The Hungarian Algorithm Calculator is a powerful tool used to solve optimization problems known as the assignment problem. It finds the optimal assignment of tasks to resources, minimizing the total cost or maximizing the total profit. This calculator employs the Hungarian algorithm, a method that efficiently solves assignment problems by iteratively reducing the problem to a series of steps until an optimal assignment is achieved.
Formula of Hungarian Algorithm Calculator
The Hungarian Algorithm Calculator follows these steps:
Step1: Subtract the minimum value in each row from all the values in that row.
Step2: Subtract the minimum value in each column from all the values in that column.
Step3: Cover all zeros with the minimum number of lines.
Step : Test for optimality. If the number of lines drawn is equal to the number of rows or columns, an optimal assignment is found. If not, proceed to step 5.
Step5: Determine the smallest uncovered value (let it be k) and subtract it from all uncovered values. Then add it to all the values intersected by the lines. Return to step 3.
Step6: The optimal assignment is obtained from the resulting matrix.
You'll need to represent your problem as a matrix of costs or distances, and then apply the Hungarian algorithm steps iteratively until an optimal assignment is found.
General Terms Table
| Term | Description |
|---|---|
| Assignment | The task of assigning resources to tasks in an optimal way. |
| Optimization | The process of finding the best solution among alternatives. |
| Algorithm | A step-by-step procedure for solving a problem. |
| Matrix | A rectangular array of numbers arranged in rows and columns. |
| Cost | The value representing the expense or effort required. |
| Optimal | The best possible solution. |
This table provides general terms related to the Hungarian Algorithm Calculator, helping users understand key concepts without needing to calculate each time.
Example of Hungarian Algorithm Calculator
Suppose we have a scenario where three workers (W1, W2, W3) are assign to three tasks (T1, T2, T3). The cost matrix representing the cost of assigning each worker to each task is as follows:
| T1 | T2 | T3 | |
|---|---|---|---|
| W1 | 5 | 9 | 1 |
| W2 | 10 | 3 | 2 |
| W3 | 8 | 7 | 4 |
Using the Hungarian Algorithm Calculator, we can find the optimal assignment of workers to tasks. After calculation, the optimal assignment would be:
W1 -> T3
W2 -> T2
W3 -> T1
Most Common FAQs
The Algorithm Calculator is use to find the optimal assignment of tasks to resources, minimizing costs or maximizing profits.
The algorithm works by iteratively reducing the assignment problem to a series of steps until an optimal assignment is find. It involves subtracting row and column minima, covering zeros, and testing for optimality.
Yes, the calculator is applicable to various real-life scenarios such as workforce scheduling, job assignment, and resource allocation.
The calculator provides accurate results based on the input cost matrix and follows the rigorous steps of the algorithm to find the optimal assignment.
Yes, the calculator is capable of handling large datasets efficiently, making it suitable for complex optimization problems.