Question

If a linear program has more than one optimal solution, does this mean that it doesn’t matter which solution is selected?

Answer 1

Solution :

Yes, it doesn't matter which solution selected from multiple optimal solution for assignment problem.

The multiple optimal solutions will arise in a linear program with more than one set of basic solutions that can minimize or maximize the required objective function. Sometimes, the multiple optimal solutions are called the alternative basic solution.

In case of an assignment problem, it is likely to have two or additional ways to remove an assured number of zeros. This situation shows multiple optimal solutions with the identical optimal value of objective function. Therefore, it can be said that the total cost or total profit will remain identical for different sets of allocation in an assignment problem.

In case of the simplex method, the presence of multiple optimal solutions is specified by a condition under which a non-basic variable in the last simplex table displays the optimal solution to the problem and the net amount of contribution is zero. The decision creator will use the most suitable set of the basic solution as the solution of the linear program when the problem has multiple optimal solutions.