Physical assets replacement: an analytical approach

TL;DR

This paper develops a mathematical approach using non-smooth analysis to determine the optimal replacement time of physical assets by identifying the minimum of their equivalent property cost functions.

Contribution

It introduces a rigorous mathematical framework to analyze the economic life of assets, improving upon previous intuitive methods.

Findings

Mathematical classification of cost function minima

Identification of the optimal replacement point

Enhanced understanding of asset economic life

Abstract

The economic life of an asset is the optimum length of its usefulness, which is the moment that the asset's expenses are minimum. In this paper, the economic life of physical assets, such as industry machine and equipment, can be interpreted as the moment that the minimum is reached by its equivalent property cost function, defined as the sum of all equivalent capital and maintenance costs during its life. Many authors in classical papers have used principles of engineering economic to solve the assets replacement problem. However, in the literature, the main attributes found were proved with intuitive ideas instead mathematical analysis. Therefore, in this paper the main goal is to study these principles of engineering economic with mathematical techniques. Here, is used non-smooth analysis to classify all the possibilities for the minimum of a class of equivalent property cost functions of assets. The minimum of these function gives the optimum moment for the asset to be replaced, i.e., its economic life.