(i)
Degeneracy; Degeneracy occurs when the number of rows
plus the number of columns less one is not equal to the number of occupied
cells.
(ii)
A slack variable: This is a variable that is added to an
inequality to make it equal e.g. incase
the supply and demand are not equal.
(iii)
Balanced transportation model: This is a model in which
the total demand and total supply are
equal.
Initial distribution using LCM
|
Source
|
D1
|
D2
|
D3
|
D4
|
D5
|
Supply
|
 S1 |
 10 |
  12 |
 2
25000
|
 3
25000
|
4
|
50,000
|
 S2 |
 4
15000
|
10
|
 9 |
 2
5000
|
8
|
20,000
|
 S3 |
 9
10000
|
 15
15000
|
 3 |
 12 |
1
10000
|
35,000
|
|
Demand
|
25,000
|
15,000
|
25,000
|
30,000
|
10,000
|
105,000
|
Test for degeneracy
M= no of rows n = number of columns
M+n-1= number of occupied cells
3+5-1=7
No degenerate
Test for optimality
v + m=t
5
12 2 3 -3
|
Source
|
D1
|
D2
|
D3
|
D4
|
D5
|
Supply
|
|
S1
0
|
10
|
12
|
2
25000
|
3
25000
|
4
|
50,000
|
|
S2
-1
|
4
15000
|
10
|
9
|
2
5000
|
8
|
20,000
|
|
S3
4
|
9
10000
|
15
15000
|
3
|
12
|
1
10000
|
35,000
|
|
Demand
|
25,000
|
15,000
|
25,000
|
30,000
|
10,000
|
105,000
|
Unoccupied cells actual cost - v + m difference
S1d1 10 0+5 5
S1d2 12 0+12 0
S1d5 4 0+-3 7
S2d2 10 -1+12 -1
S2d3 9 -1+2 8
S2d5 8 -1+-3 12
S3d3 3 4+2 -4
S3d4 12 4+3 5
The
solution is not optimum as the negative numbers indicate that the unoccupied
cells need to be allocated so as to reduce the cost further by the number I.e.
s2d2 by 1 and s3d3 by 4
Initial
basic feasible solution =(2 X 25000 + 3 X 25000 + 4 X 15000 + 2 X 5000 + 9 X
10000 + 15 X 15000 + 1 X 10000)
=KSH
520000
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