
110 Introduction to Linear Optimization and Extensions with MATLAB
R
Using as an initial basis B
0
the columns associated with x
1
, x
2
, and x
3
,
the following summary of the iterations is obtained:
Table 3.1 Example of cycling
Iteration Entering Leaving Basic variables Obj value
0 x
1
= 0, x
2
= 0, x
3
= 1 0
1 x
4
x
1
x
4
= 0, x
2
= 0, x
3
= 1 0
2 x
5
x
2
x
4
= 0, x
5
= 0, x
3
= 1 0
3 x
6
x
4
x
6
= 0, x
5
= 0, x
3
= 1 0
4 x
7
x
5
x
6
= 0, x
7
= 0, x
3
= 1 0
5 x
1
x
6
x
1
= 0, x
7
= 0, x
3
= 1 0
6 x
2
x
7
x
1
= 0, x
2
= 0, x
3
= 1 0
At the end of iteration 6, the simplex method revisits the initial basis
B
0
. Thus, the simplex method will cycle indefinitely and never terminate in
this case if the entering and leaving variable ...