A Robust AHP–TOPSIS Framework for Optimal Biodiesel Blend Selection Based on Emission Profiles, Fuel Properties and Blend Prices

Abstract

This study evaluates eight biodiesel blend types and determines the overall optimal blend by applying two established multi-criteria decision-making methods: the Analytic Hierarchy Process (AHP) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The selected blends represent widely produced and utilized feedstocks that are reported in the previous literature. In the proposed methodology, AHP is employed to determine the weights for both emissions-related subcriteria, quantified through Global Warming Potential scores and property-related subcriteria, thereby reducing the subjectivity often encountered in earlier studies. Furthermore, two boundary alternatives, defined as the “Best” and “Worst” based on international standards, are introduced to enhance the robustness of the normalization procedure. The weights determined via AHP are subsequently integrated into the TOPSIS framework to rank the biodiesel alternatives. This combined AHP-TOPSIS approach addresses a gap in the literature, as no previous study has compared the best performing blends from different sources to identify a single optimal alternative. The results indicate that a 20% sunflower biodiesel blend (SN20) achieves the highest ranking. Sensitivity analyses, including the incorporation of an additional economic criterion, consistently reaffirm SN20’s superior performance. This study offers a transparent and reproducible method that can guide future biodiesel blend evaluations and reduce subjectivity in comparative assessment.

1. Introduction

Climate change, largely driven by rising greenhouse gas (GHG) emissions, is a major challenge. The energy sector contributes the highest share (34%) of these emissions, primarily from fossil fuel consumption [1]. Reducing dependance on fossil fuels and transitioning to cleaner energy sources is critical for sustainable development. Among renewable alternatives, biodiesel has gained attention due to its ability to reduce Carbon Dioxide (CO₂) emissions while maintaining a comparable engine performance [2]. The world demand of biofuels is driven primarily by the transport sector, netting 4 EJ (159.2 billion Liters) in 2021, with a biodiesel share of around 35% [3].

Biodiesel is produced through the transesterification reaction of oils with alcohol, mainly methanol, and is classified into three categories according to the oil feedstock: first-generation (edible oils and oilseeds), second-generation (non-edible oils and organic waste) and third-generation (algae and used cooking oils) [4]. The use of biodiesel alone in diesel engines is not yet favorable. Despite its environmental advantages and improved fuel properties and engine performance, biodiesel presents challenges such as poor cold flow properties, lower oxidation stability and higher Nitrogen Oxide (NO_x) emissions compared to petroleum diesel [5]. Blending biodiesel with petroleum diesel is a practical solution to improve fuel properties while maintaining cost-effectiveness [6]. The world is realizing the importance of fuel source diversification. Argentina, for example, being the number one exporter, is setting a 10% mandate on diesel blending, while the European Union, being the number one producer, is requiring that 10% of its transport energy be based on renewable energy. Brazil, Indonesia, Thailand, China and others have implemented mandates for biodiesel blending [7]. However, the challenge remains of finding the best feedstock and blending volume.

Multi-criteria decision-making (MCDM) techniques, such as the “Analytic Hierarchy Process” (AHP), “Technique for Order Preference by Similarity to an Ideal Solution” (TOPSIS), “Vlsekriterijumska Optimizacija I Kompromisno Resenje” (VIKOR), fuzzy methods, etc., have been widely applied to identify optimal biodiesel blends based on performance, fuel properties and emissions. Sivaraja et al. (2017) [8] explored fish oil biodiesel blends ranging from B0 to B100 (with 20% increment) using three different hybrid techniques: the “Fuzzy Analytic Hierarchy Process” (FAHP) for computing weights, coupled with TOPSIS, VIKOR or “ELimination Et Choix Traduisant la REalité” (ELECTRE). A 20% biodiesel blend (B20) was found to be the best. Erdoğan et al. (2019) [9] used two hybrid techniques, AHP coupled with MOORA and “Stepwise Weight Assessment Ratio Analysis” (SWARA) coupled with “Multi-Objective Optimization on the basis of Ratio Analysis” (MOORA), to choose the best blend among vegetable oil biodiesel and animal fat biodiesel blends. The best was the 20% vegetable oil biodiesel blend. In another study, biodiesel blends from algae have been studied using TOPSIS. B20 was chosen to be the best [10]. An AHP-TOPSIS hybrid technique was implemented by Mehra et al. (2023) [11] to choose the best among B10-B20 to B100 (with 20% increment) blends, with B10 found to be the best. AHP is a very common technique used to assign weights to criteria because of its simplicity and ability to give scores as percentages. On the other hand, unlike ELECTRE and “Preference Ranking Organization Method for Enrichment Evaluation” (PROMETHEE), which utilize a pairwise comparison between alternatives, TOPSIS is the method that allows for using the raw data, without prior normalization or subjective judgment [12]. The combination of these two techniques is not new and was used by Abdulvahitoglu & Kilic (2022) [13] to evaluate the best oilseed for biodiesel among soybean, cotton, camelina and rapeseed. However, this study did not target any blends. Therefore, it is evident that the AHP and TOPSIS methods complement each other, as the former sets the relative importance of evaluation criteria and the latter ranks the alternatives based on their proximity to the ideal solution, thereby providing a comprehensive framework for the best biodiesel blend selection.

Previous studies have primarily focused on selecting the best blend from individual feedstocks or even by comparison through individual criteria such as the study of Chaitanya et al. 2020 [14], which assessed Pungam oil biodiesel blends via the combination of AHP-TOPSIS methods, using only engine emissions as comparative criteria. To our knowledge, no studies tried conducting a comparative analysis of the top-performing blends across different biodiesel types. No study has systematically evaluated the best blend from each biodiesel source and ranked them as alternatives to determine the overall optimal biodiesel blend. This leaves a gap in the ability to identify which source and which blending volume offers the optimal performance across both technical and environmental criteria. This paper addresses this gap by evaluating the top biodiesel blends from eight of the most widely used feedstocks worldwide in biodiesel production. This novel approach not only ranks the “best among the best” blends, but also provides a comprehensive framework for decision-makers to select biodiesel blends that balance performance, emissions and cost-effectiveness.

2. Materials and Methods

The work plan as outlined in Figure 1 begins with the selection of evaluation criteria, followed by the identification of the appropriate MCDM techniques. AHP is then used to determine the relative weight of the selected criteria, with data sourced from similar studies for the first set of criteria and generated through a Life Cycle Assessment (LCA) approach for the second set of criteria. For TOPSIS, data preparation includes defining two reference alternatives, named “Best” and “Worst”, based on criteria limits and standards. The study reviewed different biodiesel blends and identified the best one from each feedstock. The selected blends constitute the “alternatives” for the TOPSIS analysis. The TOPSIS data matrix is then built while using assumptions to fill data gaps. A sensitivity analysis is conducted to validate the results.

2.1. Criteria Selection

The common criteria used to assess biodiesel blends in a Compression Ignition (CI) diesel engine are performance and emissions [13]. While performance criteria such as brake power (BP), torque and Brake-Specific Fuel Consumption (BSFC) vary with engine types, speeds, power, etc. [15], fuel properties directly influence engine performance and can be used to assess, indirectly, the performance of the selected biodiesel blends. Density, viscosity, heating value and flash point are the fuel properties selected as subcriteria for this study, with density and viscosity to be minimized, and heating value and flash point to be maximized, following the subsequent logic.

• Density: Higher density reduces brake thermal efficiency (BTE) and increases fuel consumption due to greater fuel mass per injection [16,17].
• Viscosity: Higher viscosity hinders fuel atomization, increases exhaust temperatures and reduces engine torque.
• Heating Value: This determines the energy released during combustion. Lower values increase fuel consumption and reduce engine power.
• Flash Point: This indicates fuel safety for proper storage and handling. The higher the flash point the better and safer it is to operate with [17].

On the other hand, the emission subcriteria selected are Carbon Dioxide (CO₂), Carbon Monoxide (CO), Nitrogen Oxides (NO_x) and Unreacted Hydrocarbon (UHC). These subcriteria need to be minimized.

2.2. Decision-Making Methods

2.2.1. AHP

The Analytic Hierarchy Process (AHP) is a method created by L. Saaty (1980) [18] and is an MCDM technique that enables decision-makers to divide problems into a hierarchy of criteria and subcriteria, using a pairwise comparison to obtain their weights. The AHP technique transforms decision-makers’ assessments into numerical scores that can be used to determine the overall importance of each alternative. Its scale of values ranges from 1 (equal importance) to 9 (extreme importance) and from 1 to 1/9 (lesser importance). AHP can be used either with quantifiable or with intangible criteria. It alleviates subjectivity and gives a score between 0 and 1 that can be directly used as a weight [19]. However, it can be very sensitive to a weight shift in complex problems, so a consistency check is of major importance [20].

The AHP begins by structuring the decision problem into a hierarchy composed of the overall objective, the evaluation criteria, the subcriteria and the set of alternatives. Subsequently, pairwise comparisons are carried out at each hierarchical level. These comparisons are represented in an n × n judgment matrix, where the element in the ith row and ^jth column (a_ij) reflects the relative importance of element i over element j.

-

Normalization of the matrix: Each element of the matrix is divided by the sum of its corresponding column. This procedure produces a normalized matrix in which the sum of each column is equal to one.

-

Derivation of local weights: The local weight of each subcriterion is obtained by averaging the normalized values across each row of the matrix.

$$w_j={\displaystyle \frac{{{\sum }_{i=0}^{i}a}_{ij}}{n}}$$

(1)

-

Computation of global weights: To determine the overall contribution of each subcriterion, the local weights are aggregated through multiplication with the corresponding weights of the higher-level criteria, yielding the global weights.

-

Total score determination: The global weights of each alternative are then summed according to the additive model of Multi-Attribute Utility Theory (MAUT), thereby producing the total score for each alternative. It is worth mentioning that this step was not carried out. The global weights of the subcriteria were obtained using AHP to be used later in TOPSIS for the alternatives ranking.

-

Inconsistency check: AHP provides a measure of inconsistency, while comparing the pairwise elements. The consistency ratio CR is calculated by dividing the consistency index CI by the random index RI. The consistency index CI is defined as follows:

$$CI={\displaystyle \frac{{\mathsf{\lambda }}_{max}-n}{n-1}}$$

(2)

where ${\mathsf{\lambda }}_{max}$ is the largest eigenvalue of the matrix and n is the number of criteria or alternatives.

$${\mathsf{\lambda }}_{max}={\displaystyle \frac{1}{n}} {\sum }_{i=1}^{i=n}{\displaystyle \frac{i^{th} entry in {Aw}^T}{i^{th} entry in {Aw}^T}}$$

(3)

The random consistency index (RCI) is a reference value that depends on the size of the matrix and is obtained from

Table 1. Random consistency index table based on matrix size.

Number of Requirements	2	3	4	5	6	7	8	9	10
RCI	0	0.58	0.90	1.12	1.24	1.32	1.41	1.45	1.51

:

Consistency Ratio: $CR={\displaystyle \frac{CR}{RCI}}$

When the consistency ratio is less than 0.1, CR ≤ 0.1, the pairwise comparisons are considered consistent [18].

2.2.2. TOPSIS

“Technique for Order Preference by Similarity to an Ideal Solution” is a method created by Hwan and Yoon in 1981 to provide a multi-criteria decision-making technique that ranks alternatives based on their closeness to the ideal solution [21]. This method requires constructing a decision matrix formed from the alternatives and criteria, their relative weights and the objective of each criterion, whether it is to be minimized or maximized. Then the decision matrix is normalized and weighed. The positive and negative ideal solutions are then determined so that the distance between the alternatives and the positive and negative ideal solutions can be calculated. Finally, ranking the alternatives is carried out by calculating the relative closeness of the alternatives to the ideal solution. The mathematical model of TOPSIS is as follows:

-

Normalize the decision matrix: The following formula can be used for data normalization.

$$r_{ij}\left(\mathrm{x}\right)={\displaystyle \frac{x_{ij}}{\sqrt{\sum _{i=1}^m{x}_{ij}^2}}} i=1,\dots , m ;j=1, \dots , n$$

(4)

-

Calculate the weighted normalized decision matrix: According to the following formula, the normalized matrix is multiplied by the weight of the criteria.

$$v_{ij}\left(\mathrm{x}\right)=w_j{r}_{ij}\left(x\right) i=1,\dots , m ;j=1, \dots , n$$

(5)

-

Determine the positive ideal and negative ideal solutions: The aim of the TOPSIS method is to calculate the distance of each alternative from positive and negative ideals. Therefore, in this step, the positive and negative ideal solutions are determined according to the following formulas.

$$A^{+}=\left(v_1^{+},v_2^{+}, \dots , v_n^{+}\right)$$

(6)

$$A^{-}=(v_1^{-},v_2^{-}, \dots , v_n^{-+})$$

(7)

so that

$$v_j^{+}=\left\{\left(max{ v}_{ij}\left(x\right)\right| jϵj_1) , \left(min{ v}_{ij}\left(x\right)\right| jϵj_2)\right\} i=1,\dots , m$$

(8)

$$v_j^{-}=\left\{\left(min v_{ij}\left(x\right)\right| jϵj_1) , \left(max{ v}_{ij}\left(x\right)\right| jϵj_2)\right\} i=1,\dots , m$$

(9)

where j₁ and j₂ denote the negative and positive criteria, respectively.

-

Distance from the positive and negative ideal solutions: In this step, the calculation of the distances between each alternative and the positive and negative ideal solutions is obtained by using the following formulas.

$$d_i^{+}=\sqrt{{\sum }_{j=1}^n{[v_{ij}\left(x\right)-v_j^{+}\left(x\right)]}^2} , i=1, \dots , m$$

(10)

$$d_i^{-}=\sqrt{{\sum }_{j=1}^n{[v_{ij}\left(x\right)-v_j^{-}\left(x\right)]}^2} , i=1, \dots , m$$

(11)

-

Calculate the relative closeness degree of alternatives to the ideal solution: In this step, the relative closeness of each alternative to the ideal solution is obtained by the following formula. If the relative closeness degree has value near to 1, it means that the alternative has a shorter distance from the positive ideal solution and longer distance from the negative ideal solution.

$$C_i={\displaystyle \frac{d_i^{-}}{(d_i^{+}+d_i^{-})}} , i=1, \dots , m$$

(12)

In this study, TOPSIS is implemented to rank the biodiesel blends and determine the best option. The criteria weights were obtained from AHP computation as stated above. An innovative approach is introduced by adding two reference alternatives representing the best and worst solutions based on the upper and lower limits of each subcriterion. When a limit value is unavailable, the optimum value from the existing alternative is used.

2.3. Criteria Weights

Previous studies developed the relationships among property subcriteria based on their impact on engine performance and safety. The expert-assigned property weights used by Abdulvahitoglu & Kilic (2022) [13] were isolated, normalized and converted back to an AHP scale in order to build the comparison matrix. As for the emission subcriteria, an LCA approach is used to quantify the impact of these emissions on the “Climate Change” impact category by using the Global Warming Potential (GWP) of each substance. GWP can be defined as a measurement for the greenhouse effectivity to an equal mass of CO₂, measured in kilograms of CO₂ equivalent (kgCO_2-eq). So, in order to normalize the data, CO₂ is chosen as a reference substance. According to the Intergovernmental Panel on Climate Change (IPCC) sixth report, the GWPs for CO and NO_x are, respectively, nine times and four times more important than CO₂ for a time horizon of 100 years [1,22]. UHC is mainly composed of VOCs, namely C1 and C2 hydrocarbons, followed by aldehydes, paraffins and aromatics, respectively [23]. In this context, the GWP of UHC is considered as the arithmetic mean of the halogen-free VOCs that have a published GWP factor, taken to the nearest unit. This includes methane (25), ethane (6), propane (3), butane (4), isobutane (3), pentane (5) and isopentane (5). The GWPs for the emission subcriteria are summarized in

Table 2. GWP of the emission subcriteria.

Subcriteria	GWP
CO2	1
CO	9
NOx	4
UHC	7

.

2.4. TOPSIS Data Preparation

2.4.1. Limit Values

According to the American Society of Testing and Material (ASTM) and the Euronorm (EN), limit values of physical parameters can be found, related to petroleum diesel, B100 and B6 to B20 diesel. Limits of viscosity and flash point are defined by ASTM D7467 [24]. EN 14213 [25] specifies the limits for heating value, while EN 14214 [26] is the reference for the upper limit of density and EN 590 [27] is the one for the lower limit of density. Values of property limits are found in

Table 3. Property subcriteria limits.

Property	Test Method	Lower Limit	Upper Limit	Reference
Heating Value, (MJ/kg)	DIN 51900	37	/	[25]
Flash Point (°C)	D93	52	/	[24]
Viscosity, mm2/s at 40 °C	D240	1.9	4.1	[24]
Density at 15 °C	EN ISO 3675	820	900	[26,27]

.

Limits for emissions differ from one country to another and from one region to another. EU test limits are used to assess the criteria according to the EU emission standards, stage EURO VI, revised in 2021. Only CO₂ values were taken from the US Emission Standards for medium-heavy-duty (MHD) diesel engines. Values brought in g/bhph are converted to g/kwh following the conversion formula:

$$1 \mathrm{g}/\mathrm{b}\mathrm{h}\mathrm{p}\mathrm{h}=1.341 \mathrm{g}/\mathrm{k}\mathrm{W}\mathrm{h}$$

(13)

Values of emission limits can be found in

Table 4. Emission subcriteria limits.

Emission (g/kWh)	NORM	Upper Limit	Reference
CO	EURO VI	1.5	[28]
HC	EURO VI	0.13
NOx	EURO VI	0.4
CO2	USA Emissions Standard	618.2	[29]

.

Conversions from g/kWh unit to ppm or vol% are performed according to the following formulas [30]:

$$CO\left(\mathrm{g}/\mathrm{k}\mathrm{W}\mathrm{h}\right)=35.91\times CO\left(\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{\%}\right)$$

(14)

$${CO}_2\left(\mathrm{g}/\mathrm{k}\mathrm{W}\mathrm{h}\right)=63.470\times {CO}_2\left(\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{\%}\right)$$

(15)

$$HC\left(\mathrm{g}/\mathrm{k}\mathrm{W}\mathrm{h}\right)=2.00\times {10}^{-3}HC\left(\mathrm{p}\mathrm{p}\mathrm{m}\right)$$

(16)

$${NO}_x\left(\mathrm{g}/\mathrm{k}\mathrm{W}\mathrm{h}\right)=6.63\times {10}^{-3}{NO}_x\left(\mathrm{p}\mathrm{p}\mathrm{m}\right)$$

(17)

2.4.2. Best Blends Based on Feedstock

Based on statistics provided by the International Energy Agency (IEA) report on the world production volumes of biodiesel, rapeseed, soybean, palm and waste cooking methyl esters are selected. Corn, sunflower, jatropha and mahua methyl esters complete the list, as they show a promising future for industrial production [31].

The alternatives to be selected from these feedstocks are biodiesel blends that have already been studied, with values for properties and emissions being presented and published. The best blend from each feedstock is selected by comparing the criteria studied to choose the optimum values. A lower Brake-Specific Fuel Consumption (BSFC), a higher torque and lower emissions were the basis for the selection.

Table 5. Main data table containing all alternatives and respective values with respect to the subcriteria, engine details, references, rationale behind choosing the specific blend and objective of the criteria to be minimized or maximized to be used in TOPSIS.

Biodiesel Feedstock	Engine Details	Mix	Density (kg/m3)	Kinematic Viscosity (Cst)	Flash Point (°C)	Calorific Value (LHV—MJ/kg)	CO (% Vol)	NOx (ppm)	CO2 (% Vol)	UHC (ppm)	Ref.	Rationale For Choosing Best Blend
Rapeseed	Single Cylinder 4 Stroke Engine 5.95 kW @ 1500 rpm	RB25	849.9	3.45	77.8	43.47	0.167	1923	12.77	374.6	[32,33,34,35]	Best by Raman et al., 2019
Soybean	Single Cylinder 3.5 kW @ 1500 RPM	SOB20	850.5	4.65	61.0	40.40	0.28	687	11.02	41.98	[36,37]	Best by Gangolu et al., 2022
Palm oil	Single Cylinder 4 Stroke Engine 3.68 kW @ 1500 rpm	PB40	851.0	4.46	90.0	40.20	0.440	102	11.83	82.65	[38,39,40]	Best by Deepanraj et al., 2011
Used Cooking Oil	Single Cylinder 4 Stroke Engine 4.4 kW @ 1500 rpm	WC40	865.0	5.40	78.0	40.20	0.04	615	2.60	18.90	[41]	Optimum values of performance and emissions
Corn	Single Cylinder 4 Stroke Engine 4.2 kW @ 1500 rpm	CB20	846.0	3.34	73.0	41.75	0.05	1362	7.08	33.89	[42,43]	Best by Rama Krishna Reddy et al., 2022
atropha	Single Cylinder 4 Stroke Engine 7.4 kW @ 1500 rpm	JB10	837.0	2.91	88.0	40.85	0.130	2200	7.25	53.28	[44,45]	Optimum values of performance and emissions
Sunflower	Single Cylinder 4 Stroke Engine 3.73 kW @ 1500 rpm	SN20	839.0	3.26	86.0	44.80	0.040	685	3.20	27.03	[46,47]	Optimum values of performance and emissions
Mahua	Single Cylinder 5.9 kW @ 1500 RPM	MB20	854.0	2.57	85.0	42.21	0.217	1523	4.80	30.69	[48,49]	Optimum values of performance and emissions
Best	-	-	820	1.9	90	44.8	0	0	0	0	Table 3	-
Worst	-	-	900	4.1	52	37	0.042	60.28	9.74	64.94	Table 3 and Table 4	-
Objective	-	-	Min	Min	Max	Max	Min	Min	Min	Min	-	-

provides the full data set needed for conducting the MCDM analysis.

2.5. Assumptions and Working Mode

• Upper limits of flash point and heating value are not regulated, as the higher it is the better. The lower limit for the emission subcriteria is zero.
• As emission values vary with engine type, power and speed, and to ensure consistency, these values were taken from studies that used a single-cylinder, four-stroke engine operating at 1500 rpm with a BP of less than 7.5 kW.
• These engines can be considered light-duty diesel engines mainly because of their low power output.
• The main criteria, properties and emissions are considered to be equally weighted for the first part of the simulation.

2.6. Sensitivity Analysis Method

After the TOPSIS analysis, a sensitivity analysis is performed to verify the reliability of the results, in four steps. First, the main criteria weights are adjusted to observe their effect on the ranking. Second, the “Best” and “Worst” reference alternatives are removed to assess their impact on the final results. Third, the emission data are adjusted by considering the effect of aftertreatment systems to simulate real-life conditions. Finally, the break-even blend price is added as a third criterion to provide a more realistic assessment.

3. Results and Discussion

3.1. Criteria Weights Evaluation by AHP

3.1.1. The Hierarchy

Figure 2 shows the hierarchy followed to calculate the AHP scores.

3.1.2. AHP Calculations

The pairwise comparison for the property subcriteria is based on the normalized weights of Abdulvahitoglu & Kilic (2022) [13]. However, the pairwise comparison of the emission subcriteria is based on the scientific value developed in Section 2.3.

Table 6. Comparative matrix of subcriteria.

Criteria	Properties				Emissions
Subcriteria	Density	Viscosity	Flash Point	HV	Subcriteria	CO	CO2	NOx	UHC
Density	1	1/2	2	1/3	CO	1.00	9.00	2.00	2.00
Viscosity	2	1	3	1/2	CO2	1/9	1.00	1/4	1/7
Flash	1/2	1/3	1	1/5	NOx	1/2	4.00	1.00	1/2
Heating Value	3	2	5	1	UHC	1/2	7.00	2.00	1.00

shows the comparative matrices.

After computing using the AHP method, the local weights were represented in

Table 7. Local and global weights of the subcriteria.

Criteria	Properties				Emissions
Subcriteria	Density	Viscosity	Flash Point	Heating Value	CO	CO2	NOx	UHC
Local Weights	0.16	0.27	0.09	0.48	0.46	0.05	0.19	0.31
Global Weights	0.08	0.14	0.04	0.24	0.23	0.02	0.09	0.15

.

The highest weight is attributed to “Heating Value”, as this property directly affects engine performance in terms of brake power and torque. Viscosity comes in second place, as it affects atomization and fuel consumption. Density is in third place, as it is a relative measure to viscosity and heating value, and it affects both [17]. Flash point has the least importance because it is a property related to safety, in a study that lays importance on performance.

Carbon Monoxide has a higher impact on climate change and thus the highest weight value, followed by UHC and NO_x. Stepwise calculations can be found in Tables S1 and S2 in the Supplementary Materials.

3.1.3. Comparison of AHP Scores

The expert-assigned AHP scores are based on the subjective judgment of the experts in the field. The subjectivity creates a limitation in the AHP application. The use of GWP-based AHP scores, alleviates subjectivity and provides scientific numbers for a better comparison and improved decision-making process.

Table 8. Comparison on local weights of the subcriteria.

Subcriteria	CO	CO2	NOx	UHC	Reference
Expert-Assigned Weights	0.13	0.24	0.56	0.07	[11]
GWP-Based Weights	0.46	0.05	0.19	0.31	This Study
Percentage Difference	+253%	−81%	−66%	+340%

shows the difference between the expert-assigned and the GWP-based AHP scores.

The discrepancy is clear mainly in NO_x weight, which has 81% less of an effect because of its lower effect on GWP, and in CO and UHC, with a 253% and 340% increase because of their higher GWP effect. This is reflected in the difference in scores of the GWP-based weights compared to the subjective judgment of the experts.

3.1.4. AHP Global Weights

The global weights shown in

Table 9. Global subcriteria weights.

Subcriteria	Density	Viscosity	Flash	Heating Value	CO	CO2	NOx	UHC	SUM
Weight	0.08	0.14	0.04	0.24	0.23	0.02	0.09	0.15	1

are calculated, assuming the two main criteria, properties and emissions to be equally weighted. Heating value has the highest impact, followed by CO, UHC and viscosity.

3.1.5. AHP Inconsistency Check

Tables S3 and S4 in the Supplementary Materials show the inconsistency check tables for matrix 1. The ratio CI/RI is less than 0.1, so matrix 1 is consistent. The inconsistency check tables for matrix 2 are in Tables S5 and S6 in the Supplementary Materials. The ratio CI/RI is less than 0.1, so matrix 2 is also consistent.

3.2. Biodiesel Blend Ranking

TOPSIS Calculations

TOPSIS analysis is implemented on the data of Table 5. Tables S7–S12 in the Supplementary Materials show the steps for TOPSIS calculations, from normalization, the weighted normalized decision matrix, the positive and negative ideal solutions, $v_j^{+}$ and $v_j^{-}$, the positive and negative ideal distance values, d_i⁺ and d_i⁻, and the relative closeness to the ideal solution C_i*. Finally, the alternative rankings are presented in

Table 10. Final ranking of biodiesel blends.

Score	Blend	Index
1	Best	1
0.884	Sunflower—SN20	2
0.834	Corn—CB20	3
0.821	Used CO—WC40	4
0.778	Worst	5
0.736	Jatropha—JB10	6
0.653	Mahua—MB20	7
0.545	Soybean—SOB20	8
0.392	Palm oil—PB40	9
0.391	Rapeseed—RB25	10

.

SN20 was found to be the best alternative, with a score of 0.884. Two more alternatives were ranked above the worst, CB20 and WC40, with scores of 0.834 and 0.821, respectively. The other alternatives were ranked below the worst, with a score less than 0.778. A reasonable explanation is that emission values were way above the higher limits.

3.3. Sensitivity Analysis

3.3.1. Sensitivity Analysis on Criteria Weights

Varying the main criteria weights can seriously affect the final results. Weights of the two main criteria, properties and emissions are varied between 0 and 1 in a step of 0.05, and so the subcriteria weights change accordingly, affecting the final ranking results.

Figure 3 shows how the final alternative rankings change as the weight of the “Properties” criterion increases. The “Best” alternative remains in the first position, as it represents the ideal solution. However, increasing the weight of the “Properties” and reducing the importance of “Emissions” causes significant shifts in ranking. WC40, initially ranked second, drops to the last position due to its poor fuel properties, despite being the best performer in emissions. In contrast, JB10 improves from 6th to 2nd, and MB20 rises from 7th to 3rd. CB20 achieved relative stability, while SN20 consistently ranks among the top alternatives ranging between 2nd and 4th place. SOB20 remains at the bottom of the list, fluctuating between 8th and 9th place. As the importance of “Emissions” decreases, more alternatives make it above the worst rank limit. Only PB40 and SOB20 remain outside the acceptable range. Figure 4 further clarifies that at low “Properties” weights, the ranking is primarily influenced by CO emissions. As the weight of “Properties” increases, “Heating Value” becomes the dominant factor affecting the final decision.

3.3.2. Sensitivity Analysis on Alternatives

The effect of adding the two boundary alternatives is studied. By removing the “Best” and “Worst” alternatives, no changes in the TOPSIS ranking were seen; however, the only change was in the relative closeness values (

Table 11. Blend ranking without best and worst alternatives.

Score	Blend	Index
0.968	Sunflower—SN20	1
0.900	Corn—CB20	2
0.867	Used CO—WC40	3
0.801	Jatropha—JB10	4
0.706	Mahua—MB20	5
0.590	Soybean—SOB20	6
0.421	Palm oil—PB40	7
0.410	Rapeseed—RB25	8

). Therefore, the addition of these two alternatives was essential to define acceptable limits and place the alternatives within an acceptable blend range for better selection.

3.3.3. Exhaust Emission Reduction

As seen in the data in Table 5, not all emission values meet regulatory limits. This is because the data reflects direct exhaust measurements without aftertreatment. Aftertreatment systems are essential for diesel engines to comply with strict regulations like EURO VI. Electronic-controlled fuel injection improves emission control, but is not sufficient on its own [50]. Exhaust aftertreatment systems like Exhaust Gas Recirculation (EGR) reduce NO_x emissions by lowering combustion temperatures, but they increase UHC and CO emissions. The Diesel Oxidation Catalyst (DOC) oxidizes UHC and CO into CO₂, achieving reductions of 73% and 80%, respectively [51]. The Selective Catalytic Reduction (SCR) system removes over 90% of NO_x using NH₃ as a reductant, while CO₂ emissions can be reduced by 12.4% [52].

By applying the new reduction percentages to the emission values from the data in Table 5,

Table 12. Table of data after applying exhaust aftertreatment systems.

	Density	Kinematic Viscosity	Flash Point	Calorific Value	CO	NOx	CO2	UHC
Rapeseed—RB25	849.91	3.45	77.77	43.47	0.033	38.457	11.187	101.142
Soybean—SOB20	850.50	4.65	61.00	40.40	0.056	13.740	9.654	11.335
Palm oil—PB40	851.00	4.46	90.00	40.20	0.088	2.040	10.363	22.316
Used CO—WC40	865.00	5.40	78.00	40.20	0.008	12.300	2.278	5.103
Corn—CB20	846.00	3.34	73.00	41.75	0.010	27.240	6.202	9.150
Jatropha—JB10	837.00	2.91	88.00	40.85	0.026	44.000	6.351	14.386
Sunflower—SN20	839.00	3.26	86.00	44.80	0.008	13.700	2.803	7.298
Mahua—MB20	835.00	3.20	85.00	43.92	0.043	30.460	4.205	8.286
Best	820.0	1.90	90.0	44.80	0.000	0	0.00	0.00
Worst	900.0	4.10	52.0	37.00	0.042	60.28	9.74	64.94
Objective	Min	Min	Max	Max	Min	Min	Min	Min

is generated.

The new TOPSIS results, based on these adjusted values, are shown in

Table 13. Blend ranking with exhaust aftertreatment.

Score	Blend	Index
1	Best	1
0.880	Sunflower—SN20	2
0.828	Corn—CB20	3
0.809	Used CO—WC40	4
0.729	Jatropha—JB10	5
0.640	Mahua—MB20	6
0.526	Soybean—SOB20	7
0.440	Worst	8
0.408	Rapeseed—RB25	9
0.372	Palm oil—PB40	10

.

The new ranking, based on equal weights for “Properties” and “Emissions”, places SN20 at the top, followed by CB20 and WC40. The best–worst window now includes more blends, with only RB25 and PB40 outside the acceptable range.

3.3.4. Effect of Blend Prices on Final Selection

The economic aspect is crucial for the study. Biodiesel prices vary by feedstock and production location.

Table 14. Blend break-even prices.

Biodiesel Blend	Diesel Price ($/kg) [53]	B100 Break-Even Price ($/kg)	Break-Even Price of Blends ($/kg)	Reference
Rapeseed—RB25	1.459	1.549	1.481	[54]
Soybean—SOB20	1.459	1.448	1.457
Palm oil—PB40	1.459	1.67	1.543
Used CO—WC40	1.459	2.864	2.021
Corn—CB20	1.459	1.446	1.456
Jatropha—JB10	1.459	5.233	1.836
Sunflower—SN20	1.459	2.275	1.622
Mahua—MB20	1.459	1.294	1.426	[55]

shows the break-even prices for the eight biodiesel blends, the final blend prices calculated based on Brazilian diesel prices [53] and the percentage of biodiesel only [54].

The model was updated to include a new criterion, “Break-Even Price”, equally weighted, and the TOPSIS analysis data in Table 12 (data with exhaust aftertreatment) was updated with the break-even price of blends. The updated ranking is shown in

Table 15. Blend ranking with break-even price criterion.

Score	Blend	Index
1	Best	1
0.858	Sunflower—SN20	2
0.833	Corn—CB20	3
0.723	Used CO—WC40	4
0.692	Jatropha—JB10	5
0.657	Mahua—MB20	6
0.547	Soybean—SOB20	7
0.436	Rapeseed—RB25	8
0.415	Worst	9
0.394	Palm oil—PB40	10

.

Based on the equal weight approach, the results after including the economic analysis are the same as Section 3.3.3 but with different scores. SN20 remains at the top of the list, followed by CB20 and WC40.

3.3.5. Discussion of Results

In order to better understand the results of the sensitivity analysis in accordance with the original results, Figure 5 better visualizes the blend scores in comparison to the original results. After removing the boundary alternatives, the top four blends increased their scores by less than 10%, while the bottom four blends show a decrease in score by a maximum of 23%, except for RB25, which showed an increase of about 5%, all without a change in ranking. After applying the exhaust aftertreatment reduction percentage to the emissions data, all blends showed a decrease in their scores, except for RB25, which slightly increased from 0.392 to 0.408, while moving up one place to rank number 7. Finally, and most importantly, after introducing the economic factor, denoted by the break-even price of the blends, the CB20 score was not affected; however, all other blend scores showed a decrease of up to 28%, except for the RB25 score, which increased by around 12%, moving also one place to rank number 7. It is important to note that the results highlighted SN20 as the optimal blend, demonstrating its superiority in emission control and operational efficiency. Moreover, Figure 5’s trends emphasized the robustness of SN20 and indicated a notable decrease in performance consistency among other blends when various changes were applied.

SN20 is approved to be suitable for direct use in engines without any modifications, achieving emission reductions with a high engine performance [56].

In contrast, other blends do perform well in specific scenarios, especially WC40. When prioritizing emission values, WC20 is ranked 2nd, but drops to the bottom of the ranking when it comes to its properties. In fact, blends with a higher oxygen content often yield lower emissions, but may present trade-offs in terms of energy content [15].

On the other hand, corn biodiesel proved it is one of the most consistent blends in the upper ranks, not only due to its properties and low emissions values but also to its economic viability [42,43]. Rahman et al. (2021) [57] assessed up to 71 biodiesel types through computational software using only their properties as criteria. Even though the alternatives assessed were not blends of biodiesel, sunflower, along with corn biodiesel, performed fairly in the ranking. Abdulvahitoglu & Kilic (2022) [13] compared four biodiesel types, rapeseed, camelina, soybean and cottonseed, by means of three criteria, properties, performance and emissions. Rapeseed biodiesel was found to be the best, surpassing soybean biodiesel. These findings do not align with this study, as SOB20 outperformed RB25. This is mainly due to the difference in comparing pure biodiesel to its corresponding blend. A comparison with similar literature cannot be performed because no studies compared the best blends of biodiesel from different types.

This study refines the selection criteria for biodiesel blends and incorporates a comprehensive approach encompassing economic viability through a break-even pricing analysis. Such integration is vital, as economic considerations often dictate the feasibility of adopting the blend use in commercial applications. However, this study is not without limitations. The reliance on data from one specific geographic region, i.e., Brazil, may not universally apply, and further validation across different regional settings would enhance the robustness of the findings. Moreover, while the AHP-TOPSIS method minimizes subjectivity, it is crucial to acknowledge that the property subcriteria weights are still assigned based on the assumptions drawn from the literature.

4. Conclusions

This study applied a combined AHP–TOPSIS framework to identify the best-performing biodiesel blend among the eight most widely used biodiesel feedstocks worldwide. The methodology introduced two key innovations. First, the weighting of emissions-related subcriteria was determined through AHP method by using the GWP values as basis for comparison. Thereby reducing subjectivity compared to expert judgment approaches. Second, two boundary alternatives, “Best” and “Worst”, were constructed using international standard norms, so that TOPSIS classification could provide a clear border line and ensure a clearer benchmarking reference.

The results consistently indicated that the 20% sunflower biodiesel blend (SN20) achieved the highest ranking across both technical and environmental criteria. Sensitivity analyses further demonstrated the stability of this finding, as SN20 maintained its top position even when introducing an additional economic criterion through break-even prices. In contrast, WC40 performed best when emissions alone were prioritized, while JB10 was preferred when only properties were considered. These findings underline the strength of the integrated AHP–TOPSIS framework in capturing trade-offs among multiple criteria and reducing bias in biodiesel blend evaluations.

From a policy perspective, SN20 may serve as a benchmark option in regions with reliable access to sunflower oil feedstock. Meanwhile, WC40 represents a sustainable pathway in regions where waste cooking oil is abundant, aligning with circular economy goals and minimizing competition with food crops. The framework developed in this study therefore provides decision-makers with a robust, transparent and reproducible tool to guide biodiesel blend adoption strategies tailored to local resource availability and policy priorities.

Future research should extend this approach by considering additional life cycle impact categories, such as photooxidant formation for emissions-based weighting. Furthermore, applying alternative MCDM techniques alongside AHP–TOPSIS would enable a cross-validation of results and strengthen the methodological robustness. Expanding the analysis to include crop yields in specific regions would improve the realism of feedstock selection and enhance policy relevance. Finally integrating fourth-generation biodiesel feedstocks, such as algae and other non-food crops, would also provide insights into the long-term sustainability and scalability of biodiesel production.