2 Prentice Ha, Inc, a publisher headquartered in New Jersey, want to assien thre

Question

2 Prentice Ha, Inc, a publisher headquartered in New Jersey, want to assien three recently hired college graduate, Jones, Smith and Wilson to regional sales district in Omaha, Dallas and Miami. But the firm also has an opening in New York and would sent one of the three there if it were more economical than a move to Omaha, Dallas, or Miami. It will cost $1000 to relocate Jones to New York, $800 to relocate Smith ther, and S1500 to move Wilson. What is the optimal assignment of personnel to office? OMAHA MIAM DALLAS Office Hiree Jones Smith Wilson $800 $500 $500 1,100 S1,200 $1,600 $1,300 $1,000 $2,300

Explanation / Answer

Since we have to find the optimal assignment, we will use the Hungarian Matrix method to solve the problem , please fins the below steps to calculate Step 1: Validate if it is a N*N matrix, I.e. no of rows equal to no. of columns, if its not then add a dummy row or dummy column Step 2: Subtract the Smallest entry i.e. number in each row from all the entries of its row Step 3: Subtract the smallest entry in ach column from all the entries of its column. Step 4 : Draw lines through appropriate rows and columns so that all the zero entries of the cost matrix are covered and the minimum number of such lines is used Step 4: Test for Optimality 1) If the minimum number of covering lines is n, an optimal assignment of zereos is possible and we are finished 2) If the minimum number of covering lines is less than n, an optimal assignment of zeroes is not yet possible. In that case proceed to step 5 Step 5: Determine the smallest entry not covered by any line. Subtract this entry from each uncovered row, and then add it to each covered column. Return to step 3 Execting Step 1 Office Omaha Miami Dallas Newyork Names Jones 800 1100 1200 1000 Smith 500 1600 1300 800 Wilson 500 1000 2300 1500 Adding dummy Row 800 1100 1200 1000 500 1600 1300 800 500 1000 2300 1500 0 0 0 0 Executing step 2 0 300 400 200 0 1100 800 300 0 500 1800 1000 0 0 0 0 Executing step 3 and Step 4 0 0 0 0 0 800 400 100 0 200 1400 800 0 0 0 0 Covering lines is passing through row 1, row 4, column 1 , thus sum of covering lines is 3 Since the number of covering lines is not equal to N, thus executing step 5 (currently number od lines is 3) 100 0 0 0 100 700 300 0 100 100 1300 700 100 0 0 0 Again checking the step 3, now the number of covering lines is equal to N, hence we stop and have the optimum solution. 100 0 0 100 0 600 200 100 0 0 1200 800 100 0 0 100 Ans: Since the total cost for this assignment is zero, it must be an optimal assignment. The Bold zeroes are the solution Now highlighting the ans in real matrix Office Omaha Miami Dallas Newyork Names Jones 800 1100 1200 1000 Smith 500 1600 1300 800 Wilson 500 1000 2300 1500 1. So, Jones must be sent to Dallas at cost $1200 2. Smith must be sent Omaha at a cost of $500 3. Wilson must be sent to Miami at a cost of $1000. Thus we get an optimum assignment of the personal to differnet offices

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