Optimal Assignment Problem

Optimal Assignment Problem-70
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.But the cost will remain the same for different sets of allocations.

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Reduce the new matrix given in the following table by selecting the smallest value in each column and subtract from other values in that corresponding column.

In column 1, the smallest value is 0, column 2 is 4, column 3 is 3 and column 4 is 0.

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".

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

Optimal Assignment Problem Growing Up Asian In Australia Essays

The row wise reduced matrix is shown in table below.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. Write down the assignment results and find the minimum cost/time.Note: While assigning, if there is no single zero exists in the row or column, choose any one zero and assign it.Subtract 3 from all other values that are not covered and add 3 at the intersection of lines. Here in table minimum number of lines drawn is 4 which are equal to the order of matrix. Strike off remaining zeros if any in that row or column. Formulate the Model | Trial and Error | Solve the Model Use the solver in Excel to find the assignment of persons to tasks that minimizes the total cost. Strike off the remaining zeros in that column or row, and repeat the same for other assignments also.If there is no single zero allocation, it means multiple numbers of solutions exist.The assignment costs for dummy cells are always assigned as zero.Select the smallest element of the whole matrix, which is NOT COVERED by lines.


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