The single local optimization of max-plus linear systems is considered. For both the cases that the decision variables are real and non-negative, it is proven that the locally optimal solutions exist, in particular, for the single local optimization without the non-negative constraint, the locally optimal solution is unique. Two polynomial algorithms are developed to find the locally optimal solutions by solving systems of max-plus linear equations with affine equality constraints. Furthermore, the single local optimization is applied to design the scheduling scheme of computer operating systems, so that the completion time of the overall task are the earliest.