Special cases in LPP

1. Degeneracy: This occurs in LPP when one or more of the variables in the base have zero value in the RHS column, or during any stage in the iteration, when there is a tie in the ‘θ’ values of two rows.
2. Alternate optimum: If a non-basic variable has Cj-Zj value as zero, there exists an alternate optimum solution. Graphically, if the objective function is parallel to a binding constraint, then the same optimal value is obtained at more than one corner points.
3. Unbounded solution: An unbounded solution occurs when it is not possible to select the variable which should leave the base. This happens when there is no non-negative ‘θ’ value. In such a case, the value of the entering variable can be increased indefinitely, without violating any constraint. So the solution space in the graph is said to be unbounded.
4. Infeasible solution: This occurs when the entire iteration has ended, but an artificial variable is still present in the base. Such a solution is a false solution.
5. Unrestricted (unconstrained) variable: Some variables may be encountered where they can take any value, positive or negative. To take care of such variables, they are substituted with 2 other variables, that themselves are non-negative, but whose difference may be negative.