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