In this paper, a graphical algorithm (GrA) is presented for an investment optimization problem. This algorithm is based on the same Bellman equations as the best known dynamic programming algorithm (DPA) for the problem but the GrA has several advantages in comparison with the DPA. Based on this GrA, a fully-polynomial time approximation scheme is proposed having the best known running time. The idea of the GrA presented can also be used to solve some similar scheduling or lot-sizing problems in a more e ffective way