| Summary: | The problem of equipment replacement is traditionally analyzed by two discrete methodologies: dynamic programming and cash flow indicators. It was noticed that these methodologies cannot verify if (i) the optimal moment of equipment replacement is unique and (ii) if there were any physical assets that did not need to be replaced, that is, from the economical point of view, an equipment without optimal moment of substitution. Accordingly, in this work, the authors used an approach with continuous functions to solve this type of problem. In the process of establishing these functions, we obtained non-differentiable functions (in the classical sense). Therefore, a non-smooth modeling analysis was used. From the obtained results, it is possible to affirm that the optimal moment of substitution is unique. It has also been found that there may be equipment with no optimum moment for replacement. Moreover, it was also possible to formulate a model to calculate the optimum moment of equipment substitution by continuous function, according to the maintenance costs, the acquisition value, the depreciation rate and the discount rate.
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