Modelo para avaliação da vida útil econômica de máquinas e equipamentos utilizando a programação dinâmica e o método de Monte Carlo

Abstract

The replacement study of capital goods provides to the company an overview about the useful life of its assets and provides planning for effecting, within an optimal time, the exchange of the present good by a substitute that may offer advantages with respect to Costs of operation and maintenance, being possible to obtain the maximization of revenues. This dissertation proposes a model for evaluation of economic useful life of machines and equipment making use of dynamic programming (PD) with the generation of random numbers by the Monte Carlo method (MMC). The model includes variables definition that will be used, the application of the Monte Carlo method to the variables, calculation of the present values, dynamic programming calculations with the objective of defining the maximum revenues, the programming development using MatLab software and validation of model. The simulations were performed using the discount rates based on the IPCA, CDI, IGP-M, Selic and Selic targets. The use of Monte Carlo method allowed the generation of a series of policies for each simulation, being analysed statistically as a way to verify the one that would best represent the replacement policy and consequently defined the economic useful life of the good. The model was applied to a vertical milling centre and showed flexibility in the information of the input data when using the programming in the software MatLab. It was observed that in addition to generating a range of possibilities the PD+MMC model can assist the decision maker regarding the strategy to be used in the replacement of machine. The PD + MMC calculations, for a 15-year planning horizon, using the five discount rates, provided replacement policies with economic life estimated 3-year economic life for the CDI, Selic and Selic and Useful life over 15 years for the IPCA and IGP-M rates. The PD+MMC calculations for a planning horizon of 15 years, using the five discount rates, provided replacement policies with three years useful life estimate for CDI, Selic and target Selic rates and for the IPCA and plus than fifteen years useful life for IPCA and IGP-M rates. By means of the statistical analyzes it was possible to define that the substitution policy that presented the highest reliability was the one that used the IPCA / IBGE, which generated the highest revenue and the longest useful life of the machine, over 16 years, presenting a significance of 77, 56% for policy frequency.