Optimization models as applied to equipment replacement problems: review and trends

Abensur, Eder Oliveira; Santos, Bruna Pereira; Bandeira, Anselmo Alves

doi:10.1590/1806-9649-2023v30e4022

Eder Oliveira Abensur

conceptualization of this project

theoretical and methodological approach

literature review

data collection

data analysis

manuscript writing

final manuscript revision

Universidade Federal do ABC – UFABC, Santo André, SP, Brasil. E-mail: eder.abensur@ufabc.edu.br; bruna.pereira@aluno.ufabc.edu.br

http://orcid.org/0000-0002-7792-7758

Bruna Pereira Santos

conceptualization of this project

theoretical and methodological approach

literature review

data collection

data analysis

manuscript writing

Universidade Federal do ABC – UFABC, Santo André, SP, Brasil. E-mail: eder.abensur@ufabc.edu.br; bruna.pereira@aluno.ufabc.edu.br

http://orcid.org/0009-0009-2398-2792

Anselmo Alves Bandeira

conceptualization of this project

Universidade Federal da Bahia – UFBA, Salvador, BA, Brasil. E-mail: anselmo@ufba.br

http://orcid.org/0000-0001-8412-1405

Symbol	Description
A	Net cash flow of the asset at the end of a period
C	Acquisition and installation costs of the purchased asset
S	Residual value of the asset at the end of a period
t	Asset age
K	Keep the existing equipment
P or R	Replace the existing equipment
n	Stage n = 1, 2, 3, …,N
i	Minimum attractive rate
f_n(t)	Function that represents the discounted present value of all cash flows related to an asset of age t and work life n

Category	Description	Main observed techniques	Contributions to ERP
Network visualization approach ^* * high level of complementarity; ** high level of complementarity.Source: prepared by the authors.	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	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 *	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 **	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 **	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	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	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

{N V P}_{n, i} = \sum_{j = 1}^{n} [\frac{{- O P C - (M V}_{j} {- M V}_{j - 1}) - i {M V}_{j} + I R (O P C + D e p) \pm I R ({M V}_{n} - (P V - n D e p)}{{(1 + i)}^{j}}]

f^{*} n (t) = m a x \{\begin{matrix} f_{n} (t, K) = A (t) + {(1 + i)}^{- 1} {f^{*}}_{n + 1} (t + 1) \\ f_{n} (t, P) = C - S (t) + A (0) {(1 + i)}^{- 1} {f^{*}}_{n + 1} (t) \end{matrix}\}

f_{i} (t) = {m i n}_{m_{i} : t - m_{i} n_{i} \geq 0} \{\begin{matrix} α^{t - m_{i} n_{i}} \sum_{j = 1}^{m_{i}} α^{(j - 1) n_{i}} p ({n^{*}}_{i}) + f_{i - 1} (t - m_{i} {n_{i}}^{*}) \\ t = 0,1, 2, \dots ., T \end{matrix}\}

f^{*} n (t) = m i n \{\begin{matrix} f_{n} (t, K) = A (t) + {(1 + i)}^{- 1} {f^{*}}_{n + 1} (t + 1) \\ f_{n} (t, P) = C - S (t) + A (0) {(1 + i)}^{- 1} {f^{*}}_{n + 1} (t) \end{matrix}\}

[1] Source: prepared by the authors.

Brasil

Brasil

Optimization models as applied to equipment replacement problems: review and trends

Modelos de otimização aplicados ao problema de substituição de equipamentos: revisão e tendências

Abstract