Removing Infeasibility in LP Problem

In linear programming (LP) problems, infeasibility means that there is no feasible solution that satisfies all the constraints. Infeasibility can occur due to various reasons such as conflicting constraints, inconsistent data, or incorrect formulation of the problem. In such cases, the LP problem cannot be solved using standard optimization techniques.

To remove infeasibility, one of the following approaches can be taken:

1. Removing a Constraint:

Removing a constraint can make the problem feasible by relaxing the system of constraints. This approach is usually taken when the infeasibility is caused by a single constraint that is too restrictive. By removing this constraint, the feasible region is expanded, and a solution may become feasible. However, this approach should be taken with caution as removing a constraint may change the nature of the problem and the optimal solution.

2. Adding a Variable:

Adding a variable can also make the problem feasible by introducing more degrees of freedom into the system. This approach is usually taken when the infeasibility is caused by the lack of variables to satisfy all the constraints. By adding a variable, the feasible region is expanded, and a solution may become feasible. However, this approach should be taken with caution as adding a variable may increase the complexity of the problem and the computation time.

3. Adding a Constraint:

Adding a constraint can make the problem feasible by restricting the feasible region. This approach is usually taken when the infeasibility is caused by the lack of constraints to satisfy all the variables. By adding a constraint, the feasible region is reduced, and a solution may become feasible. However, this approach should be taken with caution as adding a constraint may make the problem more restrictive and reduce the feasible region further.

Conclusion:

In conclusion, to remove infeasibility in LP problems, one can remove a constraint, add a variable, or add a constraint. However, each approach should be taken with caution as it may change the nature of the problem and the optimal solution.