01 converting maximization assignment problem into minimization problem

Converting Maximization Assignment Problem Into Minimization Assignment Problem

Presented By:-

B.A.N.V.HANUMANTHA RAO

10PA1E0001

Quantitative Analysis for Business Decisions

GUIDED BY:-Mr. M.S.R.MURTHY

Introduction• An assignment problem case of a

transportation problem where the sources are assignees and destinations are tasks.

• The objective the total cost or to maximize the total profit of allocation.

• This gives rise to cost differences.

• Each job requires different skills and the capacity.

Q. A company has six job to be process by six machines the following table gives the return in rupees the job is assign to j machines how should job can be assign to the machines so to maximizes the overall return.

9 22 58 11 19 27

43 78 72 50 63 48

41 28 91 37 45 33

74 42 27 49 39 32

36 11 57 22 25 18

3 56 53 31 17 28

Steps for Problem• Steps1:- Convert maximization problem into

minimization problem select the largest element in the way of matrix or profit matrix subtracting from the highest element. Here 91 is the largest subtracting from very elements.

• Steps2:- Subtract the minimum element from each row from the other elements of the same row of the given matrix.

• Steps3:- Modify the resulting matrix by substract the smallest element of each column from the other element of same column.

• Steps4:- Draw the minimum number of horizontally and vertically line to cover all the zero in the resulting matrix. Let the minimum no. of lines be N. if N=the no. of rows of the given matrix, make zero assignment to get the obtain solution. If N is less than the number of rows, goto step4

• Step5:- Determine the smallest element of all the uncovered element. Substract it from all the uncovered element and add the same at the intersection.

• Step6:- Repeat step4 and step5 until the number of lines become equal to the number of rows.

• Step7:- Examine the rows one by one until a single zero element is found. Make this zero as to make the assignment crossout all the zero in the column of make zero.

• Step8:- Repeat step7 until number unmarks zero is lefts. If there are more than the one unmark zero in any row.

• Step9:- Thus, exactly one mark will be their in each row and column. The assignment corresponding to mark zero will give the about optimal solution.

Minimization Table 82 69 33 80 72 64

48 13 19 41 28 43

50 63 0 54 46 58

17 49 64 42 52 59

55 80 34 69 66 73

88 35 38 60 74 63

Apply Hungarian Method

49 36 0 47 39 31

35 0 6 28 15 30

50 63 0 54 46 58

0 32 47 25 35 42

21 46 0 35 32 39

53 0 3 25 39 28

Tick The Row Have No Assignment

49 36 22 24 3

35 0 6 3 2

50 63 0 29 31 30

32 47 0 20 14

21 46 0 10 17 11

53 0 3 24 0

0

0

0

0

46 33 0 19 21

35 0 9 3 2

47 60 26 28 27

32 50 0 20 14

18 43 0 7 14 8

53 0 6 24 0

0

0

0

0

0

46 33 7 19 21

35 0 16 3 2

40 53 19 21 20

32 57 0 20 14

11 36 0 7 1

53 13 0 24 0

0

0

0

0

0

9 22 58 11 19

43 78 72 50 48

41 28 37 45 33

42 27 49 39 32

36 11 57 25 18

3 53 31 17 28

27

63

91

74

22

56

• All machine are assgin to you one job solve is optimal the optimal allocation 1 VI , 2 V ,3 III,4 I,5 IV, 6 II

• Maximum profit is 27+63+91+74+22+56=333