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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 the second phase, the solution is optimized on iterative basis.
In a given problem, if the number of rows is not equal to the number of columns and vice versa, then add a dummy row or a dummy column.
The assignment cost is the sum, over all pairs, of the flow between a pair of facilities multiplied by the distance between their assigned locations.
The quadratic assignment problem (QAP) was introduced by Koopmans and Beckman in 1957 in the context of locating "indivisible economic activities".
Subtract this smallest element with all other remaining elements that are NOT COVERED by lines and add the element at the intersection of lines.
Optimal Assignment Problem Salaries Of Professional Athletes Essay
Leave the elements covered by single line as it is. Take any row or column which has a single zero and assign by squaring it.The overall measure of performance is the total cost of the assignment, so the objective is to minimize this quantity. To make the model easier to understand, name the following ranges. Total Cost equals the sumproduct of Cost and Assignment. The result should be consistent with the picture below. With this formulation, it becomes easy to analyze any trial solution. We shall describe next how the Excel Solver can be used to quickly find the optimal solution. You have the choice of typing the range names or clicking on the cells in the spreadsheet. We show that a solution of the optimal assignment problem can be obtained as the limit of the solution of an entropy maximization problem, as a deformation parameter tends to infinity.This allows us to apply entropy maximization algorithms to the 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. Summary: The objective of the Quadratic Assignment Problem (QAP) is to assign \(n\) facilities to \(n\) locations in such a way as to minimize the assignment cost.Strike off the remaining zeros, if any, in that row and column (X).Repeat the process until all the assignments have been made.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.