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THE MODIFIED DISTRIBUTION (MODI) METHOD Or UV METHOD

The problem encountered in the stepping stone method of optimality test can be overcome try MODI method because we don’t have to evaluate the empty cells one by one, all of them can be evaluated simultaneously. This is considerably time saving. The method has the following steps.

Step – I

Set up the cost matrix of the problem only with the costs in those cells in which allocations have been made.

X

Y

A

Rs.2000

B

Rs.2500

Rs.2700

C

Rs.1700

 

Step II.

Let there be set of number Vj (V1, V2) across the top of the matrix and a set of number U; (U1, U2, U3) across the left side so that their sums equal the costs entered in the matrix shown above.

V1=0        200

V2=200

2500

U1

Rs.2000

2500

U2

Rs.2500

Rs.2700

1500

U3

 

Rs.1700

 

U1+V1 =2000           U2+V2=2700

U2+V1 =2500           U2+V2= 1700

Let V1 = 0 then U1 = 2000, U2= 2500

V2 =2700 – 2500 = 200

U3=1500

Step III.

Leave the already filled cells vacant and fill the vacant cells with sums of Ui and Vj. This is shown in the matrix below:

0          V1

200     V2

2000

U1

2200   (V1+V2)

2500

U2

1500

U3

1500   (U2+V1)

Step IV.

Subtract the vacant values now filled in step III from the original cost matrix. This will result in cell evaluation matrix and is shown below for the example in hand.

5380-2200=3180

2550-1500=1050

 

Step V.

If any of the cell evaluation turns out to be negative, then the feasible solution is not optimal. If the values are positive the solution is optimal. In the present example, since both the cell evaluation values are positive, the feasible solution is optimal.

Let us take another example where some of the evolutions turns out to be negative to explain the entire procedure.

Let us assume the following transportation model for this purpose.

Distribution centres → (Press in the centre)

P

Q

R

S

Supply

Plants

A

200

300

1100

700

6 (100)

B

100

0

600

100 (1)

1 (100)

10 (300)

C

500

800

1500

900

17 (Total)

Demand

7

5

3

2

(100)

(300)

(500)

(600)