配给特定代理的成本。该过程首先通过减小矩阵开始，这涉及从每行和每列中减去最小值，并将其从该行或列中的所有其他值中减去。这一步骤确保每行和每列中至少有一个零，这是下一步的关键。一旦矩阵被减少，算法就会继续用最少的线覆盖所有的零。如果使用的线的数量等于行数（或列数），则可以使用当前的零集进行最优分配。如果没有，算法将继续寻找最小的未覆盖值，从所有未覆盖的元素中减去它，并将其添加到被两条线覆盖的元素中。这个迭代过程将持续，直到找到一个最优分配。匈牙利分配法的高效性使其成为解决许多实际应用中分配问题的首选。例如，在物流中，公司通常需要将送货卡车分配给路线，以最小化燃料成本。同样，在项目管理中，任务必须根据团队成员的技能和可用性分配，以确保及时完成项目。此外，匈牙利分配法不仅限于最小化成本；它还可以根据特定问题的要求进行调整，以最大化利润或优化其他指标。这种多功能性是其在学术研究和行业应用中仍然受欢迎的原因之一。总之，理解匈牙利分配法对于任何参与资源分配或优化领域的人来说都是至关重要的。它的系统方法不仅为复杂问题提供了解决方案，还增强了决策过程。随着各行业不断发展并变得更加数据驱动，这种算法的相关性可能会增加，使其成为各个领域专业人士工具箱中的宝贵工具。