How can I check if a solution of an LP is unique?

Question

I want to check if my linear program has just one solution or infinite ones. How can I do that using PuLP?

Answer 1

In practice, there are virtually always multiple solutions because of numerical tolerances, that is, allowing small violations of primal and dual feasibility in the solutions.

I suppose you are rather referring to multiple different optimal bases for your LP. This can be checked by testing for degeneracy: Check whether there are basic variables that are on one of their bounds (or tight basic constraints) and check whether there are non-basic variables with 0 reduced costs or dual multipliers.

These checks can only be done if your LP solution is a basic solution in the first place, coming from a simplex-type optimization.