A greedy algorithm is any algorithm that follows the problem-solving heuristic of making the locally optimal choice at each stage. In many problems, a greedy strategy does not produce an optimal solution, but a greedy heuristic can yield locally optimal solutions that approximate a globally optimal solution in a reasonable amount of time.

The greedy algorithm can occasionally fail based on the choices it makes. It is effective when making locally optimal choices that consistently lead to the best overall solution. However, it may not succeed when a short-term decision blocks access to a better long-term option. It can fail sometimes, depending upon the choices it makes.

Moreover, "greedy algorithms" is only a category of optimization algorithms, for a given problem, there can be lots of different greedy algorithms, so it does not make much sense to ask "if applying greedy algorithm on a problem will yield optimal solution".

As a consequence of the main theorem in , it is shown in that even for the polynomially solvable assignment problem the greedy algorithm may produce the unique worst possible solution. The authors of posed the problem of obtaining results, which show that the greedy algorithm fails on other combinatorial optimization problems.