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OPERATIONS RESEARCH
TRANSPORTATION PROBLEM-
NWCM(UNBALANCED)
DR.T.SIVAKAMI
ASSISTANTPROFESSOR
DEPARTMENTOFMANAGEMENTSTUDIES
BONSECOURSCOLLEGEFORWOMEN,THANJAVUR
NORTH WEST CORNER METHOD
1.Solve the following transportation problem by using
NWCM
R1 R2 R3 Supply
S1 4 8 8 76
S2 16 24 16 82
S3 8 16 24 77
Deman
d
72 102 41
Solution:
• The given transportation problem is unbalanced
• convert unbalanced into balanced.
• Introduce dummy column with the value of 20
STEP 1:
4 8 8 0 76
16 24 16 0 82
8 16 24 0 77
72 102 41 20
STEP 2:
4
8 8 0
16 24 16 0
8 16 24 0
72
76
82
77
72 102 41 20
4
Step:3
8 8 0
24 16 0
16 24 0
4
82
77
102 41 20
4
98
Step:4
24
16 0
16 24 0
82
77
98 41 20
82
16
Step:5
16
24 0
77
16 41 20
16
61
Step:6
24
0
61
41 20
41
20
Step:7
0 20
20
20
Total transportation cost:
=[4×72]+[8×4]+[24×82]+[16×16]+[24×41]+[0×20]
=288+32+1968+256+984+0
=Rs.3528.
2.Solve the transportation problem by using
NWCM
M1 M2 M3 M4 M5 Supply
F1 4 2 3 2 6 8
F2 5 4 5 2 1 12
F3 6 5 4 7 7 14
Dema
nd
4 4 6 8 8
Solution:
• The given transportation problem is
unbalanced
• Convert the unbalance into balance.
• Introduce the dummy column with the
value of 4.
Step:1
4 2 3 2 6 0
5 4 5 2 1 0
6 5 4 7 7 0
8
12
14
4 4 6 8 8 4
Step:2
4
2 3 2 6 0
5 4 5 2 1 0
6 5 4 7 7 0
8
12
14
4 4 6 8 8
4
4
4
Step:3
2
3 2 6 0
4 5 2 1 0
5 4 7 7 0
4
12
14
4 6 8 8 4
4
Step:4
5 2 1 0
4 7 7 0
12
14
6 8 8 4
6
6
Step:5
2
1 0
7 7 0
6
14
8 8 4
6
2
Step:6
7
7 0
2 8 4
14
2
12
Step:7
7 0 12
8 4
8
4
Step:8
0
4
4
4
Total transportation
cost=[4×4]+[2×4]+[5×6]+[2×6]+[7×2]+[7×8]+[0×4]
=16+8+30+12+14+56+0
=Rs.136.
3.Solve the transportation problem by using
NWCM.
5 1 8 7 5 15
3 9 6 7 8 25
4 2 7 6 5 42
7 11 10 4 9 35
30 20 15 10 20
Demand
Supply
Solution:
• The given transportation problem is unbalanced .
• Convert the unbalanced into balanced.
• Introduce the dummy column with the value of 20
Step:1
5 1 8 7 5 0
3 9 6 7 8 0
4 2 7 6 5 0
7 11 10 4 9 0
15
25
42
35
30 20 15 10 20
22
Step:2
5
1 8 7 5 0
3 9 6 7 8 0
4 2 7 6 5 0
7 11 10 4 9 0
15
25
42
35
30 20 15 10 20
22
1
5
15
Step:3
3
9 6 7 8 0
4 2 7 6 5 0
7 11 10 4 9 0
25
42
35
15 20 15 10 20
22
1
5
10
Step4:
9 6 7 8 0
2 7 6 5 0
11 10 4 9 0
10
42
35
20 15 10 20
22
1
0
10
Step 5:
2
7 6 5 0
11 10 4 9 0
42
35
10 15 10 20
22
10
32
Step 6:
7
6 5 0
10 4 9 0
32
35
15 10 20
22
15
17
Step 7:
6 5 0
4 9 0
17
35
10 20 22
10
7
Step 8:
5
0
9 0
7
35
20 22
7
13
Step 9:
9 0
35
13 22
13
22
Step10:
0
22
22
22
Total transportation
cost=[5×15]+[3×15]+[9×10]+[2×10]+[7×15]+[6×10]+[5×7]+[9×13]+[0×22]
=75+45+90+20+105+60+35+117+0
=Rs.547.

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NWCM Methods for Solving Transportation Problems