Where do I look to calculate the total cost after solving the assignment problem?
Conditions
- The optimal assignment has been determined from the reduced matrix.
- The original cost matrix is available.
Reasoning, step by step
- List the person-job pairs from the circled zeros.
- Look up the cost for each pair in the original matrix.
- Sum these costs to get the total optimum cost.
Example
The assignments are A->2, B->3, C->4, D->1. The original costs are 12, 7, 11, and 8. The total cost is .
Common misconceptions
- Summing the values from the reduced matrix, which are mostly zeros.
- Using the row or column minima instead of the original costs.
Watch the explanation
Connected concepts
Explore next
Related questions
To select independent zeros, scan the reduced matrix for rows or columns with only one available zero. Circle that zero and strike out other zeros in the same row and column.
Conditions: The matrix has been reduced using row and column operations.; The goal is to find n independent zeros for an n x n matrix.
The presenter avoids selecting a zero when a row has two zeros because the goal is to find a set of independent zeros where each row and column has exactly one selected zero. Choosing arbitrarily from a row with multiple zeros might lead to conflicts later, so the process is postponed until the zero pattern is more constrained.
Conditions: The matrix has undergone row and column reduction.; The goal is to find an optimal assignment.
A balanced assignment problem means that the number of rows (persons) is equal to the number of columns (jobs). This allows for a one-to-one assignment where each person is assigned to exactly one job.
Conditions: The cost matrix is square (same number of rows and columns).; Each job is to be assigned to exactly one person.
Column reduction is the second step of the Hungarian method. It involves taking the matrix obtained after row reduction, finding the minimum element in each column, and subtracting this minimum value from all elements in that same column.
Conditions: The matrix must have already undergone row reduction.; The problem is a balanced assignment problem.
The purpose of step three is to inspect the reduced matrix row by row and count how many zeros each row contains. This helps determine if a unique assignment can be made or if further steps are needed to isolate independent zeros.
Conditions: The matrix has undergone row and column reduction.; The goal is to find an optimal assignment.
Answers are generated from source material and independently checked. Consult the original video or creator if something is unclear.