2.1. General Structure of the Model
This study proposes a decision support model to assist small and medium-sized enterprises (SMEs) and public entities in selecting and prioritizing vehicle alternatives for fleet renewal. The model was developed to deal with the subjective and uncertain nature of assessments carried out by decision-makers, incorporating multiple economic, environmental, and operational criteria.
The developed model (
Figure 1) combines two main components: the evaluation of vehicle technological alternatives based on the Fuzzy TOPSIS method and the calculation of an auxiliary priority index (FRPI) to support the renewal of the existing fleet. The goal is to provide a complete decision-making tool for fleet managers who face multiple decision criteria in a context of uncertainty.
The proposed model aims to support strategic fleet renewal decisions by combining two complementary approaches:
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Multicriteria evaluation of vehicle technological alternatives, based on the Fuzzy TOPSIS method (Technique for Order Preference by Similarity to Ideal Solution), allows for comparing different replacement options according to multiple criteria. Fuzzy methods can transform linguistic evaluations into quantifiable values in the form of fuzzy numbers, representing the uncertainty and ambiguity inherent in human preferences. The Fuzzy TOPSIS method ranks alternatives based on their relative distance to the ideal (most desirable) and anti-ideal (least desirable) solutions.
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Calculate the FRPI (Fleet Renewal Priority Index), which prioritizes current fleet vehicles that must be replaced, based on real data such as age, maintenance, and environmental impact.
The model was developed to deal with the subjective and uncertain nature of assessments carried out by decision-makers, incorporating multiple economic, environmental, and operational criteria.
The Fuzzy TOPSIS method supports evaluating external acquisition options, whereas the FRPI index prioritizes existing fleet replacements. This articulation promotes an integrated approach that transcends simple technical and economic considerations of vehicles by offering a structured decision solution with flexibility for diverse organizational contexts, mainly SMEs and public entities.
2.2. Fuzzy TOPSIS Steps
The Fuzzy TOPSIS method is an extension of the classic TOPSIS method that incorporates the uncertainty and subjectivity of human evaluations. Its application in this model aims to compare different technological vehicle alternatives based on multiple criteria, expressed in linguistic terms.
The process consists of the following steps:
In this model (
Table 1), the method is used to compare different vehicle technology alternatives based on multiple criteria expressed in linguistic terms. Each alternative is evaluated according to the defined criteria, and these evaluations are converted into triangular fuzzy numbers (TFNs) (1) and organized in a fuzzy decision matrix (2). The fuzzy matrix is normalized to allow comparability between criteria. In the case of maximization criteria (such as energy independence or ease of loading), the values are normalized about the highest observed value. For criteria to be minimized (such as costs and emissions), a proportional inversion is applied. This step corresponds to expression (3). After normalization, each fuzzy value is multiplied by the corresponding criterion weight through scalar-fuzzy multiplication, generating the weighted fuzzy matrix that reflects the relative importance of each criterion in the decision (4). Then, two reference solutions are determined: the Fuzzy Positive Ideal Solution (FPIS), composed of the best TFN values in all criteria, and the Fuzzy Negative Ideal Solution (FNIS), composed of the worst ones. For each alternative, its fuzzy distance to the ideal solution (5) and the anti-ideal solution (6) is then calculated, using the Euclidean distance between TFNs. Finally, the degree of relative proximity of each alternative (7) to the ideal solution is calculated, allowing its ordering. The closer this value is to 1, the more appropriate the alternative is for the decision.
Table 1 summarizes the process mathematically.
Table 1.
Fuzzy TOPSIS method: Equations Summary *.
Table 1.
Fuzzy TOPSIS method: Equations Summary *.
No. | Step | Expression |
---|
(1) | Triangular Fuzzy Number (TFN) | ) |
(2) | Fuzzy Decision Matrix | |
(3) | Normalization for Benefit Criteria | |
(4) | Weighted Fuzzy Matrix | |
(5) | Distance to Ideal Solution (FPIS) | |
(6) | Distance to Negative-Ideal Solution (FNIS) | |
(7) | Relative Closeness Coefficient | |
To justify the selection of Fuzzy TOPSIS in this study, a brief comparison with alternative MCDM methods is presented below.
While MCDM offers a wide array of techniques [
37]—hierarchical methods, such as Fuzzy AHP and Fuzzy ANP [
40], compromise ranking methods, such as VIKOR [
41], and outranking approaches, such as ELECTRE and PROMETHEE [
42]—Fuzzy TOPSIS was chosen because it practically aligned with the capacities and needs of the organization for decision-making. From a computational standpoint, Fuzzy TOPSIS is easier and conceptually much more straightforward than Fuzzy AHP, which requires thorough pairwise comparisons and consistency checking [
43]. This makes it especially suitable for SME and public entities with limited analytical resources, while still producing a clear, standardized ranking of alternatives based on proximity to ideal and anti-ideal solutions.
A further advantage arises with Fuzzy TOPSIS in the evaluation of automotive technologies, as these involve criteria that are often not strictly numeric; these include perceived environmental impact, expectations of autonomy, or operational risk. The method formalizes qualitative judgments using fuzzy triangular membership functions to form a coherent decision matrix [
44,
45,
46]. This type of liberty lends further sophistication in simulating decision contexts and accounting for economic, environmental, and operational aspects within one evaluation framework. By contrast, compromise-based methods like VIKOR prioritize balancing conflicting objectives but yield results that can be less transparent and more sensitive to weight adjustments [
41,
47]. ELECTRE, on the other hand, handles discordant and incomparable alternatives using outranking thresholds, but requires careful tuning of concordance–discordance parameters and results in partial orderings which may complicate operational interpretation [
48].
While these methods offer analytical depth, their relative complexity and reduced interpretability led us to choose Fuzzy TOPSIS as the most effective balance of robustness and ease-of-use, particularly in sustainability-oriented decision-making environments with limited expertise.
Although some of the alternative MCDM methods discussed do not natively operate under fuzzy logic, they are commonly compared in the literature with fuzzy extensions, and their methodological characteristics offer valuable points of contrast when evaluating decision-making suitability under uncertainty.
2.3. Fleet Renewal Priority Index
An organizational fleet management decision involves the analysis of future technological alternatives and determining which vehicles should be replaced as a matter of urgency, all while simultaneously considering operational, economic, and environmental factors. While there are standard methods, such as Life Cycle Cost (LCC) or predictive maintenance methods (Condition-Based Maintenance), many require detailed data, long histories, or onboard sensors, limiting their applicability to SMEs or public entities with limited resources.
Moreover, Life Cycle Sustainability Assessment (LCSA) approaches are also confronted with significant methodological challenges [
49]. In a systematic review of the automotive industry, inconsistencies in the choice of functional units, system boundaries, and indicators are highlighted that affect the balanced integration of the three pillars of sustainability: economic, environmental, and social. This lack of harmonization leads to the impossibility of utilizing models like LCC or LCSA in strategic-level asset replacement management.
On the other hand, traditional fleet renewal models based on economic metrics, such as the EUAC (Uniform Annual Equivalent Cost), are often used to identify the optimal timing for vehicle or equipment replacement based on minimizing the equivalent annual cost. Studies such as those by Almobarek et al. [
50] and Kauffmann et al. [
51] demonstrate their usefulness in asset management but also reveal a significant limitation: their exclusive focus on the financial dimension, without integrating environmental impact or operational functional wear and tear.
In this context, the Fleet Renewal Priority Index (FRPI) is proposed as a complementary and accessible approach that allows for the simultaneous incorporation of three critical dimensions—vehicle age, annual maintenance cost, and average CO2 emissions—in a continuous, weighted, and interpretable manner. FRPI aims to support strategic vehicle replacement decisions based on readily available data, adapting to the reality of organizations with technical and financial constraints, and thus complementing more complex models such as Fuzzy TOPSIS, which focus on future technology selection.
A fleet management research background is used as a basis for choosing the criteria included in the FRPI. These indicators are widely recognized as relevant to supporting strategic operational efficiency, cost-effectiveness, or environmental responsibility decisions. Combined, they attempt to provide as much vehicle condition and renewal requirement assessment as feasible without resorting to an advanced system or some sensor-based data. Together, they provide for a realistic priority model that often suffers from practical constraints and objectives of many organizations.
The vehicle age is a main determinant of fleet assets’ functional and financial performance [
3,
52]. Operating and maintenance costs increase with age, whereas vehicle reliability and fuel efficiency tend to decline. Boudart and Figliozzi [
53] found that older buses suffer much higher operating and maintenance costs for each mile, thus highlighting the urgency for timely replacement to minimize lifecycle costs. Conversely, pollution emissions tend to increase with older vehicles, with the degradation of the engines over time [
54]. These lines of reasoning justify considering the age in the FRPI model.
The annual maintenance cost criterion captures the financial burden of operating aging or underperforming vehicles. Maintenance costs are a significant component of the total cost of ownership and are often used as a proxy for mechanical degradation. According to the recent research carried out by Crespo del Castillo and Parlikad [
55], combining the two approaches—predictive and preventive maintenance—can optimize asset management and at the same time lessen unforeseen expenses. Without advanced monitoring systems, annual cost summaries are the basis for deciding which equipment to replace first. This is especially relevant for SMEs and public entities that lack the infrastructure to implement condition-based maintenance systems.
The CO
2 emissions criterion reflects growing concerns over environmental performance and regulatory compliance. Integrating emissions into strategic fleet decisions aligns with sustainability goals and regulatory standards. Studies by Castillo and Álvarez [
56] and Corazza et al. [
54] encourage incorporating emissions models to track and manage environmental impact. These models support emission reduction strategies and are widely used in fleet sustainability planning. Although this paper does not rely on sophisticated simulation tools, emission bands allow for realistic approximations of vehicle environmental performance. Moreover, while the FRPI framework has not yet undergone formal expert panel validation, its structure was reviewed informally with fleet managers from both private and public organizations. Their feedback confirmed the practical relevance and interpretability of the three criteria used, supporting the real-world applicability of the proposed index.
The FRPI is an auxiliary indicator that supports vehicle replacement decisions in organizational fleets. Its function systematically identifies vehicles requiring the most urgent replacement based on multiple performance factors. Instead of a linear weighted average, this model uses continuous penalty functions that are better suited to capturing non-linear variations and cumulative effects over time.
The FRPI value (
Table 2) is obtained by the weighted combination of three penalizing functions, as shown in the general expression (8). The index considers three fundamental dimensions: vehicle age, annual maintenance cost, and average carbon dioxide (CO
2) emissions. Each of these variables is converted to a scale between 0 and 1 through a specific function, which simulates the increasing impact of ageing, economic inefficiency, and environmental impact. The penalty associated with vehicle age is modelled by an increasing exponential function (9), reflecting that older vehicles represent increased operational risks and costs. The annual maintenance cost is treated by a limited linear function (10), which reaches a maximum from a reference value. CO
2 emissions are treated similarly, increasing linear penalties from a minimum emissions level (11). The weights assigned to each criterion may be changed according to the organization’s priorities. The result enables the classification of fleet vehicles according to the priority of their replacement, thus providing structured support for decision-making.
Table 2.
FRPI calculation: penalty functions and structure.
Table 2.
FRPI calculation: penalty functions and structure.
No. | Step | Expression |
---|
(8) | General | |
(9) | Vehicle age penalty function | |
(10) | Maintenance cost penalty function | |
(11) | CO2 emissions penalty function | |
The penalty functions used in the FRPI calculation were defined based on realistic assumptions and adjusted to fleet management practices. For the age of the vehicle, an increasing exponential function with a rate of 0.15 was adopted to reflect a progressive penalty from 10 years onwards, saturating close to the maximum value in vehicles over 15 years old. The annual maintenance cost was treated as a limited linear function, with a reference value of €2000, which is considered the reasonable upper threshold for light vehicles in a business context. In terms of CO2 emissions, the starting penalty point is set at 100 g/km, which is in line with current standards of ecological efficiency and rises to a maximum of 300 g/km, thus including most traditional cars. The bands are adjustable according to the strategic or regulatory objectives of the company. In relation to carbon dioxide emissions, the initial threshold for penalties is established at 100 g per kilometre, which aligns with prevailing ecological efficiency standards, and escalates to a ceiling of 300 g per kilometre, thereby encompassing most conventional automobiles. These parameters are subject to modification.
In summary, while alternative indicators exist that individually assess costs, emissions, or operational performance, the FRPI stands out for integrating these dimensions in an aggregated manner, with adjustable penalty functions, allowing for clear, transparent, and adaptable prioritization of replacements to each organization’s strategic priorities. This approach makes the FRPI particularly useful for resource-constrained contexts, such as SMEs, and represents an innovative contribution to supporting sustainable fleet renewal decisions.