# Optimal Assignment Problem

Result: The optimal solution: Conclusion: it is optimal to assign Person 1 to task 2, Person 2 to Task 3 and Person 3 to Task 1.

Result: The optimal solution: Conclusion: it is optimal to assign Person 1 to task 2, Person 2 to Task 3 and Person 3 to Task 1.

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The model we are going to solve looks as follows in Excel. For this problem, we need Excel to find out which person to assign to which task (Yes=1, No=0).

For example, if we assign Person 1 to Task 1, cell C10 equals 1. What is the overall measure of performance for these decisions? Explanation: The SUM functions calculate the number of tasks assigned to a person and the number of persons assigned to a task.

In row A, the smallest value is 13, row B is 15, row C is 17 and row D is 12.

The row wise reduced matrix is shown in table below.

In particular, the Sinkhorn algorithm leads to a parallelizable method, which can be used as a preprocessing to handle large dense optimal assignment problems.

## How To End A Research Proposal - Optimal Assignment Problem

This parallel preprocessing allows one to delete entries which do not belong to optimal permutations, leading to a reduced instance which becomes solvable with limited memory requirements.

The objective of the problem is to assign a set of facilities to a set of locations in such a way as to minimize the total assignment cost.

The assignment cost for a pair of facilities is a function of the flow between the facilities and the distance between the locations of the facilities.

The column-wise reduction matrix is shown in the following table.

Take the smallest element of the matrix that is not covered by single line, which is 3. Now, draw minimum number of lines to cover all the zeros and check for optimality. Select a row that has a single zero and assign by squaring it.

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