Sustainable Cold-Chain Vehicle Selection: A Novel AYBI-MUNRA MCDM Model

Abstract

The part of the food supply chain that uses the most resources for transportation is the cold supply chain. For this reason, vehicle selection in the cold supply chain is a crucial task. Because there are several alternative vehicles and different criteria, choosing a vehicle is a challenging issue for decision makers. Six distinct cold-chain vehicle options were assessed with twelve sustainability (economic, environmental, and technological) criteria using an integrated Multi-Criteria Decision Making (MCDM) model. The main contribution and novelty of this study include developing a new Accordance-Yielding-Based Integration (AYBI) method for determining criteria weights. For vehicle evaluation and selection, the Multiple Normalization Rating Analysis (MUNRA) technique is applied. According to the AYBI, it was determined that Purchase Price (PP) is the most crucial criterion, followed by Infrastructure and Service Accessibility (ISA) and Load Capacity (LC), and Noise Emissions (NE) is the least significant criterion. According to the MUNRA results, the Twin-Axle Refrigerated Trailer (TRT) performs the best, followed by the Frigorific Trailer (Standard) (FT) and Double-Axle Refrigerated Truck (DART). The results also show that the developed AYBI method provides some advantages in the procedure of determining criteria weights. A sensitivity study verified the AYBI-MUNRA approach’s stability under various weight situations, and comparative analysis demonstrated its resilience in comparison to other MCDM methodologies.

1. Introduction

The cold supply chain requires the highest use of resources in the transportation and supply of food products. Spoilage of food products during the supply process is a serious problem. Approximately 30% of food products deteriorate after production [1,2]. The cold supply chain is one of the most important strategies used to prevent disruptions and reduce losses [3,4]. Raut et al. [5] stated that the use of cold logistics tools greatly reduces spoilage in the supply of food products. However, the need to keep products at a certain level of coldness, especially from production to delivery to the consumer, causes the vehicles used in the cold supply chain to produce high carbon emissions. The solution to this contradiction constitutes the source of the vehicle selection problem in the cold supply chain. However, there are limited studies in the literature on which type of vehicle is more sustainable to use in the cold supply chain.

Vehicle selection is a difficult decision problem for decision makers because there are many alternative vehicles and various criteria to consider. While compact refrigerated panel van-type vehicles are suitable for urban transportation, double-deck refrigerated trailers are more suitable for out-of-city high-capacity load transportation. Moreover, all these vehicles differ when evaluated in terms of various and sometimes conflicting criteria, such as investment cost, depreciation, capacity, operating cost and environmental impact, and none is the best in all criteria. Multi-Criteria Decision Making (MCDM) techniques are frequently used in the literature to evaluate alternative tools according to these conflicting criteria.

MCDM techniques in logistics and transportation have been widely used in the literature on logistics and supply chain issues, but they are still insufficient in sustainable vehicle selection in the cold supply chain. In existing studies, tool alternatives were evaluated within a narrow scope, and they increased the complexity of the decision model by adding only fuzzy and gray numbers to the model, without contributing to practicality [6,7]. When studies addressing sustainability in the cold supply chain are examined, it is seen that these studies are limited to route optimization for a specific fleet [8,9].

In this study, an integrated MCDM model, including Accordance-Yielding-Based Integration (AYBI) and Multiple Normalization Rating Analysis (MUNRA) methods, was developed to evaluate six different cold-chain vehicle alternatives through twelve sustainability (economic, environmental, technical) criteria. These alternatives are cold-chain panel van, light truck, single-axle truck, double-axle truck, standard trailer and double-decker trailer. The data collected from twelve decision makers via a survey were analyzed with AYBI, and the criterion weights were found. Three normalizations, linear, vector and non-linear, were combined with MUNRA to rank the alternatives using these criterion weights [10].

This study contributes to the literature in three aspects. The first contribution is that in MCDM studies, all vehicle types used in the cold supply chain were evaluated for the first time. In the second contribution, a new criterion weighting method, the AYBI method, is introduced to the literature. In the third contribution, a transparent and applicable MCDM model for cold supply chains was developed by working entirely with crisp data and benefiting from the knowledge of the direct decision maker. Apart from these contributions, this study, in the next section, after a deep literature review, elaborates on research gaps and their fulfillment by this model.

This study is organized as follows. First, in the second section, the literature on sustainability in the cold supply chain, sustainable vehicle selection and MCDM applications in transportation was examined. In the third section, AYBI and MUNRA methods are explained. In Section 4, the analyses are presented. In Section 5, conclusions, limitations, and recommendations for future research are provided.

2. Literature Review

2.1. Cold-Chain Logistics and Sustainability

The cold chain encompasses all placement, transportation, and storage activities that maintain the temperature of the product at a predetermined value, from loading onto the vehicle to the delivery point. While perishable food products are proportionally more common in cold chains, transportation is also carried out in the pharmaceutical, chemical, and medical sectors. Behdani et al. [3] noted that the high energy consumption and undesirable temperature deviations in cold-chain vehicles create significant complexity compared to dry bulk transportation. In this study, they stated that refrigeration technology, insulation quality, and load capacity are the most important determinants of cold-chain performance.

Other studies show a positive and consistent relationship between cold-chain performance and spoilage rates of food products. Raut et al. [5] demonstrated that utilizing third-party logistics reduces losses in the supply chain of agricultural products. Zhang et al. [11] examined the environmental and economic aspects of transport mode choices in cold-chain transportation and revealed that these decisions, along with the vehicle technologies used, significantly affect the total carbon emissions of the supply chain. The results show that vehicle selection is not merely an operational preference, but a strategic decision that has direct and measurable effects on sustainability performance.

Studies conducted at the network level also support these findings. Matskul et al. [9] optimized cold-chain logistics networks by considering environmental impacts and showed that network structure and vehicle assignment decisions together shape emission levels. Ghahremani-Nahr et al. [12], in their integrated transportation model developed for fruit and vegetable supply chains, considered the interaction between load consolidation, route planning, and refrigerated vehicle performance. Zheng et al. [8] demonstrated that low-emission routes can be determined using the particle swarm optimization method for route selection in multimodal cold-chain transportation. However, in this study, the vehicle fleet was not considered as a decision variable but rather as one of the fixed inputs of the model.

There is a general consensus in the literature that carbon emissions from refrigeration systems used in the transportation process are one of the priority intervention areas in the decarbonization of the cold chain. Pata et al. [13] examined different modes of transport in European countries within the framework of the environmental Kuznets curve and determined that even with increasing levels of economic development, road transport maintains a higher emission intensity compared to rail and inland waterway transport. Arora et al. [14] analyzed the factors hindering the widespread adoption of the cold supply chain in developing countries; they identified inadequate infrastructure, high initial investment costs, and a lack of knowledge regarding alternative vehicle technologies as the main obstacles. Hashemi-Tabatabaei et al. [7], on the other hand, developed an interval-valued Fermatean fuzzy decision-making framework that considers CO₂ emissions, energy consumption, and temperature reliability as key criteria in supplier evaluation. Similarly, Pro-Nuño et al. [4] examined developments in the cold-chain sector in the post-pandemic period and revealed that electrification in last-mile refrigerated transport had increased, particularly due to advances in urban emission regulations and battery technologies.

The common point highlighted in these studies is that cold-chain sustainability cannot be achieved solely through route optimization or network design. Characteristics such as vehicle technology, purchase cost, energy consumption, emission levels, range capacity, and compatibility with existing infrastructure directly affect the environmental performance of logistics systems. In other words, the performance level achievable by route and planning models is largely determined by the characteristics of the vehicle fleet used. Wiangkam et al. [15] also emphasize that vehicle fleet composition should be one of the key evaluation criteria in the selection of cold-chain logistics service providers operating in the food sector. When these findings are considered together, the necessity of addressing vehicle selection decisions in cold-chain transportation with systematic and multi-criteria approaches becomes clear. Therefore, the multi-criteria cold-chain vehicle selection approach proposed in the present study addresses a significant need in the literature.

2.2. Sustainable Vehicle Selection in Transportation

Studies on sustainable vehicle selection have increased significantly in recent years, particularly with the rise of regulations regarding fleet emissions, the increasing prevalence of alternative fuel vehicles, and the growing use of MCDM methods as decision support tools. Ogryzek et al. [16] demonstrated that effective transportation network design, supported by appropriate vehicle selection criteria, can improve sustainability performance in economic, social, and environmental dimensions. This study provided an important foundation for subsequent research by showing that vehicle evaluation should be approached not only from a cost-focused perspective but also from a multi-dimensional one.

Galkin et al. [17], addressing the impact of environmental conditions on vehicle fleet planning, emphasized that seasonal temperature variations are particularly decisive in energy consumption and fuel requirements in refrigerated transport operations. Their research results show that if the differences between summer and winter periods are not considered, both operating costs and emission levels are estimated to be lower than they actually are. This finding highlights the need to consider environmental conditions when determining vehicle selection criteria in cold-chain transportation.

Görçün et al. [6] present one of the studies most similar to this study in the existing literature. Using an intuitive fuzzy group decision-making approach, the researchers evaluated sustainable refrigerated road vehicles for use in food logistics and considered criteria such as technical specifications, economic performance, and compliance with cold-chain standards in the selection process. The study’s significant contribution is that it directly addresses vehicle selection within the context of food logistics. However, the research focuses only on refrigerated trailers and is conducted in a fuzzy decision environment. The current study, on the other hand, expands this scope by covering different vehicle classes, from panel vans to double-decker trailers, and using a new weighting approach in a clearer decision environment based on expert evaluations.

Studies conducted in the transportation sector, outside of the cold chain, also provide important findings regarding sustainable vehicle selection. Fan et al. [18], in their bibliometric review of transportation-related carbon emissions, identified vehicle technology, fuel type, and load-handling efficiency as key factors determining emission levels. Aytekin et al. [19] analyzed logistics strategies using MCDM methods. Tsao and Banyupramesta [20] created an optimal fleet deployment model necessary for sustainability in maritime logistics. Jia et al. [21] analyzed third-party logistics service-provider companies.

Studies on shared mobility and alternative transport modes provide additional methodological context. Saha et al. [22] apply a consensus-based Fermatean fuzzy MCDM model to evaluate shared micro-mobility systems for sustainable cities, finding that sustainability criteria extend beyond emissions to include noise, infrastructure, and accessibility. This finding motivates the inclusion of noise emissions and infrastructure and service accessibility in the twelve-criterion set used here. Ecer et al. [23] apply Logarithmic Percentage Change-driven Objective Weighting (LOPCOW) and Measurement Alternatives and Ranking according to Compromise Solution (MARCOS) approaches with interval-valued fuzzy neutrosophic information to sustainable aviation fuel supplier evaluation, demonstrating the practical value of multi-normalization-based ranking procedures for energy and transport decisions where expert knowledge is the primary data source. Simsek et al. [24] combine machine learning and MCDM to assess supply chain resilience in green logistics, showing that hybrid computational approaches can handle the complexity of multi-dimensional sustainability assessment.

Rossi et al. [25], by examining intermodal transportation systems used in the transportation of perishable food products, showed that rail–road combinations can reduce not only carbon emissions but also product losses. However, it was emphasized that sufficient cold-chain infrastructure is required at transfer points to obtain these advantages. This situation is reflected in the current study.

2.3. MCDM Methods in Logistics and Transportation

MCDM methods have become widely used in logistics and transportation research over the last two decades [26,27,28] due to the need to simultaneously address the economic, environmental, and social dimensions of sustainability assessments. The increasing complexity of decision-making problems and the need for transparent, practical, and applicable analytical approaches for decision-making experts have increased the use of MCDM methods. Sun et al. [29] examined Industry 4.0 applications in sustainable transportation and found that MCDM methods are one of the most frequently used techniques in evaluating the sustainability of smart transportation systems. Faramarzi-Oghani et al. [30] compared commonly used meta-heuristic methods in the sustainability of supply chains and showed that MCDM techniques provide the necessary performance evaluation infrastructure for optimization.

The number of studies indicating the effective use of MCDM techniques in decision problems occurring in supply chains is constantly increasing. Ulutaş et al. [31] evaluated the performance of logistics companies with the integrated fuzzy Preference Selection Index (PSI)–Pivot Pairwise Relative Criteria Importance Assessment (PIPRECIA)–Combined Compromise Solution (CoCoSo) technique. The findings of this study show that uncertainties arising from evaluations based on the subjective judgments of decision makers can be effectively managed using hybrid criterion weighting and alternative ranking techniques. Goodarzi et al. [32] evaluated the sustainability of intermodal logistics companies and showed that MCDM techniques provide more accurate results in the simultaneous evaluation of conflicting criteria under the broader goals of economy, the environment, and service.

Calculating criterion weights plays a crucial role in the application of MCDM techniques. The most frequently used criterion weighting methods in the supply chain include techniques such as Step-wise Weight Assessment Ratio Analysis (SWARA), the Best-Worst Method (BWM), the Full Consistency Method (FUCOM), and LOPCOW. When deciding which method to use, researchers consider factors such as the amount of data required for decision-making, the ease of calculation, and the consistency of the calculated criterion weights. The AYBI method used in this research is also a criterion weighting method based on expert opinion. However, AYBI differs from other techniques because it provides coefficients such as the Discrimination Index and Consensus Index, which reveal the consistency of decision makers’ subjective judgments. Thus, it is possible to analyze not only the criterion weights but also their reliability.

The MUNRA method is a new MCDM approach introduced to the literature by Ulutaş et al. [10] as an alternative ranking method. The most important characteristic of MUNRA is that it integrates linear, vector, and nonlinear normalizations in alternative ranking. Thus, it prevents the consistency of alternative ranking results from being reduced by relying on a single normalization. In this respect, the MUNRA method differs from other frequently used methods that use a single normalization, such as the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and VišeKriterijumska Optimizacija I Kompromisno Rešenje (VIKOR). Ulutaş et al. [10] showed that MUNRA yields highly consistent findings through comparative analyses and Spearman correlation tests.

Applications of MUNRA in different areas also prove the consistency of the method. Akbulut [33] evaluated the environmental, social, and governance (ESG) risks of manufacturing companies with a hybrid MCDM model including MUNRA and showed that MUNRA can produce accurate findings in multi-stakeholder decision-making environments. Yalvaç et al. [34] used LOPCOW and MUNRA methods together with Fermatean fuzzy sets to prioritize strategies for managing work–family conflict and revealed that the ranking results did not change significantly in the sensitivity analyses performed. Similarly, Çaylan et al. [35], in their study on organizational learning, integrated MUNRA with the Comparative Weighting Evaluation Based on the Best Criteria (COWEB) weighting technique and global fuzzy sets, showing that the method can be successfully applied in different disciplines.

Another notable issue in the literature is the debate surrounding the use of fuzzy and grey-number-based MCDM methods. While these methods offer significant advantages in situations where decision makers have uncertainty in their assessments, they are more complex in terms of application and interpretation. This reveals that, especially for non-expert users, it can reduce the comprehensibility and applicability of decision support systems. In contrast, it is stated that exact MCDM methods based on structured expert evaluations can produce quite robust results and are easier to interpret when supported by inter-rater reliability analyses [6,7]. These evaluations constitute one of the main justifications for preferring an exact data-based approach in the present study.

Bosković et al. [36] also reached a similar conclusion. The researchers showed that exact MCDM methods based on expert opinions can produce applicable and reliable rankings in the evaluation of infrastructure investments. This finding supports the fact that the methodological approach adopted in the present study has a strong foundation, both theoretically and practically.

2.4. Research Gaps and Positioning of the Present Study

The review above reveals three interconnected gaps that the present study addresses. First, no published study applies a comprehensive MCDM framework to the evaluation of sustainable frigorific road vehicles across all major vehicle classes. The main focus areas are supplier selection [37,38,39,40], risk management [41,42,43,44], and service provider selection [28,45,46,47]. Only Görçün et al. [6] come close but are limited to the trailer segment and use a fuzzy environment. Second, the criterion sets used in existing vehicle selection studies rarely combine economic, environmental, and technical-operational dimensions with the specificity required for cold-chain applications. Criteria such as infrastructure and service accessibility, noise emissions, and charging or refueling duration have been identified in urban transport and green fleet studies but have not been consolidated into a cold-chain vehicle evaluation framework. Third, new subjective weighting methods with formal agreement diagnostics remain underrepresented in logistics MCDM applications relative to their potential utility, and MUNRA has not previously been applied in the transportation domain.

Three limitations of existing weighting approaches in group decision settings motivated the use of AYBI.

First, objective methods such as Entropy [48] and CRITIC [49] derive weights only from data dispersion and ignore the expert’s judgment of importance, while subjective methods such as AHP [50], BWM [51] and SWARA [52] depend on individual comparisons or rankings. In a panel, individual weight vectors are then usually combined in a separate step (for example, by an arithmetic or geometric mean), and the profile of the experts and the degree of disagreement among them are not part of the weighting core.

Second, the simple mean of expert ratings treats all experts as equal and gives no information about whether the experts agree on a criterion. Two criteria with the same mean rating are treated identically even if experts agree on one and disagree strongly on the other.

Third, SIWEC, the closest group method, uses only the dispersion of each expert’s own ratings and does not consider expert profile or agreement on individual criteria.

Table 1 summarizes the positioning of the present study relative to the most closely related prior work.

Table 1. Positioning of the present study relative to closely related prior work.

Study	Criteria	Method	Vehicle Scope	Environment	Cold Chain
Görçün et al. [6]	Inner height, Inner width, Internal length, Capacity, Total weight, Number of authorized services, Axle load, 5th wheel height, Empty weight, Gooseneck	IF-MCDM	Reefer trailers only	Fuzzy	Yes
Aytekin et al. [19]	Ease of access, Transportation security, Transportation fee, Land use status, Freight transportation, Being ergonomic, Regulation of competition legislation and regulations, Incentives for transport, Increasing transport efficiency	Multi-MCDM	Transport modes	Crisp	No
Hashemi-Tabatabaei et al. [7]	Employee health & Safety, Rerouting, Product life-cycle, Environmental management system, Product price, Surplus inventory, Restorative capacity	IV-FF Z-LMAW	Cold-chain suppliers	Fuzzy	Yes
Goodarzi et al. [32]	Costs, GHG emissions, Noise pollution, Traffic congestion, Accidents	Multi-objective	Intermodal network	Crisp	Partial
Saha et al. [22]	Price, Weight, Capacity, Speed, Charge time, Length, Maintenance cost	FF MOOAFMF	Micro-mobility	Fuzzy	No
Ulutaş et al. [10]	Flexibility, Analytics tools, Technology Integration, Automation in supply-chain operations, Technology capability, Digital innovation, Digital collaboration, Digital education & training, Lack of information security and privacy, Lack of information sharing	MUNRA	Digital suppliers	Crisp	No
Ecer et al. [23]	Flexibility, Price, Firm size, Stability, Technological capability, R&D investments, On-time delivery, Reliability, Quality, Customer satisfaction, Responsibility, Reputation, Collaborations with society, Compliance with legislation, Green design, Waste, Green logistics, Green production, Green image	LOPCOW-MARCOS	Aviation fuel supply	Fuzzy	No
Present study	Purchase price, Operating and energy cost, Maintenance cost, Greenhouse gas emission, Energy consumption, Noise emissions, Driving range, Charging/Refueling time, Battery capacity, Power and acceleration performance, Load capacity, Infrastructure and service accessibility	AYBI-MUNRA	All frigorific classes (A1–A6)	Crisp	Yes

As Table 1 illustrates, the present study is the only one that combines full frigorific vehicle class coverage, a crisp decision environment, and an explicit cold-chain focus. The integration of AYBI for criterion weighting and MUNRA for alternative ranking has not previously been applied in the transportation or cold-chain logistics domain, adding a dual methodological dimension to the empirical contribution.

3. Materials and Methods

This section represents a new AYBI method for obtaining criteria weights. The AYBI algorithm has been explained in detail through seven steps and 11 equations. Apart from that, this section also shows the algorithm of the MUNRA method used for vehicle selection in a cold supply chain.

3.1. AYBI Method (Accordance-Yielding-Based Integration)

Step 1. A decision matrix containing expert opinions on the criteria is constructed. This matrix is presented in Equation (1), where x_tj is the score given by expert t to criterion j, k is the number of experts, and n is the number of criteria.

$$X={\left[x_{tj}\right]}_{k\times n}$$

(1)

Step 2. The Discrimination Index (RI_t) of each expert is obtained from the standard deviation σ_t of the scores that expert t assigned across all criteria. An expert who differentiates more between criteria carries more information and has a higher Discrimination index.

$${RI}_t={\displaystyle \frac{{\sigma }_t}{{\displaystyle {\sum }_{t=1}^k}{\sigma }_t}}$$

(2)

Step 3. The Criterion Discrimination Coefficient (CDC_j) is obtained from the standard deviation σ_j of the scores given to criterion j by all experts. It depends only on the dispersion of the criterion itself, takes the value 1 under full consensus, decreases monotonically as disagreement grows, and is defined for every σ_j ≥ 0.

$${CDC}_j={\displaystyle \frac{1}{1+{\sigma }_j}}$$

(3)

Step 4. The average score of each criterion (AV_j) is obtained using Equation (4), as the sum of the scores of the k experts for criterion j divided by k.

$${AV}_j={\displaystyle \frac{{\displaystyle {\sum }_{t=1}^k}{x}_{tj}}{k}}$$

(4)

Step 5. The values in the decision matrix are normalized using Equation (5), where u_tj is the normalized score and max(x_tj) is the highest score given to criterion j among all experts.

$$u_{tj}={\displaystyle \frac{x_{tj}}{\mathit{max}\left(x_{tj}\right)}}$$

(5)

Step 6. S_j aggregates the normalized scores weighted by the sum of the expert profile weight (e′_t) and the discrimination index (RI_t). T_j is the consensus-adjusted score. G_j adds the average score, and both terms are divided by their sums over the criteria, so that each contributes exactly half of the final weight.

$$S_j={\displaystyle \sum _{t=1}^k}\left(\left(u_{tj}\times e_t^{\prime }\right)+{RI}_t\right)$$

(6)

T_j = S_j × CDC_j

(7)

$$G_j={\displaystyle \frac{T_j}{{\displaystyle {\sum }_{j=1}^n}{T}_j}}+{\displaystyle \frac{{AV}_j}{{\displaystyle {\sum }_{j=1}^n}{AV}_j}}$$

(8)

The $e_t^{\prime }$ value shown in Equation (6) represents the expert normalized weight, which is determined by taking into account the experience (exp_t) and education level (edu_t) of expert t. In Equations (9) and (10), e_t is the raw expert weight, exp_t and edu_t are the experience and education scores, and φ is the balance parameter between the two.

e_t = φexp_t + (1 − φ)edu_t

(9)

$$e_t^{\prime }={\displaystyle \frac{e_t}{{\sum }_{t=1}^k{e}_t}}$$

(10)

The φ value shown in Equation (9) (φ ∈ [0, 1]) is taken as 0.5 in this study. The scoring table for experience and education levels is presented in Table 2.

Table 2. Experience years and education levels.

Educational Backgrounds	Points	Experience	Points
High school or below	1	1–5 years	1
Associate degree	2	6–10 years	2
Bachelor’s degree	3	11–15 years	3
Master’s degree	4	16–20 years	4
PhD or above (PhD, Post-doc, Assoc. Prof., Prof.)	5	21 years and above	5

Step 7. In the final step, the weight of each criterion (w_j) is obtained using Equation (11), by dividing G_j by the sum of G_j over all n criteria, so that the weights sum to one.

$$w_j={\displaystyle \frac{G_j}{{\displaystyle {\sum }_{j=1}^n}{G}_j}}$$

(11)

Equations (8) and (9) are linear combinations with equal coefficients. In Equation (8), the two terms ${\displaystyle \frac{T_j}{{\displaystyle {\sum }_{j=1}^n}{T}_j}}$ and ${\displaystyle \frac{{AV}_j}{{\displaystyle {\sum }_{j=1}^n}{AV}_j}}$ are both divided by their sums over the criteria, so they are unit-sum vectors on the same scale, and each contributes exactly half of the final weight. Equal coefficients were chosen because there is no prior information that favors the consensus-adjusted score over the direct mean rating, or the reverse, and because equal-weight averaging is a common and transparent way of combining weighting information (see Section 4 for the supporting literature). The same convention is used for the experience and education scores in Equation (9) (φ = 0.5). The equal coefficients are a convention and not a proven optimum. Because both terms are normalized to unit sum, moderate departures from equal coefficients would change the weights only slightly, and a check in which the coefficient of the first term in Equation (8) was varied between 0 and 1 did not change the ranking of the alternatives; the coefficients can nevertheless be adapted by users who have a justified preference for one of the components.

3.2. MUNRA (Multiple Normalization Rating Analysis)

• Step 1. Aggregated Decision Matrix Construction

Since the opinions of multiple decision makers were taken into account in this study, these opinions were combined using the Bonferroni mean operator [53] to obtain an aggregated decision matrix.

$$B{M}^{p,q}\left(a_1,a_2,\dots ,a_n\right)={\left({\displaystyle \frac{1}{n\left(n-1\right)}}{\displaystyle \sum _{\begin{array}{c}i,j=1\\ i\ne j\end{array}}^n}{a}_i^p\hspace{0.17em}{a}_j^q\right)}^{{\displaystyle \frac{1}{p+q}}}$$

(12)

In Equation (12), the values of p and q are taken to be 1. The steps of the MUNRA method are as follows [10]. The method begins with an aggregated decision matrix A of order m × n, where m denotes the number of alternatives and n the number of criteria:

$$\begin{array}{cccc}& A={\left[a_{ij}\right]}_{m\times n}& & \end{array}$$

(13)

Each entry a_ij records the performance of alternative i on criterion j.

• Step 2. Normalization

MUNRA applies three distinct normalization procedures in sequence to reduce the dependence of rankings on any single scaling assumption.

In linear normalization, each data point is scaled according to the highest or lowest value in the column.

$$\begin{array}{cccc}& r_{ij}={\displaystyle \frac{a_{ij}}{\mathit{max}\left(a_{ij}\right)}},j\in BNF& & \end{array}$$

(14)

$$\begin{array}{cccc}& r_{ij}={\displaystyle \frac{\mathit{min}\left(a_{ij}\right)}{a_{ij}}},j\in NBNF& & \end{array}$$

(15)

In vector normalization, normalization is done according to Euclidean magnitude. In cost criteria, a transformation is made such that higher values indicate better performance:

$$\begin{array}{cccc}& y_{ij}={\displaystyle \frac{a_{ij}}{\sqrt{{\displaystyle {\sum }_{i=1}^m}{a}_{ij}^2}}},j\in \mathrm{BNF}& & \end{array}$$

(16)

$$\begin{array}{cccc}& y_{ij}=1-{\displaystyle \frac{a_{ij}}{\sqrt{{\displaystyle {\sum }_{i=1}^m}{a}_{ij}^2}}},j\in \mathrm{NBNF}& & \end{array}$$

(17)

In nonlinear normalization, an asymmetric sensitivity structure is developed. For benefit criteria, squaring the ratio makes the difference between high-performing criteria more pronounced, while for cost criteria, cubing the ratio makes the difference between low-performing criteria more prominent.

$$\begin{array}{cccc}& p_{ij}={\left({\displaystyle \frac{a_{ij}}{\max \left(a_{ij}\right)}}\right)}^2,j\in \mathrm{BNF}& & \end{array}$$

(18)

$$\begin{array}{cccc}& p_{ij}={\left({\displaystyle \frac{\min \left(a_{ij}\right)}{a_{ij}}}\right)}^3,j\in \mathrm{NBNF}& & \end{array}$$

(19)

In Equations (14)–(19), BNF represents the benefit criteria and NBNF represents the cost criteria. Linear and vector normalizations allow for a proportional comparison of the criteria, while nonlinear normalization reduces distortion caused by excessively high or low data and mitigates their effects on the final ranking of alternatives.

• Step 3. Weighted Aggregation Within Each Normalization Scheme

Criterion weights w_j are applied independently to each normalized set. The weighted combined score for alternative i in each scheme is as follows:

$$\begin{array}{cccc}& r_i^{\prime }={\displaystyle \sum _{j\in \mathrm{BNF}}}{w}_j{r}_{ij}+{\displaystyle \sum _{j\in \mathrm{NBNF}}}{w}_j{r}_{ij}& & \end{array}$$

(20)

$$\begin{array}{cccc}& y_i^{\prime }={\displaystyle \sum _{j\in \mathrm{BNF}}}{w}_j{y}_{ij}+{\displaystyle \sum _{j\in \mathrm{NBNF}}}{w}_j{y}_{ij}& & \end{array}$$

(21)

$$\begin{array}{cccc}& p_i^{\prime }={\displaystyle \sum _{j\in \mathrm{BNF}}}{w}_j{p}_{ij}+{\displaystyle \sum _{j\in \mathrm{NBNF}}}{w}_j{p}_{ij}& & \end{array}$$

(22)

• Step 4. Final Score Computation

The scores of the three scheme levels are integrated into a single utility value.

$$\begin{array}{cccc}& v_i=\alpha \hspace{0.17em}{r}_i^{\prime }+\beta \hspace{0.17em}{y}_i^{\prime }+\gamma \hspace{0.17em}{p}_i^{\prime }& & \end{array}$$

(23)

The linear, vector and nonlinear normalizations are those of the original MUNRA method [10], where they are justified in detail. Their combination with equal weights (α = β = γ = 1/3) reduces the dependence of the ranking on a single normalization. Alternatives are ranked according to v_i; the alternative with the highest score is determined as the best alternative.

4. Application

In this study, 12 criteria and six alternatives related to the subject were selected from the literature by two academics with research experience in the field of logistics. The criteria and frigorific vehicles identified are presented below.

The criteria are as follows:

• Purchase Price (PP): the initial acquisition cost of the vehicle, including the refrigeration unit.
• Operating and Energy Cost (OEC): the recurring cost of running the vehicle, mainly energy (fuel or electricity), including the energy used for refrigeration.
• Maintenance Cost (MC): the cost of scheduled and unscheduled maintenance and repair of the vehicle and its refrigeration unit.
• Greenhouse Gas Emission (GGE): the greenhouse gas emissions (CO₂ equivalent) released during vehicle operation.
• Energy Consumption (EC): the amount of energy consumed per unit of operation, reflecting the energy efficiency of the vehicle and its refrigeration system.
• Noise Emission (NE): the noise level produced by the vehicle and its refrigeration unit during operation.
• Driving Range (DR): the distance the vehicle can travel on a full battery charge or tank of fuel.
• Charging/Refueling Time (RT): the time required to recharge the battery or to refuel the vehicle.
• Battery Capacity (BC): the on-board energy storage capacity of the vehicle, i.e., the battery for electric and hybrid vehicles and the fuel tank for conventional vehicles.
• Power and Acceleration Performance (PAP): the engine or motor power and the acceleration capability of the vehicle, including the ability to cope with load and gradients.
• Load Capacity (LC): the maximum payload and cargo volume the vehicle can carry per trip.
• Infrastructure and Service Accessibility (ISA): the availability of charging or fueling stations, service points and spare parts along the operating routes.

While five (DR, BC, PAP, LC and ISA) of these criteria were identified as beneficial, the remaining criteria were identified as non-beneficial.

The vehicles are as follows:

• Refrigerated Panel Van (RPV);
• Frigorific Box Truck (FBT);
• Single-Axle Refrigerated Truck (SART);
• Double-Axle Refrigerated Truck (DART);
• Frigorific Trailer (Standard) (FT);
• Twin-Axle Refrigerated Trailer (TRT).

The six alternatives were defined in the expert survey by their intended use and load capacity. Refrigerated Panel Vans (RPVs) are compact vehicles of up to 3.5 t for urban last-mile distribution, Frigorific Box Trucks (FBTs) carry 3.5 to 7.5 t for short-distance regional distribution, and Single-Axle Refrigerated Trucks (SARTs) carry 7.5 to 18 t over medium distances between regions. Double-Axle Refrigerated Trucks (DARTs) are high-capacity vehicles of 18 to 26 t for interregional transport, Standard Frigorific Trailers (FTs) serve long-distance and international transport with high volume, and Twin-Axle Refrigerated Trailers (TRTs) offer the maximum capacity for long-distance transport. The survey did not specify the propulsion technology or the refrigeration unit type of the vehicles, and the experts rated each class according to the typical vehicles of that class in the sector.

These 12 criteria and six vehicles were presented to 12 experts in the field. The educational backgrounds and years of experience of the experts from whom the data were obtained are presented in Table 3.

Table 3. Experts’ educational backgrounds and years of experience.

Experts’ Codes	Experience Area	Educational Backgrounds	Experience
EXP-1	Logistics	PhD	25
EXP-2	Logistics	MSc	5
EXP-3	Logistics	BC	2
EXP-4	Logistics	BC	4
EXP-5	Logistics	MSc	6
EXP-6	Logistics	BC	5
EXP-7	Logistics	BC	13
EXP-8	Logistics	BC	3
EXP-9	Logistics	MSc	2
EXP-10	Logistics	MSc	14
EXP-11	Logistics	MSc	5
EXP-12	Logistics	PhD	16

The experts first weighted the criteria using a scale from one (Least Important) to nine (Most Important). The decision matrix showing the experts’ ratings of the criteria is presented in Table 4.

Table 4. The decision matrix for criteria.

Criteria Type	Cost	Cost	Cost	Cost	Cost	Cost
Criteria	PP	OEC	MC	GGE	EC	NE	σt	RIt
EXP-1	9	7	7	5	7	3	1.7495	0.0897
EXP-2	9	8	6	9	9	7	1.1282	0.0578
EXP-3	8	9	8	9	9	6	1.1146	0.0571
EXP-4	9	7	5	7	9	4	1.7123	0.0878
EXP-5	9	8	7	5	6	3	1.9695	0.1010
EXP-6	8	9	8	9	9	6	1.1146	0.0571
EXP-7	7	9	9	9	9	9	1.5643	0.0802
EXP-8	9	9	9	5	5	6	1.6765	0.0859
EXP-9	7	7	6	4	5	4	1.1146	0.0571
EXP-10	7	9	8	8	9	5	1.3114	0.0672
EXP-11	9	5	5	3	7	3	2.8710	0.1472
EXP-12	9	9	6	9	5	5	2.1794	0.1117
Criteria Type	Benefit	Cost	Benefit	Benefit	Benefit	Benefit
Criteria	DR	RT	BC	PAP	LC	ISA	σt	RIt
EXP-1	8	8	7	9	9	7	1.7495	0.0897
EXP-2	7	9	9	7	7	9	1.1282	0.0578
EXP-3	8	7	9	6	7	8	1.1146	0.0571
EXP-4	8	9	8	9	9	9	1.7123	0.0878
EXP-5	3	7	6	6	9	7	1.9695	0.1010
EXP-6	8	7	7	6	9	8	1.1146	0.0571
EXP-7	5	9	9	5	7	8	1.5643	0.0802
EXP-8	9	9	9	9	9	9	1.6765	0.0859
EXP-9	6	6	6	5	7	7	1.1146	0.0571
EXP-10	9	8	9	6	8	9	1.3114	0.0672
EXP-11	9	1	9	9	9	7	2.8710	0.1472
EXP-12	6	6	8	2	7	9	2.1794	0.1117

After the decision matrix is established, the experts’ discrimination index is obtained using Equation (2). For EXP-1, this value is calculated as follows:

$${RI}_1={\displaystyle \frac{{\sigma }_1}{{\displaystyle {\sum }_{t=1}^k}{\sigma }_t}}={\displaystyle \frac{1.7495}{1.7495+\cdots +2.1794}}=0.0897$$

Once this value is determined, the standard deviation of the criteria (σ_j), the Criterion Discrimination Coefficient (CDC_j), and the average values (AV_j) of the criteria are calculated. For the PP criterion, CDC_j and AV_j values are calculated with Equations (3) and (4) as follows:

$${CDC}_1={\displaystyle \frac{1}{1+{\sigma }_j}}=\left({\displaystyle \frac{1}{1+0.8876}}\right)=0.5298$$

$${AV}_1={\displaystyle \frac{{\displaystyle {\sum }_{t=1}^k}{x}_{tj}}{k}}={\displaystyle \frac{9+\cdots +9}{12}}=8.3333$$

These values are calculated in the same way for the other criteria. These values are presented in Table 5.

Table 5. The criteria σ_j, CDC_j, AV_j values.

Values	PP	OEC	MC	GGE	EC	NE
σj	0.8876	1.2792	1.4142	2.2896	1.7816	1.8320
CDCj	0.5298	0.4387	0.4142	0.3040	0.3595	0.3531
AVj	8.3333	8.0000	7.0000	6.8333	7.4167	5.0833
Values	DR	RT	BC	PAP	LC	ISA
σj	1.8505	2.2496	1.2060	2.1515	0.9962	0.9003
CDCj	0.3508	0.3077	0.4533	0.3173	0.5010	0.5262
AVj	7.1667	7.1667	8.0000	6.5833	8.0833	8.0833

The values in the decision matrix are normalized using Equation (5). The normalized value for the EXP-1 expert under the PP criterion is calculated as follows.

$$u_{11}={\displaystyle \frac{x_{11}}{\mathit{max}\left(x_{tj}\right)}}={\displaystyle \frac{9}{9}}=1$$

Other values are normalized in a similar way. The normalization matrix is presented in Table 6.

Table 6. The normalized matrix.

Criteria	PP	OEC	MC	GGE	EC	NE
EXP-1	1.0000	0.7778	0.7778	0.5556	0.7778	0.3333
EXP-2	1.0000	0.8889	0.6667	1.0000	1.0000	0.7778
EXP-3	0.8889	1.0000	0.8889	1.0000	1.0000	0.6667
EXP-4	1.0000	0.7778	0.5556	0.7778	1.0000	0.4444
EXP-5	1.0000	0.8889	0.7778	0.5556	0.6667	0.3333
EXP-6	0.8889	1.0000	0.8889	1.0000	1.0000	0.6667
EXP-7	0.7778	1.0000	1.0000	1.0000	1.0000	1.0000
EXP-8	1.0000	1.0000	1.0000	0.5556	0.5556	0.6667
EXP-9	0.7778	0.7778	0.6667	0.4444	0.5556	0.4444
EXP-10	0.7778	1.0000	0.8889	0.8889	1.0000	0.5556
EXP-11	1.0000	0.5556	0.5556	0.3333	0.7778	0.3333
EXP-12	1.0000	1.0000	0.6667	1.0000	0.5556	0.5556
Criteria	DR	RT	BC	PAP	LC	ISA
EXP-1	0.8889	0.8889	0.7778	1.0000	1.0000	0.7778
EXP-2	0.7778	1.0000	1.0000	0.7778	0.7778	1.0000
EXP-3	0.8889	0.7778	1.0000	0.6667	0.7778	0.8889
EXP-4	0.8889	1.0000	0.8889	1.0000	1.0000	1.0000
EXP-5	0.3333	0.7778	0.6667	0.6667	1.0000	0.7778
EXP-6	0.8889	0.7778	0.7778	0.6667	1.0000	0.8889
EXP-7	0.5556	1.0000	1.0000	0.5556	0.7778	0.8889
EXP-8	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000
EXP-9	0.6667	0.6667	0.6667	0.5556	0.7778	0.7778
EXP-10	1.0000	0.8889	1.0000	0.6667	0.8889	1.0000
EXP-11	1.0000	0.1111	1.0000	1.0000	1.0000	0.7778
EXP-12	0.6667	0.6667	0.8889	0.2222	0.7778	1.0000

After the normalization matrix is obtained, the normalized weight of each expert ($e_t^{\prime }$) is calculated. The expert normalized weight for EXP-1 is calculated with Equations (9) and (10) as follows.

e₁ = 0.5 × exp₁ + (1 − 0.5) × edu₁ = 0.5 × 5 + (1 − 0.5) × 5 = 5

$$e_1^{\prime }={\displaystyle \frac{e_1}{{\sum }_{t=1}^k{e}_t}}={\displaystyle \frac{5}{5+\cdots +4.5}}=0.1449$$

The expert normalized weights for other experts are calculated in the same way. These values are shown in Table 7.

Table 7. The expert normalized weights for each expert.

Experts	${\mathit{e}}_{\mathit{t}}^{\mathbf{\prime }}$
EXP-1	0.1449
EXP-2	0.0725
EXP-3	0.0580
EXP-4	0.0580
EXP-5	0.0870
EXP-6	0.0580
EXP-7	0.0870
EXP-8	0.0580
EXP-9	0.0725
EXP-10	0.1014
EXP-11	0.0725
EXP-12	0.1304

Following this calculation step, the S_j, T_j and G_j values and criteria weights are obtained. These values are calculated with Equations (6)–(8) and (11) as follows for the PP criterion.

$$S_1={\displaystyle \sum _{t=1}^k}\left(\left(u_{ij}\times e_t^{\prime }\right)+{RI}_t\right)=\left(\left(1\times 0.1449\right)+0.0897\right)+\cdots +\left(\left(1\times 0.1304\right)+0.1117\right)=1.9291$$

T₁ = S_j × CDC_j = 1.9291 × 0.5298 = 1.0220

$$G_1={\displaystyle \frac{T_1}{{\displaystyle {\sum }_{j=1}^n}{T}_j}}+{\displaystyle \frac{{AV}_1}{{\displaystyle {\sum }_{j=1}^n}{AV}_j}}={\displaystyle \frac{1.0220}{1.0220+\cdots +0.9965}}+{\displaystyle \frac{8.3333}{8.3333+\cdots +8.0833}}=0.2106$$

$$w_1={\displaystyle \frac{G_1}{{\displaystyle {\sum }_{j=1}^n}{G}_j}}={\displaystyle \frac{0.2106}{0.2106+\cdots +0.2049}}=0.1053$$

These values are obtained in the same way for the other criteria. The results of the AYBI method are presented in Table 8.

Table 8. The results of the AYBI method.

Criteria	PP	OEC	MC	GGE	EC	NE
Sj	1.9291	1.8889	1.7746	1.7585	1.8068	1.5475
Tj	1.0220	0.8287	0.7350	0.5345	0.6495	0.5464
Gj	0.2106	0.1850	0.1630	0.1384	0.1580	0.1198
wj	0.1053	0.0925	0.0815	0.0692	0.0790	0.0599
Criteria	DR	RT	BC	PAP	LC	ISA
Sj	1.7842	1.7955	1.8808	1.7101	1.8953	1.8937
Tj	0.6259	0.5525	0.8526	0.5427	0.9495	0.9965
Gj	0.1525	0.1442	0.1877	0.1364	0.1996	0.2049
wj	0.0763	0.0721	0.0938	0.0682	0.0998	0.1024

Based on the results of the AYBI method, the criteria are listed as follows: PP, ISA, LC, BC, OEC, MC, EC, DR, RT, GGE, PAP and NE. The PP criterion was identified as the most important criterion, while the NE criterion was identified as the least important. To examine whether the criteria carry overlapping information, the pairwise Spearman correlations between the importance ratings given by the 12 experts were calculated. The mean absolute correlation across all 66 criterion pairs is 0.347, and only 7.6% of the pairs have a correlation of 0.7 or higher, which indicates that the criteria are not strongly redundant. The strongest association is observed between Operating and Energy Cost and Greenhouse Gas Emission (ρ = 0.721), followed by Energy Consumption and Greenhouse Gas Emission (ρ = 0.567), whereas Operating and Energy Cost and Energy Consumption are only weakly related (ρ = 0.185). The criteria represent different dimensions (monetary cost, physical energy use and environmental impact). Nevertheless, the partial overlap between OEC and GGE may give the cost-emission dimension a somewhat higher implicit weight, and this is acknowledged as a limitation. To show what the additional AYBI components contribute, the AYBI weights were compared with the weights obtained directly from the mean expert ratings. The two weight vectors are strongly correlated (Spearman ρ = 0.953, Pearson r = 0.907, Kendall τ = 0.884), and the maximum absolute difference is 0.0103 (for PP and ISA). The AYBI weights are more discriminating (coefficient of variation 0.181 versus 0.124), mainly because of the agreement coefficient CDC_j, which raises the weights of the criteria on which the experts agree. The expert-level components ($e_t^{\prime }$ and RI_t) change the weights by less than about 0.007. Kendall’s coefficient of concordance among the experts was W = 0.255 (tie-corrected, p < 0.001), indicating significant but only moderate agreement, which supports the use of CDC_j. The equal coefficients in Equations (8) and (9) follow a common convention. Equal-weight averaging is a common way of combining weighting information, for example, in the combination of AHP, CRITIC and Entropy weights [54], and criteria weights may also be refined with data-driven information on the relations between criteria [55]. After determining the weights of the criteria, the MUNRA method is used to rank the frigorific vehicles. After the criteria weights were determined, the same 12 experts rated each of the six vehicle alternatives on each of the 12 criteria on a scale from one to nine. The experts were informed of the criterion types, and each score expresses the level of the criterion for the vehicle: for cost criteria (PP, OEC, MC, GGE, EC, NE and RT), a higher score indicates a higher level of cost, emission, consumption, noise or time, and for benefit criteria (DR, BC, PAP, LC and ISA), a higher score indicates a higher level of the desired characteristic. The original ratings of the 12 experts are provided in Appendix A. Then, the experts’ opinions are combined using the Bonferroni mean operator to create an aggregated decision matrix. This matrix is presented in Table 9.

Table 9. The aggregated matrix.

Criteria	PP	OEC	MC	GGE	EC	NE
RPV	8.0679	6.2085	6.5621	5.7840	7.7352	6.6241
FBT	7.4019	6.8191	6.6492	5.9658	7.4904	6.5528
SART	6.8964	6.9870	6.8235	6.1398	7.0732	5.7261
DART	7.0528	7.0700	6.7386	6.6367	7.4924	5.6381
FT	6.5355	7.1478	6.8169	6.8843	6.9740	5.5487
TRT	6.7868	7.2321	6.8124	6.4468	7.2195	5.7128
Criteria	DR	RT	BC	PAP	LC	ISA
RPV	5.3001	6.4608	5.8023	6.2981	5.4411	8.2444
FBT	5.8956	6.6287	6.4784	6.1311	6.2945	8.1613
SART	6.3042	5.8608	7.2363	6.8158	6.9783	7.4853
DART	7.0561	6.2097	7.5729	7.2426	7.7411	7.4019
FT	7.0421	6.2861	8.2444	7.1467	8.2425	7.3875
TRT	7.7274	6.4503	8.2425	7.3916	8.5767	7.2216

Equations (14) and (15) are applied to this combined decision matrix for linear normalization. The results of these normalization operations are presented in Table 10. After this, Equations (16) and (17) are applied for vector normalization. The vector-normalized decision matrix is presented in Table 11. Finally, the nonlinear normalization process is performed using Equations (18) and (19). The nonlinear normalized decision matrix is presented in Table 12.

Table 10. The linear normalized matrix.

Criteria	PP	OEC	MC	GGE	EC	NE
RPV	0.8101	1.0000	1.0000	1.0000	0.9016	0.8377
FBT	0.8829	0.9105	0.9869	0.9695	0.9311	0.8468
SART	0.9477	0.8886	0.9617	0.9421	0.9860	0.9690
DART	0.9267	0.8781	0.9738	0.8715	0.9308	0.9841
FT	1.0000	0.8686	0.9626	0.8402	1.0000	1.0000
TRT	0.9630	0.8585	0.9633	0.8972	0.9660	0.9713
Criteria	DR	RT	BC	PAP	LC	ISA
RPV	0.6859	0.9071	0.7038	0.8521	0.6344	1.0000
FBT	0.7629	0.8842	0.7858	0.8295	0.7339	0.9899
SART	0.8158	1.0000	0.8777	0.9221	0.8136	0.9079
DART	0.9131	0.9438	0.9186	0.9798	0.9026	0.8978
FT	0.9113	0.9323	1.0000	0.9669	0.9610	0.8961
TRT	1.0000	0.9086	0.9998	1.0000	1.0000	0.8759

Table 11. The vector normalized matrix.

Criteria	PP	OEC	MC	GGE	EC	NE
RPV	0.5388	0.6337	0.6022	0.6264	0.5695	0.5480
FBT	0.5768	0.5977	0.5969	0.6147	0.5831	0.5529
SART	0.6057	0.5877	0.5864	0.6035	0.6064	0.6093
DART	0.5968	0.5828	0.5915	0.5714	0.5830	0.6153
FT	0.6264	0.5783	0.5868	0.5554	0.6119	0.6214
TRT	0.6120	0.5733	0.5870	0.5836	0.5982	0.6102
Criteria	DR	RT	BC	PAP	LC	ISA
RPV	0.3276	0.5827	0.3237	0.3751	0.3045	0.4394
FBT	0.3645	0.5719	0.3614	0.3652	0.3522	0.4349
SART	0.3897	0.6215	0.4037	0.4060	0.3905	0.3989
DART	0.4362	0.5989	0.4225	0.4314	0.4332	0.3945
FT	0.4353	0.5940	0.4600	0.4257	0.4612	0.3937
TRT	0.4777	0.5834	0.4599	0.4403	0.4799	0.3848

Table 12. The nonlinear normalized matrix.

Criteria	PP	OEC	MC	GGE	EC	NE
RPV	0.5316	1.0000	1.0000	1.0000	0.7329	0.5878
FBT	0.6883	0.7547	0.9612	0.9113	0.8071	0.6071
SART	0.8511	0.7016	0.8894	0.8360	0.9585	0.9099
DART	0.7957	0.6772	0.9235	0.6620	0.8065	0.9532
FT	1.0000	0.6553	0.8920	0.5931	1.0000	1.0000
TRT	0.8930	0.6327	0.8938	0.7222	0.9014	0.9163
Criteria	DR	RT	BC	PAP	LC	ISA
RPV	0.4704	0.7465	0.4953	0.7260	0.4025	1.0000
FBT	0.5821	0.6912	0.6175	0.6880	0.5386	0.9799
SART	0.6656	1.0000	0.7704	0.8503	0.6620	0.8243
DART	0.8338	0.8407	0.8437	0.9601	0.8146	0.8061
FT	0.8305	0.8105	1.0000	0.9348	0.9236	0.8029
TRT	1.0000	0.7501	0.9995	1.0000	1.0000	0.7673

After these normalized matrices are obtained, the results of the MUNRA method and the ranking of frigorific vehicles are determined using Equations (20)–(23). These results are presented in Table 13.

Table 13. The results of MUNRA method.

Results	${\mathit{r}}_{\mathit{i}}^{\mathbf{\prime }}$	${\mathit{y}}_{\mathit{i}}^{\mathbf{\prime }}$	${\mathit{p}}_{\mathit{i}}^{\mathbf{\prime }}$	vi	Rankings
RPV	0.8575	0.4839	0.7205	0.6873	6
FBT	0.8758	0.4939	0.737	0.7022	5
SART	0.9152	0.512	0.8187	0.7486	4
DART	0.9237	0.5166	0.821	0.7538	3
FT	0.9453	0.5258	0.8723	0.7811	2
TRT	0.9492	0.5285	0.8722	0.7833	1

According to the results of the MUNRA method, frigorific vehicles are ranked as follows: TRT, FT, DART, SART, FBT and RPV. Thus, the TRT was identified as the best frigorific vehicle, while the RPV was identified as the vehicle with the lowest performance.

To verify the reliability and stability of the MUNRA method, a comparative analysis was conducted using 15 different MCDM methods: Simple Additive Weighting (SAW), TOPSIS, Weighted Aggregated Sum Product Assessment (WASPAS), MARCOS, Complex Proportional Assessment (COPRAS), Additive Ratio Assessment (ARAS), Multi-Objective Optimization by Ratio Analysis (MOORA), Multi-Attribution Border Approximation Area Comparison (MABAC), Evaluation Based on Distance from Average Solution (EDAS), Operational Competitiveness Ratings Assessment (OCRA), Square-Root-based Evaluation Method (SREM), Preference using Root Value based on Aggregated Normalizations (PROVAN), Compromise Ranking of Alternatives from Distance to Ideal Solution (CRADIS), Alternative Prioritization and Assessment System (ALPAS), and Compromise Ranking From Alternative Solutions (CORASO). The consistency of rankings among the methods was measured using Spearman’s rank correlation coefficient, and the significance of each coefficient was tested with the exact two-sided permutation test (n = 6, no tied ranks). The ranking produced by MUNRA was identical to the rankings of 13 methods (ρ = 1.000, p = 0.0028). A lower but still significant correlation was obtained with the MABAC and PROVAN methods (ρ = 0.8857, p = 0.0333). The average Spearman correlation across the 15 methods was 0.9848. TRT was identified as the best alternative and RPV as the worst alternative by all methods. These results indicate that the ranking is stable across the methods considered; they support the stability of the ranking stage and do not, by themselves, validate the AYBI weights.

To evaluate the robustness of the ranking with respect to the criteria weights, a sensitivity analysis was carried out at three perturbation levels (±20%, ±40% and ±50%) with two complementary procedures. In the first, 3000 weight vectors were generated at each level by multiplying each AYBI weight independently by a factor drawn from a uniform distribution between 1 − δ and 1 + δ (δ = 0.20, 0.40, 0.50) and renormalizing the vector to sum to one. In the second, an Artificial Bee Colony (ABC) algorithm (30 food sources, 100 iterations, scout limit of 15) searched within the same bounds for the weight vector that is most damaging to the ranking, i.e., the one that minimizes the Spearman correlation with the original ranking and the score gap between neighboring alternatives. In both procedures, MUNRA was reapplied to every weight vector, and the resulting ranking was compared with the original ranking using Spearman’s rank correlation coefficient. The results are presented in Table 14.

Table 14. Results of the sensitivity analysis.

Perturbation	Monte Carlo: Total Sim.	Ranking Changes	Change (%)	Mean ρ	Min. ρ	ABC Worst Case: Min. ρ	Worst-Case Ranking
±20%	3000	271	9.0	0.9947	0.8857	0.8857	FT, TRT, SART, DART, FBT, RPV
±40%	3000	881	29.4	0.9793	0.8857	0.8857	FT, TRT, SART, DART, FBT, RPV
±50%	3000	1046	34.9	0.9738	0.8286	0.6571	FT, SART, TRT, DART, RPV, FBT

In the Monte Carlo analysis, the original ranking was preserved in 91.0%, 70.6% and 65.1% of the simulations at the ±20%, ±40% and ±50% levels, respectively, and the mean Spearman correlation remained above 0.97 at all levels. At ±20% and ±40%, the changes were limited to the two pairs of closely scored alternatives, FT and TRT (0.7811 and 0.7833) and SART and DART (0.7486 and 0.7537), while RPV and FBT kept the last two positions in all simulations. At ±50%, RPV and FBT exchanged positions in a small number of simulations. The ABC search shows that, within ±20% and ±40%, even the most unfavorable weight vector only swaps these two close pairs (minimum ρ = 0.8857). At ±50%, a weight vector exists that moves TRT to the third place and RPV above FBT (minimum ρ = 0.6571), which indicates that the ranking cannot be considered invariant under extreme weight changes. The results therefore show that the separation between the large vehicles (FT, TRT, DART, SART) and the small vehicles (FBT, RPV) is stable for moderate changes of the weights, whereas the order within the close pairs depends on the weights and should be interpreted with caution.

The newly developed AYBI method was compared with Simple Weight Calculation (SIWEC), which is also a group decision-making method. SIWEC considers only the decision maker’s rating consistency (row-based standard deviation) when determining the importance of criteria. AYBI, however, expands on this logic by evaluating four different sources of information together: expert profile (education/experience weight, e_t), discriminating power of the expert’s ratings (RI_t), the degree of inter-expert agreement at the criterion level (CDC_j), and the average importance level of the criterion (AV_j). This multidimensional structure provides AYBI with richer interpretation capabilities compared to SIWEC; for example, it can additionally report that a criterion carries a high weight despite differences of opinion among experts.

There is also a difference in terms of structural robustness: in SIWEC, if an expert assigns equal scores to all criteria, that expert’s contribution is completely nullified. An expert who assigns identical scores to all criteria has zero contribution in SIWEC, whereas AYBI keeps a contribution through $e_t^{\prime }$ and RI_t; this is a structural difference and not a proven superiority.

Empirically, the two methods showed strong convergence in the actual 12-expert × 12-criteria dataset used in the study (Spearman’s ρ = 0.972). A Monte Carlo simulation with 1000 scenarios per panel size showed that the mean Spearman correlation between the AYBI and SIWEC weights increases with the size of the expert panel, from 0.75 for four experts and six criteria to 0.91 for 12 experts and 12 criteria and 0.95 for 20 experts and 15 criteria. The agreement is therefore weaker for small panels, which is consistent with the stronger influence of the constant term RI_t when few experts are available.

These findings demonstrate that the AYBI criterion weights used as input in the MUNRA ranking phase are not only internally consistent but also are consistent with a well-established alternative method (SIWEC). A bootstrap over experts (5000 resamples) retained TRT as the best alternative in 99.1% of the samples and the full ranking in 98.7%, and the leave-one-expert-out analysis gave a mean Spearman correlation of 0.985 (minimum 0.937) with the original ranking. These analyses assess the consistency and robustness of the results with respect to the expert panel and the weights. They do not, by themselves, establish the superiority of AYBI over other weighting methods.

5. Discussion

This study provides a comprehensive MCDM model that combines the AYBI weight calculation method and the MUNRA alternative ranking method to assess six cold-chain vehicles according to 12 criteria. The study presents the practical value of the AYBI and MUNRA methods, as it shows its ability to provide consistent results compared with other MCDM techniques. The findings present policymakers and managers with a useful decision approach for assessing frigorific vehicles. Integrating the Discrimination Index (RI_t) and Criterion Discrimination Coefficient (CDC_j) of AYBI with MUNRA’s multi-normalization offers practitioners an easy-to-use, transparent approach that eliminates complex mathematical calculations to deal with uncertainty in decision making.

For presenting a solid framework for evaluating sustainability performance of cold-chain vehicles, a novel hybrid MCDM method was developed in this study by integrating AYBI and MUNRA methods. The benefits of the developed framework and main findings are discussed below.

First, the AYBI and MUNRA techniques offered advantages in the decision analysis. The AYBI technique includes the experience and education level of experts in the analysis, which accounts for the expert profile in the weighting. The application of the MUNRA technique for assessing alternatives presented a consistent way to manage normalizations in the analysis. It merges with linear, vector, and nonlinear normalizations and therefore provides a more stable ranking.

Second, the AYBI findings found that Purchase Price (0.1053), Infrastructure and Service Accessibility (0.1024), Load Capacity (0.0998), Battery Capacity (0.0938), and Operating/Energy Cost (0.0925) criteria are very significant. On the other hand, Power and Acceleration Performance and Noise Emissions criteria were found to be the least significant. High weight scores of Purchase Price and Operating/Energy Cost criteria show that cold-chain vehicles are capital intensive investments, and they require constant energy use to maintain refrigeration. The significance of Infrastructure and Service Accessibility and Battery Capacity criteria reflects that clean energy vehicles cannot effectively be used unless there is a reliable charging or fuel network and adequate energy in the vehicle. Load Capacity is also important when considering cold-chain vehicles as it highlights the desire for scale economy for each trip to decrease costs and energy needs. Contrary to the above-mentioned criteria, Power and Acceleration Performance and Noise Emissions were found to be the least significant criteria, as cost, energy demand, and capacity were superior from an operational viewpoint in frigorific vehicle decision-making. The weighing results suggest that economic criteria are still significant and central in the analysis. The significance of infrastructure and service accessibility criteria reflects that sustainability is not only affected by truck specifications but also operational support. Load Capacity is another criterion found to be significant because it balances efficiency of transportation in sustainability. Noise level was found to be the least important, and this demonstrates that noise receives different levels of priority in the practice of logistics compared to other criteria.

The MUNRA analysis results suggested that the most preferable alternative among cold-chain vehicles is Twin-Axle Refrigerated Trailers (0.7833), which is followed by Standard Frigorific Trailers (0.7811), Double-Axle Refrigerated Trucks (0.7538), Single-Axle Refrigerated Trucks (0.7486), Frigorific Box Trucks (0.7022), and Refrigerated Panel Vans (0.6873). The alternative ranking results show that sustainable vehicle selection in the cold chain is dominated by operational requirements other than performance criteria.

Twin-Axle Refrigerated Trailers and Standard Frigorific Trailers obtained the highest scores because the expert panel gave high importance to purchase price, infrastructure and service accessibility, load capacity and energy-related costs, and these vehicle classes were rated favorably on load capacity, driving range and battery capacity. These results should not be read as a general statement that larger vehicles are more sustainable. Both trailer classes were rated less favorably on greenhouse gas emissions and noise than the smaller vehicles, and their advantage depends on the operating context: it applies to long-distance and high-volume transport, where the load carried per trip is high. For urban last-mile distribution, short routes or low-emission zones, criteria such as noise, emissions, maneuverability and access restrictions would carry more weight, and the ranking could differ. The sensitivity analysis supports this reading: the separation between the large and the small vehicles is stable for moderate changes of the weights, but the order within the close pairs (FT-TRT and SART-DART) depends on the weights. Refrigerated Panel Vans and Frigorific Box Trucks ranked lowest under the weights of this study, mainly because of their low load capacity and driving range, although they are well suited to urban distribution and have low noise emissions. Double and Single Axle Refrigerated Trucks showed an intermediate performance.

Comparative analysis shows that the developed integrated model including AYBI and MUNRA methods has high correlation (ρ = 0.9848) with 15 alternative MCDM techniques. TRT ranking first and RPV ranking the last in 16 techniques shows that the model is robust and stable. The sensitivity analysis showed that the separation between the large vehicles (FT, TRT, DART, SART) and the small vehicles (FBT, RPV) is preserved for moderate changes of the weights (up to ±40%), whereas the order within the close pairs (FT-TRT and SART-DART) is weight-dependent. Comparative analysis provided the robustness of the AYBI-MUNRA approach compared to other MCDM techniques, while sensitivity analysis showed stability for moderate weight changes, with weight-dependent order only within the close pairs FT-TRT and SART-DART.

6. Conclusions

The results indicate that, under the criteria and weights of this study, high-capacity vehicles such as TRT and FT are preferable for long-distance and high-volume transport, intermediate vehicles such as DART and SART for regional distribution, and smaller vehicles such as RPV and FBT remain relevant for urban distribution, where noise, access and last-mile constraints matter more than load capacity. The ranking should therefore be interpreted according to the operating context and not as a general ordering of the sustainability of vehicle size.

There are several limitations of this study. First, it only uses 12 criteria and six alternative vehicles. Increasing the criteria to include temperature stability, safety or social impacts in future studies could provide more comprehensive findings regarding the sustainability performance of vehicles. Also, expanding vehicles in future studies to reflect zero-emission solutions, including hydrogen trucks, will provide a more comprehensive outlook for future predictions. Second, this study only uses crisp techniques. The developed framework could be improved in future studies by integrating uncertainty. Third, the research can benefit from using probabilistic MCDM techniques and AI-based decision making, as this could further improve the usability of the decision model in complicated and data-intensive environments. Fourth, costs and battery performance were assessed with baseline data, not dynamic, real-time data. Therefore, using real-time or dynamic data in future studies will provide more accurate results. Fifth, the opinions of 12 experts, who are professionals in the logistics sector, were considered in this study. Even though their insights were useful, this does not reflect the whole picture, including the perspectives of food suppliers, truck operators, and customers. Sixth, the analysis is performed using the criteria selected, their weights, and the selected alternatives in a given geography. In future studies, the analysis may be applied in different countries, in different urban or rural systems, and in different sectors. Seventh, no scenarios were involved in this study; however, considering alternative scenarios on carbon tax, subsidies, cost, and emissions would give better outcomes for future predictions. Eighth, there is no standardization in vehicle alternatives, as the aim was to consider all the vehicles used in cold chains; however, this led to differences in the specifics of vehicles and, as a result, difference performances in the criteria. To counteract this, a standard functional unit cost per ton-kilometer can be used in future studies.

Ninth, the propulsion technology and the refrigeration unit type of the vehicle classes were not specified in the expert survey, temperature-control performance was not considered as a separate criterion, and the Operating and Energy Cost and Greenhouse Gas Emission criteria show a partial overlap (ρ = 0.721), which may give the cost-emission dimension a somewhat higher implicit weight.

Tenth, the dispersion-based component RI_t of AYBI acts as a scaling term and does not reweigh individual experts, and a high dispersion of an expert’s ratings may reflect inconsistency as well as discriminating power. Eleventh, the influence of RI_t on the criteria ranking is larger for small expert panels, and the agreement of AYBI with simpler approaches (the mean ratings and SIWEC) shows consistency and does not prove superiority; the AYBI weights differ from the mean-rating weights mainly through the agreement coefficient CDC_j. Twelfth, the ranking of the alternatives is based on expert judgments and is sensitive to the weights within the pairs of closely scored vehicles (FT-TRT and SART-DART). Thirteenth, the equal coefficients in Equations (8) and (9) are a convention and not a proven optimum; they had no effect on the ranking of the alternatives in this study, but other coefficients may be preferable for other expert panels or decision problems.

Future research can compare the alternatives under a common transport task using a functional unit (for example, per ton-kilometer of temperature-controlled cargo), specify the propulsion and refrigeration systems of each vehicle class, and add temperature-control performance as a criterion. AYBI can also be tested against other group weighting methods on larger expert panels, extended to fuzzy or grey environments, and applied to other decision problems such as green supplier selection or location selection.