Network visualization approach
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A recurrence formula (transition) is defined to calculate the changes in variable values between different states of the analyzed asset (retention or replacement) at specific stages (years) |
Deterministic dynamic programming, Stochastic dynamic programming, Integer linear programming and Mixed linear programming |
A logical structure that is easily comprehensible and adaptable to various mathematical programming techniques, facilitating the determination of the optimal moment of replacement in discrete time |
Multi-criteria analysis
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Decision-making models based on two or more criteria, such as costs, reliability, and time between stops, rely on the behaviors of variables that influence the ERP cash flow. The limit values and weights assigned to each criterion are defined by managers or experts |
HPA Promethee, Promethee II |
More decision criteria other than costs. There is the possibility of defining a common optimal solution that would not be possible because of the individual behavior of the analyzed variables |
Simulation *
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The variables that impact the ERP cash flow, including acquisition value, operating costs, market value, and discount rate, are estimated using the selected simulation technique |
Monte Carlo simulation Metaheuristics (e.g., genetic algorithms) |
The ERP cash flow variables are subjected to randomness |
Real options
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The option to buy or sell equipment is determined through a stochastic calculation involving operating costs, asset residual value, and ERP cash flow |
Geometric Brownian motion |
The ERP cash flow variables are subjected to randomness |
Continuous functions **
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ERP expenses such as operating costs (maintenance, depreciation), capital, and market value are converted into mathematical functions |
Differential calculation |
The optimal moment for replacement in continuous time and identification of assets that do not require replacement due to the absence of an optimal point in their mathematical functions |
Fuzzy logic
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ERP expenses (capital, operating, residual value) are converted to fuzzy numbers with a variation within limits established by a formation rule |
Triangular fuzzy numbers |
Uncertainty with regard to ERP expenses |
Machine learning
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The data define the guidelines for action in each situation, and rule updates are based on recorded data |
Data regression statistical algorithms (e.g., neural network, decision trees, random forest, SVM, naive Bayes) |
Predictive maintenance applications using online-collected data to estimate the remaining service life of crucial equipment components |