# Hungarian Method

May 12th, 2015
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The cost of allocating methods to requirements can be represented by a cost matrix in which each element represents the cost Cij of allocating the ith method to the jth requirement

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HungarianMethodHUNGARIANMETHODThe cost of allocatingmethods torequirements can berepresented by a costmatrix in which eachelement representsthe cost Cij ofallocating the ithmethod to the jthrequirement12jn1C11C12C1jC1n2C21C22C2jC2niCi1CijCinCn1CnjCnnnThe fundamental principleof this method is that if anassignment problem ismodified by adding orsubtracting a constantfrom all of the elements ina row or column of a costmatrix then the optimalsolution of the modifiedproblem is the same asthe optimal solution of theoriginal problem.The algorithm is asfollows:Step 1: Locate thesmallest cost in each ROWof the cost matrix. Subtractthis cost from each cost onthat row. This results in a0 in each row of the costmatrix.Step 2: Determine if asolution to the modifiedproblem exists that has a costof zero i.e. there must be nindependent 0s where n is thenumber of rows or columns.Check by drawing the minimalset of lines through the 0s thatresulted from step1 (lines aredrawn across rows or downcolumns). If fewer than n lineswill cover all 0s then theoptimal solution has not beenfound proceed to step 3.Step 3. Repeat step 1on the columns. Againdraw the minimal set oflines to cover all 0s. Ifthe minimal set of linesis n the optimal solutionhas been found - if notproceed to step 4.Step 4: Starting with thematrix from step 3. Call theelemen

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