Assignment problem: Difference between revisions

Revision as of 23:16, 14 December 2005

Revision as of 23:25, 14 December 2005

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Then we perform row operations on the matrix. To do this, the lowest of all ai [i belonging to 1-4] is taken and is subtracted from the other elements in that row. This will lead to at least one zero in that row [We get multiple zeros when there are two equal elements which also happen to be the lowest in that row]. This procedure is repeated for all rows. We now have a matrix with at least one zero per row. Now we try to assign tasks to agents such that each agent is doing only one task and the penalty incurred in each case is zero. This is illustrated below.

['''Note-I havent used the matrix notation since formatting is not possible with that]'''

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<s>d1' &nbsp; 0' &nbsp;&nbsp; d3' &nbsp; d4'</s> <br/>

'''Note that since-Since a verticle line cannot be drawn iI have used a horizontal line to cut the 1st column.'''

From the elements that are left, find the lowest value. Subtract this from all elements that are not struck. Add this to elements that are present at the intersection of two lines. Leave other elements unchanged. Now assign the tasks using above rules. Repeat the procedure till an assignment is possible.