When dealing with maintenance and replacement policies for finite or infinite periods, the cost parameters tend to vary owing to inflationary trends. If the objective is to minimize the total cost incurred during a given planning period, the computational time required to obtain the solution increases as the planning horizon increases. A similar effect is also seen for other parameters. In such cases it is preferred to obtain solutions of good quality that require less computational time. This paper discusses the benefits drawn from the already available Branching Algorithm. With minor modifications to the algorithm, the reduction in the number of nodes created and the computation time required are very significant. The solutions are compared with the solutions of the Branching Algorithm for a wide range of parameters.