Special Cases in simplex
method applications
Stat 261
Special cases
Degeneracy
Alternative (optima)
Unbounded solutions
Infeasible solution
Degeneracy
If the optimal solution one or more of the original variables
has‘0’ value,then this is called degenerate optimal solution.
Example:
Z  3x  9 x
Subject to x 1  4x 2  8
x 1  2x 2  4
x1 , x 2  0
Alternative (optima)
If there is a ‘0’ under a non-basic variables in Z-row that’s
means there are many solutions.
Example:
Z  2 x1  4 x2
Subject to x 1  2x 2  5
x1  x 2  4
x1 , x 2  0
Or by graphical method,
if the slope z-row equal slope one of the constraints.
Unbounded solution
If under any non-basic , there are all minus or zero’s
values , then the LP has unbounded solution.
Z  2 x1  x 2
Subject to x 1  x 2  10
2x 1  40
x1 , x 2  0
Unbounded solution space with
bounded objective value
Max
Z  6 x1  2 x2
Subject to
2x1  x 2  2
x1  4
x1 , x 2  0
Infeasible solution
• Example:
Z  3x1  2 x 2
Subject to 3x 1  4x 2  12
2x 1  x 2  2
x1 , x 2  0