Q.

1 A company ha one surplus truck in each of the cities A,B,C,D & E and one deicit truck in each of the cities 1,2,3,4,5&
6. The distance between the cities in K.M. is shown in the matrix below. Find the assignment of trucks from each cities in
surplus to cities in deficit so that the totl distance covered by truck is minimum.

1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 14 10 13 13 12
E 8 12 11 7 13 10

Solution

In assignment problem the number of rows must equeal to no. of column. So, we add a dummy row 'F'

1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 14 10 13 13 12
E 8 12 11 7 13 10
F 0 0 0 0 0 0

1 2 3 4 5 6 formula avail
A 0 1 0 0 0 0 1 1
B 0 0 0 0 0 1 1 1
C 0 0 1 0 0 0 1 1
D 1 0 0 0 0 0 1 1
E 0 0 0 1 0 0 1 1
F 0 0 0 0 1 0 1 1
formula 1 1 1 1 1 1
demand 1 1 1 1 1 1

TP cost 38
 Q.3 A production control superintendent finds the following information on his desk. In department A,B & C, the no. of
surplus pallates is 18,27 & 21 respectively.In department G,H,I & J, the no, of pallates rquired is 14,12,23 & 17
respectively. The time in minutes to move a pallet from one departmnent to another is given below.

G H I J Supply
A 13 25 12 21 18
B 18 23 14 9 27
C 23 15 12 16 21
Demand 14 12 23 17

Solution

Column1 G H I J Formula Supply

A 14 0 4 0 18 18
B 0 0 10 17 27 27
C 0 12 9 0 21 21
Formula 14 12 23 17 66
Demand 14 12 23 17 66

TP cost 811
Q.5 Consider the following transhipment problem with two sources and two destinations, the costs for shipment in Rs.
are given below. Determine the optimal shippig schedule

source destinatio Supply

S1 S1 D1 D2
Source S1 0 1 6 2 4
S2 1 0 8 2 5
Destination D1 0 7 0 3
D2 1 0 1 0
Demand 3 6

Solution

source destinatio Supply

S1 S1 D1 D2
Source S1 0 1 6 2 4
S2 1 0 8 2 5
Destination D1 0 7 0 3 9
D2 1 0 1 0 9
Demand 9 9 3 6

source destination 3 2
S1 S1 D1 D2 formula supply
Source S1 3 1 0 0 4 4
S2 0 5 0 0 5 5
Destination D1 6 0 3 0 9 9
D2 0 3 0 6 9 9
Formula 9 9 3 6 27
Demand 9 9 3 6 27

TS cost 1